Miscellaneous

Factor completely: \(5x² - 45\)

Factor: \(3x² - 2x - 5\)

Area is x² + 20x + 99. Find the length if width is (x + 9).

Factor: \(5x² + 7x + 2\)

Factor completely: \(4x² - 16\)

A patio area is x² - 10x + 24. If the width is (x - 6), find the length.

Factor: \(x² + 12x + 32\)

Find the trinomial that is NOT factorable

Rectangle area is x² - 2x - 24. Find possible dimensions.

Factor: \(4x² + 4x + 1\)

Factor completely: \(2x² - 18\)

Factor completely: \(3x² + 3x - 18\)

Factor: \(1/4x² - x - 3\)

Two numbers add to 10 and multiply to 21. What are the numbers?

Product of two integers is 30. One is 7 more than the other. Find them.

The area of a poster is x² - 3x - 10. If the height is (x - 5), what is the base?

A student writes 2x² - 8 = 2(x-4)(x+4) What is the mistake?

9x² - 16 = (3x - 4)(3x + __)

Factor completely: \(5x² - 10x - 15\)

Factor 6x² + 7x - 3. A student uses 9 and -2 to split 7x. Is this step correct?

A student factors 2x² - 5x - 3 as (2x + 1)(x - 3). Is this correct?

In the expression 4x² - 11x + 6, the signs in the binomial factors must be

A triangle has area (1/2)bh. If the area is (1/2)(x² + 5x + 4) and the base is (x + 1), what is the height?

Factor: \(25x² + 70x + 49\)

Factor completely: \(3x³ - 12x\)

(x - 4y)(x + 3y) = x² + __xy - 12y²

The product of two consecutive integers is 110. Find the smaller positive integer.

Factor: \(3x² - 10x + 8\)

Factor: \(x² - 15x + 56\)

Area is x² - x - 2. Find dimensions.

Factor completely: \(5x³ - 5x\)

In the factorization 3x² + bx + 10 = (3x + 2)(x + 5), what is the value of b?

Which expression equals (x + 5y)(x - 2y)?

Factor: \(x² - 16x + 64\)

x² - 5x - 6 Is the factorization correct? (x-6)(x+1)

The height (feet) of a ball thrown upward is h(t) = -16t² + 32t + 48 Factoring gives -16(t-3)(t+1) When does the ball hit the ground?

Factor: \(6x² - 7xy - 3y²\)

Area is x² - 12x + 20. If x = 11, what are the dimensions?

Factor completely: \(2x³ - 32x\)

Factor: \(6x² + 11x - 10\)

4x² - 12x + ___ = (2x - 3)²

Factor: \(x² - 12x + 20\)

Factor: \(4x² + 20x + 25\)

3x² + 7x + 2 = (3x + __)(x + 2)

The product of two integers is 72. One integer is 1 more than the other. Find the positive integers.

Factor: \(x² + 18x + 81\)

The area of a sail is x² + 10x + 24. Find the factors.

Factor: \(12x² + 17x + 6\)

Factor: \(4x² + 28x + 49\)

A rectangle has area x² + 5x + 6 (square units). Factoring gives (x+2)(x+3) What are possible dimensions?

Which trinomial cannot be factored using integers?

Factor: \(x² - 11x + 18\)

The area of a deck is x² + 8x + 12. If x = 4, what is the width if the length is (x + 6)?

Factor completely: \(x³ - 2x² - 9x + 18\)

(x + 6)² = x² + __x + 36

Factor: \(x² + 14x + 45\)

The product of two consecutive even integers is 80. If x represents the smaller integer, the equation is x(x + 2) = 80. What is the smaller integer?

Factor completely: \(3x³ + 9x² - 30x\)

Consecutive positive integers multiply to 132. Find the larger one.

A student expands (4x + 3)(x - 1) and gets 4x² + x - 3. Is their work correct?

Factor: \(5x² - 18x - 8\)

Factor: \(5x² - 13x - 6\)

Which constant makes x² + 10x + ___ a perfect square trinomial?

Factor: \((log x)² - 5(log x) + 6\)

Height is h = -16(t - 2)(t + 0.5). How long is the ball in the air?

Factor: \(10x² + 11x - 6\)

(x + 3)(x + 5) = x² + __x + 15

Factor completely: \(2x³ - 8x\)

Factor completely: \(6x² - 24\)

A student writes x² + 7x + 10 = (x+5)(x+5). What is the mistake?

A rectangle has area x² + x - 20. If x = 10, what is the actual area?

Factor: \(3x² + 6x + 3\)

Factor: \(3x² - 16x + 5\)

In the pattern (a + b)² = a² + 2ab + b², why is the middle term '2ab' and not just 'ab'?

The area of a rug is x² + 7x + 10. If the length is (x + 5), what is the width?

Which expression shows 2x² + 7x + 5 with the middle term split correctly for factoring by grouping?

Factor: \(x² - 3\)

Factor completely: \(3x² - 27\)

Factor completely: \(4x³ + 12x² - 40x\)

Factor: \(2x² + 13x + 15\)

Area of a frame is x² - 4x - 32. One side is (x - 8). Find the other.

Factor: \(4x² + 11x - 3\)

Consecutive integers multiply to 156. Find the smaller one.

The height (feet) of a ball thrown upward is h(t) = -16t² + 64t (t = time in seconds) Factoring gives -16t(t-4) What does t = 4 represent?

Factor: \(3x³ - 21x² + 30x\)

A student writes x² - 8x + 12 = (x-6)(x+2) What is the mistake?

Factor: \(3x² - 2x - 8\)

Which of these trinomials cannot be factored using integers (Prime)?

A picture frame has an area of x² - x - 12. If one side is (x - 4), what must the other side be?

Factor: \(x² - 4x - 21\)

Factor: \(x² - 2x + 1\)

Factor: \(x² + 2xy + y² - z²\)

Factor: \(4x² + 4x - 3\)

Factor: \(2sin²θ + sinθ - 1\)

Factor: \(x² + 13x + 40\)

Factor: \(x² - 3x - 40\)

Factor: \(2x² - x - 6\)

The product of two consecutive integers is 42. Setting up x(x+1) = 42 leads to x² + x - 42 = 0 Factoring gives (x+7)(x-6). What are the two positive integers?

A ball's height is h = -(t - 5)(t + 1). At what time is the ball at its highest point (midpoint of roots)?

(2x + 5)(3x - 4) = 6x² + __x - 20

Factor: \(2x² + 5x + 3\)

Factor: \(3x² + 14x + 8\)

Factor: \(x² + 3x - 18\)

Factor: \(9x² - 30x + 25\)

Factor completely: \(4x³ + 4x² - 24x\)

Factor completely: \(3x³ + 12x² + 9x\)

Factor: \(x² + 15x + 54\)

Factor: \(6x² - 7x + 2\)

Factor completely: \(5x² + 25x + 30\)

A storage unit has floor area x² + 13x + 40. Find the width if length is (x + 8).

Factor: \(√3x² + 11x + 6√3\)

Factor completely: \(5x² - 5x - 30\)

A rectangular field has area x² - 14x + 45. Find the perimeter in terms of x.

An object is thrown and hits the ground at t = 2 and t = 6. What could be the factors of the equation?

Factor: \(x² - 12x + 36\)

x² + 6x + 8 Is the factorization correct? (x+4)(x+2)

Factor: \(4x² + 8x - 5\)

Factor: \(x² + 4x + 4\)

Which cannot be factored with integers?

Factor completely: \(7x² - 7x - 42\)

Which cannot be factored?

Factor: \(6x² + x - 1\)

A square garden has an area of x² + 6x + 9. What is the length of one side?

A box has a base area of x² + 11x + 18. Find the length and width.

Factor: \(x² - 26x + 169\)

Rectangle area is x² + 5x - 14. Find dimensions.

A student writes 4x² + 20x + 24 = (2x + 4)(2x + 6) What step did they miss?

Factor: \(x² - 30x + 225\)

Factor: \(6x² - 19x + 10\)

Factor: \(2x² + 11x + 5\)

5(x² + 4x - 12) = 5x² + __x - 60

Factor: \(x² + 2x + 1\)

Factor completely: \(2x³ + 14x² + 20x\)

Which trinomial equals (x + 2)(x - 5)?

Factor: \(x² + 2x - 15\)

Which of the following advanced trinomials is considered 'Prime'?

Factor: \(2x² - 2√10x + 5\)

x² - 2x - 15 Is the factorization correct? (x+5)(x-3)

Factor: \(x² - 12x + 27\)

The product of two consecutive even integers is 48. If the smaller is 2x, we get 2x(2x+2) = 48 Giving 4x² + 4x - 48 = 0 Which pair solves this?

Factor completely: \(2x² + 2x - 24\)

x² + 9x + 14 = (x + __)(x + 7)

Two numbers multiply to 48 and have a difference of 2. What are the positive numbers?

For the trinomial 4x² - 17x + 4, what is the correct AC product and the magic pair?

Factor: \(x² - 2x - 24\)

A backyard has area x² + 15x + 56. Find the dimensions.

Factor: \(x² + 24x + 144\)

A ball reaches height h = 0 at t = 5. Which factor must be in its height equation?

To factor 6x² + 7x - 3 using grouping, how should the middle term 7x be split?

For 5x² - 13x - 6, which pair multiplies to -30 (AC) and adds to -13?

Which is a Prime Trap?

Two numbers add to 15 and multiply to 56. What are they?

Product of two consecutive integers is 90. Find them.

Factor: \(x² - 20x + 100\)

x² - 4y² = (x - __y)(x + 2y)

Factor: \(x² - 6x - 16\)

x² - 13x + 40 A student factors it as (x-10)(x-4). Why is this wrong?

Factor: \(x² + 3xy + 2y²\)

Factor completely: \(3x² - 3x - 18\)

Factor: \(2x² + 7xy + 3y²\)

A rectangle has an area represented by x² + 5x + 6. If the area is length times width, which dimensions are possible?

Using the discriminant (b² - 4ac), which of these is NOT factorable over integers?

Factor completely: \(x³ + 5x² + 6x\)

Factor: \(x² + 11x + 24\)

Factor: \(x² + 4x - 12\)

Factor completely: \(2x² + 16x + 30\)

For 3x² + 11x + 6, what pair of numbers multiplies to 18 (AC) and adds to 11?

Factor: \(x² - 10x + 16\)

Factor: \(x² - 4√2x + 6\)

A diver jumps from a board. The time to hit the water is found by factoring t² - 2t - 8 = 0. How many seconds until they hit?

Factor: \(x² - 14x + 48\)

Factor completely: \(x⁶ - 9x³ + 8\)

Factor completely: \(-3x² + 15x - 18\)

Simplify: \((x² - 4) / (x² + 4x + 4)\)

The product of two consecutive positive integers is 42. This forms the equation x² + x - 42 = 0. Which pair of integers is the solution?

Projectile equation factors to -16(t - 1)(t + 1). When does it land?

Factor completely: \(3x² + 18x + 27\)

Which trinomial equals (4x - 1)(x + 3)?

Area is x² + 16x + 63. Find the length if width is (x + 7).

Which can be factored?

Factor: \(16x² + 24x + 9\)

Factor: \(x² + 10x + 25\)

Factor: \(x⁴ + 4\)

If a projectile's height is factored as h = -16(t - 4)(t + 0.5), why do we ignore the root t = -0.5?

Factor: \(6x² - x - 2\)

Factor: \(3x² + 13x + 4\)

Factor: \(8x² + 22x + 5\)

If a student writes (3x - 1)(x + 2) for 3x² + 5x - 2, what is the middle term of their product?

Factor: \(x² - x - 2\)

Which pair multiplies to -20 and adds to -1?

A rectangular pool has an area of x² + 12x + 35. What is the sum of the length and width if they are represented by the factors?

Simplify: \((x³ - 1) / (x² - 1)\)

3x² - 11x + ___ = (3x - 2)(x - 3)

Factor: \(x² + 6x - 27\)

Rectangle area is x² + 18x + 80. Find dimensions.

Factor completely: \(4x² - 20x + 24\)

Factor: \(4x² - 40x + 100\)

Factor: \(x² + x - 30\)

Factor completely: \(6x² + 6x - 72\)

A path's area is x² + 13x + 40. Which factor represents a dimension?

Factor: \(4x² - 4x - 15\)

Factor: \(x² + 16x + 63\)

Factor: \(3x² - 17x + 10\)

If (x - 4)(ax + 1) = 3x² - 11x - 4, what is the value of a?

Factor: \(2x² - 11x + 12\)

Factor: \(x² - 10x + 21\)

If a and c are both positive in ax² + bx + c, and b is negative, the factors must be

Factor: \(100x² - 20x + 1\)

The product of two consecutive odd integers is 35. What are the integers?

Height factors to -16(t - 3)(t + 1). What is the height at t = 0?

Factor: \(3x² - 5x - 2\)

A student factors x² + 6x + 12 as (x+2)(x+6). Is this correct?

Factor completely: \(x⁴ - 10x² + 9\)

Factor: \(2x² + 9x + 10\)

Factor completely: \(4x² + 16x + 12\)

Factor: \(6x² + 7x + 2\)

A rocket is launched. Its height is h = -16t² + 64t + 80. After factoring out the GCF (-16), you get -16(t² - 4t - 5). What are the roots of this motion?

Ball height is h = -16(t - 4)(t + 1). How high is it at t = 1?

Factor: \(x² - 17x + 72\)

The height of a ball is given by h(t) = -16(t - 3)(t + 1). At what positive time 't' does the ball hit the ground (height = 0)?

A student expands (x + 3)² as x² + 9. What did they forget?

A student says x² + 25 factors into (x + 5)(x - 5). Why are they wrong?

Factor: \(x² - 5/6x + 1/6\)

Factor: \(x² + 22x + 121\)

Factor: \(x² + 4x - 21\)

A garden has area x² + 7x + 12. The length is (x+4). What is the width in factored form?

Factor: \(x² - 14x + 49. A student writes (x + 7)(x - 7). What is the error?\)

Factor completely: \(3x² - 12x + 12\)

Area of a room is x² + 14x + 48. If one side is (x + 8), find the other.

A square has area x² - 10x + 25. What is the perimeter?

x² + bx + 100 = (x + 10)². What is the value of b?

Factor completely: \(10x² - 50x + 60\)

Factor completely: \(2x³ - 2x² - 12x\)

A student says x² + 25 = (x+5)(x-5). What is the error?

A window's area is x² - 4x - 21. Find the width if the length is (x + 3).

Which of the following is a factor of 6x² - 5x - 4?

Which expression is the result of squaring the binomial (3x - 4)?

Factor completely: \(2x³ + 4x² - 30x\)

Which expression equals (2x - 3)²?

Factor: \((x² - 1)² - 11(x² - 1) + 24\)

Factor: \(x² + 5x - 24\)

Factor completely: \(2x² - 4x - 16\)

Factor: \(x² - 5x - 14\)

Factor: \(4x² - 15x - 4\)

2x² - 18 = 2(x - 3)(x + __)

If (2x + 3) is a factor of 2x² + kx - 15, what is k?

Factor: \(4x² + 19x - 5\)

x² - xy - 12y² Is the factorization correct? (x+4y)(x-3y)

Factor: \(x² - 13x + 36\)

Why is (2x - 3)(x - 4) the wrong factorization for 2x² - 11x + 12?

Factor: \(1/9x² - 1/4y²\)

Factor completely: \(6x² + 12x - 18\)

Factor: \(x² + 5x + 6\)

Factor completely: \(4x² - 36\)

Factor: \(x² - 25\)