Factoring Trinomials
Practice factoring trinomials using sum-and-product reasoning and sign rules.
Practice Question Set
7 quick practice checks
Topic Progress
Saved on this device and updated across practice sessions.
Multiply (x - 7)(x + 3). What is the resulting middle term?
In x² + 2x - 24, the constant is negative (-24). This tells you that the two factors must have
A student factors x² - 5x + 6 as (x - 1)(x - 6). Why is this wrong?
Factor: \(x² + 11x + 30\)
Factor: \(x² - 7x - 18\)
Factor: \(x² + 8x + 15\)
Factor: \(x² - 14x + 48\)
Factor: \(x² - 9x + 20\)
If a trinomial is x² + bx + c (where b and c are both positive), what will the signs in the factors be?
x² + 9x + ___ = (x + 5)(x + 4)
x² + ___x + 12 = (x + 6)(x + 2)
For x² - 3x - 10, the factors have opposite signs. Which factor must get the negative sign to result in -3x?
Factor: \(x² + 18x + 80\)
Factor: \(x² + 14x + 45\)
Factor: \(x² + 5x - 14\)
In x² - 8x + 15, the constant is positive (+15) but the middle is negative (-8). This means both factors must be
Factor: \(x² - 6x - 16\)
Factor: \(x² + 13x + 40\)
Factor: \(x² + 17x + 72\)
A student says x² + 5x - 6 factors into (x + 2)(x + 3). What mistake did they make?
Factor: \(x² + 21x + 110\)
Factor: \(x² - 4x - 21\)
Factor: \(x² + 2x - 8\)
Factor: \(x² - 5x - 36\)
Factor: \(x² + 12x + 32\)
Factor: \(x² + 4x - 12\)
Factor: \(x² - 12x + 27\)
Factor: \(x² - x - 30\)
For x² - 13x + 42, find the pair that multiplies to 42 and adds to -13.
Is (x + 4)(x + 2) the correct factorization for x² + 6x + 8?
Factor: \(x² - 3x - 40\)
Factor: \(x² - 2x - 24\)
Factor: \(x² - 10x + 21\)
Factor: \(x² - 15x + 54\)
Factor: \(x² + 15x + 50\)
Factor: \(x² + 10x + 24\)
Factor: \(x² - 16x + 60\)
Factor: \(x² - 4x - 32\)
Factor: \(x² - 1x - 56\)
Factor: \(x² + 16x + 63\)
Factor: \(x² + 20x + 100\)
In the trinomial x² - x - 20, the constant is -20 and the middle coefficient is -1. Which pair fits?
Factor: \(x² - 2x - 35\)
Which pair of numbers multiplies to -24 and adds to +2?
x² - x - 12 = (x - 4)(x + ___)
Factor: \(x² - 11x + 18\)
Factor: \(x² + 19x + 90\)
Factor: \(x² + 1x - 20\)
To factor x² + 7x + 10, you need two numbers that multiply to 10 and add to 7. What are they?
Factor: \(x² + 3x - 10\)