Solve by Factoring

Which equation has the solutions x = 0 and x = 2?

To solve (2x - 6)(x + 5) = 0, we solve 2x - 6 = 0 and x + 5 = 0. What are the two values for x?

In x² + 6x = 0, the 'c' value is 0. This means you should always factor by

If an equation is already factored as (x + 8)(x - 1) = 0, the two solutions are found by setting each factor to

If a quadratic equation has solutions x = 4 and x = -3, what were its two factors?

True or False: \(To solve x(x - 5) = 10, you can just say x = 10 or x - 5 = 10.\)

Based on the factors (x - 8) and (x - 3), the solutions are

Solve: \(-x² - 5x = 0.\)

Find two numbers that multiply to 24 and add to -11.

If a solution is x = 0, what is the simplest factor for that root?

The factors are (x + 5)(x - 3) = 0. The roots are

The factored form of x² + 7x + 10 = 0 is (x + 5)(x + 2) = 0. Therefore, the solutions are

Since 36 is 6² and 12 is 2x6, the expression forms a perfect square trinomial. The only solution is

If the factors are (x - 4)(x + 3) = 0, the solutions are

After factoring 5x(x + 4) = 0, one solution is x = -4. What is the other solution?

First factor out the GCF 2. You get 2(x² + 7x + 12) = 0. What are the factors of the trinomial?

If the constant 'c' is negative, like in x² + 2x - 15 = 0, what do we know about the signs of the factors?

Rewrite x² = 11x - 24 in standard form so it can be factored.

Using the factors (x - 5)(x + 4) = 0, the solutions are

First, multiply the whole equation by -1 to get x² - x - 20 = 0. The factors are

Factor 4x² - 8x into 4x(x - 2). The solution from the factor '4x' is

In the equation 5x² + 20x = 0, the first step is to factor out the GCF. What is the GCF?

Solving an equation by factoring is the same as finding what part of the graph?

Step 1: \(Divide by 2 to get x² - 4 = 0. Step 2\)

This factors into (2x - 1)(2x + 1) = 0. The solutions are

To solve 3x² - 27 = 0 by factoring, first factor out the GCF (3). This leaves 3(x² - 9). The final solutions are

In the equation x² - 2x - 8 = 0, the factors must have

Solve: \((3x - 1)(2x + 5) = 0.\)

The Zero Product Property states that if a • b = 0, then either 'a' must be zero or ___ must be zero.

Factor out x to get x(x - 9) = 0. The solutions are

Solve: \(x² - 49 = 0.\)

The factors are (x - 6)(x + 2) = 0. The solutions are

Solve: \(x² - 6x + 9 = 0. (Hint\)

To solve x² + 5x = 6 by factoring, what must you do first?

To solve 2x² + 5x + 3 = 0, you could use the 'AC method'. What is the product of A and C?

When factoring by grouping, if you have x(x + 3) + 2(x + 3), what is the common binomial factor?

Factor out 10: \(10(x² - 4) = 0. Factor the rest\)

We factor quadratic equations so that we can use which property to find the roots?

To factor x² - x - 12, we need numbers that multiply to -12 and add to -1. These are

The equation x² - 100 = 0 factors into (x - 10)(x + 10) = 0. The solutions are called

Solve: \(-2x² + 10x = 0. Factor out -2x first.\)

Based on the factors (x + 3) and (x + 4), the solutions are

If the solution to a factor is x = -7, what did the factor look like?

If x² - 2x - 8 = 0 factors into (x - 4)(x + 2) = 0, what is the solution set?

Which of these equations CANNOT be solved by simple factoring into integers?

To factor x² + 7x + 10, you need two numbers that multiply to 10 and add to

The factors are x(x + 6) = 0. The solutions are

The factored form is (2x + 3)(x + 1) = 0. One solution is x = -1. What is the other?

When a quadratic factors into two identical factors, like (x - 5)², the solution is called a

To solve x² - 4x = 12, you must first rewrite it as