Solve by Factoring

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solve: \(x² - 6x + 9 = 0. (Hint\)

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

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

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

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

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

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

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

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

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

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

Solve: \(-x² - 5x = 0.\)

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solve: \(x² - 49 = 0.\)

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

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

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

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

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

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