Review Solving by Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, rewrite the equation in the form ax^2 + bx + c = 0, factor it into (px + q)(rx + s) = 0, and then set each factor equal to zero.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to solve for a variable?

Back

To solve for a variable means to find the value of that variable that makes the equation true.

Tags

CCSS.7.EE.B.4A

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the first step in solving x^2 + 3x - 10 = 8 by factoring?

Back

The first step is to rearrange the equation to set it equal to zero: x^2 + 3x - 18 = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What are the factors of x^2 + 3x - 18?

Back

The factors of x^2 + 3x - 18 are (x + 6)(x - 3).

Front

How do you check your solution after factoring?

Back

To check your solution, substitute the values back into the original equation to see if they satisfy it.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the constant term in a quadratic equation?

Back

The constant term (c) in a quadratic equation affects the position of the parabola on the y-axis and can influence the number of real solutions.

Tags

CCSS.HSF-IF.C.7A

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero, and they correspond to the values that make each factor equal to zero.

Tags

CCSS.HSF-IF.C.7C