Factoring Quadratics Mixed

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b. These numbers will be used to write the expression as (x + p)(x + q), where p and q are the two numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a quadratic expression when a ≠ 1?

Back

When a ≠ 1, use the method of grouping or the ac method. Multiply a and c, find two numbers that multiply to ac and add to b, then rewrite the expression and factor by grouping.

Front

What is the significance of the leading coefficient in a quadratic expression?

Back

The leading coefficient (a) affects the direction of the parabola's opening and its width. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a polynomial with a common factor?

Back

To factor a polynomial with a common factor, identify the greatest common factor (GCF) and factor it out of each term.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form x² + bx + c into the form (x + p)² = q, making it easier to solve or graph.

Tags

CCSS.HSA-REI.B.4B