Factoring Quadratics

Front

What is factoring in algebra?

Back

Factoring in algebra 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 and a ≠ 0.

Front

What are the common methods for factoring quadratics?

Back

Common methods for factoring quadratics include: 1) Factoring by grouping, 2) Using the quadratic formula, 3) Recognizing special products (like difference of squares, perfect square trinomials), and 4) Trial and error.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial is factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of x² - 81?

Back

The factored form of x² - 81 is (x - 9)(x + 9), which is an example of the difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression 25x² - 9?

Back

The expression 25x² - 9 can be factored as (5x - 3)(5x + 3), which is also a difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

What are the factors of the quadratic 3x² - 17x + 10?

Back

The factors of the quadratic 3x² - 17x + 10 are (x - 5)(3x - 2).

Front

How do you factor x² - 10x + 24?

Back

To factor x² - 10x + 24, look for two numbers that multiply to 24 and add to -10. The factors are (x - 4)(x - 6).

Front

What is the factored form of x² + 16x + 15?

Back

The factored form of x² + 16x + 15 is (x + 1)(x + 15).