Factor Polynomials

Front

What is factoring in mathematics?

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 polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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 polynomial?

Back

To factor a quadratic polynomial, find two numbers that multiply to the constant term (c) and add to the linear coefficient (b).

Front

What is the factored form of x² - 4?

Back

(x + 2)(x - 2) - This is an example of the difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of x² - 49?

Back

(x + 7)(x - 7) - This is also an example of the difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of x² - 4x - 32?

Back

(x - 8)(x + 4) - This is found by identifying two numbers that multiply to -32 and add to -4.

Front

What is the factored form of k² - 2k - 24?

Back

(k + 4)(k - 6) - This is found by identifying two numbers that multiply to -24 and add to -2.

Front

What is the factored form of 3x² + 18x + 15?

Back

3(x + 5)(x + 1) - First factor out the GCF (3), then factor the quadratic.