Factoring 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 are the factors of the polynomial k² + 7k + 10?

Back

(k + 2)(k + 5)

Front

How do you factor the polynomial x² - 5x - 36?

Back

(x + 4)(x - 9)

Front

What are the factors of the polynomial x² + x - 6?

Back

(x + 3)(x - 2)

Front

What is the factored form of n² + 16n + 63?

Back

(n + 7)(n + 9)

Front

How do you factor the polynomial x² - 17x + 72 completely?

Back

(x - 9)(x - 8)

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.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the parabola when the polynomial is graphed and influences the end behavior of the polynomial.