Factor Polynomials

Front

What is a polynomial?

Back

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

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the area of a rectangle formula?

Back

The area of a rectangle is calculated as Area = Length × Width.

Front

How do you find the length of a rectangle if you know the area and width?

Back

To find the length, divide the area by the width: Length = Area / Width.

Front

What is the difference of squares?

Back

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

Front

Factor the polynomial x² - 36.

Back

(x + 6)(x - 6) - This is an example of the difference of squares.

Front

What is the sum of two numbers if their product is 63 and one number is 7?

Back

The other number is 9, since 7 + 9 = 16 and 7 × 9 = 63.

Front

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

Back

Look for two numbers that multiply to c and add to b, then express it as (x + m)(x + n).

Front

What is the product of (x + 7)²?

Back

x² + 14x + 49 - This is found by applying the square of a binomial formula.

Front

What is the factored form of k² + 7k + 10?

Back

(k + 2)(k + 5) - This is found by identifying two numbers that add to 7 and multiply to 10.