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 does GCF stand for?

Back

GCF stands for Greatest Common Factor, which is the largest factor that two or more numbers have in common.

Front

How do you find the GCF of 8r^3 and 16r^2?

Back

The GCF is 8r^2, as it is the highest factor that divides both terms.

Front

Factor the polynomial: 3x^2 - 7x + 2

Back

(x - 2)(3x - 1)

Front

Factor the expression: x^2 - 5x

Back

x(x - 5)

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all terms of the polynomial.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states: a^2 - b^2 = (a - b)(a + b).

Front

Factor the expression: x^2 - 9

Back

(x - 3)(x + 3) - this is an example of the difference of squares.

Front

What is the quadratic formula?

Back

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