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 difference of squares?

Back

The difference of squares is a special factoring technique used for expressions in the form a² - b², which can be factored as (a + b)(a - b).

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers or expressions share. It is used to simplify expressions before factoring.

Front

How do you factor by grouping?

Back

To factor by grouping, you group terms in pairs, factor out the GCF from each pair, and then factor out the common binomial factor.

Front

Factor the polynomial: x² - 36

Back

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

Front

Factor the polynomial: 5n³ - 10n² + 3n - 6

Back

(5n² + 3)(n - 2) - This can be factored by grouping.

Front

Factor the polynomial: n² + 16n + 63

Back

(n + 7)(n + 9) - This is a trinomial that can be factored into two binomials.

Front

Factor the polynomial: 8r³ - 16r²

Back

8r²(r - 2) - Factor out the GCF first.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.