Factoring Binomials

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 5 or 3x^2 - 2.

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 binomial: x^2 - 16.

Back

(x - 4)(x + 4) - This is a difference of squares.

Front

What is the formula for factoring a perfect square trinomial?

Back

The formula is a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.

Front

Factor the expression: x^2 - 36.

Back

(x - 6)(x + 6) - This is a difference of squares.

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

Factor the expression: x^3 - 4x.

Back

x(x - 2)(x + 2) - Factor out the common term x first.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains three terms, such as x^2 + 5x + 6.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient affects the shape and direction of the graph of the polynomial and can influence the factoring process.