Factoring

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 factor?

Back

A factor is a number or algebraic expression that divides another number or expression evenly, without leaving a remainder.

Front

How do you factor a quadratic expression of the form ax^2 + bx + c?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers to split the middle term, then factor by grouping.

Front

What is the factored form of x^2 - 5x + 6?

Back

(x - 2)(x - 3) because -2 and -3 multiply to 6 and add to -5.

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: r^2 - 16r + 60.

Back

(r - 6)(r - 10) because -6 and -10 multiply to 60 and add to -16.

Front

What is the factored form of k^2 + 7k + 10?

Back

(k + 2)(k + 5) because 2 and 5 multiply to 10 and add to 7.

Front

How do you factor a trinomial?

Back

To factor a trinomial, look for two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of 3v^2 - 4v - 7?

Back

(3v - 7)(v + 1) because -7 and 1 multiply to -7 and add to -4.

Front

What is the factored form of x^2 + 11x + 24?

Back

(x + 3)(x + 8) because 3 and 8 multiply to 24 and add to 11.