Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is typically written as (x - p)(x - q), where p and q are the roots of the equation.

Front

Factor the expression: x² - 2x - 15

Back

(x - 5)(x + 3)

Front

Factor the expression: n² + 16n + 63

Back

(n + 7)(n + 9)

Front

Factor the expression: n² + 5n - 6

Back

(n - 1)(n + 6)

Front

Factor the expression: r² - 16r + 60

Back

(r - 6)(r - 10)

Front

Factor the expression: a² - a - 12

Back

(a - 4)(a + 3)

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to identify the coefficients of the quadratic expression in the form ax² + bx + c.

Front

What does it mean if a quadratic expression cannot be factored?

Back

It means that the expression does not have rational roots, and it may be expressed in its simplest form or solved using the quadratic formula.

Front

What is the relationship between the roots and the factors of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the equation.