7.6 Factoring when a > 1

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 does it mean when a > 1 in factoring?

Back

It means that the leading coefficient of the quadratic expression is greater than 1, which affects how we factor the expression.

Front

Factor the expression: 3x² + 5x - 12

Back

(3x - 4)(x + 3)

Front

Factor the expression: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

Factor the expression: 6x² + 5x − 6

Back

(3x − 2)(2x + 3)

Front

Factor the expression: 2n² + 13n + 15

Back

(2n + 3)(n + 5)

Front

Factor the expression: 5n² - 6n - 27

Back

(5n + 9)(n - 3)

Front

What is the first step in factoring a quadratic expression when a > 1?

Back

Identify the leading coefficient and ensure the expression is in standard form (ax² + bx + c).

Front

What is the 'ac' method in factoring?

Back

The 'ac' method involves multiplying the leading coefficient (a) by the constant term (c) to find two numbers that multiply to ac and add to b.

Front

What are the signs of the factors if the quadratic expression is in the form ax² + bx + c?

Back

The signs of the factors depend on the signs of b and c. If c is positive, both factors will have the same sign; if c is negative, the factors will have different signs.