Flashcard on Factoring (AC Method)

Front

What is the AC Method in factoring?

Back

The AC Method is a technique used to factor quadratic expressions of the form ax² + bx + c by finding two numbers that multiply to ac and add to b.

Front

Factor the expression: 4x² - 25x + 25

Back

(x-5)(4x-5)

Front

Factor the expression: 2m² + 3m - 9

Back

(m + 3)(2m - 3)

Front

What are the steps to factor a quadratic expression using the AC Method?

Back

1. Identify a, b, and c in ax² + bx + c. 2. Calculate ac. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the middle term using these numbers. 5. Factor by grouping.

Front

Factor the expression: 2x² - 13x - 70

Back

(2x+7)(x-10)

Front

Factor the expression: 5x² - 28x + 32

Back

(5x-8)(x-4)

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors, which are simpler expressions that multiply together to give the original expression.

Front

Factor the expression: 4n² - 17n - 15

Back

(n-5)(4n+3)

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the shape of the parabola represented by the quadratic expression and influences the factoring process.