Factoring Quadratic Expressions

Definition: The process of writing a quadratic as a product of its factors – two binomials.

A quadratic expression is an expression in the form: ax² + bx + c.

Factoring a quadratic (leading coefficient of 1):
To factor a quadratic in the form x² + bx + c, find two factors of c whose sum is b.

Factoring a quadratic (leading coefficient ≠ 1):
To factor a quadratic in the form ax² + bx + c (where a ≠ 1), after pulling out any common factors, find two numbers whose product is equal to the product if a and c, and whose sum is equal to b.factoring-quadratic-expressions-13-728

More information:

Factoring By Grouping

Factoring Sum and Differences

Complete the Square

Example: Factor 3x² + 11x + 10.

Solution:

Step 1: Determine two numbers whose product is 30 (from 3 × 10) and whose sum is 11.
These are 5 and 6.

Step 2: Expand 11x into two terms with coefficients 5 and 6.
3x² + 6x + 5x + 10

Step 3: Factor by grouping.
3x(x + 2) + 5(x + 2)

Step 4: Factor again.
(x+2)(3x+5)

3x² + 11x + 10 = (x+2)(3x+5)

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