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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

4. Factoring Quadratic Expressions

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Exercise 32 Page 221

If possible, factor out the greatest common factor before anything else.

GCF: 3
Expression: 3(a^2+3)

Practice makes perfect

To completely factor the given expression, we will first identify the greatest common factor.

Factor Out the GCF

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 3.

3a^2+9

SplitIntoFactors

Split into factors

( 3)a^2+( 3)3

Factor out 3

3(a^2+3)

Sum of Two Squares

The expression we want to factor is the sum of squares. 3(a^2+3) ⇔ 3( a^2 + sqrt(3)^2) Unluckily — or not! — there is nothing we can do to factor the above expression. The reason for this is that it is the sum and not the difference of two squares. A common misconception is that it is possible to factor the sum of two squares as though it was a difference of two squares. Take care not to make this mistake!

Extra

Difference of Two Squares

If an expression shows a difference of perfect squares, we can factor it using a formula. a^2 - b^2 ⇔ (a+b)(a-b) Note that this only works if we have a difference of two perfect squares. Let's see some examples.

Expression	Rewrite as Perfect Squares	Apply the Formula
x^2-100	x^2- 10^2	(x+10)(x-10)
4x^2-36	(2x)^2- 6^2	(2x+6)(2x-6)
25x^2y^4-49z^6	(5xy^2)^2- (7z^3)^2	(5xy^2+7z^3)(5xy^2-7z^3)

Subchapter links

Lesson Check p.221

Practice and Problem-Solving Exercises p.221-223

Standardized Test Prep p.223

Mixed Review p.223