Factor+GCF

= When in doubt...Try to factor the GCF out! =

== The first thing you want to do when trying to factor out any quadratic expression is check to see if you can factor out the GCF. The Greatest Common Factor of the terms in a quadratic expression is the largest constant, variable, or product of a constant and variable that can go into each term. The GCF of the terms 3x 2, -6x, and 15 is 3 because 3 is the largest number that goes into 3, -6, and 15 AND not all terms have an x that can be factored out. So to factor the expression 3x2 - 6x + 15 == 1.) Factor out the GCF (divide by 3 for each term) 3x2 ÷ 3 = x2 -6x ÷ 3 = -2x 15 ÷ 3 = 5 2.) You bring the 3 outside the and put inside the parentheses all the terms you just took the GCF out of. So 3(x2 - 2x + 5) 3.) Since you cannot factor out anything else, that would be your final answer. Check your answer by multiplication.

3x 3 ÷ 3x = x 2 9x 2 ÷ 3x = 3x 27x ÷ 3x = 9
Bring the GCF out of the parentheses and rewrite the remaining terms inside the parentheses

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