x^2+6x+9 is divided by x+3
Answers
1.1 Factoring x2 + 6x + 9
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3. + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
x2 + 3x + 3x + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization
1.2 Cancel out (x+3) which appears on both sides of the fraction line.
Final answer is (x+3)
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