middle term splitting of x^2+27x-182
Answers
Answer:
STEP1:Trying to factor by splitting the middle term
1.1 Factoring x2+27x+182
The first term is, x2 its coefficient is 1 .
The middle term is, +27x its coefficient is 27 .
The last term, "the constant", is +182
Step-1 : Multiply the coefficient of the first term by the constant 1 • 182 = 182
Step-2 : Find two factors of 182 whose sum equals the coefficient of the middle term, which is 27 .
-182 + -1 = -183 -91 + -2 = -93 -26 + -7 = -33 -14 + -13 = -27 -13 + -14 = -27 -7 + -26 = -33 -2 + -91 = -93 -1 + -182 = -183 1 + 182 = 183 2 + 91 = 93 7 + 26 = 33 13 + 14 = 27 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 13 and 14
x2 + 13x + 14x + 182
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+13)
Add up the last 2 terms, pulling out common factors :
14 • (x+13)
Step-5 : Add up the four terms of step 4 :
(x+14) • (x+13)
Which is the desired factorization