x^2+32x+252 class 9
solution please give fast it's argent
Answers
Answer:
1.1 Factoring x2-32x+252
The first term is, x2 its coefficient is 1 .
The middle term is, -32x its coefficient is -32 .
The last term, "the constant", is +252
Step-1 : Multiply the coefficient of the first term by the constant 1 • 252 = 252
Step-2 : Find two factors of 252 whose sum equals the coefficient of the middle term, which is -32 .
-252 + -1 = -253
-126 + -2 = -128
-84 + -3 = -87
-63 + -4 = -67
-42 + -6 = -48
-36 + -7 = -43
-28 + -9 = -37
-21 + -12 = -33
-18 + -14 = -32 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -14
x2 - 18x - 14x - 252
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-18)
Add up the last 2 terms, pulling out common factors :
14 • (x-18)
Step-5 : Add up the four terms of step 4 :
(x-14) • (x-18)
Which is the desired factorization
Equation at the end of step
1
:
(x - 14) • (x - 18) = 0
STEP
2
:
Theory - Roots of a product
x^2+32x+252 = 0
x^2+18x+14x+252=0
x(x+18)+14(x+18) =0
(x+14)(x+18) =0
Therefore; x= -14 or x= -18