dabdab806
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -3 x2 - 12x - 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-12) Add up the last 2 terms, pulling out common factors : 3 • (x-12) Step-5 : Add up the four terms of step 4 : (x-3) • (x-12) Which is the desired factorization
dabdab806
Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
Answers & Comments
Answer:
1.) (x–3) • (x–12)
2.) (3x + 1)²
3.) 25 • (3x³+2y²) • (3x³+2y²)
4.) (xy³+10) • (x²y⁶–10xy³+100)
Step-by-step explanation:
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The first term is, x2 its coefficient is 1 .
The middle term is, -15x its coefficient is -15 .
The last term, "the constant", is +36
Step-1 : Multiply the coefficient of the first term by the constant 1 • 36 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -15 .
-36 + -1 = -37 -18 + -2 = -20 -12 + -3 = -15 That's it
x2 - 12x - 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-12)
Which is the desired factorization
-9 + -1 = -10 -3 + -3 = -6 -1 + -9 = -10 1 + 9 = 10 3 + 3 = 6 That's it