factorize y^2+13y+40
Answers
Answer:
y²+8y+5y+40
y(y+8)+5(y+8)
(y+8)(y+5)
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Answer:
y^2+13y+40 = (y+8)(y+5)
Step-by-step explanation:
Factoring y2+13y+40
The first term is, y2 its coefficient is 1 .
The middle term is, +13y its coefficient is 13 .
The last term, "the constant", is +40
Step-1 : Multiply the coefficient of the first term by the constant 1 • 40 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is 13 .
-40 + -1 = -41
-20 + -2 = -22
-10 + -4 = -14
-8 + -5 = -13
-5 + -8 = -13
-4 + -10 = -14
-2 + -20 = -22
-1 + -40 = -41
1 + 40 = 41
2 + 20 = 22
4 + 10 = 14
5 + 8 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 5 and 8
y2 + 5y + 8y + 40
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y+5)
Add up the last 2 terms, pulling out common factors :
8 • (y+5)
Step-5 : Add up the four terms of step 4 :
(y+8) • (y+5)
Which is the desired factorization
Final result :
(y + 8) • (y + 5)