what is the sum and product of 4x2-81=0
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what is the sum and product of 4x2-81=0
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Answer:
The first term is, 4x2 its coefficient is 4 .
The middle term is, +36x its coefficient is 36 .
The last term, "the constant", is +81
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 4 • 81 = 324
Step-2 : Find two factors of 324 whose sum equals the coefficient of the middle term, which is 36 .
-324 + -1 = -325
-162 + -2 = -164
-108 + -3 = -111
-81 + -4 = -85
-54 + -6 = -60
-36 + -9 = -45
-27 + -12 = -39
-18 + -18 = -36
-12 + -27 = -39
-9 + -36 = -45
-6 + -54 = -60
-4 + -81 = -85
-3 + -108 = -111
-2 + -162 = -164
-1 + -324 = -325
1 + 324 = 325
2 + 162 = 164
3 + 108 = 111
4 + 81 = 85
6 + 54 = 60
9 + 36 = 45
12 + 27 = 39
18 + 18 = 36 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 18 and 18
4x2 + 18x + 18x + 81
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+9)
Add up the last 2 terms, pulling out common factors :
9 • (2x+9)
Step-5 : Add up the four terms of step 4 :
(2x+9) • (2x+9)
Which is the desired factorization
M