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Jayden Glover
Mathematics
12 January, 06:22
Factorization : 3a2-10a+8
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Tony Cooke
12 January, 06:24
0
Step-by-step explanation:
3a² - 10a + 8
1. find delta and √delta
∆ = (-10) ²-4*3*8=100-96=4
√∆=2
2. find a1, a2 with formulas (because ∆>0)
a1 = (10+2) / 6 = 2
a2 = (10-2) / 6=4/3
Note: ka²+la+m = k (a-a1) (a-a2)
So answer is 3 (a-2) (a-4/3) = (3a-4) (a-2).
OR: we can find a root from factors 8 (it is 2) and then:
3a²-10a+8 = 3a² - 6a - 4a + 8 = 3a (a-2) - 4 (a-2) = (3a-4) (a-2)
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Demarcus Gilbert
12 January, 06:38
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(a - 2) • (3a - 4)
Step-by-step explanation:
(3a2 - 10a) + 8
Trying to factor by splitting the middle term
2.1 Factoring 3a2-10a+8
The first term is, 3a2 its coefficient is 3.
The middle term is, - 10a its coefficient is - 10.
The last term, "the constant", is + 8
Multiply the coefficient of the first term by the constant 3 • 8 = 24
Find two factors of 24 whose sum equals the coefficient of the middle term, which is - 10.
-24 + - 1 = - 25
-12 + - 2 = - 14
-8 + - 3 = - 11
-6 + - 4 = - 10 That's it
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and - 4
3a2 - 6a - 4a - 8
Add up the first 2 terms, pulling out like factors:
3a • (a-2)
Add up the last 2 terms, pulling out common factors:
4 • (a-2)
Add up the four terms of step 4:
(3a-4) • (a-2)
Which is the desired factorization
Final result:
(a - 2) • (3a - 4)
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