Factorization : 3a2-10a+8

(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)

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)