Question

Factorization : 3a2-10a+8

Answer 1

Answer:

 (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)

Answer 2

Answer:

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)