Question

Find the factors of given polynomial 3ysquare-14y+8

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Answer 1

Answer:

(3y+2)⋅(y+4)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(3y2 + 14y) + 8

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 3y2+14y+8

The first term is, 3y2 its coefficient is 3 .

The middle term is, +14y its coefficient is 14 .

The last term, "the constant", is +8

Step-1 : Multiply the coefficient of the first term by the constant 3 • 8 = 24

Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 14 .

-24 + -1 = -25

-12 + -2 = -14

-8 + -3 = -11

-6 + -4 = -10

-4 + -6 = -10

-3 + -8 = -11

-2 + -12 = -14

-1 + -24 = -25

1 + 24 = 25

2 + 12 = 14 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 12

3y2 + 2y + 12y + 8

Step-4 : Add up the first 2 terms, pulling out like factors :

y • (3y+2)

Add up the last 2 terms, pulling out common factors :

4 • (3y+2)

Step-5 : Add up the four terms of step 4 :

(y+4) • (3y+2)

Which is the desired factorization

Final result :

(3y + 2) • (y + 4)