6y^2-16y-21 factorise
Answers
Answer:
(4y - 3) • (4y + 7)
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2".
STEP1:Equation at the end of step 1
(24y2 + 16y) - 21
STEP2:Trying to factor by splitting the middle term
2.1 Factoring 16y2+16y-21
The first term is, 16y2 its coefficient is 16 .
The middle term is, +16y its coefficient is 16 .
The last term, "the constant", is -21
Step-1 : Multiply the coefficient of the first term by the constant 16 • -21 = -336
Step-2 : Find two factors of -336 whose sum equals the coefficient of the middle term, which is 16 .
-336 + 1 = -335 -168 + 2 = -166 -112 + 3 = -109 -84 + 4 = -80 -56 + 6 = -50 -48 + 7 = -41 -42 + 8 = -34 -28 + 12 = -16 -24 + 14 = -10 -21 + 16 = -5 -16 + 21 = 5 -14 + 24 = 10 -12 + 28 = 16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 28
16y2 - 12y + 28y - 21
Step-4 : Add up the first 2 terms, pulling out like factors :
4y • (4y-3)
Add up the last 2 terms, pulling out common factors :
7 • (4y-3)
Step-5 : Add up the four terms of step 4 :
(4y+7) • (4y-3)
Which is the desired factorization
Final result :
(4y - 3) • (4y + 7)
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