factorise the following 6y²+17y-14
Answers
Answer:
( 2y - 7 ) • ( 3y + 2 )
Step-by-step explanation:
STEP1:Equation at the end of step 1 ((2•3y2) - 17y) - 14 STEP2:Trying to factor by splitting the middle term
2.1 Factoring 6y2-17y-14
The first term is, 6y2 its coefficient is 6 .
The middle term is, -17y its coefficient is -17 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 6 • -14 = -84
Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is -17 .
-84 + 1 = -83 -42 + 2 = -40 -28 + 3 = -25 -21 + 4 = -17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 4
6y2 - 21y + 4y - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
3y • (2y-7)
Add up the last 2 terms, pulling out common factors :
2 • (2y-7)
Step-5 : Add up the four terms of step 4 :
(3y+2) • (2y-7)
Which is the desired factorization
Final result :
(2y - 7) • (3y + 2)
Answer:
the factors are
y = 2/3
and y = -7/2