divide 6x²-13x-6 by 2x-3
Answers
Answer:
3x-2
Step-by-step explanation:
STEP1 : Equation at the end of step 1
STEP2:
6x2 - 13x + 6 Simplify ————————————— 2x - 3
Trying to factor by splitting the middle term
2.1 Factoring 6x2 - 13x + 6
The first term is, 6x2 its coefficient is 6 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 6 • 6 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -13 .
-36 + -1 = -37 -18 + -2 = -20 -12 + -3 = -15 -9 + -4 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -4
6x2 - 9x - 4x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-3)
Add up the last 2 terms, pulling out common factors :
2 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(3x-2) • (2x-3)
Which is the desired factorization
Canceling Out :
2.2 Cancel out (2x-3) which appears on both sides of the fraction line.
Final result :
3x - 2
Step-by-step explanation:
6−13x+6x
2
=6−9x−4x+6x
2
=3(2−3x)−2x(2−3x)
=(2−3x)(3−2x)
Divide by −3+2x
=
−(3+2x)
(2−3x)(3−2x)
=−2+3x=3x−2