Math

Question Find the value of cc if 2x32x-3 is a factor of 8x26x+c8x^2-6x+c.

Studdy Solution

STEP 1

Assumptions1. x3x-3 is a factor of 8x6x+c8x^{}-6x+c . We need to find the value of cc

STEP 2

Since 2x2x- is a factor of 8x26x+c8x^{2}-6x+c, we can say that 8x26x+c8x^{2}-6x+c is divisible by 2x2x-. So, if we substitute xx such that 2x=02x-=0, the value of 8x26x+c8x^{2}-6x+c should be zero.

STEP 3

Find the value of xx that makes 2x3=02x-3=0.
2x3=02x -3 =0

STEP 4

olve the equation for xx.
2x=32x =3x=32x = \frac{3}{2}

STEP 5

Substitute x=32x = \frac{3}{2} into the equation 8x2x+c8x^{2}-x+c.
8(32)2(32)+c=08\left(\frac{3}{2}\right)^{2} -\left(\frac{3}{2}\right) + c =0

STEP 6

implify the equation.
8(94)6(32)+c=08\left(\frac{9}{4}\right) -6\left(\frac{3}{2}\right) + c =0

STEP 7

Further simplify the equation.
189+c=018 -9 + c =0

STEP 8

olve the equation for cc.
c=18c = -18

STEP 9

Calculate the value of cc.
c=9c = -9The value of cc is -9.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord