factor the expression completely 6xcube minus 4xsquare minus 16x
Answers
Step-by-step explanation:
MATHS
What must be subtracted from 16x
3
−8x
2
−4x+7 so that the resulting expression has 2x+1 as a factor?
Share
Study later
VIDEO EXPLANATION
ANSWER
If any function let, f(x) is a polynomial and another function is g(x) polynomial having less degree than the f(x). Now if g(x) is a factor of f(x) then g(x) should divide the f(x) leaving no remainder. This means :
f(x)=g(x).q(x)
where q(x) is the quotient .
Now 2x+1 is a factor of 16x
3
−8x
2
−4x+7 then, it should divide by 2x+1 having zero remainder.
Now on dividing :
2x+1
16x
3
−8x
2
−4x+7
=8x
2
−8x+2 with having remainder 5 .
⇒16x
3
−8x
2
−4x+7=(8x
2
−8x+2)(2x+1)+5
Now if we subtract 5 from the given polynomial then
⇒(16x
3
−8x
2
−4x+7)−5
⇒16x
3
−8x
2
−4x+2
⇒
2x+1
16x
3
−8x
2
−4x+2
=8x
2
−8x+2
Now 2x+1 is a factor of our new polynomial.
So, we have to subtract 5 from 16x
3
−8x
2
−4x+7 for having 2x+1 as a factor.