Question

factor the expression completely 6xcube minus 4xsquare minus 16x​

Answer 1

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?

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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.