Question

One factor of the polynomial 3x3 + 20x2 - 21x + 88 is (x + 8). what is the other factor of the polynomial? (note: use long division.)
oa (3x2 - 4x+11)
b. (3x - 4x)
c. (3x2 +11)
d. (3x2 + 4x - 11)

Answer 1

The other factor of the polynomial is a. 3x2-4x+11

Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)

We need to find another factor using long division method

So,

We will divide the polynomial by the factor to find the another factor

Therefore,

$\sqrt[x+8]{3x^3+20x^2-21x+88}$

Now calculating

First multiplying $3x^2$ with (x+8) so , $3x^2$ will be in the quotient

We get $3x^3+24x^2$

simplifying the calculation for $3x^3+20x^2$ and $3x^3+24x^2$

We get the remainder is $-4x^2-21x+88$

Second we will multiply -4x with (x+8) Where -4x will be in the quotient

We get $-4x^2-32x$ and then we will simplify the equation

We get 11x +88 as a remainder

The quotient we get is $3x^2-4x$

Third we will multiply +11 with (x+8) Where +11 will be in the quotient

we get 11x+88

Simplifying the equation we get the remainder 0

So the quotient we get is  (3x2 - 4x+11)

Hence the another factor of the polynomial is  (3x2 - 4x+11)

Learn more about Long division method here

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