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,
[tex]\sqrt[x+8]{3x^3+20x^2-21x+88}[/tex]
Now calculating
First multiplying [tex]3x^2[/tex] with (x+8) so , [tex]3x^2[/tex] will be in the quotient
We get [tex]3x^3+24x^2[/tex]
simplifying the calculation for [tex]3x^3+20x^2[/tex] and [tex]3x^3+24x^2[/tex]
We get the remainder is [tex]-4x^2-21x+88[/tex]
Second we will multiply -4x with (x+8) Where -4x will be in the quotient
We get [tex]-4x^2-32x[/tex] and then we will simplify the equation
We get 11x +88 as a remainder
The quotient we get is [tex]3x^2-4x[/tex]
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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