How do i determine which binomial is not a factor of 4x^4 -21x^3 -46x^2 + 219x + 180?

Question

a) x+4
b) x+3
c) x-5
d)4x+3

explain . show how to get the answer please?

Answer 1

a)

If binomial (x+4) is a factor of the above polynomial, then the value of the polynomial for x=-4 would be zero. Let us try whether it is so or not.

So find the value of
4(-4)^4 -21(-4)^3 -46(-4)^2 + 219*(-4) + 180

It is 936 and not zero, therefore (x+4) IS NOT a factor of the polynomial.

b) c) and d)

Do the same (i.e. insert -3, 5, and -3/4 into polynomial) and find that in all three cases you get zero value of the polynomial.

Using Excell simplifies the calculations.
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Answer 2

How do i determine which binomial is not a factor of 4x^4 -21x^3 -46x^2 + 219x + 180?
I am assuming you are only looking for one answer,
here use long division to find,
a) x + 4 is the one not a factor.
4x^3 + 37x^2 - 194x + 557
x + 4 (4x^4 -21x^3 -46x^2 + 219x + 180)
4x^4 16x^3
37x^3 - 46x^2 + 219x + 180
37x^3 + 148x^2
-194x^2 + 219x + 180
-194x^2 + 776x
557x + 180
557x + 2228
- 2048
You have a reminder of -2048
Therefore, x + 4 isnt a factor of
4x^4 -21x^3 -46x^2 + 219x + 180.

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