Determine for which polynomials (x+2) is a factor. Explain your answer. P(x)=x^4-3x^3-16x-12 Q(x)=x^3-3x^2-16x-12

Jaya Legge

Jaya Legge

Answered question

2021-09-15

Determine for which polynomials (x+2) is a factor. Explain your answer.
P(x)=x43x316x12

Q(x)=x33x216x12

Answer & Explanation

averes8

averes8

Skilled2021-09-16Added 92 answers

We have to show if (x+2) is a factor of the polynomials P(x)=x43x316x12 and Q(x)=x33x216x12 or not.
To check the factor we have to see whether (x+2) satisfies the given polynomials.
If it satisfies the given polynomial or gives the answer 0 i.e P(x)=0 or Q(x)=0 we will say that it is a factor of the polynomial, if it doesn't satisfy the given polynomial we will say that it is not a factor of the polynomial.
First, we will put x+2=0x=2
Now, we will substitute x=-2 in the given polynomials P(x) and Q(x) and see if it is a factor of these polynomials or not.
Now,
P(2)=(2)43(2)316(2)12
P(2)=16+24+3212
P(2)=60
therefore, P(2)0
hence, x=2 is not a factor of the polynomial P(x)
Now,
Q(2)=(2)33(2)216(2)12
Q(2)=812+3212
Q(2)=0
therefore, Q(2)=0
Hence, x=2 is a factor of the polynomial Q(x)

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