Use the factor theorem to determine if the given binomial is a factor of f(x). f(x)=x^4+8x^3+11x^2-11x+3, x+3

Aneeka Hunt 2021-02-16 Answered
Use the factor theorem to determine if the given binomial is a factor of f(x).
f(x)=x4+8x3+11x211x+3,x+3
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Expert Answer

averes8
Answered 2021-02-17 Author has 92 answers

Step 1
To decide if the given binomial divides the polynomial f(x), using the factor theorem
Step 2
Recall the factor theorem: (xa) is a factor of the polynomial f(x) if and only if f(a)=0. Apply this in the present case with a=3, that is , test whether f(-3) is zero or otherwise.
f(x)=x4+8x3+11x211x+3.
f(3)=81216+99+33+3=0
So, (x+3) is a factor of f(x)
Step 3
Result: x+3 is a factor of f(x) (see factorization above)
f(x)=x4+8x3+11x211x+3
=(x+3)(x3+5x24x+1)

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