SOLUTION: Which statements are true about the polynomial function? {{{ f(x) = x^4 + 5x^3 - x^2 - 5x }}} Select EACH correct answer. A. f(x) divided by (x + 5) has a remainder of 0.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Which statements are true about the polynomial function? {{{ f(x) = x^4 + 5x^3 - x^2 - 5x }}} Select EACH correct answer. A. f(x) divided by (x + 5) has a remainder of 0.       Log On


   



Question 1127752: Which statements are true about the polynomial function?
+f%28x%29+=+x%5E4+%2B+5x%5E3+-+x%5E2+-+5x+
Select EACH correct answer.
A. f(x) divided by (x + 5) has a remainder of 0.
B. (x - 5) is a factor of f(x).
C. f(5)= 0
D. f(x)= 0 when x = -5.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+f%28x%29+=+x%5E4+%2B+5x%5E3+-+x%5E2+-+5x+
Select EACH correct answer.
A. f%28x%29 divided by %28x+%2B+5%29 has a remainder of 0.
factor +f%28x%29:
+f%28x%29+=+x%5E4+%2B+5x%5E3+-+x%5E2+-+5x+
+f%28x%29+=+%28x%5E3+%2B+5x%5E2+-+x+-+5%29x+
+f%28x%29+=+x%28%28x%5E3+%2B+5x%5E2%29+-+%28x+%2B+5%29%29+
+f%28x%29+=+x%28x%5E2%28x+%2B+5%29+-+%28x+%2B+5%29%29+
+f%28x%29+=+x%28x%5E2+-1%29+%28x+%2B+5%29+
+f%28x%29+=+%28x%5E3+-x%29+%28x+%2B+5%29+
so,
x%5E4+%2B+5x%5E3+-+x%5E2+-+5x+=+%28x%5E3+-+x%29+%2A+%28x+%2B+5%29+%2B+0 -> A is correct

B. %28x+-+5%29+is+a+factor+of+%7B%7B%7Bf%28x%29-> NOT correct

C. f%285%29=+0-> NOT correct
+f%28x%29+=+5%5E4+%2B+5%2A5%5E3+-+5%5E2+-+5%2A5+=1200

D. f%28x%29=+0 when x+=+-5.->correct
use factored form:
+0+=+%28x%5E3+-x%29+%28x+%2B+5%29+
+0+=+%28x+%2B+5%29++=>x=-5

so, you need to choose all correct answers and they are:
A. f%28x%29 divided by %28x+%2B+5%29 has a remainder of 0.
D. f%28x%29=+0 when x+=+-5.