SOLUTION: Please help Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). f(x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). f(x)       Log On


   

Question 616638: Please help
Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient).
f(x) = 8x3 + 31x2 + 23x + 6; c = -3

A) Yes; f(x) = (x + 3)(8x2 + x + 2)
B) Yes; f(x) = (x - 3)(8x2 + 7x - 2)
C) No
D) Yes; f(x) = (x + 3)(8x2 + 7x + 2)


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

f(x) = 8x3 + 31x2 + 23x + 6; c = -3

f(-3) = 0, yes, (x+3) is a factor

Using synthetic Division

-3	8	31	23	6

		-24	-21	-6

	8	7	2	0

f(x) = 8x3 + 31x2 + 23x + 6 = (x+3)(8x^2 + 7x + 2)