SOLUTION: Use the Factor Theorem to determine whether the first polynomial is a factor of the second. x + 3; 2x^3 + x^2

SOLUTION: Use the Factor Theorem to determine whether the first polynomial is a factor of the second. x + 3; 2x^3 + x^2 - 13x +6

Question 982439: Use the Factor Theorem to determine whether the first polynomial is a factor of the second.
x + 3; 2x^3 + x^2 - 13x +6
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Same as synthetic division to check the roots -3 for the polynomial function 2x^3+x^2-13x+6.

If remainder is 0, then -3 is a root and x+3 is a factor. That's what the Factor Theorem means.

-3________|______2______1_______-13_______6
__________|
__________|____________-6_______15________-6
__________|_____________________________________
________________2_____-5________2________0

Remainder IS zero, so x+3 is a factor of the given polynomial function.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use the Factor Theorem to determine whether the first polynomial is a factor of the second.
x + 3; 2x^3 + x^2 - 13x +6
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If x+3 is a factor, f(-3) = 0
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Using synthetic division you get:
-3)....2....1....-13....6
.......2....-5....2...|..0
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Since the remainder is zero, f(-3)=0, and x+3 is a factor.
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Cheers,
Stan H.
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