Question 1004098: Which of the following is a factor of (x^4-27x^2-14x+120)
A. x+2 , B. x-3 , C. x+4 , D. x+5
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Simplify (x^3+5x^2+5x-2) divided by (x+2).
A, x^2-3x-1 , B. x^2-3x+1, C. x^2+3x-1 , D. x^2+3x+1
thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first problem to get you started.
The best way to do this problem is to check each answer choice
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Let's check choice A. This factor is x+2, so solve x+2 = 0 to get x = -2
Plug in x = -2 and evaluate
y = x^4-27x^2-14x+120
y = (-2)^4-27(-2)^2-14(-2)+120 ... replace each x with -2
y = 56
The result y = 56 is NOT zero, so x = -2 is NOT a root of the polynomial.
Since x = -2 is NOT a root of the polynomial, this means x+2 is NOT a factor of the polynomial.
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Let's check choice B. This factor is x-3, so solve x-3 = 0 to get x = 3
Plug in x = 3 and evaluate
y = x^4-27x^2-14x+120
y = (3)^4-27(3)^2-14(3)+120 ... replace each x with 3
y = -84
The result y = -84 is NOT zero, so x = 3 is NOT a root of the polynomial.
Since x = 3 is NOT a root of the polynomial, this means x-3 is NOT a factor of the polynomial.
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Let's check choice C. This factor is x+4, so solve x+4 = 0 to get x = -4
Plug in x = -4 and evaluate
y = x^4-27x^2-14x+120
y = (-4)^4-27(-4)^2-14(-4)+120 ... replace each x with -4
y = 0
The result y = 0 is zero, so x = -4 is definitely a root of the polynomial.
Since x = -4 is a root of the polynomial, this means x+4 is a factor of the polynomial.
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Let's check choice D. This factor is x+5, so solve x+5 = 0 to get x = -5
Plug in x = -5 and evaluate
y = x^4-27x^2-14x+120
y = (-5)^4-27(-5)^2-14(-5)+120 ... replace each x with -5
y = 140
The result y = 140 is NOT zero, so x = -5 is NOT a root of the polynomial.
Since x = -5 is NOT a root of the polynomial, this means x+5 is NOT a factor of the polynomial.
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Summary:
Only x+4 is a factor of the polynomial. So only choice C is the answer.
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