SOLUTION: Factor the following polynomial completely: 1. 9y4 + 42y3 + 49y2 2. x3 + 6x2 - x � 6 3. 8x3 + 125 4. a. Write a polynomial that can be used to represent the prod

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Question 87052: Factor the following polynomial completely:
1. 9y4 + 42y3 + 49y2
2. x3 + 6x2 - x � 6
3. 8x3 + 125
4. a. Write a polynomial that can be used to represent the product of any 3 consecutive even integers.
b. Use any 3 consecutive even integers to verify that your polynomial represents the product of the 3 integers.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Factor the following polynomial completely:
1. 9y^4 + 42y^3 + 49y^2
= y^2(9y^2+42y+49)
= y^2(3y+7)(3y+7)
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2. x^3 + 6x^2 - x � 6
(x-1)(x^2+7x+6)
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3. 8x3 + 125
= (2x)^3+5^3
=(2x+5)((2x)^2-(2x)*5+5^2)
=(2x+5)(4x^2-10x+25)
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4. a. Write a polynomial that can be used to represent the product of any 3 consecutive even integers.
f(x) = (2x)(2x+2)(2x+4)
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b. Use any 3 consecutive even integers to verify that your polynomial represents the product of the 3 integers.
Let x= 3
f(3) = 6*8*10= 480
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Cheers,
Stan H.