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Question 449967: Factor the polynomial:
1. x^2 - 49.
2. 2a^4 - 21a^3 + 49a^2
3. y^3 + 2y^2 - 81y - 162
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 1. x^2 - 49
This is the difference of two squares: x^2-49 = (x+7)(x-7)
2. 2a^4 - 21a^3 + 49a^2
This has a factor of a^2: 2a^4 - 21a^3 + 49a^2 = a^2(2a^2 - 21a + 49)
The expression inside the parentheses can be further factored as:
2a^2 - 21a + 49 = (2a-7)(a-7)
So the factorization is 2a^4 - 21a^3 + 49a^2 = a^2(2a-7)(a-7)
3. y^3 + 2y^2 - 81y - 162
By long division, you can confirm that y+2 is one of the factors, with a remainder y^2-81
This can be further factored: y^2-81 = (y+9)(y-9)
So the factorization is y^3 + 2y^2 - 81y - 162 = (y+2)(y+9)(y-9)
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