Question 65095
(a + 2b)^2 
Answer:
= a^2 + 4ab + 4b^2 
cannot be multiplied out any further 
4x^2 + 9 
Answer:
cannot be factored in the Real Number System

Factor the expression 4x^2 - 9 
Answer:
(2x-3)(2x+3)
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Factor the expression 9x^2 - 12x + 4 
=(3x-2)^2
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Factor 16x^2 + 40xy + 25y^2
=(4x+5y)^2
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8x^3 + 1
Answer: 
= (2x + 1)(4x^2 - 2x + 1) 
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Factor the expression x^3 + 8y^3
=(x+2y)(x^2-2xy+4y^2)
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Factor the expression x^9 - 27y^6 
=(x^3-3y^2)(x^6-3x^3y^2+9y^4)
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You are told that f(x) is a polynomial, and you are told that when we divide x+1 into f(x) then the remainder is 0. Based on this information, which of these statements is necessarily true? 
Answer:
f(-1) = 0 
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Divide x + 1 into f(x) = 2x^3 + 3x^2 + 9x + 5. Write your answer in the form given by the Division Algorithm; in other words, write your answer as: 2x^3 + 3x^2 + 9x + 5 = q(x)(x+1) + r(x) for some polynomials q(x) and r(x).
If you know synthetic division:
-1)....2....3....9....5
.......2....1....8.|.-3
f(x)=(2x^2+x+8)(x+1)-3
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Cheers,
Stan H.