SOLUTION: (a + 2b)^2 = a^2 + 4b^2 = a^2 + 4ab + 4b^2 = a^2 + 2ab + 2b^2 cannot be multiplied out any further 4x^2 + 9 = (2x + 3)^2 = (4x + 9)^2 = (3x + 2)^2

Question 65095: (a + 2b)^2
= a^2 + 4b^2
= a^2 + 4ab + 4b^2
= a^2 + 2ab + 2b^2
cannot be multiplied out any further
4x^2 + 9
= (2x + 3)^2
= (4x + 9)^2
= (3x + 2)^2
cannot be factored

Factor the expression 4x^2 - 9 .
Factor the expression 9x^2 - 12x + 4
Factor 16x^2 + 40xy + 25y^2

8x^3 + 1
= (2x + 1)(4x^2 - 2x + 1)
= (2x - 1)(4x^2 + 2x + 1)
= (2x + 1)(4x^2 + 2x - 1)
cannot be factored because it is the sum of two cubes
Factor the expression x^3 + 8y^3
Factor the expression x^9 - 27y^6
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? f(1) = 0
f(0) = 1
f(-1) = 0
f(0) = -1

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).

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(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)
-----------------
Factor the expression 9x^2 - 12x + 4
=(3x-2)^2
----------------
Factor 16x^2 + 40xy + 25y^2
=(4x+5y)^2
------------
8x^3 + 1
Answer:
= (2x + 1)(4x^2 - 2x + 1)
---------------
Factor the expression x^3 + 8y^3
=(x+2y)(x^2-2xy+4y^2)
-----------------------
Factor the expression x^9 - 27y^6
=(x^3-3y^2)(x^6-3x^3y^2+9y^4)
-----------------
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
-------------
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
----------
Cheers,
Stan H.

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