Question 195047: regarding algebra factorising: question is 4X + 8 = 4(X + 2)
i was given this question and answer but was not told how to work it out, i understnad how to get 4(X) (4X times 1 equals 4 (X) but i cant see how + 2 is found.
do i have the right idea or am i missing something out.
thanks
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 4x +8
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if we divide both terms by 2, and the multiply both by 2, the expression stays the same.
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(2) 4x/(2) + (2) 8/(2)
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now lets take out the common factors of the numerator, 2
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(2) { 4x/2 +8/2 }
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and now simplify each term
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(2) { 2x +4}
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Normally we do not do all of these steps, we simply define the greatest common factor, and extract it from the expression,,,being careful to respect all of the terms.
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For example:
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3x3 +6x^2 +9x
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The greatest common number factor is 3, and the greatest common variable factor is x
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(3x) { 3x^3/3x +6x^2 /3x +9x/3x }
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3x ( x^2 +2x +3)
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we can check the answer by distributing,
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3x(x^2) = 3x^3 ok,,,3x (2x) = 6x^2 ok,,,3x (3)=9x ok
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one more example, this time with negatives
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5x4 -15x^3 +20x^2 -25x
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greatest common number is 5, greatest common variable is x, therefore 5x
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5x{ 5x^4/5x - 15x^3/5x +20x^2 5x -25x/5x }
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simplying
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5x { x^3 - 3x^2 +4 x - 5 }
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checking: 5x(x^3)=5x^4,,ok,,,,5x (-3x^2)= -15x^3,,ok,,,5x(4x)=20x^2,ok,,,,5x( -5) =-25x, ok.
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just take it step by step, until it becomes second nature
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Good Luck,,,,keep up hard work
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