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Question 731867: How do i work this one out and then factor it? please help.
4(a + 3)2 – (a + 3) – 18
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How do i work this one out and then factor it? please help.
4(a + 3)2 – (a + 3) – 18
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I don't know what you mean by "work this one out," but it can be factored
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Use ^ (Shift 6) for exponents
4(a + 3)^2 – (a + 3) – 18
sub x for (a+3) temporarily
4x^2 – x – 18
It will be either (x + m)*(4x + n) or (2x + m)*(2x + n)
Since the x term has an odd coefficent, it can't be (2x + m)*(2x + n).
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It will be (x + m)*(4x + n)
Find a pair of factors of 18 that fit.
The signs will be different since it's -18
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18 has 3 pairs of factors
1*18
2*9
3*6
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(x + m)*(4x + n)
The n has to be the odd number, so it's 1, 3 or 9 (either + or minus)
Now it's trial and error.
(x + 2)*(4x - 9) works
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Sub back (a+3) for x
= (a+3+2)*(4a+12-9)
= (a+5)*(4a+3)
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You can expand 4(a + 3)^2 – (a + 3) – 18 first
= 4a^ + 24a + 36 - a - 3 - 18
= 4a^2 + 23a + 15
That might be slightly easier since it's all positive numbers.
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