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Assuming that it is +15, the answer is either (x + 5)(x + 3) or (x - 5)(x - 3). The sign to be used is the same as that of 8x.
The above assumption is based on the fact that if the constant term were -15 there is no simple factorisation.
x2 + 8x + 15 = (x + 3) (x + 5).
(x + 5)(x + 2)
x2 + 8x = -15 x2 + 8x + 15 = 0 since 15 = 5 x 3 and 5 + 3 = 8, then (x + 5)(x + 3) = 0 x + 5 = 0 or x + 3 = 0 x = -5 or x = -3
If you notice, 8x + 4 = 4(2x + 1), but there is an odd coefficient for x2, so there is guaranteed to be some remainder (that is 8x + 4 is not a factor of the polynomial): (24x3 - 5x2 - 48x - 8) ÷ (8x + 4) = 3x2 - 2x - 5 - (x2 - 12)/(8x + 4)
3x3 - 24x2 + 45x = 3x(x2 - 8x + 15) = 3x(x2 - 3x - 5x + 15) = 3x[ x(x - 3) - 5(x - 3) ] = 3x(x - 5)(x - 3)
x² + 8x + 15 = (x + 5)(x + 3)
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x2 + 8x + 15 = (x + 3)(x + 5)
x2-8x+15 = (x-3)(x-5)
x2 + 8x + 15 = (x + 3) (x + 5).
(x-4)(x-4)
-(x + 5)(x + 6)
(x + 9)(x + 2)
3x3 - 24x2 + 45x = 3x*(x2 - 8x + 15) = 3x*(x - 3)*(x - 5)
(x + 5)(x + 2)
x2 - 2x - 15 = 0
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