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Q: Factor the polynomial x2 plus 8x plus 7?

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x2-8x+16 = (x-4)(x-4) when factored

2x(x2+2x+4)

(x-4)(x-4)

(x - 4)(x - 4)

x² + 8x + 15 = (x + 5)(x + 3)

x2 + 8x + 15 = (x + 3)(x + 5)

x2 + 8x + 15 = (x + 3) (x + 5).

(x + 6)(x + 2)

That does not factor neatly.

x2-8x+15 = (x-3)(x-5)

8x(x2-x+1)

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)

x2 + 8x = x(x+8)

(x + 8)(x + 1)

(x+1)(x+9)

16 does that.

(x + 6)(x + 2)

(x-3)(x+8)

(x-3)(x+7)

(x - 3)(x - 3)

(x-2)(x-3)

x2 + 12x + 32 = (x + 8)(x + 4)

(x + 8)(x + 1)

x2 + 8x + 12 = (x + 6) (x + 2)

(x+1)(x+9)