To factor this trinomial, we can use the technique of factoring by grouping. This involves rewriting the trinomial as the sum of two binomials, and then finding two factors of the constant term (15) that add up to the coefficient of the middle term (8).
We start by writing the trinomial as:
(x^2 + 8x + 15) = (x^2 + 5x + 3x + 15)
Now, we can see that 3 and 12 are factors of 15 that add up to 8, so we can rewrite the expression as:
(x^2 + 8x + 15) = (x^2 + 5x + 3x + 15) = (x^2 + 5x + 3x) + (0x + 15)
= (x(x + 5) + 3(x + 5)) + (0x + 15)
= (x + 3)(x + 5)
Therefore, the other factor is (x + 3). The correct answer is (x + 3).
In mathematics, a number or algebraic expression is a factor if it evenly divides another number or expression, leaving no residue. For instance, the exact values of 12 3 = 4 and 12 6 = 2 show that 3 and 6 are factors of 12. 1, 2, 4, and 12 make up the remaining factors of 12.
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