Question

topic 3: factoring polynomials

1. ( x^2 + 3x - 40 )

Explanation:

Step1: Find two numbers

We need two numbers that multiply to $-40$ (the constant term) and add up to $3$ (the coefficient of the $x$ term). Let's list the factor pairs of $40$: $(1, 40), (2, 20), (4, 10), (5, 8)$. Now, we need one positive and one negative number since their product is negative. Let's check: $8$ and $-5$. $8\times(-5) = -40$ and $8 + (-5) = 3$. Perfect.

Step2: Factor the quadratic

Using the numbers we found, we can factor $x^2 + 3x - 40$ as $(x + 8)(x - 5)$. Let's verify: $(x + 8)(x - 5) = x^2 - 5x + 8x - 40 = x^2 + 3x - 40$, which matches the original polynomial.

Answer:

$(x + 8)(x - 5)$