Question

4
multiple choice 8.6 points

1. which of the following is

a factor of $3k^2 + 5k - 8$
a) $3k - 1$
b) $3k - 8$
c) $k + 8$
d) $3k + 8$
$\bigcirc$ $3k + 8$
$\bigcirc$ $3k - 8$
$\bigcirc$ $3k - 1$
$\bigcirc$ $k + 8$
clear my selection

Explanation:

Step1: Factor the quadratic trinomial

We need to factor $3k^2 + 5k - 8$. Find two numbers that multiply to $3\times(-8)=-24$ and add to $5$. These numbers are $8$ and $-3$. Split the middle term:
$$3k^2 + 8k - 3k - 8$$

Step2: Group and factor by pairs

Group the first two and last two terms, then factor out common terms:
$$k(3k + 8) - 1(3k + 8)$$
Factor out $(3k + 8)$:
$$(3k + 8)(k - 1)$$

Answer:

D) $3k+8$