Question 5 Factor: $$ 3 x^{2}+10 x+8 $$ (A) $$ (3 x+2)(x+4) $$ (B) $$ (3 x+4)(x+2) $$ pry (C) $$ (3 x+1)(x+8) $$ (D) $$ (3 x+2)(3 x+4) $$

Question

UpStudy AI · Accepted Answer

We are given the quadratic expression

$$
3x^2+10x+8.
$$

**Step 1.** Multiply the coefficient of $$x^2$$ by the constant term:

$$
3 \times 8 = 24.
$$

**Step 2.** Find two numbers whose product is $$24$$ and whose sum is $$10$$. The numbers $$4$$ and $$6$$ satisfy:

$$
4 \times 6 = 24 \quad \text{and} \quad 4 + 6 = 10.
$$

**Step 3.** Rewrite the middle term $$10x$$ using $$4x$$ and $$6x$$:

$$
3x^2 + 4x + 6x + 8.
$$

**Step 4.** Factor by grouping:

Group the first two terms and the last two terms:

$$
(3x^2 + 4x) + (6x + 8).
$$

Factor out the common factors from each group:

$$
x(3x + 4) + 2(3x + 4).
$$

**Step 5.** Notice that $$(3x + 4)$$ is common in both groups:

$$
(3x + 4)(x + 2).
$$

Thus, the factored form of the quadratic is:

$$
(3x + 4)(x + 2).
$$

The correct answer is option (B).
The factored form of $$3x^2 + 10x + 8$$ is $$(3x + 4)(x + 2)$$.

Question 5 Factor: \( 3 x^{2}+10 x+8 \) (A) \( (3 x+2)(x+4) \) (B) \( (3 x+4)(x+2) \) pry (C) \( (3 x+1)(x+8) \) (D) \( (3 x+2)(3 x+4) \)