QuestionJune 7, 2025

Factor completely: 3x^2+8x+4 square

Factor completely: 3x^2+8x+4 square
Factor completely:
3x^2+8x+4
square

Solution
4.4(186 votes)

Answer

(3x + 2)(x + 2) Explanation 1. Identify the quadratic expression The expression is 3x^2 + 8x + 4. 2. Find two numbers that multiply to ac and add to b Here, a = 3, b = 8, c = 4. We need numbers that multiply to 3 \times 4 = 12 and add to 8. These numbers are 6 and 2. 3. Rewrite the middle term using these numbers Rewrite 8x as 6x + 2x: 3x^2 + 6x + 2x + 4. 4. Factor by grouping Group terms: (3x^2 + 6x) + (2x + 4). Factor each group: 3x(x + 2) + 2(x + 2). 5. Factor out the common binomial Factor out (x + 2): (3x + 2)(x + 2).

Explanation

1. Identify the quadratic expression<br /> The expression is $3x^2 + 8x + 4$.<br /><br />2. Find two numbers that multiply to $ac$ and add to $b$<br /> Here, $a = 3$, $b = 8$, $c = 4$. We need numbers that multiply to $3 \times 4 = 12$ and add to $8$. These numbers are $6$ and $2$.<br /><br />3. Rewrite the middle term using these numbers<br /> Rewrite $8x$ as $6x + 2x$: $3x^2 + 6x + 2x + 4$.<br /><br />4. Factor by grouping<br /> Group terms: $(3x^2 + 6x) + (2x + 4)$.<br /> Factor each group: $3x(x + 2) + 2(x + 2)$.<br /><br />5. Factor out the common binomial<br /> Factor out $(x + 2)$: $(3x + 2)(x + 2)$.
Click to rate: