How do you factor #3x^2 + 7x + 2#?

Question

Eli Assouline · Accepted Answer

(3x + 1)(x + 2)

Use the new AC Method to factor trinomials (Socratic Search) #y = 3x^2 + 7x + 2 =# 3(x = p)(x + q) Converted trinomial #y' = x^2 + 7x + 6 = #(x + p')(x + q') Factor pair of (6) --> (1, 6). This sum is 7 = b. Then p' = 1 and q' = 6. Back to y, #p = 1/3# and #q = 6/3 = 2.# #y = 3(x + 1/3)(x + 2) = (3x + 1)(x + 2)#

Nathan Axel · Answer

undefined To factor the quadratic expression 3x^2 + 7x + 2, you need to find two numbers that multiply to give you the product of the coefficient of x^2 term (3) multiplied by the constant term (2), which is 6, and add up to the coefficient of the x term (7). The numbers are 6 and 1. So, you can rewrite the expression as (3x + 1)(x + 2).

Avery Alexander · Answer

undefined To factor the quadratic expression 3x^2 + 7x + 2, you can use the factoring by grouping method or the quadratic formula. Here, factoring by grouping is applicable.

First, multiply the coefficient of the x^2 term (3) by the constant term (2), which gives you 6.

Then, find two numbers that multiply to give you 6 and add to give you the coefficient of the x term (7). These numbers are 6 and 1.

Next, split the middle term (7x) using the two numbers found in the previous step. So, the expression becomes 3x^2 + 6x + x + 2.

Now, factor by grouping:
(3x^2 + 6x) + (x + 2)

Take out the common factors from each pair:
3x(x + 2) + 1(x + 2)

Now, notice that (x + 2) is a common factor:
(x + 2)(3x + 1)

So, the factored form of 3x^2 + 7x + 2 is (x + 2)(3x + 1).