How do you factor the expression #3x^2+7x-6#?

Question

Eva Abramson · Accepted Answer

(3x - 2)(x + 3)

Use the systematic new AC Method to factor trinomials (Socratic Search) #y = 3x^2 + 7x - 6 =# 3(x + p)(x + q) Converted trinomial: #y' = x^2 + 7x - 18 = #(x + p')(x + q'). p' and q' have opposite signs. Factor pairs of (ac = -18) --> (-2, 9). This sum is 7 = b. Then p' = -2 and q' = 9. Therefor, #p = (p')/a = -2/3# and #q = (q')/a = 9/3 = 3.# Factored form: y = 3(x - 2/3)(x + 3) = (3x - 2)(x + 3)

Ethan Adkins · Answer

undefined To factor the expression 3x^2 + 7x - 6, you need to find two numbers that multiply to give you (3 * -6) = -18 and add to give you 7 (the coefficient of the middle term, x).

The two numbers are 9 and -2.

So, you can rewrite the expression as:

3x^2 + 9x - 2x - 6

Now, group the terms:

(3x^2 + 9x) + (-2x - 6)

Factor out the greatest common factor from each group:

3x(x + 3) - 2(x + 3)

Now, you can see that both groups have a common factor of (x + 3):

(x + 3)(3x - 2).

Savannah Anderson · Answer

undefined To factor the expression $3x^2 + 7x - 6$, we need to find two numbers that multiply to give $3 \times (-6) = -18$ and add to give $7$. These numbers are $9$ and $-2$. Then, we can rewrite the expression as:
$$3x^2 + 9x - 2x - 6$$
Next, we group the terms:
$$(3x^2 + 9x) + (-2x - 6)$$
Now, we factor out the greatest common factor from each group:
$$3x(x + 3) - 2(x + 3)$$
Finally, we factor out the common binomial factor $x + 3$:
$$(x + 3)(3x - 2)$$
So, the factored form of the expression $3x^2 + 7x - 6$ is $(x + 3)(3x - 2)$.