3v^2+10v+8
Do you want to factor this? If so, factor 8 into two factors that will add to 10 when one of them is multiplied by 3.
3v^2 + 10v + 8.
Factor using AC Method:
A * C = 3 * 8 = 24 = 4 * 6,
Group the 4 terms in 2 factorable
pairs:
(3V^2 + 6) + (4V + 8),
3V(V + 2) + 4(V + 2),
(V + 2) (3V + 4).
fail
The expression 3v^2 + 10v + 8 is a quadratic trinomial. To simplify or factor it, you can follow these steps:
Step 1: Check if the trinomial can be factored by finding two numbers whose product is equal to the product of the coefficient of the squared term (3) and the constant term (8), and whose sum is equal to the coefficient of the linear term (10). The constant term in this case is positive.
Step 2: The product of 3 and 8 is 24, so we need to find two numbers that multiply to give 24 and add up to 10. The two numbers that satisfy these conditions are 4 and 6.
Step 3: Now, rewrite the middle term of the trinomial (10v) using the numbers found in the previous step (4 and 6):
3v^2 + 4v + 6v + 8
Step 4: Group the terms:
(3v^2 + 4v) + (6v + 8)
Step 5: Factor out the common factors from each group:
v(3v + 4) + 2(3v + 4)
Step 6: Notice that (3v + 4) appears in both groups. Thus, you can factor it out:
(3v + 4)(v + 2)
Therefore, the fully factored form of the expression 3v^2 + 10v + 8 is (3v + 4)(v + 2).