PLEASE HELP ME :(Sari is teaching her best friend factor trinomials with a leading coefficient greater than 1. She starts with the trinomial 2x^2 + 5x + 3.Show/describe all of the steps for finding the factorization of the trinomial. Be sure to include the final factorization in your description.
Accepted Solution
A:
Answer:2x² + 5x + 3 = (2x + 3)(x + 1)
Step-by-step explanation:* Lets explain how to factor a trinomial in the form ax² ± bx ± c:- Look at the last term c # If the c term is a positive number, then its factors r , s will both
be positive or both be negative # a has two factors h and k # The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs
# If the c term is a negative number, then either r or s will be negative, but not both.
# a has two factors h and k # The brackets are (hx + r)(kx - s) or (hx - r)(kx + s)where a = hk , c = rs and b = rk - hs
* Lets solve the problem
∵ The equation is 2x² + 5x + 3 = 0
∵ The general form of the equation is ax² + bx + c = 0
∴ a = 2 , b = 5 , c = 3∵ c is positive∴ Its factors r and s have same sign∵ c = 3∵ 3 = 3 × 1
∴ r = 3 and s = 1 ∵ a = 2 ∵ The factors of a are h , k
∵ 2 = 2 × 1
∴ h = 2 and k = 1 ∵ The brackets are (hx + r)(kx + s)
∴ 2x² + 5x + 3 = (2x + 3)(x + 1)