Q:

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)