Question

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.

Answer 1

The factorization of 2x² + 5x + 3 is (2x + 3)(x + 1)

Answer 2

The factorization of 2x² + 5x + 3 is (2x + 3)(x + 1)

Explanation:

* Lets explain how to factor a trinomial in the form ax² ± bx ± c:

- Look at the c term first.

# If the c term is a positive number, then its factors r , s will both

be positive or both be negative it depends on the sign of b, if b

positive then both are positive if b negative then both are 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) where a = hk , c = rs and b = rk - hs

* Lets solve the problem

∵ The equation is 2x² + 5x + 3

∵ The general form of the trinomial is ax² + bx + c

∴ a = 2 , b = 5 , c = 6

∵ c is positive

∴ Its factors r and s have same sign

∵ a = 2

∵ The factors of a are h , k

∵ 2 = 2 × 1

∴ h = 2 and k = 1

∵ The factors of c are r , s

∵ 3 = 3 × 1

∴ r = 3 and s = 1

∵ The brackets are (hx + r)(kx - s)

∴ 2x² + 5x + 3 = (2x + 3)(x + 1)

∴ The factorization of 2x² + 5x + 3 is (2x + 3)(x + 1)