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19 April, 09:05

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.

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  1. 19 April, 09:26
    0
    The factorization of 2x² + 5x + 3 is (2x + 3) (x + 1)

    Step-by-step 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)
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