which statement about $4x^{2}+19x - 5$ is true?\none of the factors is $(x - 4)$.\none of the factors is…

which statement about $4x^{2}+19x - 5$ is true?\none of the factors is $(x - 4)$.\none of the factors is $(4x + 1)$.\none of the factors is $(4x - 5)$.\none of the factors is $(x + 5)$.

which statement about $4x^{2}+19x - 5$ is true?\none of the factors is $(x - 4)$.\none of the factors is $(4x + 1)$.\none of the factors is $(4x - 5)$.\none of the factors is $(x + 5)$.

Answer

Explanation:

Step1: Factor the quadratic expression

We use the AC - method for factoring (ax^{2}+bx + c) (here (a = 4), (b=19), (c=-5)). First, find (a\times c=4\times(- 5)=-20). We need two numbers that multiply to (-20) and add up to (19). The numbers are (20) and (-1). Rewrite the middle - term: (4x^{2}+20x - x-5). Group the terms: ((4x^{2}+20x)-(x + 5)). Factor out the greatest common factor from each group: (4x(x + 5)-1(x + 5)). Then, (4x^{2}+19x - 5=(4x - 1)(x + 5)).

Answer:

D. One of the factors is ((x + 5))