the factorization of $x^{2}+3x - 4$ is modeled with algebra tiles. what are the factors of $x^{2}+3x - 4$…

the factorization of $x^{2}+3x - 4$ is modeled with algebra tiles. what are the factors of $x^{2}+3x - 4$? (x + 4) and (x - 4) (x + 3) and (x - 4) (x + 4) and (x - 1) (x + 3) and (x - 1)

the factorization of $x^{2}+3x - 4$ is modeled with algebra tiles. what are the factors of $x^{2}+3x - 4$? (x + 4) and (x - 4) (x + 3) and (x - 4) (x + 4) and (x - 1) (x + 3) and (x - 1)

Answer

Explanation:

Step1: Recall factoring quadratic form

For a quadratic expression (ax^{2}+bx + c) (here (a = 1), (b=3), (c=-4)), we need to find two numbers (m) and (n) such that (m\times n=ac=- 4) and (m + n=b = 3).

Step2: Find the two - numbers

The numbers are (4) and (-1) since (4\times(-1)=-4) and (4+( - 1)=3).

Step3: Rewrite the middle term

Rewrite (x^{2}+3x - 4) as (x^{2}+4x-x - 4).

Step4: Group the terms

((x^{2}+4x)-(x + 4)).

Step5: Factor out common factors from each group

(x(x + 4)-1(x + 4)).

Step6: Factor out the common binomial factor

((x + 4)(x-1)).

Answer:

C. ((x + 4)) and ((x - 1))