select the correct answer.\nwhat is the complete factorization of $x^{2}+4x - 45$?\na. $(x + 15)(x - 3)$\nb…

select the correct answer.\nwhat is the complete factorization of $x^{2}+4x - 45$?\na. $(x + 15)(x - 3)$\nb. $(x - 9)(x + 5)$\nc. $(x + 9)(x - 5)$\nd. $(x - 15)(x + 3)$

select the correct answer.\nwhat is the complete factorization of $x^{2}+4x - 45$?\na. $(x + 15)(x - 3)$\nb. $(x - 9)(x + 5)$\nc. $(x + 9)(x - 5)$\nd. $(x - 15)(x + 3)$

Answer

Answer:

C. ((x + 9)(x - 5))

Explanation:

Step1: Analyze the quadratic form

For a quadratic (ax^{2}+bx + c) (here (a = 1), (b=4), (c=-45)), we need two numbers (m) and (n) such that (m\times n=ac=- 45) and (m + n=b = 4).

Step2: Find the two numbers

We look for two numbers. The pairs of factors of (-45) are: ((-1,45)), ((1,-45)), ((-3,15)), ((3,-15)), ((-5,9)), ((5,-9)). We find that (9\times(-5)=-45) and (9+(-5)=4).

Step3: Factor the quadratic

Using the formula (x^{2}+bx + c=(x + m)(x + n)), we have (x^{2}+4x-45=(x + 9)(x - 5)). We can also check by expanding ((x + 9)(x - 5)=x^{2}-5x+9x-45=x^{2}+4x-45).