Question

COSEddQuestions9.75725 pes1Karina wants to solve the following quadratic equation by factoring154.r? – 25.1 +6=0She started the problem as shown below. Help her finish factoring, show all your steps, and solve for x,Show Your WorkCorrect answer

Answer 1

To factor the given equation, rewrite the middle terms as binomials.

`4x^2-24x-x+6=0`

Group the terms and then factor out the common monomial from each group.

`4x(x-6)-(x-6)=0`

Factor the common binomial factor.

`(4x-1)(x-6)=0`

Since the factored form of the expression at the left is

`(4x-1)(x-6)=0`

we may obtain the values inside the squares by multiplying the factors. We may use the FOIL method to obtain each term.

Thus, we get the following.

Product of the first terms:

`(4x)(x)=4x^2`

Product of the Outer Terms:

`(4x)(-6)=-24x`

Product of the Inner Terms:

`(-1)(x)=-x`

Product of the Last Terms:

`(-1)(-6)=6`

Thus, the terms inside the first figures should be -x and -24x, respectively.