Question

I dont understand the method the teacher is using and trying to understand the process that shows when the problem is scanned

Answer 1

One method to factor a trinomial in its standard form is the X-box method.

`ax^2+bx+c=0\Rightarrow\text{ Trinomial in standard form }`

The first step for this method is to multiply a and c and place ac at the top:

`\begin{gathered} m^2+3m-28 \\ a=1 \\ b=3 \\ c=-28 \\ ac=1\cdot-28 \\ ac=-28 \end{gathered}`

The second step is to place b at the bottom:

The third step is to find two numbers that multiply to the top number ac and add to the bottom number b. For this, we can use the factors of -28. The factors of -28 are 1,2,4,7,14,28,-1,-2,-4,-7,-14, and -28.

`\begin{gathered} \text{ Multiply }\rightarrow\text{ Adding} \\ -1\cdot28=-28\text{ }\rightarrow-1+28=27 \\ -2\cdot14=-28\rightarrow-2+14=12 \\ $$\boldsymbol{-4\cdot7=-28\rightarrow-4+7=3}$$ \\ -7\cdot4=-28\rightarrow-7+4=-3 \\ -14\cdot2=-28\rightarrow-14+2=-12 \\ -28\cdot1=-28\rightarrow-28+1=-27 \end{gathered}`

As we can see, the factors of -28 that serve us are -4 and 7 because multiplied they give as a result -28 and added they give as a result 3.

Finally, we can write the initial trinomial in its factored form using the two middle numbers from the third step.

`$$\boldsymbol{m}^{\boldsymbol{2}}\boldsymbol{+3m-28=(m-4)(m+7)}$$`