Question

Complete the equation to show two equivalent expressions. g2 – 4g – 21 = (g – )(g + )

Answer 1

Answer:

$g^2-4g-21=(g-7)(g+3)$

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

$(g-a)(g+b)$

expanding this expression we get:

$g^2+bg-ag-ab$

$g^2+(b-a)g-ab$

Thus we have

$g^2-4g-21=g^2+(b-a)g-ab$

from here we see that for both sides of the equation to be equal, it must be that

$b-a=-4$

$-ab=-21$.

Getting rid of the negative signs we get:

$a-b=4$

$ab=21$

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for $a$ and $b$ systematically.

The solutions to this set are $a=7$ and $b=3$. (you have to guess on this—it's easier)

Therefore, we have

$(g-a)(g+b)=(g-7)(g+3)$

which completes our equation

$\boxed{ g^2-4g-21=(g-7)(g+3)}$

Answer 2

Answer:

I think that the answer is -7&3