Question

Can u help me with this thank you Which expression is the completely factored form of the expression x2-3x-28 .

Answer 1

Answer:

( x + 4)( x -7 )

Explanation:

We are asked to factor the following expression.

$x^2-3x-28$

Meaning, we have to write the above in the following form

$(x+a)(x+b)$

Now, expanding the above gives

$(x+a)(x+b)=x^2+(a+b)x+ab$

Upon comparing the RHS of the above with our expression, we find that

$\begin{gathered} a+b=-3 \\ ab=-28 \end{gathered}$

In other words, what two numbers sum to -3 and have a product of -28?

Well, if our two numbers are -4 and 7 then

$\begin{gathered} 4*-7=-28 \\ 4+-7=-3 \end{gathered}$

Hence, the factored form of our expression is

$(x+4)(x-7)$