Question

if u can help me with this it would be great.

Answer 1

you really need to find 2 numbers that added to the half number and multiplied the last number

You can do this by applying GFC for the last number

1.

$\begin{gathered} 12\text{ | 2} \\ 6\text{ | 2} \\ 3\text{ | 3} \\ 1\text{ } \end{gathered}$

so we have 2x2x3, or we can group to find the correct sum

than, we will take 4x3

$\begin{gathered} a=4 \\ b=3 \\ c=-7 \end{gathered}$

we need the two numbers to be negative so that both the addition and the multiplication match

c is the half number, for this reason is -7, from the expresion

$x^2-7x+12=0$

so

$\begin{gathered} a=-4 \\ b=-3 \\ c=-7 \end{gathered}$

check

$\begin{gathered} a\times b=12 \\ -4\times-3=12 \end{gathered}$$\begin{gathered} a+b=c \\ (-4)+(-3)=-7 \end{gathered}$

so, the solve is

$\begin{gathered} (x+a)(x+b) \\ (x+(-4))(x+(-3)) \\ (x-4)(x-3) \end{gathered}$

And you can aplly the same method for the following exercises