QUESTION 1
The given binomial is;
[tex](x+9)(3x-4)[/tex]
First terms are multiplied: [tex]x\times 3x=3x^2[/tex]
Outside terms are multiplied: [tex]x\times -4=-4x[/tex]
Inside terms are multiplied: [tex]9\times 3x=27x[/tex]
Last terms are Multiplied: [tex]9\times -4=-36[/tex]
This gives us;
[tex]=3x^2-4x+27x-36[/tex]
[tex]=3x^2+23x-36[/tex]
QUESTION 2
We want to factor
[tex]6r^5s+4r^4s^2-8r^2s[/tex]
The HCF is [tex]2r^2s[/tex]
We factor to get;
[tex]2r^2s(3r^3+2r^2s-4)[/tex]
QUESTION 3;
[tex]x^2+x-2=0[/tex]
Split the middle term;
[tex]x^2+2x-x-2=0[/tex]
Factor
[tex]x(x+2)-1(x+2)=0[/tex]
[tex](x+2)(x-1)=0[/tex]
[tex](x+2)=0,(x-1)=0[/tex]
[tex]x=-2,x=1[/tex]
The solutions are;
[tex]x=-2[/tex] and [tex]x=1[/tex]
These are the x-intercepts of the graph of the function
[tex]f(x)=x^2+x-2[/tex]
