Question

Multiply. (x – 4)(x^2 – 5x + 3)?

1) x^3 + 3x^2 + 11x – 12
2) x^3 – 5x^2 + 13x – 12
3) x^3 – 9x^2 + 23x – 12
4) x^3 – x^2 + 17x – 12

Answer 1

3) `x^3-9x^2+23x-12`

Explanation:

`(x-4)(x^2-5x+3)`

Always take the first term of the first brackets (i.e. `x`) and multiply it by each term in the second bracket. Then do the same for `-4` and simplify the expanded expression:

`x*x^2=x^3`
`x*-5x=-5x^2`
`x*3=3x`

`-4*x^2=-4x^2`
`-4*-5x=20x`
`-4*3=-12`

Therefore,

`(x-4)(x^2-5x+3)=x^3-5x^2+3x-4x^2+20x-12`
`(x-4)(x^2-5x+3)=x^3-9x^2+23x-12`

Answer 2

Option 3

Explanation:

Observe that the solutions to choose from all have different `x^2` and different `x` terms. So we can pick on either of these to make our selection.

I choose the `x` term

`"First bracket"color(white)("dd")S"econd bracket"`
`color(white)("dd")obrace(color(white)(".dd")xcolor(white)("d"))color(white)("dddd") xxobrace(color(white)("dddd")3color(white)("ddddd"))=+color(white)(".")3x`
#color(white)("dd")(-4)color(white)("dddd") xxcolor(white)( "dd")(-5x)color(white)("d.d")=ul(color(white)(".")+20xlarr" Add")#
`color(white)("dddddddddddddddddddddddddddd")23x`

Of the choices option 3 has `23x`