Question

A) Expand and simplify (4x + 3)(2x - 5)

(2)
+
b) Factorise x2 + 5x + 6
(2)
Total marks: 4

Answer 1

a.
`8x^(2) -14x-15`

b.
`(x+3)(x+2)`

Explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

`4x*2x=8x^(2)`

For O, take the outer terms and multiply

`4x*-5=-20x`

For I, take the inner terms and multiply

`3*2x=6x`

For L, take the last terms and multiply

`3*-5=-15`

After that, add all of them up

`8x^(2) +(-20x)+6x+(-15)=8x^(2)-14x-15`

B. Since the equation is in the form x^2+bx+c,

`(x+?)(x+?)`

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

`(x+3)(x+2)`