Question

Which expression is equivalent to x^2 + 5x - 6? Explain how.

(1) (x + 3) (x - 2)

(2) (x + 2) (x - 3)

(3) (x - 6) (x + 1)

(4) (x + 6) (x - 1)

Answer 1

(4) (x + 6)(x - 1)

Explanation:

Hello!

Given expression

`x { }^(2) + 5x - 6`

Find numbers when they are multiplied gives 6 and when they are added which gives 5.

Thus, these numbers are -1 & 6.

`x {}^(2) + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )`

Can also check the multiplied values of these two values.

Hope it helps!

Answer 2

(4)

Explanation:

Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).

Multiples are: +6 and -1

input the two multiples in place of the middle term (+5x)

=x^2+6x-1x-6

Collect like terms

=x(x+6)-1((x+6)

Answer= (x+6)(x-1)

Confirm answer above:

Open bracket

x(x-1)+6(x-1)

x^2-x+6x-6

x^2+5x-6 (initial equation).