Question

Which trinomial is factored?

x2 + 3x – 6
x2 + 5x – 6
x2 + 3x – 2
x2 + x – 6

Answer 1

Answer: The correct answer is D on edge.

Explanation:

Answer 2

Answer: The correct options are (B)
`x^2+5x-6` and (D)
`x^2+x-6.`

Step-by-step explanation: we are given the correct trinomial that can be factored.

We know that a trinomial of the form
`x^2+ax+b` can be factored if we find two real numbers 'c' and 'd' such that

c + d = a and c × d = b.

Option (A) is

`x^2+3x-6.`

Here, a = 3 and b = -6.

Since there are no 'c' and 'd' such that c + d = 3 and c × d = -6, so this trinomial cannot be factored.

Option (B) is

`x^2+5x-6.`

Here, a = 5 and b = -6.

Since -6 + 1 = -5 and -6 × 1 = -6, so this trinomial can be factored. The factorization is as follows:

`x^2+5x-6\\\\=x^2+6x-x-6\\\\=x(x+6)-1(x+6)\\\\=(x-1)(x+6).`

Option (C) is

`x^2+3x-2.`

Here, a = 3 and b = 2.

Since there are no 'c' and 'd' such that c + d = 3 and c × d = -2, so this trinomial cannot be factored.

Option (D) is

`x^2+x-6.`

Here, a = 1 and b = -6.

Since 3 + (-2) = 1 and 3 × (-2) = -6, so this trinomial can be factored. The factorization is as follows:

`x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x+3)\\\\=(x-2)(x+3).`

Thus, Options (B) and (D) are correct.