Answer: The correct options are (B) [tex]x^2+5x-6[/tex] and (D) [tex]x^2+x-6.[/tex]
Step-by-step explanation: we are given the correct trinomial that can be factored.
We know that a trinomial of the form [tex]x^2+ax+b[/tex] can be factored if we find two real numbers 'c' and 'd' such that
c + d = a and c × d = b.
Option (A) is
[tex]x^2+3x-6.[/tex]
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
[tex]x^2+5x-6.[/tex]
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:
[tex]x^2+5x-6\\\\=x^2+6x-x-6\\\\=x(x+6)-1(x+6)\\\\=(x-1)(x+6).[/tex]
Option (C) is
[tex]x^2+3x-2.[/tex]
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
[tex]x^2+x-6.[/tex]
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:
[tex]x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x+3)\\\\=(x-2)(x+3).[/tex]
Thus, Options (B) and (D) are correct.
Answer: The correct answer is D on edge.
Step-by-step explanation:
