Question

Mrs campbell gave her algebra 1 students a list of trinomials to factor for homework. which of these can be factored into two binomials

A. x^2+3x+2
B. x^2+4x+5
C. x^2+5x+7
D. x^2+6x+10

Answer 1

A

Explanation:

A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0.

The discriminant for trinomial
`ax^2+bx+c` is he expression
`D=b^2-4ac.`

Check all options:

A.

`D=3^2-4\cdot 1\cdot 2=9-8=1,`

then

`x_(1,2)=(-b\pm√(D))/(2a)=(-3\pm√(1))/(2)=-2,\ -1.`

Thus,

`x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).`

B.

`D=4^2-4\cdot 1\cdot 5=16-20=-4<0,`

so this trinomial cannot be factored.

C.

`D=5^2-4\cdot 1\cdot 7=25-28=-3<0,`

so this trinomial cannot be factored.

D.

`D=6^2-4\cdot 1\cdot 10=36-40=-4<0,`

so this trinomial cannot be factored.