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students were asked to write a trinomial that could not be factored using integers. which students followed the given directions.
pat x2 + 3x- 10
sam x2+x-12
mel x2+2x-1
lee x2+2x-3​

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ANSWER

Mel followed the right direction.

EXPLANATION

Pat's trinomial is;

[tex] {x}^{2} + 3x - 10[/tex]

There are factors of -10 that sums up to 3.

[tex]5 + - 2 = 3[/tex]

Hence this trinomial could be factored into (x-2)(x+5)

Sam's trinomial:

[tex] {x}^{2} + x - 12[/tex]

There are factors of -12 that sums up to 1.

4+-3=1

[tex] {x}^{2} + x - 12 = (x + 4)(x - 3)[/tex]

Mel's trinomial:

[tex] {x}^{2} + 2x - 1[/tex]

There are no factors of -1 that sums to 2.

This trinomial cannot be factored.

Lee's trinomial:

[tex] {x}^{2} + 2x - 3[/tex]

There are factors of -3 that sums up to 2

3+-1=2

[tex] {x}^{2} + 2x + 3 = (x + 3)(x - 1)[/tex]

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