Determine a value for a that would make this expression factorable then factor completely: 2x^2-5x^2-18x+a

Answer 1

As written you have 2x^2 - 5x^2 - 18x + a

= -3x^2 -18x + a

divide by -3

(-3)(x^2 -6x + a) If a = 9 then it equals

(-3)(x-3)^2

but you probably meant 2x^3 as the leading term of the expression

then a=45

2x^3 - 5x^2 -18x + 45 factors into

2x^2(x-5/2) -18(x - 5/2)

(2x^2-18)(x-5/2) =

2(x^-9)(x-5/2) =

2(x+3)(x-3)(x-2.5)

Answer 2

If you factor by grouping you can take an x² out of the first 2 terms.

This gives you with x² (2x + 5)

You want the last 2 terms to be something times (2x + 5)

Since you have -18x, this would be (2x) (-9)

If you take out -9 (2x + 5) you would get -18x -45

That means a = -45