factor the following polynomial completely: using the fact that x + 2 is a factor =2x^3 + 7x^2 - 3x - 18?

Question

i need it immediately, can u do it with explanation, thanks.. love lots and godbless

Answer 1

I assume you know how to do synthetic substitution?

−02 | +02 +07 −03 −18
−−−| +00 −04 −06 +18
−−−−−−−−−−−−−−−−
−−−| +02 +03 −09 +00

So after dividing by x + 2, you're left with:

(x + 2)(2x² + 3x - 9)

Which factors further to:

(x + 2)(2x − 3)(x + 3)

Answer 2

have you ever found out the field technique? that's the place you draw a normal field with 4 squares, the 1st field includes the 1st term which may well be x^2, the final field could have -18. what's x^2 multiply by skill of -18? that must be -18 nonetheless spectacular? because of the fact one million situations a extensive style is that extensive style...discover the mulitples of -18 Mulitple factors of -18: -18 and one million -one million and 18 -3 and 6 -6 and 3 -2 and 9 -9 and a couple of What 2 numbers provides as much as furnish you 3? you're able to placed those 2 numbers interior the the rest squares, doesnt matter the place..pull out the GCF enable's see... it ought to be the two -6 and 3 or -3 and 6 spectacular? properly the respond is -3 and 6 components 3x the respond is (x-3)

Answer 3

2X^3+7x^2-3x-18 and x+2 is a factor - so that means that x+2 divides that poly with no remainder. when we do that :

_____2x^2+3x-9________
x+2 |2x^3+7x^2-3x-18

so 2X^3+7x^2-3x-18 = (x+2)(2x^2+3x-9). But 2x^2+3x-9 can be factored further, 2x^2 is 2x *x,, 9 is 3*3, and the middle term 3x is 2x*3 -x*3. so that means that poly breaks down to (2x-3)(x+3), so the complete factorization of 2x^3+7x^2-3x-18 is (x+2)(2x-3)(x+3)

Answer 4

2x^3+7x^2-3x-18
=2x^2(x+2)+3x(x+2)-9(x+2)
=(x+2)(2x^2+3x-9)
=(x+2)(2x^2+6x-3x-9)
=(x+2){2x(x+3)-3(x+3)}
=(x+2)(x+3)(x-3)