ChatterBank2 mins ago

# Answers

Best Answer

No best answer has yet been selected by loz58. Once a best answer has been selected, it will be shown here.

For more on marking an answer as the "Best Answer", please visit our FAQ.2x^3 + x^2 -13x +6 = 0

If (x - 2) is a factor of the above, then it can be written

(x - 2) (f(x)) = 0

so either (x -2) = 0 or f(x) = 0

If x - 2 = 0 then x = 2

Put x = 2 into the original equation and see if it equals 0.

If it does, then (x - 2) was a factor of the given expression.

So

(x - 2) (ax^2 + bx + c) = 0

Since this has to expand to 2x^2 + . . . etc

then x multiplied by ax^2 has to = 2x^3

so therefore a = 2

(x - 2) (2x^2 + bx + c) = 0

Now to determine b, look at the x^2 term

(x) multipied by (bx) + (-2) times (2x^2) has to = + x^2

so bx^2 -4x^2 = x^2

so b = 5

(x - 2) (2x^2 + 5x + c) = 0

Now to determine c, look at the term without x

(-2) multipied by (c) = 6

so c = -3

That gives (x - 2) (2x^2 + 5x - 3) = 0

Double-check by expanding this to confirm that all terms agree.

. . . . . . . . . . . . . . . . . . . .

(x - 2) (2x^2 + 5x - 3) = 0

so either (x - 2) = 0 . . . so

**x = 2 is one solution**

or (2x^2 + 5x - 3) = 0

You could now attempt to factorise the quadratic (2x^2 + 5x - 3) but there are no integer factors.

You will have to use the formula for solving a quadratic to give the remaining two roots

x = (-b +/- SQR (b^2 - 4ac)) / 2a

This wil give you

**the remaining two solutions.</b**

**
You can also do a long diviison of 2x3+x2-13x+6 of x-2 **

and you do it in the classic fashion:

x+2 into 2x3 goes 2x2 times, and x+2 times 2x2 is 2x3+4x2 and so you write:

_ 2x2__________

x-2 I 2x3 + x2 -13x + 6

2x3 - 4x2

--------------

-5x2 this is where you subtract

and then you say x-2 into -5x2 goes -5x times and -5x times x-2 is -5x2 + 10

put that under and subtract....

and I think along the top you will generate

2x2 - 5x +3 along the top

and you do it in the classic fashion:

x+2 into 2x3 goes 2x2 times, and x+2 times 2x2 is 2x3+4x2 and so you write:

_ 2x2__________

x-2 I 2x3 + x2 -13x + 6

2x3 - 4x2

--------------

-5x2 this is where you subtract

and then you say x-2 into -5x2 goes -5x times and -5x times x-2 is -5x2 + 10

put that under and subtract....

and I think along the top you will generate

2x2 - 5x +3 along the top

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