need help with coming uo with the 0 they are placing in the equation

Question

3x4 + x2 -4x +5

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x2 +2x

Answer 1

I think you might be asking about the method used to divide the two polynomials.

To divide 3x⁴ + x² -4x + 5 by x² + 2x you MUST put in placeholder zeros in each of the missing terms. Notice that "3x⁴ + x² -4x + 5" is missing an x³ term? So you MUST put in 0x³ in the polynomial in order to do the division. So it becomes: "3x⁴ + 0x³ + x² -4x + 5". And, to be consistent, we'll do the same with "x² + 2x". It is missing a constant term at the end so "x² + 2x + 0". Adding these "zero terms" doesn't change the problem but it make the division work out. So the problem becomes:

Then you start dividing just like you do any long division problem with numbers. You ask, how many times does x² go into 3x⁴? Or another way to think about it is, "What do you multiply x² by to get 3x4? The answer is 3x². So you put 3x² above like this:

Then multiply 3x² by x² + 2x + 0 and but the result below like this:

And subtract, putting the answer below and then repeat the process until you get to the remainder.

Answer 2

The expression does not have a zero, that is a value of x that makes the rational expression equal to zero.

Review the post for accuracy.

Answer 3

It is NOT necessary to fill the divisor with terms having either a zero coefficients or a zero constant, unless they are between two other terms.

It is necessary to do so for the dividend.

3x^2 - 6 x + 7

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x^2 + 2x | 3x^4 + 0x^3 + x^2 -4x + 5

- ( 3x^4 + 6x^3 )

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- 6x^3 +x^2 -4x + 5

- ( - 6 x^3 - 6x^2 )

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7 x^2 -4x + 5

- ( 7 x^2 + 14x )

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-18x +5

-18x +5 is the remainder.

You could also write it as ( -18x + 5) / ( x^2 + 2x )

and add it to the quotient, 3x^2 - 6x + 7.

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