Question

Help me please please please please please ​

Answer 1

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Answer 2

Answer:
`x^3-x^2`

This is the same as writing x^3-x^2

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Step-by-step explanation:

We divide the two given polynomials. We can apply synthetic division.

The numerator polynomial is
`x^4+3x^3-4x^2` which is the same as
`1x^4+3x^3-4x^2+0x+0`

The sequence of coefficients are: {1,3,-4,0,0}. Those coefficients will be used to set up the synthetic division table in the top row.

The denominator polynomial x+4 means -4 is the test root since it's the solution to x+4 = 0. This -4 goes to the upper left corner.

Check out the diagram below.

The yellow cell in the bottom row represents the remainder. Everything else in the bottom row are coefficients to the quotient polynomial. The coefficients {1,-1,0,0} means we get
`1x^3-1x^2+0x+0` which simplifies to
`x^3-x^2` and that's the final answer.

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Let's check the answer. Multiplying
`(x+4)` with
`(x^3-x^2)` should get us
`x^4+3x^3-4x^2`

Let's see if that happens.

`(x+4)(x^3-x^2)\\\\y(x^3-x^2) \ \text{ ... where } y = x+4\\\\x^3*y-x^2*y\\\\x^3*(x+4)-x^2*(x+4)\\\\x^3*x+x^3*4-x^2*x-x^2*4\\\\x^4+4x^3-x^3-4x^2\\\\x^4+3x^3-4x^2\\\\`

We get the proper product we're after, so the answer is confirmed.

Basically we were given expressions for A and B and computed C = A/B to get the final answer C. This check section is us computing A = BC to confirm the answer.