Question

Dividing Polynomials with Tables Isiah is dividing 2x3 - x2 + 2x + 5 by x + 1 using a division table. His work is shown here. What is the value of A?

Answer 1

Answer:

5

Step-by-step explanation:

We are asked to find the value of A. We know from the question that we need to have the sum of -3x and (A)x equal the third term of the original polynomial, which is 2x. written out in an equation, it looks like this.

$-3x+(A)x=2x$

We can simplify the equation if we add 3x to both sides, which then leaves us with this.

$(A)x=5x$

We can further simplify the equation by dividing both sides by x. This leaves us with our last equation for this problem.

$A=5$

Finally, we have our answer. We can also verify that this is a valid integer by multiplying our, now completed, quotient by the divisor and adding the remainder, which in this case, our remainder is 0, so we will not be including it in our operation.

$(x+1)(2x^{2}-3x+5)$

If our calculations were all correct, the product of these polynomials should equal our dividend, verifying our integer is valid; lo' and behold, it is.

$2x^{3}-x^{2}+2x+5$