We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a binomial in the form (x - a), then our remainder will be P(a).

We are dividing:

$(x^2+5x+7)\div(x+k)$

So, a polynomial by a binomial factor.

Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.

We want our remainder to be 3. So, P(a)=P(-k)=3.

Therefore:

$(-k)^2+5(-k)+7=3$

Simplify:

$k^2-5k+7=3$

Solve for k. Subtract 3 from both sides:

$k^2-5k+4=0$

Factor:

$(k-1)(k-4)=0$

Zero Product Property:

$k-1=0\text{ or } k-4=0$

Solve:

$k=1\text{ or } k=4$

So, either of the two expressions:

$(x^2+5x+7)\div(x+1)\text{ or } (x^2+5x+7)\div(x+4)$

Will yield 3 as the remainder.

5 0

2 years ago

Which of these equations represent functions? Check all that apply.

AVprozaik [17]

A is quadratic function
B is equation of a circle
C is equation of a line
D is hiperbolic funciotn

5 0

2 years ago

HELP!! What is the surface area?

irakobra [83]

Answer:

10 & 5.5 is 20

and

6 & 5 is 11

3 0

2 years ago