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

3 years ago

Plz help me by answering these circled questions in steps plz

igor_vitrenko [27]

a- is -28 and i’m working out the rest for you now

3 0

3 years ago

Find the next item in the sequence. 15, 30, 45, 60, ...

amid [387]

The rate of change is 15. We know this because 30 - 15 = 15, 45 - 30 = 15, and 60 - 45 = 15.

The next item in the sequence would be 75, since 60 + 15 = 75.

4 0

3 years ago

Read 2 more answers

6(2) - 7(8 + 6 - 3(2)

san4es73 [151]

Answer:

-44

Step-by-step explanation:

12-7(8+6-6)

12-7(8)

12-56

-44

7 0

2 years ago

Read 2 more answers