Find the values of k so that each remainder is three.
10. (x^2+ 5x + 7) = (x + k)

Step-by-step explanation:

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:

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:

Simplify:

Solve for k. Subtract 3 from both sides:

Factor:

Zero Product Property:

Solve:

So, either of the two expressions:

Will yield 3 as the remainder.

d i think

step-by-step explanation: