Dividing the polynomial $$ P(x) $$ by $$ x+2 $$ yields a quotient $$ Q(x) $$ and a remainder of 7 . If $$ Q(2)=-1 $$, find $$ P(-2) $$ and $$ P(2) $$. $$ P(-2)=\square $$ $$ P(2)=\square $$

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UpStudy AI · Accepted Answer

We start with the division algorithm for polynomials:

$$
P(x) = (x+2)Q(x) + 7
$$

**Step 1: Calculate $$ P(-2) $$**

Substitute $$ x = -2 $$:

$$
P(-2) = (-2+2)Q(-2) + 7 = 0 \cdot Q(-2) + 7 = 7
$$

Thus,

$$
P(-2) = 7
$$

**Step 2: Calculate $$ P(2) $$**

Substitute $$ x = 2 $$ and use the given $$ Q(2) = -1 $$:

$$
P(2) = (2+2)Q(2) + 7 = 4(-1) + 7 = -4 + 7 = 3
$$

Thus,

$$
P(2) = 3
$$
$$ P(-2) = 7 $$ $$ P(2) = 3 $$

Dividing the polynomial by yields a quotient and a remainder of 7 . If , find and .

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