To find the remainder when the polynomial px² + 7x + 3 is divided by x + 4, we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial f(x) by a linear polynomial of the form x – c is simply f(c).
In our case, we need to evaluate the polynomial at x = -4 since we have x + 4. Therefore, we substitute -4 into the polynomial:
f(-4) = p(-4)² + 7(-4) + 3
Calculating each term:
- p(-4)² = p(16) = 16p
- 7(-4) = -28
- 3 = 3
Now, combining these results, we get:
f(-4) = 16p – 28 + 3 = 16p – 25
Thus, the remainder when px² + 7x + 3 is divided by x + 4 is 16p – 25.