What is the remainder when the polynomial px^2 + 7x + 3 is divided by x – 4?

To find the remainder when px² + 7x + 3 is divided by x – 4, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x – a, the remainder is f(a).

In this case, we need to evaluate the polynomial at a = 4. This means we will substitute 4 into the polynomial:

f(4) = p(4)2 + 7(4) + 3

Calculating that gives:

f(4) = p(16) + 28 + 3

Now, simplifying further:

f(4) = 16p + 31

Thus, the remainder when dividing px² + 7x + 3 by x – 4 is 16p + 31.

In summary, the remainder is dependent on the value of p. If you know the specific value of p, you can easily compute the numerical remainder.