Divide f(x) = x cubed - 4x squared + 2x + 7 by (x - 3). What remainder does the Remainder Theorem give?

1. The Remainder Theorem says that dividing by x minus k leaves the remainder f(k). 2. Here the divisor is x - 3, so k is 3. 3. Evaluate f(3), starting with 3 cubed, which is 27. 4. Next comes negative 4 times 9, which is negative 36. 5. Next comes 2 times 3, which is 6, and finally the constant 7. 6. Adding gives 27 minus 36 plus 6 plus 7, which is 4. 7. So the remainder is 4, and it is not 0, so x - 3 is not a factor. 8. A remainder of 0 would assume the divisor is a factor without testing it. 9. A remainder of 7 reads off the constant term instead of evaluating at 3. 10. A remainder of 10 comes from using k equal to negative 3 by mistake. _Source: OpenStax Precalculus (CC BY 4.0), section 3.6 Zeros of Polynomial Functions_