Evaluating Polynomials Using Long Division

This video tutorial teaches how to evaluate polynomials for given values using substitution and long division. It begins with a simple example of substituting a value into a polynomial and solving it step-by-step. The tutorial then explains the long division method for polynomials, addressing common misunderstandings such as sign changes in binomials. The remainder theorem is introduced to verify solutions. Finally, the video covers advanced polynomial evaluation using long division, emphasizing the importance of placeholders for exponent terms.

What is the result of substituting X = 3 into the polynomial X^2 + 2X - 7?

• 5

• 8

• 10

• 12

When using long division to evaluate polynomials, what is a common mistake?

• Using the wrong divisor

• Skipping the subtraction step

• Not changing the sign when forming a binomial

• Forgetting to multiply terms

What is the first term obtained when dividing X^2 + 2X - 7 by X - 3 using long division?

• X

• 2X

• 5X

• 3X

According to the remainder theorem, what does the remainder represent when dividing a polynomial P(X) by X - a?

• The value of P(X) at X = 0

• The constant term of P(X)

• The value of P(a)

• The leading coefficient of P(X)

What is the remainder when evaluating the polynomial 2X^3 - 7 for X = -3 using long division?

• 0

• -61

• -27

• 61