Understanding the Remainder Theorem

What is the main purpose of the remainder theorem?

• To solve quadratic equations

• To find the quotient of polynomial division

• To directly find the remainder of polynomial division

• To simplify polynomials

In synthetic division, what is the first step when dividing by a binomial like X + 2?

• Add 2 to all coefficients

• Divide all coefficients by 2

• Set X + 2 equal to zero and solve for X

• Multiply all coefficients by 2

What is the remainder when using synthetic division for the polynomial x^4 + 7x^3 + 5x^2 - 4x + 15 divided by X + 2?

• 3

• 5

• 0

• 7

How does the remainder theorem simplify finding the remainder of a polynomial division?

• By adding the coefficients

• By multiplying the coefficients

• By substituting the root of the divisor into the polynomial

• By using long division

What is the result of substituting X = -2 into the polynomial x^4 + 7x^3 + 5x^2 - 4x + 15?

• 3

• 0

• 7

• 5

In the second example, what is the value of P(3) for the polynomial 2x^4 - 5x^3 - 3x^2 + x - 5?

• -2

• 0

• 5

• 2

What is the significance of the exponent being even or odd in the remainder theorem?

• It has no significance

• It affects the coefficients

• It changes the degree of the polynomial

• It determines the sign of the result

What is the remainder when dividing 7x^2 - 2x^3 + 1 by X + 1 using the remainder theorem?

• 3

• 0

• 5

• 10

Why might the remainder theorem be preferred over synthetic division?

• It provides the quotient

• It is more accurate

• It is faster and requires fewer steps

• It is easier to understand

What is the first step in applying the remainder theorem to a polynomial?

• Divide the polynomial by the divisor

• Substitute the root of the divisor into the polynomial

• Multiply the polynomial by the divisor

• Add the coefficients of the polynomial