Gr12 Mathematics: Ch 5.9 Remainder Theorem

What is the remainder when a polynomial p(x) is divided by cx - d?

p(-d/c)

p(cx)

p(d/c) (correct)

p(c/d)

Given a polynomial p(x) and a divisor cx - d, what is the general form of the polynomial division?

p(x) = (cx - d) · R + Q(x)

p(x) = (cx + d) · Q(x) - R

p(x) = (cx + d) · R - Q(x)

p(x) = (cx - d) · Q(x) + R (correct)

What is the degree of the quotient Q(x) when dividing a polynomial p(x) by a linear polynomial cx - d?

One degree less than p(x) (correct)

One degree more than p(x)

Two degrees less than p(x)

The same degree as p(x)

What is the remainder R when dividing a polynomial p(x) by a linear polynomial cx - d?

A constant Signup and view all the answers

What is the expression for the remainder R when dividing a polynomial p(x) by cx - d?

R = p(d/c) Signup and view all the answers

What is the purpose of the Remainder Theorem in polynomial division?

To find the remainder R Signup and view all the answers

What is the value of x that gives the remainder when dividing a polynomial p(x) by cx - d?

x = \frac{d}{c} Signup and view all the answers

What is the relationship between the degrees of the polynomial p(x) and the quotient Q(x) when dividing by a linear polynomial cx - d?

The degree of Q(x) is one less than the degree of p(x) Signup and view all the answers

What is the form of the remainder R when dividing a polynomial p(x) by a linear polynomial cx - d?

R is a constant Signup and view all the answers

What is the purpose of substituting \frac{d}{c} into the polynomial p(x) in the Remainder Theorem?

To find the remainder R Signup and view all the answers

What is the general form of the polynomial division when dividing p(x) by cx - d?

p(x) = (cx - d) \cdot Q(x) + R Signup and view all the answers

What is the relationship between the polynomial p(x) and the divisor cx - d in the Remainder Theorem?

p(x) is divided by cx - d to obtain the remainder Signup and view all the answers

What is the significance of the quotient Q(x) in the Remainder Theorem?

It is a polynomial of one degree less than p(x) if cx - d is a linear polynomial. Signup and view all the answers

What is the role of the divisor cx - d in the Remainder Theorem?

It determines the value of the remainder R. Signup and view all the answers

What is the advantage of using the Remainder Theorem in polynomial division?

It provides an efficient way to compute the remainder R. Signup and view all the answers

What is the relationship between the polynomial p(x) and the remainder R?

R is obtained by evaluating p(x) at x = d/c. Signup and view all the answers

What is the condition for the divisor cx - d to be a linear polynomial?

c and d are both constants. Signup and view all the answers

What is the purpose of the expression p(d/c) in the Remainder Theorem?

It is used to evaluate the remainder R. Signup and view all the answers