Gr12 Mathematics: Ch 5.8 Cubic Polynomials

What is the formula for performing long division of polynomials?

a(x) = b(x) × Q(x) - R(x)

a(x) = b(x) × R(x) + Q(x)

a(x) = b(x) × Q(x) + R(x) (correct)

a(x) = b(x) × R(x) - Q(x)

What is the first step in performing synthetic division?

Use the opposite sign of the root of the dividend polynomial.

Write the coefficients of the divisor polynomial.

Use the opposite sign of the root of the divisor polynomial.

Write the coefficients of the dividend polynomial. (correct)

What is the equation of the y-intercept of a cubic polynomial?

y = f(0) = b

y = f(x) = d (correct)

y = f(0) = a

y = f(0) = c

What is the purpose of finding the stationary points of a cubic polynomial?

To identify the turning points of the graph Signup and view all the answers

What is the first step in solving a cubic equation using the Factor and Remainder Theorem?

Find the value of k such that f(k) = 0 Signup and view all the answers

What is the general formula for synthetic division?

All of the above Signup and view all the answers

What is the purpose of analyzing the end behavior of a cubic polynomial?

To analyze the behavior of the graph as x approaches positive and negative infinity Signup and view all the answers

What is the formula for the quotient Q(x) in polynomial division?

a(x) / b(x) + R(x) Signup and view all the answers

What is the purpose of finding the x-intercepts of a cubic polynomial?

To find the roots of the polynomial equation Signup and view all the answers

What is the difference between long division and synthetic division of polynomials?

Long division is a general method, while synthetic division is a shortcut method Signup and view all the answers

What is the first step in drawing the graph of a cubic polynomial?

Find the y-intercept Signup and view all the answers

What is the relationship between the roots of a polynomial equation and its factors?

The roots correspond to the factors Signup and view all the answers

What is the purpose of analyzing the end behavior of a cubic polynomial?

To determine the shape of the graph Signup and view all the answers

What is the general form of a cubic polynomial?

ax^3 + bx^2 + cx + d Signup and view all the answers

What is the second step in solving a cubic equation using the Factor and Remainder Theorem?

Divide the polynomial by the factor x - k Signup and view all the answers

What is the purpose of finding the stationary points of a cubic polynomial?

To determine the shape of the graph Signup and view all the answers

What is the remainder when the polynomial a(x) is divided by b(x)?

R(x) Signup and view all the answers

What is the main difference between long division and synthetic division of polynomials?

Synthetic division is a shorthand method of long division Signup and view all the answers

What is the purpose of finding the stationary points of a cubic polynomial?

To determine the turning points of the graph Signup and view all the answers

When dividing a polynomial a(x) by a linear divisor x - k, what is the value of the remainder?

a(k) Signup and view all the answers

What is the relationship between the roots of a polynomial equation and its factors?

The roots of the equation are the zeros of the factors of the polynomial Signup and view all the answers

When drawing the graph of a cubic polynomial, what is the purpose of identifying the end behavior?

To identify the direction of the graph as x approaches infinity Signup and view all the answers

What is the purpose of using the Factor and Remainder Theorem to solve cubic equations?

To find the roots of the equation Signup and view all the answers

When performing synthetic division, what is the role of the opposite sign of the root of the divisor polynomial?

It is used to perform the synthetic division process Signup and view all the answers

Gr12 Mathematics: Ch 5.8 Cubic Polynomials

Questions and Answers

What is the formula for performing long division of polynomials?

What is the first step in performing synthetic division?

What is the equation of the y-intercept of a cubic polynomial?

What is the purpose of finding the stationary points of a cubic polynomial?

What is the first step in solving a cubic equation using the Factor and Remainder Theorem?

What is the general formula for synthetic division?

What is the purpose of analyzing the end behavior of a cubic polynomial?

What is the formula for the quotient Q(x) in polynomial division?

What is the purpose of finding the x-intercepts of a cubic polynomial?

What is the difference between long division and synthetic division of polynomials?

What is the first step in drawing the graph of a cubic polynomial?

What is the relationship between the roots of a polynomial equation and its factors?

What is the purpose of analyzing the end behavior of a cubic polynomial?

What is the general form of a cubic polynomial?

What is the second step in solving a cubic equation using the Factor and Remainder Theorem?

What is the purpose of finding the stationary points of a cubic polynomial?

What is the remainder when the polynomial a(x) is divided by b(x)?

What is the main difference between long division and synthetic division of polynomials?

What is the purpose of finding the stationary points of a cubic polynomial?

When dividing a polynomial a(x) by a linear divisor x - k, what is the value of the remainder?

What is the relationship between the roots of a polynomial equation and its factors?

When drawing the graph of a cubic polynomial, what is the purpose of identifying the end behavior?

What is the purpose of using the Factor and Remainder Theorem to solve cubic equations?

When performing synthetic division, what is the role of the opposite sign of the root of the divisor polynomial?

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