Introduction to polynomials (with basic operations)

Introduction to polynomials (with basic operations)

by FJ

Learning outcome

(a) To perform addition, subtraction and multiplication of polynomials.

A polynomial P(x) of degree n, is an algebraic expression of the form 

 $P\left(x\right)=a_nx^n+a_{\left(n-1\right)}x^{\left(n-1\right)}+...+a_1x+a_0$  

where n is a positive integer, and 'a' representing the coefficient of the terms

and

 $a_n\ne0$  

Now, based on your knowledge (from notes), answer the following questions.

Multiple Choice

What is the term classification of the following polynomial?
x³-7x²+3

• monomial
• binomial
• trinomial
• polynomial

Multiple Choice

What is the degree classification of this polynomial?

x²+4x-8

• binomial

• trinomial

• quadratic

• cubic

Multiple Choice

A polynomial that has two terms is a:

• polynomial
• monomial
• binomial

Multiple Choice

Which of these has a negative leading coefficient?

• x²+9x-4
• 6x-9
• -8x+8
• 9x

Multiple Choice

Which is an example of a linear polynomial?

• x²-5

• 6x+4

• 5x⁵

• 2x³-9x²

Multiple Choice

What is the leading coefficient of the following polynomial?
5x²-3x+6

• 2
• -3
• 5
• 6

Multiple Choice

Find (3x² + 6x - 1) + (4x² + 5x + 9)

• -x² + x - 10

• x² - x + 10

• 7x² + 11x + 8

• 7x² + 11x + 10

Multiple Choice

Add the following polynomials
(x³-6x²+3)+(3x³+4x-1)

• 4x³-2x²+2
• 4x³-6x²+4x+2
• -2x³+2x+2
• 4x³-2x²-2

Multiple Choice

Add the following polynomials:
(x³-2x²+3)+(2x³+3x²-1)

• 3x³-2x²+3x+2
• 3x³+x²+2
• 3x³-5x²-2
• 3x³-x²+1

Multiple Choice

Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)

• x³+2x²+5x-2
• x³+10x²+3x-2
• 3x³+2x+4x-3
• 3x³+10x²-3x-2

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8
• 2x² + 5x - 7
• -x² -6x + 8
• -2x² + 11x - 4

Multiple Choice

Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)

• 2x²+x+1
• 2x²-5x+3
• 2x²-x+1
• 4x²-5x+3

Multiple Choice

Find

 $\left(5x+2\right)\left(x^2-3x+6\right)$  

•  $5x^3-17x^2+24x+12$  

•  $5x^3-17x-24x+12$  

•  $5x^3-13x^2+24x+12$  

•  $5x^3+13x^2-24x-12$  

Multiple Choice

Given that $\left(2x^2+5\right)\left(x-4\right)=kx^3+mx^2+nx-20$ . Find the values of k, m and n. 

• k = 2, m = 8, n = - 5

• k = 2, m = 8, n = 5

• k = 2, m = - 8, n = 5

• k = 2, m = -8, n = - 5

Multiple Choice

If $\left(3x^3+mx-2\right)\left(2x^2+4\right)=\left(m+n\right)x^5+20x^3-4x^2+36x-8.$  

Find the values of m and n.

• m = - 9, n = -3

• m = 9, n = - 3

• m = 9, n = 3

• m = - 9, n = 3