Understanding Polynomials

This video tutorial by Denny Handayani on the MATLAB channel covers the basics of polynomials, including their definition, properties, and operations such as addition, subtraction, and multiplication. The video provides examples to help distinguish polynomials from non-polynomials and includes exercises to reinforce understanding. The tutorial also addresses common polynomial problems and their solutions, making it a comprehensive introduction to polynomial algebra.

What is a polynomial?

• An algebraic expression with variables having any type of exponents

• An algebraic expression with variables having fractional exponents

• An algebraic expression with variables having positive integer exponents

• An algebraic expression with variables having negative exponents

Which of the following is a polynomial?

• 2x^3 + 6x^2 - 2x + 1

• 5x^7 + 3x^2 + 7√x

• 3x^5 + 2/x - 6x + 7

• 7x^3 + 6x^2 + 3/x + 1/x^2

How do you add two polynomials?

• Divide the coefficients of terms with the same degree

• Subtract the coefficients of terms with the same degree

• Multiply the coefficients of terms with the same degree

• Add the coefficients of terms with the same degree

What is the result of subtracting Qx from Px if Px = 5x^4 + 3x^3 - 5x^2 + 6 and Qx = 4x^3 - 2x^2?

• 5x^4 + x^3 - 7x^2 + 6

• 5x^4 - x^3 + 3x^2 + 6

• 5x^4 - x^3 - 3x^2 + 6

• 5x^4 + 7x^3 - 3x^2 + 6

What is the degree of the polynomial 6x^3 - 2x^2 - 1?

• 1

• 4

• 2

• 3

What is the coefficient of x^2 in the polynomial 5x^4 - 4x^3 + 3x^2 - 2x + 1?

• 4

• 1

• 2

• 3

If Px is a polynomial of degree 4 and Qx is of degree 6, what is the degree of Px - Qx?

• 10

• 6

• 5

• 4

What is the degree of the polynomial resulting from multiplying Px of degree 5 by Qx of degree 3?

• 9

• 5

• 8

• 15

What is the degree of the polynomial 3x^2 - x^3 multiplied by 2x^3 + 6x + 1?

• 9

• 8

• 6

• 5

What is the result of adding Px = 3x^3 - 6x^2 + 12x + 3 and Qx = 2x^4 - 3x^3 + 2x^2 - 6?

• 2x^4 - 3x^3 - 4x^2 + 12x - 3

• 2x^4 + 0x^3 - 4x^2 + 12x - 3

• 2x^4 - 3x^3 + 4x^2 + 12x - 3

• 2x^4 - 3x^3 - 4x^2 + 12x + 3