University:
North Central College
Course:
MATH 152 | Calculus II
Academic year:

2024
Views:

436

Pages:

2
Author:

nesikhiyawl0

Question 1 How do you write y+1=-7(x+1) in standard form? Answer Explanation: It is a straight line equation. We have to write it in standard form. y+1=-7(x+1) y+1=-7x-7 y=-7x-7-1 y=-7x-8 Answer: y=-7x-8 Question 2 What is the leading term, leading coefficient, and degree of this polynomial F(X) = 5/6 x + 3x² - 4.3x³ - 7x⁴? Answer Explanation: The leading term of a polynomial is the term of highest degree. The leading coefficient of a polynomial is the coefficient of the leading term. The degree of a polynomial is the degree of the leading term. -7x⁴ the leading term -7 ⇒ the leading coefficient 4⇒ the degree of this polynomial Question 3 What is the leading term, leading coefficient, and degree of this polynomial 8x² + 9 + 5x³ ? Answer 1 Explanation: To determine the leading coefficient and leading term, it is necessary to write the expression in canonical form: 5x³ + 8x² + 9 The degree is the largest exponent value of the variable in any term of the expression (for an expression with multiple variables it is the maximum of the sum of exponents). Leading term: 5x³ Leading coefficient: 5 Degree: 3 Answer 2 Explanation: The leading term of a polynomial is the term with the highest degree. The leading coefficient of a polynomial is the coefficient of the leading term. The degree of a polynomial is the highest degree of its terms. Hence, leading term, leading coefficient, and degree of the polynomial is 5x³, 5, 3. Leading term, leading coefficient, and degree of the polynomial is 5x³, 5, 3 respectively. Question 4 What is the leading term, leading coefficient, and degree of this polynomial y = 4x² - 3x + 7? Answer Explanation: The degree of a polynomial is the largest exponent of a variable for any term in the polynomial (for polynomials in more than one variable it is the largest sum of exponents for any term). The leading term is the term with the largest degree. Note that the leading term is not necessarily the first term of the polynomial (unless the polynomial is written in something called canonical form). The leading coefficient is the constant within the leading term. Leading term: 4x² Leading coefficient: 4 Degree: 2 Question 5 What is the leading term, leading coefficient, and degree of this polynomial f(x) = -2x³(x+5)¹(x - 3)²? Answer Explanation: You first express the the polynomial in its canonical form consisting of a conbination of monomials, you get: -2x⁹ - 8x⁸ - 198x⁷ + 620x⁶ + 2050x⁵ - 1500x⁴ - 11250x³ The degree is the term with the greatest exponent, which is in this case 9. The leading term is -2x⁹, and the leading coefficient is -2, and the degree of this polynomial is 9.