Introduction to Linear Polynomials | Exercise 2.1

Question 4

What is the coefficient of zz in the polynomial 4z3+5z2−114z^3 + 5z^2 - 11?

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Solution
Understand the Question
  • A coefficient is the numerical multiplier of a variable term in a polynomial.
  • If a specific power of a variable does not appear in a polynomial, its coefficient is 00 because 0⋅z=00 \cdot z = 0.

Step 1 · Identify the coefficient of zz

Rewrite the polynomial by including all powers of zz in descending order: 4z3+5z2−11=4z3+5z2+0z−114z^3 + 5z^2 - 11 = 4z^3 + 5z^2 + 0z - 11

The term containing zz (or z1z^1) has a multiplying factor of 00.

Therefore, the coefficient of zz is 00.

Answer

00

Common Mistakes
  • Assuming coefficient is 1: Thinking the coefficient of a missing term is 11 instead of 00. A coefficient of 11 means the term +z+z is written explicitly.
  • Confusing constant term with coefficient: Confusing the constant term (−11-11) or other coefficients (44 or 55) with the coefficient of the requested variable zz.

More questions in Exercise 2.1

Q1

Find the degrees of the following polynomials:

(i) 2x2−5x+32x^2 - 5x + 3

(ii) y3+2y−1y^3 + 2y - 1

(iii) −9-9

(iv) 4z−34z - 3

Q2

Write polynomials of degrees 1, 2 and 3.

Q3

What are the coefficients of x2x^2 and x3x^3 in the polynomial x4−3x3+6x2−2x+7x^4 - 3x^3 + 6x^2 - 2x + 7?

Q4

What is the coefficient of zz in the polynomial 4z3+5z2−114z^3 + 5z^2 - 11?

Q5

What is the constant term of the polynomial 9x3+5x2−8x−109x^3 + 5x^2 - 8x - 10?

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