Introduction to Linear Polynomials | Exercise 2.1

Question 5

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

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Solution
Understand the Question
  • A constant term in a polynomial is the term that does not contain any variable (or corresponds to the variable raised to the power of zero, x0x^0).
  • To find it, examine each term in the polynomial and identify the standalone number along with its sign.

Step 1 · Identify the Constant Term

Given polynomial 9x3+5x2−8x−109x^3 + 5x^2 - 8x - 10

Analyzing each term:

  • 9x39x^3 contains x3x^3
  • 5x25x^2 contains x2x^2
  • −8x-8x contains xx
  • −10-10 contains no variable (x0x^0)

Therefore, the constant term is −10-10.

Answer

−10-10

Common Mistakes
  • Ignoring the Sign: Writing 1010 instead of −10-10. Always include the negative sign attached to the term.
  • Confusing Coefficients with the Constant: Mistaking the coefficient of a variable term (e.g., 99, 55, or −8-8) for the constant term.

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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