AP SSC Class 10 Maths Chapter 3 Polynomials

The AP SSC Class 10 Maths Chapter 3 Polynomials discusses polynomials and its various properties. Here, in the article, we have provided a brief explanation of polynomials and methodical solutions to the chapter questions.

What is a Polynomial?

A polynomial is an algebraic expression constructed using constants and variables. Coefficients can be raised to various powers of non-negative integer exponents. A few examples of polynomials are \(3x^{2}+5x+6\), \(x^{3}\) and \(2x+5\)

Degree of a Polynomial

If p(x) is a polynomial in x, the highest power of x in p(x) is known as the degree of the polynomial p(x).

  • A polynomial of degree 1 is known as a linear polynomial. Example, \(4x+6\)
  • A polynomial of degree 2 is known as a quadratic polynomial. Example, \(x^{2}+3x+5\)
  • A polynomial of degree 3 is known as a cubic polynomial. Example, \(a^{3}+a^{2}+a+6\)

If p(x) is a polynomial in x, and if a is a real number, then the value obtained by replacing x by a in p(x), is called the value of p(x) at x = a, and is denoted by p(a). The value of x that makes the polynomial equal to 0 is known as the zero of a polynomial.

Class 10 Maths Chapter 3 Polynomials Questions

  1. If \(p(x)=5x^{7}-4x^{6}+8x-6\), find the
    • Coefficient of \(x^7\)
    • Degree of p(x)
    • Constant term

    Solution:

    1. The coefficient of\(x^7\) is 5
    2. The degree of p(x) is 7
    3. The constant term of p(x) is -6
  1. If \(p(t)=t^{3}-1\), find the values of p(1), p(–1), p(0), p(2), p(–2).
  2. Solution:

    1. p(1) = \(p(t)=1^{3}-1=0\)
    2. p(–1) = \(p(t)=(-1)^{3}-1=-2\)
    3. p(0) = \(p(t)=0^{3}-1=-1\)
    4. p(2)=\(p(t)=2^{3}-1=7\)
    5. p(–2) =\(p(t)=(-2)^{3}-1=-9\)

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Practise This Question

Find the area to be painted for the given object. All dimensions including answer options are in cm.(Take  π = 227)