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. Refer to the below given AP SSC 1oth Class Maths Chapter 3 Polynomials Notes and Solutions and learn how to give step-by-step correct solutions for the concepts taught under the subject in class.

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 [latex]3x^{2}+5x+6[/latex], [latex]x^{3}[/latex] and [latex]2x+5[/latex]

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, [latex]4x+6[/latex]
• A polynomial of degree 2 is known as a quadratic polynomial. Example, [latex]x^{2}+3x+5[/latex]
• A polynomial of degree 3 is known as a cubic polynomial. Example, [latex]a^{3}+a^{2}+a+6[/latex]

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

Solution:

1. 1. The coefficient of[latex]x^7[/latex] is 5
   2. The degree of p(x) is 7
   3. The constant term of p(x) is -6

2. 2. If [latex]p(t)=t^{3}-1[/latex], find the values of p(1), p(–1), p(0), p(2), p(–2).

Solution:

2. 1. p(1) = [latex]p(t)=1^{3}-1=0[/latex]
   2. p(–1) = [latex]p(t)=(-1)^{3}-1=-2[/latex]
   3. p(0) = [latex]p(t)=0^{3}-1=-1[/latex]
   4. p(2)=[latex]p(t)=2^{3}-1=7[/latex]
   5. p(–2) =[latex]p(t)=(-2)^{3}-1=-9[/latex]

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