Class 10 Exam > Class 10 Notes > EXERCISE 3 - Polynomials, Class 10, Maths
EXERCISE 3 - Polynomials, Class 10, Maths PDF Download
EXERCISE 3
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
FAQs on EXERCISE 3 - Polynomials, Class 10, Maths
| 1. What are polynomials? |  |
Ans. Polynomials are algebraic expressions consisting of variables and coefficients, which are combined using the four basic mathematical operations of addition, subtraction, multiplication, and division.
| 2. What is the degree of a polynomial? | |
Ans. The degree of a polynomial is the highest power of the variable present in the polynomial. For example, the degree of the polynomial 3x^2 + 5x – 2 is 2, as the highest power of x is 2.
| 3. How do you add or subtract polynomials? | |
Ans. To add or subtract polynomials, simply combine like terms. Like terms are those that have the same variable and the same power. For example, to add the polynomials 3x^2 + 5x - 2 and 2x^2 - 3x + 4, you first group the like terms: (3x^2 + 2x^2) + (5x - 3x) + (-2 + 4), which simplifies to 5x^2 + 2x + 2.
| 4. What is the factor theorem? | |
Ans. The factor theorem states that if a polynomial P(x) is divided by (x – a), then the remainder will be zero if and only if (x – a) is a factor of P(x). In other words, if P(a) = 0, then (x – a) is a factor of P(x).
| 5. How do you find the roots of a polynomial? | |
Ans. To find the roots of a polynomial, set the polynomial equal to zero and solve for the variable. The solutions to the equation are the roots of the polynomial. For example, to find the roots of the polynomial x^2 – 4, you would set the polynomial equal to zero: x^2 – 4 = 0. Solving for x, you get x = ±2, so the roots of the polynomial are x = 2 and x = -2.
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