Test: Polynomials (Easy) - Class 10

We know that the degree is the term with the greatest exponent.

3x³ - 2x - x + 3 = 3x³ - 3x + 3 is an example of cubic polynomials. A cubic polynomial is a polynomial of degree 3. Since the highest degree is 3.

The polynomial ax² + bx + c has three terms. The first one is ax², the second is bx, and the third is c. The exponent of the first term is 2. The exponent of the second term is 1 because bx = bx¹. The exponent of the third term is 0 because c = cx⁰. Since the highest exponent is 2, therefore, the degree of ax² + bx + c is 2. Since, the degree of the polynomial is 2, hence, the polynomial ax² + bx + c can have zero, one or two zeroes. Hence, the polynomial ax² + bx + c can have at most two zeros.

To find the zero of a polynomial, we use f(x) = 0.

Then, 4x + 5 = 0 ⟹ 4x = −5 ⟹ x = -5 / 4

Hence, −5 / 4 ​ is the zero of the polynomial 4x + 5.

when x = −2; y = 4 + 2 − 6 = 0

when x = 3; y = 9 − 3 − 6 = 0

∴ -5 is zero of the polynomial

Thus, when 6x + 2 is subtracted from the given polynomial 8x⁴ + 14x³ + x² + 7x + 8, then it will be divisible by 4x² - 3x + 2.

where a_n, a_n−1,... a₂, a₁, a₀. are constants and n is a natural number.

Let p(x) = 3x² + 2x + 1

The degree of a polynomial is the highest power of x in its expression.

Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively.

Highest power of x in p(x) is = 2

Thus, the degree of p(x) is 2.

Hence, it is a quadratic polynomial.