#### If p(x) = x^{2} + x +1 and q(x) = x^{2} - x +1, then p(x) q(x) = ____.

Given polynomials are p(x) = x^{2} + x +1 and q(x) = x^{2} - x +1. p(x) q(x) = (x^{2} + x +1)( x^{2} - x +1) x^{2} (x^{2} + x +1) - x(x^{2} + x +1) + (x^{2} + x +1) x^{4} + x^{3 }+ x^{2} - x^{3 }- x^{2} – x + x^{2} + x + 1 x^{4 } + x^{2} + 1 p(x) q(x) = x^{4 } + x^{2} + 1

#### If f(x) = x^{3 }– 6x^{2}+ 11x – 6, then the value of f(x) at x = 1 is

Given polynomial is x^{3 }– 6x^{2}+ 11x – 6. f(x) = (1)^{2}+ 11(1) – 6 = 1 – 6 + 11 – 6 = 12 – 12 = 0 Hence, the value of f(x) at x = 1 is 0.

#### The degree of 5 x^{2} – 3x + 4

The highest power of a term of a polynomial is its degree. Hence, The degree of 5 x^{2}– 3x + 4 is 2

#### The polynomial x^{2} is a ____.

The polynomial consisting of one term is known as a monomial. Hence, x^{2} is monomial.

#### The degree of 7x^{2} + 8x^{8} –2x is ____.

The highest power of a term of a polynomial is its degree.
Hence, the degree of 7x^{2} + 8x^{8} – 2x is 8

#### Which of the following is 35^{th} degree binomial?

The 35^{th} degree is x^{35} + 4x

#### If f(x) = 2x^{3} – 13^{2}+ 17x + 12, then the value of f(x) at x = -3 is ____.

Given polynomial is f(x) = 2x^{3} – 13^{2}+ 17x + 12. f(-3) = 2(-3)^{3}+ 17(-3) + 12 = -54 – 117 – 51 + 12 = -210 Hence, the value of f(x) at x = -3 is -210.

#### The zero of the polynomial p(x) = x - 5

Given polynomial is p(x) = x – 5 The zero of a polynomial is the value of x that makes the polynomial equal to 0. P(x) = 0 ⇒ x - 5 = 0 ⇒ x = 5 Hence, the zero of the polynomial p(x) = x – 5 is 5

#### The polynomial 3x^{3} + 4x^{2}+ 5x - 7____.

Given polynomial is 3x^{3} + 4x^{2}+ 5x – 7. The degree of the polynomial is 3. A polynomial of degree 3 is known as a cubic polynomial. Hence, the polynomial 3x^{3} + 4x^{2}+ 5x – 7 is a cubic polynomial.