Question

Write two polynomials ()and () such that the degree of both ()and () is3 but degree of the polynomial ()+() is 1.

Answer 1

Answer:

To determine the degree of a polynomial that is not in standard form, such as {\displaystyle (x+1)^{2}-(x-1)^{2}}, one can put it in standard form by expanding the products (by distributivity) and combining the like terms; for example, {\displaystyle (x+1)^{2}-(x-1)^{2}=4x} is of degree 1, even though each summand has degree 2. However, this is not needed when the polynomial is written as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors.

Answer 2

P(x)Q(x) = (x3 − x2 + x − 1)(3x3 − 2x2)

= x3(3x2 − 2x2) − x2(3x3 − 2x2) + x(3x3 − 2x2) − (3x3 − 2x2)

= 3x6 − 2x5 − 3x5 + 2x4 + 3x4 − 2x3 − 3x3 + 2x2

= 3x6 − 5x5 + 5x4 − 5x3 + 2x2

Hope This helps you mate

#Siddharth here!