Two polynomials are given: f(x)=3x^ 4 -2x^ 2 +5

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Two polynomials are given:

f(x)=3x^{4}-2x^{2}+5, \qquad g(x)=-x^{3}+4x.

Answer the following in the order given. (i) Find the polynomial

h(x)=f(x)-g(x)

and write it in descending powers of

x

. (ii) Determine the degree and leading coefficient of

h(x)

. (iii) Calculate the

y

-intercept of

h(x)

. (iv) State, with a reason, whether the graph of

h(x)

opens in both upward and downward directions or in only one direction.