The answers are:
i) p(y) is a trinomial and q(x) is a binomial.
ii) The degree of p(y) is 2, and the degree of q(x) is 3.
iii) The value of p(-2) = 56.
iv) The coefficient [tex]y^2[/tex] is 9, and the coefficient [tex]x^3[/tex] is 1.
Step-by-step explanation:
Given: Two polynomials [tex]p(y) = 9y^2 -9y+ 2[/tex] and [tex]q(x) = x^3 -64[/tex]
Solutions:
i) p(y) has three terms, hence, p(y) is a trinomial.
q(x) has two terms, hence, q(x) is a binomial.
ii) A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
Thus, the degree of p(y) is 2, and the degree of q(x) is 3.
iii)The value of p(-2) can be calculated by putting [tex]y = -2[/tex] in the equation:
[tex]p(-2)= 9(-2)^2-9(-2)+2[/tex]
[tex]= 9(4)+18+2[/tex]
[tex]=36+18+2[/tex]
[tex]=56[/tex]
Thus, p(-2) = 56
iv) The coefficients are the numbers written before the variables.
Thus, the coefficient [tex]y^2[/tex] is 9, and the coefficient [tex]x^3[/tex] is 1.