Chapter 7, Problem 1CA

To determine

To calculate: Classify given polynomials by number of terms and order them by degree in ascending order.

Answer to Problem 1CA

a) $-4x^3$ is a monomial.

b) $6y-3y^5$ is a binomial.

c) $c^2+2+c$ is a trinomial.

d) $-10d^4+7d^2$ is a binomial.

e) $-5z^{11}+8z^{12}$ is a binomial.

f) $3b^6-12b^8+4b^4$ is a trinomial.

Ordering (as per ascending degree):

  $c^2+2+c,(-4x^3),-10d^4+7d^2,6y-3y^5,3b^6-12b^8+4b^4,-5z^{11}+8z^{12}$

Explanation of Solution

Given information: $-4x^3,6y-3y^5,c^2+2+c,-10d^4+7d^2,-5z^{11}+8z^{12},3b^6-12b^8+4b^4$ are given polynomials.

Calculation:

a)As evident from given statement, the polynomial contains only one term $(-4x^3)$

  $\therefore$ Given polynomial is a monomial, its degree is $3$ .

b) $6y-3y^5$ has two terms, $\therefore$ It is a binomial whose degree is $5$ .

c) $c^2+2+c$ has three terms, $\therefore$ It is a trinomial whose degree is $2$ .

d) $-10d^4+7d^2$ has two terms, $\therefore$ It is a binomial whose degree is $4$ .

e) $-5z^{11}+8z^{12}$ has two terms, $\therefore$ It is a binomial whose degree is $12$ .

f) $3b^6-12b^8+4b^4$ has three terms, $\therefore$ It is a trinomial whose degree is $8$ .

Ordering polynomials in ascending order (as per degree):

  $c^2+2+c,(-4x^3),-10d^4+7d^2,6y-3y^5,3b^6-12b^8+4b^4,-5z^{11}+8z^{12}$