Question

q3 - accelerated mathematics gr 8 | lesson: identifying characteristics of polynomial expressions

1. how many terms are in the polynomial $2x^{3}-3x^{4}+4x^{2}-67$

a. 3
b. 2
c. 4
d. 5

1. what is the constant term in the polynomial $x^{3}-6x^{2}+4x+12$

a. $4x$
b. 12
c. $x^{3}$
d. $-6x^{2}$

1. what is the degree of the polynomial $x^{4}-6x^{2}+2x-8$

a. 2
b. 3
c. 1
d. 8

1. which of the following polynomials has three terms?

a. $x^{2}+5x+7$
b. $6x^{3}-2$
c. $2x^{4}-3x^{2}+x+8$
d. $4x^{2}+3x$

Explanation:

Step1: Count terms in first polynomial

The polynomial $2b^5 - 3x^4 + 4a^3 - 67$ has 4 distinct terms: $2b^5$, $-3x^4$, $4a^3$, $-67$.

Step2: Identify constant term (no variable)

In $x^3 - 6x^2 + 4x + 12$, the term without a variable is 12.

Step3: Find highest exponent (degree)

In $x^4 - 6x^2 + 2x - 8$, the highest power of $x$ is 4.

Step4: Count terms for each option

• a. $x^2 + 5x + 7$ has 3 terms; b. $6x^3 - 2$ has 2 terms; c. $2x^4 - 3x^2 + x + 8$ has 4 terms; d. $4x^2 + 3x$ has 2 terms.

Answer:

1. c. 4
2. b. 12
3. d. 4
4. a. $x^2 + 5x + 7$