Question

Simplify the given polynomial expressions, and determine the degree and number of terms in each expression.

Answer 1

1)
$6 { x}^{3} - 10 {x}^{2} + 4x$
Degree: 3
Terms:3

2)
$- {x}^{5} - 3 {x}^{4} + 12 {x}^{3} - 6$
degree:5
terms:4

3) 9x^4-9
degree:4
terms:2

Answer 2

Degree and number of terms in each polynomial expression are as follow,

• $6x^{3} -10x^{2} +4x$         degree : $3$ and Number of terms : $3$
• $-x^{5} -3x^{4} +12x^{3} -6$ degree : $5$ and Number of terms : $4$
• $9x^{4} -9$                       degree : $4$ and Number of terms : $2$

What is expression?

" Expression is defined as the relation between two or more variables or numbers are represented using mathematical operation."

According to the question,

Given polynomial expression,

1. $4x + 2x^{2} ( 3x-5)$  

Simplify the given expression we get,

$4x + 6x^{3} -10x^{2}\\\\= 6x^{3} -10x^{2} +4x$

Degree of the polynomial expression : $3$

Number of terms : $3$

2. $(-3x^{4} +5x^{3} -12) + (7x^{3} -x^{5} +6)$

Simplify the given expression we get,

$-3x^{4} +12x^{3} -6 -x^{5} \\\\= -x^{5} -3x^{4} +12x^{3} -6$

Degree of the polynomial expression : $5$

Number of terms : $4$

3. $(3x^{2} -3)(3x^{2} +3)$

Simplify the given expression we get,

$9x^{4} -9$

Degree of the polynomial expression : $4$

Number of terms : $2$

Hence, degree and number of terms in each polynomial expression are as follow,

• $6x^{3} -10x^{2} +4x$         degree : $3$ and Number of terms : $3$
• $-x^{5} -3x^{4} +12x^{3} -6$ degree : $5$ and Number of terms : $4$
• $9x^{4} -9$                       degree : $4$ and Number of terms : $2$

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