QuestionIdentify the binomials from the options: A. $x^{2}+3$ , B. $8 x$ , C. $\frac{5}{7} y^{3}+5 y^{2}+y$ , D. $x^{4}+x^{2}+1$ , E. $6 x^{2}+\frac{1}{2} y^{3}$ , F. $x^{11}$ .

Studdy Solution

STEP 1

Assumptions1. A binomial is a polynomial with two terms. . The terms in a polynomial are separated by '+' or '-' signs.

STEP 2

We need to identify the polynomials that have exactly two terms.

STEP 3

Examine option A $x^{2}+3$ .This expression has two terms, $x^{2}$ and $3$ , separated by a '+' sign. Therefore, it is a binomial.

STEP 4

Examine option B $8 x$ .This expression has only one term, $8x$ . Therefore, it is not a binomial.

STEP 5

Examine option C $\frac{5}{7} y^{3}+5 y^{2}+y$ .This expression has three terms, $\frac{5}{7} y^{3}$ , $5 y^{2}$ , and $y$ , separated by '+' signs. Therefore, it is not a binomial.

STEP 6

Examine option D $x^{4}+x^{2}+1$ .This expression has three terms, $x^{4}$ , $x^{2}$ , and $1$ , separated by '+' signs. Therefore, it is not a binomial.

STEP 7

Examine option $6 x^{2}+\frac{1}{2} y^{3}$ .
This expression has two terms, $6 x^{2}$ and $\frac{1}{2} y^{3}$ , separated by a '+' sign. Therefore, it is a binomial.

STEP 8

Examine option F $x^{11}$ .
This expression has only one term, $x^{11}$ . Therefore, it is not a binomial.

STEP 9

Summarize the results.
The binomials among the given options are $x^{2}+3$ and $6 x^{2}+\frac{}{2} y^{3}$ .

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QuestionIdentify the binomials from the options: A. $x^{2}+3$ , B. $8 x$ , C. $\frac{5}{7} y^{3}+5 y^{2}+y$ , D. $x^{4}+x^{2}+1$ , E. $6 x^{2}+\frac{1}{2} y^{3}$ , F. $x^{11}$ .

Studdy Solution

STEP 1

Assumptions1. A binomial is a polynomial with two terms. . The terms in a polynomial are separated by '+' or '-' signs.

STEP 2

We need to identify the polynomials that have exactly two terms.

STEP 3

Examine option A $x^{2}+3$ .This expression has two terms, $x^{2}$ and $3$ , separated by a '+' sign. Therefore, it is a binomial.

STEP 4

Examine option B $8 x$ .This expression has only one term, $8x$ . Therefore, it is not a binomial.

STEP 5

Examine option C $\frac{5}{7} y^{3}+5 y^{2}+y$ .This expression has three terms, $\frac{5}{7} y^{3}$ , $5 y^{2}$ , and $y$ , separated by '+' signs. Therefore, it is not a binomial.

STEP 6

Examine option D $x^{4}+x^{2}+1$ .This expression has three terms, $x^{4}$ , $x^{2}$ , and $1$ , separated by '+' signs. Therefore, it is not a binomial.

STEP 7

Examine option $6 x^{2}+\frac{1}{2} y^{3}$ .
This expression has two terms, $6 x^{2}$ and $\frac{1}{2} y^{3}$ , separated by a '+' sign. Therefore, it is a binomial.

STEP 8

Examine option F $x^{11}$ .
This expression has only one term, $x^{11}$ . Therefore, it is not a binomial.

STEP 9

Summarize the results.
The binomials among the given options are $x^{2}+3$ and $6 x^{2}+\frac{}{2} y^{3}$ .

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QuestionIdentify the binomials from the options: A. x2+3x^{2}+3x2+3, B. 8x8 x8x, C. 57y3+5y2+y\frac{5}{7} y^{3}+5 y^{2}+y75​y3+5y2+y, D. x4+x2+1x^{4}+x^{2}+1x4+x2+1, E. 6x2+12y36 x^{2}+\frac{1}{2} y^{3}6x2+21​y3, F. x11x^{11}x11.

Studdy Solution

STEP 1

Assumptions1. A binomial is a polynomial with two terms. . The terms in a polynomial are separated by '+' or '-' signs.

STEP 2

We need to identify the polynomials that have exactly two terms.

STEP 3

Examine option A x2+3x^{2}+3x2+3.This expression has two terms, x2x^{2}x2 and 333, separated by a '+' sign. Therefore, it is a binomial.

STEP 4

Examine option B 8x8 x8x.This expression has only one term, 8x8x8x. Therefore, it is not a binomial.

STEP 5

Examine option C 57y3+5y2+y\frac{5}{7} y^{3}+5 y^{2}+y75​y3+5y2+y.This expression has three terms, 57y3\frac{5}{7} y^{3}75​y3, 5y25 y^{2}5y2, and yyy, separated by '+' signs. Therefore, it is not a binomial.

STEP 6

Examine option D x4+x2+1x^{4}+x^{2}+1x4+x2+1.This expression has three terms, x4x^{4}x4, x2x^{2}x2, and 111, separated by '+' signs. Therefore, it is not a binomial.

STEP 7

Examine option 6x2+12y36 x^{2}+\frac{1}{2} y^{3}6x2+21​y3.This expression has two terms, 6x26 x^{2}6x2 and 12y3\frac{1}{2} y^{3}21​y3, separated by a '+' sign. Therefore, it is a binomial.

STEP 8

Examine option F x11x^{11}x11.This expression has only one term, x11x^{11}x11. Therefore, it is not a binomial.

STEP 9

Summarize the results.The binomials among the given options are x2+3x^{2}+3x2+3 and 6x2+2y36 x^{2}+\frac{}{2} y^{3}6x2+2​y3.

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QuestionIdentify the binomials from the options: A. $x^{2}+3$ , B. $8 x$ , C. $\frac{5}{7} y^{3}+5 y^{2}+y$ , D. $x^{4}+x^{2}+1$ , E. $6 x^{2}+\frac{1}{2} y^{3}$ , F. $x^{11}$ .

Examine option A $x^{2}+3$ .This expression has two terms, $x^{2}$ and $3$ , separated by a '+' sign. Therefore, it is a binomial.

Examine option B $8 x$ .This expression has only one term, $8x$ . Therefore, it is not a binomial.

Examine option C $\frac{5}{7} y^{3}+5 y^{2}+y$ .This expression has three terms, $\frac{5}{7} y^{3}$ , $5 y^{2}$ , and $y$ , separated by '+' signs. Therefore, it is not a binomial.

Examine option D $x^{4}+x^{2}+1$ .This expression has three terms, $x^{4}$ , $x^{2}$ , and $1$ , separated by '+' signs. Therefore, it is not a binomial.

Examine option $6 x^{2}+\frac{1}{2} y^{3}$ .
This expression has two terms, $6 x^{2}$ and $\frac{1}{2} y^{3}$ , separated by a '+' sign. Therefore, it is a binomial.

Examine option F $x^{11}$ .
This expression has only one term, $x^{11}$ . Therefore, it is not a binomial.

Summarize the results.
The binomials among the given options are $x^{2}+3$ and $6 x^{2}+\frac{}{2} y^{3}$ .