Math / Algebra

Question10. Réponds aux quatre questions en te reportant à ces polynômes. \begin{tabular}{|c|c|} \hline $3 b^{2}$ & $2+p$ \\ \hline $4 s t+t-1$ & $2 x^{2}-y^{2}$ \\ \hline \end{tabular} a) Lesquels sont des binômes? b) Lesquels sont du $2^{e}$ degré ? c) Quelle est la variable du monôme? d) Quels polynômes ont un terme constant?

Studdy Solution

STEP 1

What is this asking? We're looking at a bunch of math expressions and figuring out which ones are "binomials," which ones are "2nd degree," what variable a single-termed expression uses, and which expressions have a constant number part. Watch out! Don't mix up the idea of "degree" with how many terms an expression has!
Also, remember a constant term is just a number without any variables attached.

STEP 2

1. Identify Binomials
2. Identify 2nd Degree Polynomials
3. Find the Variable in the Monomial
4. Find Constant Terms

STEP 3

A binomial is a polynomial with two terms.
Let's look at our expressions!

STEP 4

$2 + p$ has two terms: $2$ and $p$ .
So, it's a binomial!

STEP 5

$4st + t - 1$ has three terms: $4st$ , $t$ , and $-1$ .
Three terms makes it a trinomial, not a binomial.

STEP 6

$2x^2 - y^2$ has two terms: $2x^2$ and $-y^2$ .
So, it's a binomial too!

STEP 7

The degree of a polynomial is the highest power any variable is raised to.

STEP 8

In $3b^2$ , the variable $b$ is raised to the power of 2.
That makes it a 2nd degree polynomial.

STEP 9

In $2 + p$ , $p$ is the same as $p^1$ , so it's a 1st degree polynomial.

STEP 10

In $4st + t - 1$ , the term $4st$ has two variables multiplied, $s$ and $t$ , each raised to the power of $1$ .
When we add the powers together ( $1+1=2$ ), we get 2.
This makes the whole expression 2nd degree.

STEP 11

In $2x^2 - y^2$ , both $x$ and $y$ are raised to the power of 2.
So, this is also a 2nd degree polynomial.

STEP 12

A monomial is an expression with only one term. $3b^2$ is our only monomial.

STEP 13

The variable in $3b^2$ is $b$ .

STEP 14

A constant term is a number without any variables.

STEP 15

$2 + p$ has the constant term $2$ .

STEP 16

$4st + t - 1$ has the constant term $-1$ .

STEP 17

a) The binomials are $2 + p$ and $2x^2 - y^2$ . b) The 2nd degree polynomials are $3b^2$ , $4st + t - 1$ , and $2x^2 - y^2$ . c) The variable in the monomial is $b$ . d) The polynomials with a constant term are $2 + p$ and $4st + t - 1$ .

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Studdy Solution

STEP 1

STEP 2

1. Identify Binomials
2. Identify 2nd Degree Polynomials
3. Find the Variable in the Monomial
4. Find Constant Terms

STEP 3

A binomial is a polynomial with two terms.
Let's look at our expressions!

STEP 4

$2 + p$ has two terms: $2$ and $p$ .
So, it's a binomial!

STEP 5

$4st + t - 1$ has three terms: $4st$ , $t$ , and $-1$ .
Three terms makes it a trinomial, not a binomial.

STEP 6

$2x^2 - y^2$ has two terms: $2x^2$ and $-y^2$ .
So, it's a binomial too!

STEP 7

The degree of a polynomial is the highest power any variable is raised to.

STEP 8

In $3b^2$ , the variable $b$ is raised to the power of 2.
That makes it a 2nd degree polynomial.

STEP 9

In $2 + p$ , $p$ is the same as $p^1$ , so it's a 1st degree polynomial.

STEP 10

In $4st + t - 1$ , the term $4st$ has two variables multiplied, $s$ and $t$ , each raised to the power of $1$ .
When we add the powers together ( $1+1=2$ ), we get 2.
This makes the whole expression 2nd degree.

STEP 11

In $2x^2 - y^2$ , both $x$ and $y$ are raised to the power of 2.
So, this is also a 2nd degree polynomial.

STEP 12

A monomial is an expression with only one term. $3b^2$ is our only monomial.

STEP 13

The variable in $3b^2$ is $b$ .

STEP 14

A constant term is a number without any variables.

STEP 15

$2 + p$ has the constant term $2$ .

STEP 16

$4st + t - 1$ has the constant term $-1$ .

STEP 17

a) The binomials are $2 + p$ and $2x^2 - y^2$ . b) The 2nd degree polynomials are $3b^2$ , $4st + t - 1$ , and $2x^2 - y^2$ . c) The variable in the monomial is $b$ . d) The polynomials with a constant term are $2 + p$ and $4st + t - 1$ .

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Studdy Solution

STEP 1

STEP 2

1. Identify Binomials2. Identify 2nd Degree Polynomials3. Find the Variable in the Monomial4. Find Constant Terms

STEP 3

A **binomial** is a polynomial with *two* terms.Let's look at our expressions!

STEP 4

2+p2 + p2+p has two terms: 222 and ppp.So, it's a **binomial**!

STEP 5

4st+t−14st + t - 14st+t−1 has *three* terms: 4st4st4st, ttt, and −1-1−1.Three terms makes it a *trinomial*, not a binomial.

STEP 6

2x2−y22x^2 - y^22x2−y2 has two terms: 2x22x^22x2 and −y2-y^2−y2.So, it's a **binomial** too!

STEP 7

The **degree** of a polynomial is the highest power any variable is raised to.

STEP 8

In 3b23b^23b2, the variable bbb is raised to the power of **2**.That makes it a **2nd degree** polynomial.

STEP 9

In 2+p2 + p2+p, ppp is the same as p1p^1p1, so it's a **1st degree** polynomial.

STEP 10

In 4st+t−14st + t - 14st+t−1, the term 4st4st4st has two variables multiplied, sss and ttt, each raised to the power of 111.When we add the powers together (1+1=21+1=21+1=2), we get **2**.This makes the whole expression **2nd degree**.

STEP 11

In 2x2−y22x^2 - y^22x2−y2, both xxx and yyy are raised to the power of **2**.So, this is also a **2nd degree** polynomial.

STEP 12

A **monomial** is an expression with only *one* term. 3b23b^23b2 is our only monomial.

STEP 13

The variable in 3b23b^23b2 is **bbb**.

STEP 14

A **constant term** is a number without any variables.

STEP 15

2+p2 + p2+p has the constant term **222**.

STEP 16

4st+t−14st + t - 14st+t−1 has the constant term **−1-1−1**.

STEP 17

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1. Identify Binomials
2. Identify 2nd Degree Polynomials
3. Find the Variable in the Monomial
4. Find Constant Terms

A binomial is a polynomial with two terms.
Let's look at our expressions!

$2 + p$ has two terms: $2$ and $p$ .
So, it's a binomial!

$4st + t - 1$ has three terms: $4st$ , $t$ , and $-1$ .
Three terms makes it a trinomial, not a binomial.

$2x^2 - y^2$ has two terms: $2x^2$ and $-y^2$ .
So, it's a binomial too!

The degree of a polynomial is the highest power any variable is raised to.

In $3b^2$ , the variable $b$ is raised to the power of 2.
That makes it a 2nd degree polynomial.

In $2 + p$ , $p$ is the same as $p^1$ , so it's a 1st degree polynomial.

In $4st + t - 1$ , the term $4st$ has two variables multiplied, $s$ and $t$ , each raised to the power of $1$ .
When we add the powers together ( $1+1=2$ ), we get 2.
This makes the whole expression 2nd degree.

In $2x^2 - y^2$ , both $x$ and $y$ are raised to the power of 2.
So, this is also a 2nd degree polynomial.

A monomial is an expression with only one term. $3b^2$ is our only monomial.

The variable in $3b^2$ is $b$ .

A constant term is a number without any variables.

$2 + p$ has the constant term $2$ .

$4st + t - 1$ has the constant term $-1$ .