MATHEMATICS HIGH SCHOOL

Classify the following polynomials by degree and number of terms.1. 3p^3 + 2p^2 + 19p - 5

2. 5x^4 + 12

3. n^2 - 7n - 21

4. 3

5. 2x + 7

6. -8y^2

Answers

Answer 1

Answer:

Answer:

See below

Step-by-step explanation:

Let's classify the given polynomials by their degree and number of terms:

1. 4p³ + 2p² + 19p - 5

- Degree: 3 (the highest power of the variable, which is p, is 3)

- Number of terms: 4 (there are four terms in the expression)

2. 5x⁴ + 12

- Degree: 4 (the highest power of the variable, which is x, is 4)

- Number of terms: 2 (there are two terms in the expression)

3. n² - 7n - 21

- Degree: 2 (the highest power of the variable, which is n, is 2)

- Number of terms: 3 (there are three terms in the expression)

4. 3

- Degree: 0 (since it's a constant, it has no variable part)

- Number of terms: 1 (there is only one term, which is the constant 3)

5. 2x + 7

- Degree: 1 (the highest power of the variable, which is x, is 1)

- Number of terms: 2 (there are two terms in the expression)

6. -8y²

- Degree: 2 (the highest power of the variable, which is y, is 2)

- Number of terms: 1 (there is only one term, which is -8y²)

Answer 2

Answer:

Answer:

3p^3 + 2p^2 + 19p - 5

Degree: The highest exponent of the variable 'p' is 3, so the degree is 3.

Number of terms: There are 4 terms in this polynomial.

5x^4 + 12

Degree: The highest exponent of the variable 'x' is 4, so the degree is 4.

Number of terms: There are 2 terms in this polynomial.

n^2 - 7n - 21

Degree: The highest exponent of the variable 'n' is 2, so the degree is 2.

Number of terms: There are 3 terms in this polynomial.

Degree: The polynomial 3 is a constant term, and constants have a degree of 0.

Number of terms: There is 1 term in this polynomial.

2x + 7 Degree: The highest exponent of the variable 'x' is 1, so the degree is 1.

Number of terms: There are 2 terms in this polynomial.

-8y^2

Degree: The highest exponent of the variable 'y' is 2, so the degree is 2.

Number of terms: There is 1 term in this polynomial.

Therefore, the classification of the given polynomials by degree and number of terms is as follows:

3p^3 + 2p^2 + 19p - 5:

Degree: 3

Number of terms: 4

5x^4 + 12:

Degree: 4

Number of terms: 2

n^2 - 7n - 21:

Degree: 2

Number of terms: 3

Degree: 0 Degree: 0

Number of terms: 1

2x + 7:

Degree: 1

Number of terms: 2

-8y^2:

Degree: 2

Number of terms: 1

Step-by-step explanation:

In algebra, a polynomial is an expression consisting of variables (such as 'x', 'y', or 'p') raised to non-negative integer powers, combined with coefficients (constants), and combined using addition and subtraction operations. The terms within a polynomial are separated by addition or subtraction signs.

The degree of a polynomial is determined by the highest exponent (power) of the variable in the polynomial. It represents the highest power to which the variable is raised. For example, in the polynomial 3p^3 + 2p^2 + 19p - 5, the highest power of the variable 'p' is 3, so the degree of the polynomial is 3.

The number of terms in a polynomial refers to the separate parts that are added or subtracted. In the polynomial 3p^3 + 2p^2 + 19p - 5, there are four terms: 3p^3, 2p^2, 19p, and -5.

Let's break down the classification of each polynomial:

3p^3 + 2p^2 + 19p - 5:

Degree: The highest exponent of the variable 'p' is 3, so the degree is 3.

Number of terms: There are four terms in this polynomial.

5x^4 + 12:Degree: The highest exponent of the variable 'x' is 4, so the degree is 4.

Number of terms: There are two terms in this polynomial.

n^2 - 7n - 21:

Degree: The highest exponent of the variable 'n' is 2, so the degree is 2.

Number of terms: There are three terms in this polynomial.

Degree: The polynomial 3 is a constant term, and constants have a degree of 0 since they have no variables.

Number of terms: There is one term in this polynomial.

2x + 7:

Degree: The highest exponent of the variable 'x' is 1, so the degree is 1.

Number of terms: There are two terms in this polynomial.

-8y^2:

Degree: The highest exponent of the variable 'y' is 2, so the degree is 2.

Number of terms: There is Number of terms: There is one term in this polynomial.

By determining the degree and number of terms in a polynomial, we can gain insights into its properties and behavior, such as its complexity, the number of solutions it may have, or its graph's share

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The product of 5 more than p and 7?

Answers

If you would like to solve the following expression, you can do this using these steps:

the product of 5 more than p and 7:
5 more than p ... p + 5
the product ... *
(p + 5) * 7 = 7 * p + 7 * 5 = 7 * p + 35

The correct result would be 7 * p + 35.

The product of 5 more than p and 7 can be expressed algebraically as (5 + p) * 7.

This can also be expressed as 35 + 7p or 7p + 35.

3x - 17 = 46 . solve for x

Answers

Answer:

$x = 21$

Step-by-step explanation:

We can simplify this equation down until we have x isolated.

$3x - 17 = 46$

If we add 17 to both sides:

$3x = 63$

Now we can divide both sides by 3:

$x = 21$

So $x = 21$ .

Hope this helped!

Answer:
x= 21

Explaination:
3x - 17 = 46
3x = 46 + 17
3x = 63
3x/3 = 63/3
x = 21

If f(n) = - 5n - 2, then f(3) is _____.

Answers

We have f(n) = - 5n - 2
So f(3) = - 5×(3) - 2 = - 17

Can you show us how to find the discriminant of the quadratic x^2 + 2x -2 =0

Answers

Step #1:
Make sure the equation is in the form of [ Ax² + Bx + C = 0 ].

Yours is already in that form.
A = 1
B = 2
C = -2

Step #2:
The 'discriminant' for that equation is [ B² - 4 A C ].
That's all there is to it, but it can tell you a lot about the roots of the equation.

-- If the discriminant is zero, then the left side of the equation is a perfect square,
and both roots are equal.

-- If the discriminant is greater than zero, the the roots are real and not equal.

-- If the discriminant is less than zero, then the roots are complex numbers.

The discriminant of your equation is [ B² - 4 A C ] = 2² - 4(1)(-2) = 4 + 8 = 12

Your equation has two real, unequal roots.

$the\ discriminant\ of\ the\ quadratic\ ax^2+bx+c=0\n\n\Delta=b^2-4\cdot a\cdot c\n-------------------------\n\n x^2 + 2x -2 =0\n\n\Delta=2^2-4\cdot1\cdot(-2)=4+8=12\n\ndiscriminant=12$