2. simplify: (partially visible)
3. write the following in standard form: ( 11 - 17x^2 - 10x^4 + 5x^3 + 6x^5 )
4. what is the degree of the polynomial above in question #3?
5. how many terms are in the polynomial above in question #3?
6. classify the following polynomials by degree and type: (monomial, binomial, trinomial, polynomial)
( 3x^4 + 4x^2 ): ______
( -12x^2 + 2y + 10 ): ______
( 6x^2y ): ______
( 4y^5 + 3x^4 + 2x^3 + 6x ): ______
4. write an expression for the perimeter of the rectangle below.
(rectangle with length ( (9x + 5) ) and width ( (4y - 6) ))

Question

2. simplify: (partially visible)
3. write the following in standard form: ( 11 - 17x^2 - 10x^4 + 5x^3 + 6x^5 )
4. what is the degree of the polynomial above in question #3?
5. how many terms are in the polynomial above in question #3?
6. classify the following polynomials by degree and type: (monomial, binomial, trinomial, polynomial)
   ( 3x^4 + 4x^2 ): ______
   ( -12x^2 + 2y + 10 ): ______
   ( 6x^2y ): ______
   ( 4y^5 + 3x^4 + 2x^3 + 6x ): ______
4. write an expression for the perimeter of the rectangle below.
   (rectangle with length ( (9x + 5) ) and width ( (4y - 6) ))

Accepted Answer

### Question 3: Write the following in Standard Form: $ 11 - 17x^2 - 10x^4 + 5x^3 + 6x^5 $
# Answer:
$ 6x^5 - 10x^4 + 5x^3 - 17x^2 + 11 $
# Explanation:
## Step1: Recall standard form of polynomial
A polynomial in standard form is written with terms in descending order of their exponents.
## Step2: Identify exponents of each term
- For $ 6x^5 $, exponent is 5.
- For $ -10x^4 $, exponent is 4.
- For $ 5x^3 $, exponent is 3.
- For $ -17x^2 $, exponent is 2.
- For $ 11 $ (which is $ 11x^0 $), exponent is 0.
## Step3: Arrange terms in descending order
Arrange the terms from highest exponent to lowest: $ 6x^5 - 10x^4 + 5x^3 - 17x^2 + 11 $.

### Question 4: What is the degree of the polynomial above in question #3?
# Answer:
5
# Explanation:
## Step1: Recall degree of polynomial
The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.
## Step2: Identify highest exponent
In the polynomial $ 6x^5 - 10x^4 + 5x^3 - 17x^2 + 11 $, the term with the highest exponent is $ 6x^5 $ where the exponent is 5. So the degree is 5.

### Question 5: How many terms are in the polynomial above in question #3?
# Answer:
5
# Explanation:
## Step1: Recall definition of a term
A term in a polynomial is a single number, a variable, or a product of numbers and variables separated by addition or subtraction signs.
## Step2: Identify terms
In the polynomial $ 6x^5 - 10x^4 + 5x^3 - 17x^2 + 11 $, the terms are $ 6x^5 $, $ -10x^4 $, $ 5x^3 $, $ -17x^2 $, and $ 11 $. Counting these, we get 5 terms.

### Question 6: Classify the following polynomials by degree and type:
#### (i) $ 3x^4 + 4x^2 $
# Answer:
Quartic binomial
# Explanation:
- **Type**: It has 2 terms ($ 3x^4 $ and $ 4x^2 $), so it is a binomial.
- **Degree**: The highest exponent is 4, so it is a quartic (degree 4) polynomial.

#### (ii) $ -12x^2 + 2y + 10 $
# Answer:
Quadratic trinomial
# Explanation:
- **Type**: It has 3 terms ($ -12x^2 $, $ 2y $, $ 10 $), so it is a trinomial.
- **Degree**: The highest exponent among the terms is 2 (from $ -12x^2 $), so it is a quadratic (degree 2) polynomial.

#### (iii) $ 6x^2y $
# Answer:
Cubic monomial
# Explanation:
- **Type**: It has 1 term, so it is a monomial.
- **Degree**: For a term with multiple variables, the degree is the sum of the exponents. Here, exponent of $ x $ is 2 and exponent of $ y $ is 1, so degree $ = 2 + 1 = 3 $. So it is a cubic (degree 3) polynomial.

#### (iv) $ 4y^5 + 3x^4 + 2x^3 + 6x $
# Answer:
Quintic polynomial (or Quintic polynomial with 4 terms, but typically we say quintic polynomial as the type is determined by number of terms: it has 4 terms, so a polynomial with 4 terms is just called a polynomial, but by degree it's quintic)
# Explanation:
- **Type**: It has 4 terms ($ 4y^5 $, $ 3x^4 $, $ 2x^3 $, $ 6x $), so it is a polynomial (specifically a 4 - term polynomial, but the general type based on number of terms: monomial (1), binomial (2), trinomial (3), and polynomial for 4 or more).
- **Degree**: The highest exponent is 5 (from $ 4y^5 $), so it is a quintic (degree 5) polynomial.

### Question 4 (Perimeter of Rectangle): Write an expression for the perimeter of the rectangle below with length $ (9x + 5) $ and width $ (4y - 6) $
# Answer:
$ 18x + 8y - 2 $
# Explanation:
## Step1: Recall perimeter formula for rectangle
The perimeter $ P $ of a rectangle is given by $ P = 2\times(\text{length} + \text{width}) $.
## Step2: Substitute length and width
Length $ l=(9x + 5) $, width $ w=(4y - 6) $. So $ P = 2[(9x + 5)+(4y - 6)] $.
## Step3: Simplify the expression
First, simplify inside the brackets: $ (9x + 5)+(4y - 6)=9x + 4y+5 - 6=9x + 4y - 1 $.
Then multiply by 2: $ 2(9x + 4y - 1)=2\times9x+2\times4y - 2\times1 = 18x + 8y - 2 $.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 3: Write the following in Standard Form: \( 11 - 17x^2 - 10x^4 + 5x^3 + 6x^5 \)

Step1: Recall standard form of polynomial

Step2: Identify exponents of each term

Step3: Arrange terms in descending order

Question 4: What is the degree of the polynomial above in question #3?

Step1: Recall degree of polynomial

Step2: Identify highest exponent

Question 5: How many terms are in the polynomial above in question #3?

Step1: Recall definition of a term

Step2: Identify terms

Question 6: Classify the following polynomials by degree and type:

(i) \( 3x^4 + 4x^2 \)

Answer: