1. Simplify and write in standard form. Then, classify
the polynomial by degree and number of terms.
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
2. Simplify and write in standard form. Then, classify
the polynomial by degree and number of terms.
(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)
3. Simplify the product.
-3x(x^2 + 3x - 1)
4. Find the GCF of the polynomial, then factor.
8v^6 + 2v^5 - 10v^9
1. Alright, let's simplify this and see what we've got. We're subtracting here, so let's distribute that negative sign to each term in the second polynomial:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
= 5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Now let's combine like terms:
= (5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
= 2x^3 + 4x^2 - 11x + 11
So, the simplified expression is 2x^3 + 4x^2 - 11x + 11. Now let's classify it.
This polynomial has a degree of 3, since the highest exponent is 3. It also has 4 terms. So, it is classified as a cubic polynomial with 4 terms.
2. Let's simplify this expression step by step:
(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)
= 9w - 4w^2 + 10 + 8w^2 + 7 + 5w
Now let's combine like terms:
= (9w + 5w) + (-4w^2 + 8w^2) + (10 + 7)
= 14w + 4w^2 + 17
So, the simplified expression is 4w^2 + 14w + 17. Now let's classify it.
This polynomial has a degree of 2, since the highest exponent is 2. It also has 3 terms. So, it is classified as a quadratic polynomial with 3 terms.
3. To simplify the product, we need to distribute -3x to each term inside the parentheses:
-3x(x^2 + 3x - 1)
= -3x^3 - 9x^2 + 3x
So, the simplified product is -3x^3 - 9x^2 + 3x.
4. Alright, let's find the greatest common factor (GCF) of this polynomial, then we can factor it:
First, let's find the GCF. We can see that each term has a common factor of 2v^5, so the GCF is 2v^5.
Now, let's factor out the GCF:
8v^6 + 2v^5 - 10v^9
= 2v^5(4v + 1 - 5v^4)
So, the factored form of the polynomial is 2v^5(4v + 1 - 5v^4).
To answer your questions step-by-step:
1. Simplification and classification of the polynomial:
Start by simplifying the given expression:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
= 5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1 (using the distributive property)
Group like terms:
= (5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
= 2x^3 + 4x^2 - 11x + 11
Therefore, the simplified form is 2x^3 + 4x^2 - 11x + 11.
The polynomial has a degree of 3 (the highest exponent in the terms) and 4 terms, so it can be classified as a cubic polynomial with 4 terms.
2. Simplification and classification of the polynomial:
Start by simplifying the given expression:
(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)
= 9w - 4w^2 + 10 + 8w^2 + 7 + 5w (using the distributive property)
Group like terms:
= (9w + 5w) + (-4w^2 + 8w^2) + (10 + 7)
= 14w + 4w^2 + 17
Therefore, the simplified form is 4w^2 + 14w + 17.
The polynomial has a degree of 2 and 3 terms, so it can be classified as a quadratic polynomial with 3 terms.
3. Simplification of the product:
Start by simplifying the given expression:
-3x(x^2 + 3x - 1)
= -3x * x^2 - 3x * 3x - 3x * -1 (using the distributive property)
= -3x^3 - 9x^2 + 3x
Therefore, the simplified product is -3x^3 - 9x^2 + 3x.
4. Finding the GCF and factoring the polynomial:
Start by factoring out the greatest common factor (GCF).
The GCF of the coefficients is 2. The GCF of the variables is v^5.
So, the GCF of the polynomial is 2v^5.
Now, factor out the GCF:
8v^6 + 2v^5 - 10v^9
= 2v^5(4v + 1) - 2v^5(5v^4)
= 2v^5(4v + 1 - 5v^4)
Therefore, the factored form of the polynomial is 2v^5(4v + 1 - 5v^4).
To solve these polynomial problems, we'll follow certain steps. Let's answer each question step by step to help solve them:
1. To simplify and write in standard form, we'll combine like terms. Subtracting the expression on the right side from the expression on the left side, we get:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
= 5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Combining like terms, we have:
= (5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
= 2x^3 + 4x^2 - 11x + 11
So, the simplified form of the expression is 2x^3 + 4x^2 - 11x + 11.
To classify the polynomial, we determine the degree and the number of terms:
Degree: The highest power of x is 3, so the degree is 3.
Number of terms: There are 4 terms.
Therefore, the polynomial is classified as a cubic polynomial with 4 terms.
2. Again, to simplify and write in standard form, we'll combine like terms. Adding the expression inside the parentheses, we get:
(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)
= 9w - 4w^2 + 10 + 8w^2 + 7 + 5w
Combining like terms, we have:
= (9w + 5w) + (-4w^2 + 8w^2) + (10 + 7)
= 14w + 4w^2 + 17
So, the simplified form of the expression is 4w^2 + 14w + 17.
To classify the polynomial, we determine the degree and the number of terms:
Degree: The highest power of w is 2, so the degree is 2.
Number of terms: There are 3 terms.
Therefore, the polynomial is classified as a quadratic polynomial with 3 terms.
3. To simplify the product, we'll distribute -3x to each term inside the parentheses:
-3x(x^2 + 3x - 1)
= -3x * x^2 - 3x * 3x - (-3x * 1)
= -3x^3 - 9x^2 + 3x
So, the simplified product is -3x^3 - 9x^2 + 3x.
4. To find the greatest common factor (GCF) of the polynomial, we need to find the largest factor that divides evenly into each term. In this case, we can find the GCF by finding the common factors of the coefficients and the variables:
8v^6 + 2v^5 - 10v^9
= 2v^5(4v + 1 - 5v^4)
The greatest common factor is 2v^5. Now, to factor the polynomial, we can rewrite it as:
2v^5(4v + 1 - 5v^4)
So, the factored form of the polynomial is 2v^5(4v + 1 - 5v^4).
I don't see your answers, nor any show of effort on your part.
I will gladly check your work.