1. Simplify and write in standard form. Then, classify
the polynomial by degree and number of terms
[5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1]
2. Simplify and write in standard form. Then, classify
the polynomial by degree and number of terms.
[9w - 4w² + 10] + [8w² + 7 + 5w]
3. Simplify the product.
-3x [x² + 3x - 1]
That said, I can get you started.
Collect terms with like powers. For example,
[5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1]
= 5x³+3x³ + 3x²-x² -7x+4x + 10-1
now just add up the coefficients for like powers and arrange the powers in descending order. (They already are)
Terms are separated by + and - signs
The degree is the highest power.
Go for it. You can also use sites like google and wolframalpha.com to verify your work.
To simplify and write in standard form, we need to combine like terms in the given expressions.
1. Simplifying [5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1]:
Combine like terms: 5x³ + 3x³ = 8x³, 3x² - x² = 2x², -7x + 4x = -3x, and 10 - 1 = 9.
The simplified expression in standard form is 8x³ + 2x² - 3x + 9.
Classification: It is a polynomial of degree 3 (highest power of x is 3) and has 4 terms.
2. Simplifying [9w - 4w² + 10] + [8w² + 7 + 5w]:
Combine like terms: -4w² + 8w² = 4w² and 9w + 5w = 14w.
The simplified expression in standard form is 4w² + 14w + 17.
Classification: It is a polynomial of degree 2 (highest power of w is 2) and has 3 terms.
3. Simplifying -3x[x² + 3x - 1]:
Perform the multiplication: -3x * x² = -3x³, -3x * 3x = -9x², and -3x * -1 = 3x.
The simplified product is -3x³ - 9x² + 3x.
To simplify and classify the given polynomials, we will perform the operations and combine like terms.
1. [5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1]
To simplify, we will group the like terms together.
Adding the terms with the same exponent (degree):
(5x³ + 3x³) + (3x² - x²) + (-7x + 4x) + (10 - 1)
Simplifying further:
8x³ + 2x² - 3x + 9
The polynomial 8x³ + 2x² - 3x + 9 is in standard form with four terms. Its degree is 3.
2. [9w - 4w² + 10] + [8w² + 7 + 5w]
Similarly, we will group the like terms together.
Adding the terms with the same exponent (degree):
(9w + 5w) + (-4w² + 8w²) + 10 + 7
Simplifying further:
14w + 4w² + 17
The polynomial 4w² + 14w + 17 is in standard form with three terms. Its degree is 2.
3. -3x [x² + 3x - 1]
To simplify the product, we will distribute -3x to each term inside the parentheses.
-3x * x² - 3x * 3x - 3x * (-1)
Simplifying further:
-3x³ - 9x² + 3x
The product of -3x and (x² + 3x - 1) is -3x³ - 9x² + 3x. The polynomial is already in standard form with three terms. Its degree is 3.
Oh, my goodness! Are you actually putting questions here that you expect our math tutors to do for you? And are these questions in all 3 of your posts so far parts of a test??
No, no, no -- the way this works is that YOU include what YOU THINK, including where you get stuck in solving each one. Then a math tutor can help you.