examples of simplifying polynomials

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Question:Create a unique example of dividing a polynomial by a monomial and provide the simplified form. (PLEASE) Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy.

Answers:(x - 2x + x 1) : ( x- 2)= the quotient 3x +4x+ 9 and reminder 17 Here is the method for calculation 3x +4x+ 9 ------------------------ ** x-2 / 3x - 2x + x 1 \ first 3x divide by x the result is 3x **** 3x - 6x *********** 3x multiply by ( x-2) ------------------- * - ******substraction *******4x + x **********divide again by x etc +4x *******4x -8x ********** 4x multiply by x-2 --------------------* -*******substraction ....etc *********+9x - 1 *********+9x -18 -----------------------* - ************+17 ***** here is the rest because 17 can t be divided by x you can do the same way for x +x-2 / 2x -0x + 3x - 2x + x 1 \

Question:this is the question: Explain how to multiply a monomial by a polynomial. Also include examples where you need to simplify after multiplying . HELP! PLEASE AND THANK YOU .

Answers:1. Multiply term by term. 2. Add/subtract all numbers with same variables. Example: (x+1)(x +x+1) x +x +x+x +x+1 x +2x +2x+1

Question:Question 1 (Multiple Choice Worth 3 points) [7.01] Choose the correct classification of 3x4 9x3 3x2 + 6. 5th degree polynomial 4th degree polynomial 9th degree polynomial 24th degree polynomial Question 2 (Multiple Choice Worth 3 points) [7.01] Choose the polynomial written in standard form. x2y2 + xy 1 10x3 + 14x2 4x4 + x x2 + x2y + 3 5x + x3 3 Question 3 (Multiple Choice Worth 4 points) [7.04] Choose the correct simplification of x to the 9th power times y to the 14th power all over x to the 2nd power times y to the 9th power. x11y23 x12y12 x7y5 x18y16 Question 4 (Multiple Choice Worth 3 points) [7.02] Choose the correct simplification of (8x + 7) + (2x 6). 10x 1 10x + 13 10x + 1 11x Question 5 (Multiple Choice Worth 3 points) [7.02] Choose the correct simplification of (2x3 + x2 4x) (9x3 3x2). 11x3 2x2 4x 7x3 + 4x2 4x 2x3 2x2 4x 7x3 4x2 4x Question 6 (Multiple Choice Worth 3 points) [7.02] Choose the correct simplification of (4a2 + 9a 5) + (6a2 5). 10a2 + 9a 10a2 + 9a 10 2a2 + 9a 2a2 + 9a 10 Question 7 (Multiple Choice Worth 4 points) [7.04] Choose the correct simplification of x to the 2nd power over x to the 7th power. x5 x9 1 over x to the 5th power x to the 7th power times y to the 12th power all over x to the 4th power times y to the 9th power Question 8 (Multiple Choice Worth 4 points) [7.03] Choose the correct simplification of (7x3y3)2. 14x6y6 49x5y5 49x6y6 14x5y5 Question 9 (Multiple Choice Worth 3 points) [7.03] Choose the correct simplification of (x9)2. x11 x7 x81 x18 Question 10 (Multiple Choice Worth 4 points) [7.03] Choose the correct simplification of 4x0. 4 4x 1 0 Question 11 (Multiple Choice Worth 4 points) [7.04] Choose the correct simplification of x to the 7th power over x to the 3rd power. x10 1 over x to the 4th power x4 x21 Question 12 (Essay Worth 6 points) [7.01] Part 1: Explain, in complete sentences, what it means to write a polynomial in standard form. Part 2: Provide an example of a 4-term polynomial, not in standard form, and explain how to rewrite it in standard form. Question 13 (Essay Worth 6 points) [7.02] Explain, in your own words, the step-by-step process to simplifying the expression below. Include the simplified answer in your explanation. (8x2 + 5) (3x2 x + 7)

Answers:Since the questions are in multiple choice, I'll only provide the answers. 1: 4th degree polynomial 2: 10x3 + 14x2 4x4 + x 3: x7y5 4: 10x + 1 5: 7x3 + 4x2 4x 6: 10a2 + 9a 10 7: 1 over x to the 5th power 8: 49x6y6 9: x18 10: 4 11: x4 12: A polynomial in standard form is to arrange the monomials in decreasing powers. For instance, if we have 3x + x3 + 2 - 4x2, the standard form is x3 - 4x2 + 3x + 2. 13: To simplify the expression (8x2 + 5) (3x2 x + 7): First, we look at the first term of the first polynomial and find if there are like terms with the other polynomial. In this case, we have 8x2 and 3x2, when subtracted would give us 5x2. Second, we look at the next power of x. Only the second polynomial has an x with power 1. Thus, we have x (since negative of negative x provides a positive x). Third, we subtract the numerical constants for both polynomials, 5 - 7, yielding -2. Finally, we combine the results for each step: 5x2 + x - 2

Question:^ means the number next is to that power Simplify and Add (3x^2-4x+2)+(-3x^2-3x+2) Simplify and Subtract (-5x^2-7x-3)-(-7x^2-4x-2) I beleive the one's below me are monomials Simplify (-9x^3y^4) (5x^3y^4) Simplify (-4C^3d^4e^2)^2 Simplify -4x^3(2x^4-5y) Simplify (x-2) (x^2+3x-2) Simplify (5x-2) (2x-9) Simplify (5x-2) (2x-9) Simplify (4x+9y) (4x-9y)

Answers:3x^2 - 4x + 2 - 3x^2 - 3x + 2 -7x + 4 -5x^2 - 7x - 3 + 7x^2 + 4x + 2 2x^2 - 3x - 1 -45x^6y^8

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Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 1 :Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 1

Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 2 :Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 2