Determine whether the statement makes sense or does not make sense, and explain your reasoning: "When performing the division (x5 + 1) ÷ (x + 1), there’s no need for me to follow all the steps involved in polynomial longdivision because I can work the problem in my head and see that the quotient must be x4 + 1"

Q: What is the remainder when f(x) = x' - 22x 16x - 161 is divided by (x - 40)?

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Q: Part of the roof of a factory is devoted to mechanical support and part to green space. The area of…

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Q: What polynomial should be added to 2x-5 so that the sum is zero?

A: Solution...

Q: What is the remainder when the polynomial f(x) = 4x* – 3x³ + x? + 10x – 1 is divided by (x- 2). %3D

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Q: The degree of -2x5 is

A: The degree of a polynomial is the largest exponent on the variable.

Q: Use polynomial long division to divide 4x2 + 23x – 16 by x + 5. What is the quotient and remainder?

A: In long divide method , You need to eliminate the highest term available by dividing.

Q: Use synthetic division to show that 5 is a solution of x4 - 4x3 - 9x2 + 16x + 20 = 0. Then solve the…

A: Coefficients of x4 - 4x3 - 9x2 + 16x + 20 are 1, -4, -9, 16, 20  Then we use the synthetic division.…

Q: Divide the polynomial -x - 2x2 + 3 by (x - K + 11). Use synthetic division to write your answer in…

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Q: Simplify the expression to a polynomial in standard form: (2æ – 1)(3x² – 9x – 4) -

A: Standard form of a polynomial  The Standard form to represent the polynomial is as follows:- F(x) =…

Q: What is the degree of the polynomial 3x4-5x3+7x2-2x+8?

A: Degree of polynomial: The highest or the largest power of the variable denotes degree of variable…

Q: 2. Is the expression 4x³ – 3.6x? – V2 a polynomial? If so, what is its degree?

A: Let p(x)=4x3-3.6x2-2. The general form of a 3 degree polynomial with real coefficients is given by…

Q: When performing the division (x5 + 1) ÷ (x + 1), there’s no need for me to follow all the steps…

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Q: Explain why x - 1 is NOT a factor of the polynomial 15 -2 + 3.

A: Let, f(x) = x¹⁵ - x² + 3 By FACTOR THEOREM, if (x-1) is a factor of f(x) then, 1 is a zero of f(x)…

Q: what method should you use for a polynomial with 4 terms

A: The method to factor a polynomial with four term. Consider the polynomial of 4 terms is,…

Q: What is the number of terms in the polynomial (2a - 5)(a^2 -1)?

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Q: Find the quotient of the polynomials using SYNTHETIC DIVISION. Show your solution. (6x2 + x3 + 2x +…

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Q: Is the expression 4x3 - 3.6x2 - 22 a polynomial? If so,what is its degree?

A: 4x3-3.6x2-22 is polynomial because the powers are positive.

Q: The area of a rectangle is 2x^3+5x^2-x-6 sq m. Write a polynomial that represents its width if its…

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Q: What is the remainder when f(x) = 2x20 - 8x10 + x - 2 is divided by x - 1?

A: Given : The polynomial is  2x20 - 8x10 + x - 2 and dividend is x - 1.

Q: Find the quotient of the polynomials using SYNTHETIC DIVISION. Show your solution. (2x + x3 + 7x2 -…

A: We need to find the quotient of the polynomials using SYNTHETIC DIVISION (2x + x3 + 7x2 - 40) ÷ ( x…

Q: The polynomial -6x + 50x+ ax+ 24 has factors x-1 and 2x + 1. Determine the value of a.

A: Suppose px be the given polynomial such that px=-6x3+50x2+ax+24 And the factors of the polynomial…

Q: How do you find a GCF of a monomial and a polynomial, can i have  step by step showing of each type?

A: solution

Q: The value of the polynomial 5x - 4x2+3 , when x = -1

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Q: When 2x2 - 7x + 9 is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find…

A: We know that Dividend = (Divisor) (Quotient) + Remainder

Q: Simplify the polynomial (3x² + 2xy + 5y²) – (-6x² 2xy + Зу?)

A: Given polynomial3x2+2xy+5y2--6x2-2xy+3y2

Q: What is the coefficient of x^7 in the polynomial (1+x+2x^2)^12

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Q: Simplify the expression to a polynomial in standard form: (-4x2 + 3x + 3)(x² – 2x + 2)

A: We need to evaluate  (-4x2+3x+3)(x2-2x+2)

Q: Since using synthetic division, write the answer as a polynomial

A: Steps to perform while doing synthetic division: 1) To write the given problem in a division like…

Q: You divide two polynomials and obtain the result 5x^2-13x+47-102/x+2. What is the dividend

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Q: (2x – 10x + x- 2) ÷ (x+ 1)

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Q: Simplify the expression to a polynomial in standard form: (3x + 1)(x2 + 4æ – 8)

A: Topic = Polynomial

Q: the zeros of polynomial are 5 multiple of 2, and -1. write in standard form

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Q: A storage company is designing a new storage unit. Based on the dimensions shown, the volume of a…

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Q: How do you divide a polynomial long division?

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Q: what is the power of the polynomial (2x-1)¹⁰×(3x+3)⁹?

A: Let, f(x) and g(x) are linear functions of x .       The polynomial {f(x)}m.{g(x)}n   The power of…

Q: The problem involve the Remainder Theorem.

A: Given, P(x)=x500+6x101-x2-2x+4 We know by remainder theorem ,if a Polynomial function P(x) is…

Q: The problem involve the Remainder Theorem.

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Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form : 2x + 3x2…

A: A polynomial is defined as an expression which is composed of variables, constants and exponents,…

Q: Divide the polynomial 3r-7x +2 by r+1. Clearly state the quotient and the remainder.

A: To find the remainder and quotient while dividing the polynomial

Q: 4. Simplify the expression to a polynomial in standard form. (x + 10) (x² – 2x + 3)

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Q: Find the remainder when f(x) = 2x5 – 8x3 +3 is divided by 3x + 2. -

A: Long Division of Polynomials: A long division polynomial is an algorithm for dividing polynomial by…

Q: 3. 3x2- 11x - 20 = 0

A: topic - factorization

Q: Written as a simplified polynomial in standard form, what is the result when (2x + 1)² is subtracted…

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Q: What is the degree of the polynomial 9 - 3x + 4y - x2? O 1 O 2 3. O 4

A: Degree is heightest power of polynomial.

Q: For Exercise, use synthetic division to divide the polynomials. (2r* – 7x – 56x² + 37x + 84) ÷ -(1-)…

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Q: The length of a rectangle om terms of x is 3x^2+7x+9 and its width is 3x+6. a. Write a polynomial…

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Q: 2. Add one term to the polynomial expression 14x19 9x15 +11x* + 5x² + 3 to make it into a + 11x+ 5x?…

A: Consider the polynomial  14x19-9x15+11x4+5x2+3

Q: find  the remainder when the polynomial 2x4 -5x3 +12-7 is divided by (x+1)

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.…

A: Given: 20x3+8x2 and 20x3+10x

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.