Each of the following polynomials is written with its monomials ordered according to exactly one of the monomial orders: Lex, graded lex, or graded reverse lex. Determine which monomial order was used in each case. (a) 7a y4z-2ry8+2?y? (b) xy³z+ry?,2+x²z3 (c) æ+y³z+2a³y?z-4ry?z4

Q: 2. Decide if the following polynomials are reducible in Q[x]. (a) 2x3 – 3x + 3; (b) 4x3 — 5х + 2.

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Q: 3. Given the polynomials p1 = t3 – 2t2 + 1, p2 = t2 – 4, p3 = t3 + 2t, p4 = 5t. Does this set of…

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Q: Which of the following polynomials is exactly divisible by (3x + 1)? * O 6x^2 + 17x + 5 9x^2 + 6x +…

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Q: Three students used different methods to multiply polynomials. Carefully observe each student's work…

A: Here the polynomials are x-6 & x-9. The vertical terms must be x & -9 and the horizontal…

Q: Which of the following polynomials is exactly divisible by (2x- 1)? A. 2. - 5x+2 C. 42 - 16 B. 22 +…

A: The objective is to find the polynomial that is divisible by (2x-1).

Q: 7. Add or subtract the following polynomials: a. 2x2 + 3y3 - 4x2 = b. y3 + 2y3 - 8 + 2 = c. 10 -…

A: Given that   Add or subtract the following polynomials: a. 2x2 + 3y3 - 4x2

Q: Add the polynomials. (5x^4+7x^3+2x^2+25x-9) + (6x^4-9x^3+8x^2-17x+5)

A: We need to add the following polynomial 5x4+7x3+2x2+25x-9 + 6x4-9x3+8x2-17x+5

Q: Classify the following polynomials by degree and number of terms. 4p3+2p2+19p−5

A: Given: 4p3+2p2+19p-5 A polynomial with 1 term is a monomial. A polynomial with two terms is a…

Q: 2. Simplify each polynomial. Gather like terms. a)-p +5q – 8r – q+ 3p+9r +1 c) 5q - 9s – 8r + 8q –…

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Q: 10. Which of the following polynomials is NOT divisible by (3x+ 1)? A. 6x2 + 17x+ 5 B. 3x - 4x2+…

A: Use remainder theorem

Q: 1- Write the expression x* +x³ + 3x² – 3x – 4 in the of Legendre polynomials

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Q: Evaluate the following polynomials? 1.P(2)=x³–3x²–x+2 2.P(3)=2x³+2x²–4x+1 3.P(-2)=x³–8x²–2x+5

A: As per the policy we are solving first three subparts.   Please repost and specify which subparts…

Q: 6) Divide the following polynomials a) (2x³ – 3x² + 4x + 5) ÷ (x + 2) b) (16x3 – 12x² + 20x – 3) ÷…

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Q: consider two polynomials P(x) =6x+1 and Q(x)=4x2-3x+2 carry out the indicated operation and simplify…

A: Explanation of the solution is given below...

Q: Multiply the following polynomials and express your answer in simplest form. (2x-6)(x+ 11) C) 2x2 +…

A: As we know that the multiplication of  (a+b)(c+d)=ac+ad+bc+bd

Q: 8-94 c and d

A: see 2nd and 3rd step.

Q: Determine whether the following polynomials span P2. P1 - 2-x+ 6x?, p2 - 6 + x, P3 = 28 + 2x + 12x²,…

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Q: 1. Add the following trinomials 8x? – 7x – 2y, 5x? – 6x – 15y , -4x²+11x - 9y 2a. Simplify the…

A: Topic:- algebra  Note:- as per our guideline if more than three subparts posted than only first…

Q: Which of the following polynomials go to negative infinity as x approaches infinity but go to…

A: Checking option b because  Option a,c,d is positive when x approaches to infinity and negative when…

Q: A local city wants to compare the number of those with a car and those without a car, represented by…

A: Given,          A local city wants to compare the number of those with a car and those without a…

Q: determine the degree of the given polynomials. -5x2y2 - 6xy2 + x

A: Consider the provided polynomial, 5x2y2-6xy2+x Determine the degree of the given polynomial.

Q: Determine whether the following polynomials span P2. P1 = 5 - x+ 4x², p2 = 7+ x, p3 = 38 + 2x + 8x²,…

A: Determine whether the following polynomial span P2 Given information: The polynomials are…

Q: Which of the following operations on polynomials will always result in another polynomial? Select…

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Q: Simplify the following polynomial by combining like terms. 6d - 10 + 3f – 58 – 3d + 4 O -15d + 3d +…

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Q: Add or Subtract the following Polynomials listed on the attached document. 1. (4a - 6a 3a + a + 1) +…

A: Technique to be used:- 1.Write terms having same powers together. 2.Then add or subtract…

Q: 6) Divide the following polynomials c)(2x3 + 19x2 – 21x) ÷ (2x² + 21x)

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Q: Use long division to divide the following polynomials: (3ct + a3-#+1) 은 (22-2x + 1) O 3a2-5x +12 +…

A: Answer

Q: 2. Simplify the following polynomials: a) (x²-3x² + 5x-9) + (4x³ - 5x² - 8x +11) b) (3xyz - 4x² + 8)…

A: For solving this kind of problem we need to add same power of terms and simplify the equation.

Q: Find the factors of the following polynomials. 9. x? – 4 10. x2 + 4x-5 11. 3x + 6x² + 5x + 10

A: It is reuquired to find the factors of the given polynomials.

Q: Which of the following are terms in the sum of the given polynomials? 3x2,-2x2y, 2xy2, 4y2, xy2,…

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Q: Add or subtract the following polynomials. (3a + a) + (5 - 2a) + (5a°) O 2a - a+ 20 O 3a - a + 10 O…

A: Add or subtract given polynomial

Q: Which of the following polynomials is the correct simplified form of 10y3-2y3-16y2+8y2?

A: From the given problem:   10y3-2y3-16y2+8y2   Now simplifying the given polynomials:…

Q: DO NOW Simplify the following expressions by performing the indicated operation and classify new…

A: Degree of polynomial is defined as degree of highest power of variable.  Number of terms are the no.…

Q: 2. Write the polynomial in standard form. * 5w – 2w + 2w - 8 2w + 2w + 5w-8 -2w + 2w -8+5w 5w - 2w +…

A: Steps :: 1) Write the term with the highest exponent first2) Write the terms with lower exponents in…

Q: expand and simplify the following polynomial: 2 (7 – 4a) a (2a – 4) (5a + 1) 40a + 390a? + 180a O…

A: 2(7-4a)a(2a-4)(5a+1) = (14- 8a)a{ 10a2 + 2a - 20a -4}  = (14a- 8a2)( 10a2 -18 a - 4)  ={ 140a3…

Q: Q3: Find the following (if possible) • All possible polynomials in GF(4²) 3x 17 ++ 5xmod 241 = 17 5…

A: GF42=GF(16) is called the Galois Field with 16 elements.  Galois Field: A finite field or a Galois…

Q: 13. Arrange the terms of the following polynomials in descending and ascending powers of y. (a) 8+2y…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: A. Classify the following polynomials as to degree. 1. 4x2 + 3x - 7x + 8 6. 3 + 3x? 2. x + 2x - 5 7.…

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Q: Determine whether the following polynomials span P2. P1 = 4- x+ 11x2, p2 = 7+ x, p3 = 29 + x + 22x?,…

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Q: A third degree polynomial passes through the points (0,-3),(,0),(2,9), (3,30), (4,69) and (5, 132),…

A: Using Newton's forward difference method:f(x) = f(x0) + (r)∆y + (r)r-12!∆2y +  (r)r-1(r-2)3!∆3y…

Q: 14. fx)= (4x - 11x+2)(7x - 2x)+(4x +9 x)(4x -9x+1) (b) 13 (c) 14 (d) 15 (e) 16 (a) 7 (b) 8 (c) 9 (d)…

A: we have to find no. of zeros

Q: Add the following polynomial given in the first column and match them with their appropriate result.…

A:

Q: Find the phrase that describes the end behavior of the following polynomial: 150 100 -100 O Odd…

A: The given graph is,

Q: Determine whether the following polynomials span P2. P1 - 2-x+ 6x?, p2 = 7 + x, P3 = 32 + 2x + 12x²,…

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Q: 5x +...)(5x ..= 25x²–0.16yª 4 -

A: Given query is to fill the blank to make expression true.

Q: 9 Find a, b and c, given that the following pairs of polynomials are identically equa a ax? + bx + c…

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Q: 4. Which of the following describes the end behavior of the polynomial y = –x³ + x? %3D as z -oo, y…

A: Here  function is given and we have to find the end behavior of function

Q: Determine the third order polynomial below which has the following cartesian confitates (-1,-16),…

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Q: Simplify the following polynomial by combining like terms. 3x + 8x - 2- 22 +7x– 6 O 2x + 30x -8 O…

A: Combining like terms

Q: 1. Which of the following expressions are monomials with degree 2? i) 2x + 2x ii) 2x2 iii) x iv) 2x…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.