It can be proven that the expression (a +b) a - ab +b-) is equivalent to which of the following polynomial identitles O (a+b)3 O (a-b) O a3+63 O a3-63

Q: . Do the polynomials x? + 2, 2x? – x + 1,x + 2, and x² + x + 4 span P2?

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Q: 2. If the result of a polynomial division is 2x – 4x? – 5x + x+2 23 ,make at least three definitive…

A: Consider the given: If the result of the polynomial division is-2x3−4x2−5x+23x+2It means , The…

Q: 1. Simplify. (7x2 - 2x + 1) + (9x² – 4x + 5) – (4x2 + 6x - 7) b) (7a? - 4ab + 96²) – (-a? + 2ab…

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost other…

Q: Consider two polynomials P (x)=4x-5 and Q(x)=3x2+7x-2 (a.) P(x) times Q(x)= (b.) P(-5)+Q(-3)=…

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Q: 1. Show whether the given polynomials 1+4x + x², 2+ 5x + 3x2, 3x 5x, and 3+ 15x - 8x spans p,.…

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Q: Which polynomials are in standard form? Choose all answers that apply: A 5 2x a4- 8a2- 16 523 + 4x-3…

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Q: Determine whether each expression in Exercises 24–27 isa polynomial. If it is, state the degree of…

A: Determine whether each expression in Exercises 24–27 is a polynomial. If it is, state the degree of…

Q: Which of the positive integers coming from the set{1, 2, 3, 4} are upper bounds for the zeros of the…

A: The given polynomial is Px=x4-4x2-3

Q: Write the polynomial z - 2r3 -1 as product of distinct poly- nomials of degree 1 and 2.

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Q: Do the polynomials x? + 2,2x2 – x + 1,x + 2, and x² + x + 4 span P2?

A: Let u1 = x2+2, u2 = 2x2-x+1, u3 = x+2, and u4 = x2+x+4. Notice that u1 + u3 = u4. So, u1, u2, u3,…

Q: Use the definition to determine whether the polynomials x3 −4x2 +3x, x3 +6x2 +11x+6, x2 −2, and 2x+5…

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Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: According to Descartes' Rule of Signs, how many negative zeroS could the polynomial æ4 – 3x³ – 2x² +…

A: According to Descartes's rule of signs, maximum number of positive real root of a polynomial…

Q: A. Determine the factors of the given polynomial. 1. х3 + 2х2 -5х-6 2. х3 + x2- х-1 3. x3- x2- 10x-8

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Q: Exercises 108–110 will help you prepare for the material covered in the next section. 108. Multiply:…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 3. x – 6x² + x

A: We know that a polynomial with its highest degree 3 is known to be a Cubic polynomial. The general…

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

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Q: Find the polynomial to represent (3x-7)2. O 9r2 - 21x + 49 O 9x2 + 21x + 49 9z2 – 42x + 49 9x2 + 42x…

A: We have to find the polynomial which represents the given expression: 3x-72 We know the algebraic…

Q: Explain the formula for the Hermite interpolating polynomial?

A: In any polynomial function if the values for the function is known for some data points and the…

Q: 1 Determine the correct factorization of the polynomial expression given below. 128x - 54x 2x(4x -…

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Q: Show that x2 − 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

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

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Q: 3. Write down the polynomial having coordinates in B and the one with the same coordinates in B'.

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Q: Do the polynomials x³ + 2x – 4, x³ + x² – 3x + 1, and æ³ + 5 generate P3(R)? Explain. - -

A: Here generate means span.  The span of a set of vectors is the set of all linear combinations of the…

Q: How do you write polynomial funtions in standard form when the zeros are 5, 3i, and -3?

A: The polynomial with zeroes as a, b and c can be expressed as (x - a)(x - b)(x - c). This can be…

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: Which polynomial correctly combines the like terms and expresses the given polynomial in standard…

A: Given: The polynomial expression is 8mn5-2m6+5m2n4-m3n3+n6-4m6+9m2n4-mn5-4m3n3.

Q: In Exercises 35-36, divide the polynomial by the топоmial. 35. (15.x3 – 30x2 + 10x – 2) ÷ (5.x2) 36.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 23. Express the polynomial 2m -3+ 7m in standard form. 2m + 7m-3 9m -3 7m+ 2m - 3 -3+ 7m+ 2m

A: Given expression of polynomial 2m2-3+7m

Q: Ise the definition to determine whether the polynomials x3 – 4x2 + 3x, x* + 6x2 + 1la+6, x² – 2, and…

A: True

Q: Which of the following polynomial expressions factors into 3x(x + 5)(x + 2)? O 3x° - 21x2 – 30x O…

A: Given, Simplify 3xx+5x+2

Q: Assume that the polynomial 7? + bx +c = 0 in which b, cE Z, has two integer solutions. Which one of…

A: We have to equation as - x2 + bx + c = 0.......(1) The above equation (1) is a quadratic equation…

Q: 6. Which polynomials have 4 roots? Select all that apply. 3x* – 81 = 0 4x + 4x + 4 = 0 2x4 + 3x? +…

A: The root of the polynomial is measured by its degree. Degree of a polynomial is the highest power of…

Q: The standard notation of the factorial polynomial x(4) - x(3) - 2

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Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

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Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

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Q: Select the polynomial that has exactly three zeros O - 111 O 4x + 11x O 22 - 3x? + 2x2 2 x² 2x 8 -…

A: we know that if polynomial has n degree then there are at most solutions. here in option A…

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: Consider the following polynomial. m12,3 - n³z12 (a) Can the polynomial be treated as the difference…

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Q: State whether the ollowing algebraic expressions are polynomials or not. IF not, state the reason 1.…

A: We will find out the required solution.

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

A: The given graph is,

Q: What are polynomials and can you give me an example of a few?

A: Concept of polynomial is used .

Q: 2. Find the difference of the polynomials: (5x°-2x'+x)-(4x°- 3x+2x³-5x) O 9x° +3x-4x O…

A: Given,  ( 5x5 - 2x3 + x ) - (4x5 - 3x4 + 2x3 - 5x )

Q: In Exercises 12–13, subtract the polynomials. 12. (7x – 6x2 + 5x – 11) – (-8x³ + 4x2 – 6x – 3) 13.…

A: We have to subtract the one polynomial from other .

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: Multiply the polynomials. Choices for 53-57: 53. x(x+9) A) -4x +8x-6x? B) -12x* +6x -24x 5x(x* -2x)…

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Q: If the polynomials f1 and f2 are not divisible by the polynomial g, can their sum f1 + f2 be…

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Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…

Q: 2a] aS a product Of irreducible polynomials.

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Q: subtract the polynomials using the horizontal format. -4a - 5 from 6a + 2

A: The given polynomials are: ( -4a - 5) and (6a + 2) We have to subtract the polynomial ( -4a - 5)…