Use the Binomial Theorem to simplify (x – 2)3 as a polynomial ax3 + bx? + cx + d.

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

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Q: Use the binomial theorem to expand and simplify.(3t - 5s)4

A: (3t-5s)4

Q: What is the coefficient of x2y" in (5x- y)°?

A:

Q: Use the binomial theorem to expand and simplify.(x2 + 2y)3

A: To expand and simplify the given equation using binomial theorem

Q: How can you determine whether a linear binomial is a factor of a polynomial without using the…

A: to find : How can you determine whether a linear binomial is a factor of a polynomial without using…

Q: Verify whether -3 and 2 are the zeros of the polynomials x3-x2+x-6

A: polynomial p(x) is zeros at x=a if p(a)= 0,

Q: Which of the following polynomials is exactly divisible by (3x+1)? A. 6x2+17x+5 B. 9x2+6x+1 C.…

A: We have to check which of the given polynomials is exactly divisible by 3x+1. Factor theorem states…

Q: Arrange the steps in the correct order to prove the polynomial identity for the cube of a binomial…

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Q: Rewrite the polynomial in the form ax + by + c and then identily the values and c. x - 1- 2y

A: To identify the value of a,b,c

Q: Now classify the polynomial. 5x quintic binomial quadratic binomial linear monomial

A: Linear Monomial :  An expression  which has only one term whose highest degree is one.

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

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Q: What is the coefficient of x2y' in (5x- y)?

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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: 10. Determine whether the first polynomial in P3(R) can be expressed as a linear combination of the…

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Q: Use the Binomial Theorem to expand the expression (x2 + x-3)4 and write the result in simplified…

A: To Use the Binomial Theorem to expand the expression                                         (x2 +…

Q: Use the binomial theorem to expand and simplify the expression.(2x + y3)4

A: Simplify the expression: 2x+y34.   Apply Binomial theorem: a+bn=∑r=0nCrnan−rbr. Therefore,…

Q: Find the coefficient of x5 in (1 – 2x)-7 using generating function.

A: Given to find the coefficient of x5 in 1-2x-7 The generating function will be Gx=1-2x-7…

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: Show how to determine whether the binomial is a factor of the polynomial. 1. f(x) = 3x4 + 6x3 – x2 -…

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Q: What is the sum of the polynomials? (8x² - 9y² -4x] + (x²_3y² - 7x) 2-3y2-7x 8x -9y2 -4x +

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Q: Use the binomial theorem to expand and simplify.

A: Formula for binomial expansion - a+bn = nC0anb0 + nC1an-1b1 + nC2an-2b2 + nC3an-3b3 +…

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: Use the binomial theorem to expand and simplify (2x² – 4x + 7)°.

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Q: Find a, beR such that the polynomial f(x) = 6x4 – 7x3 + ax? + 3x + 2 is divisible by g(x) = x2 – x +…

A: When a polynomial is divisible by another polynomial, there is a quotient polynomial. The leading…

Q: Write P20 = x² +2r– 1 as a linear combination of the polynomials P21 = x² – x – 2, P22 = 2x² – x +…

A: We have to express polynomial P20 as a linear combination of P21,P22,P23.

Q: 2. อใน at2 a อริน 0x2

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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: Find the sum of the coefficients of ( 3x + 2y -2)⁸.

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Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - c is a factor of…

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Q: What is the 6th term of (x - 1)¹0?

A: Given problem:- what is the 6th term of (x-1)10

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

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Q: Now classify the polynomial. 5х C linear monomial quintic binomial quadratic binomial

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Q: subtract the polynomials using the vertical format. x3 + x2 - x - 1 from -2x3 + 6x2 - 3x + 8

A: Given that : The polynomials x3 + x2 - x - 1 and -2x3 + 6x2 - 3x + 8.

Q: Find the conditions that the zeroes of the polynomials Ax) =x – px+ qx – r may be in arthametic…

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Q: メ-5x1-36 ×-3x744Xー12 4 show that -24

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Q: Multiply this binomial using the box method. (x-2)(x+3)

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Q: When fully multiplied out, what is the 8th term of (x-3y)¹2?

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Q: Find the product. Show your work. (6x + 3) (x² – 4x + 4) - Show Your Work 6x3 27x2- 12x + 12 O 6x3 -…

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Q: The binomials (x- 2) and (2x +3) are the factors of which polynomial?

A: We have to find the polynomial which the binomials (x - 2) and (2x + 3) are the factors . Then ,…

Q: subtract the polynomials using the horizontal format. -3a2 - 6a + 3 from 3a2 + 6a - 11

A: A polynomial is an expression consisting of variables and coefficients, that involves only the…

Q: Expand and simplify this factorial polynomial: (x-10)^(4)

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Q: Express f(x) = 4x3 + 6x2 + 7x + 2 in term of Legendre Polynomials.

A: The Legendre equation is, 1-x2d2ydx2-2x dydx+nn+1y=0 The polynomial denoted by Pnx is called the…

Q: Find the middle term in the expansion of (3x + x/3)10.

A: Given power is 10. So the number of terms= 10+1=11   This means the 11+12=6th term will be the…

Q: subtract the polynomials using the horizontal format. 7x + 5 from 2x - 1

A: A polynomial is an expression consisting of variables and coefficients, that involves only the…

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

A: Solve the problem as shown below see if they are linear combination of each other and then verify,

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: Use the binomial theorem to expand and simplify the expression.(x2 - 3y)6

A: Use the binomial theorem to expand and simplify the expression.(x2 - 3y)6

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)…

Q: determine if the statement is true or false. If a statement is false, explain whyThe sum of two…

A: Given:The sum of two polynomials each of degree 5 will be less thanor equal to degree 5