1. Solve for the following polynomials: a. x8 + x' +3x-1 is divided by x-3x³ +4x +1 | b. 4x3 + 18x? + 15x + 28 is divided by x +4 C. 2x - 6x3 + 7x2-5x+ 1 is divided by x + 2 Your answer

Q: 47. For what value of k will the polynomial function f(x)=x²+6x² +kx -4 have the same remainder when…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Make up two polynomials, not of the same degree, with thefollowing characteristics: crosses the…

A: Here it is given that Polynomial  crosses the x-axis at - 2  touchesthe x-axis at 1, and is above…

Q: I the zeros of the given quadratic polynomials, and verify the relationship between the oefficient…

A: Explanation and solutions is given below.....

Q: Is 7x to the 3rd power a polynomials

A: A polynomial is an algebric expression with at least one term in it.Given expression is 7x3. Here…

Q: Find the polynomial of the lowest possible degree which assumes the values 3, 12, 15, 21 when x has.…

A:

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

A:

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: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

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Q: Determine whether the first polynomial can be expressed as a linear combination of other two…

A: The given polynomials are  2x^3 − 2x^2 + 12x − 6, x^3 − 2x^2 − 5x − 3, 3x^3 − 5x^2 −4x − 9

Q: Express as a polynomial. (t 2 + 2t - 5)(3t 2 - t + 2)

A: Given: t2+2t-53t2-t+2 For the polynomial, we solve the parenthesis,…

Q: Which of the following polynomials has a remainder of 1 when divided by x + 2, x + 3 and x + 5? x³ +…

A: We have to find the polynomial

Q: How many roots are there for the polynomial that factors into f(x) = (x² – 1)(x + 2)(æ – 1)2? 3.

A: no of roots = ?

Q: What is the quotient and remainder after dividing the following: f (x) = 2x3 18x? – 16x 50 by x- 10…

A: Solution

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

A:

Q: Express as a polynomial.

A: Use the identity x+y2=x2+y2+2xy.

Q: Find the polynomial in x of the third degree, which vanishes when x=-1 and x=2 has  the value 8 when…

A:

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

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Q: 8. Verify that (x2 - 1) + is a valid result for the x4 +3x2+4 polynomial long-division calculation…

A: Given : The divide the  polynomial x 6 + 2x4 + 2x2 - 4 by the polynomial  x4 + 3x2 + 4 . Result : x2…

Q: 18. Express the polynomial 6x -x +2x-4 in standard form. 6x'-2x-4 7 +2x-4 -4+2x-5x 5x +2x-4

A: standard form is the form in which polynomial is written decreasing power of x and all different…

Q: Answer the questions about the following polynomial. 1+ 5x?

A: The given polynomial is 1+5x2 Standard form of the polynomial : 5x2+1

Q: 14. Evaluate this cubic polynomial for x = 1.32, using both rounding and chopping to three digits at…

A:

Q: If x* – 1 = (x – 1) q (x), which polynomial represents q(x)? |

A: As we know that (x2-y2)=(x-y)(x+y)

Q: From the given polynomials be able to solve each by factoring or any other way of solving to find…

A:

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: Which of the following polynomials will fill in the blank to make the equation true? 2 (3x - 7x + 2)…

A: The given polynomials,3x2-7x+2+_______=2x2-10x+3

Q: Gives that f(x) 5x^3-54x^2+170x-104. And that 5+i is a zero, factor f(x) completely.

A: If 5+i is a zero then (5-i) is also a zero.

Q: (b) Find the nested form Q(x) of the polynomial /(x) = x³ + 2x2-5x + 3 and hence evaluate Q(2.6)…

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Q: If Æ(x) = 2x + 1, find Æ(a + h). 2a + 2h + 1 a + h + 1 2a + 2h + 2 2a + h + 1

A: Here we will find E(a+h),

Q: Find the least common multiple of the following pair of polynomials:x(x - 1) 2 ( x + 1)  and 4( x -…

A: The least common multiple (LCM) is the smallest quantity which is multiple of more than one…

Q: 21) Determine a polynomial that represents the area of the figure. 21) 2x + 6 3x + 3 A) 6x2 + 18 B)…

A:

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A)…

A:

Q: 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |

A: Start with Right hand side as follows.

Q: 1. Find the sum of the polynomials: (5x°-2x+x)+(4x° – 3xª +2x³-5x) O x5 +3x4-4x3+6x O 9x5+3x4-4x³+6x…

A:

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

Q: Divide the following polynomials. 1. USE THE LONG DIVISION to divide X'+ 3X² +5X+3 by X+1. 2. USE…

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Q: What is the fermat value, in polynomial form, of integer 'a', if a=x^4 + 1; p=x^2 + 1?

A: We have to find the Fermat value 'a' which is given in the following form, a=x4+1p=x2+1

Q: Use synthetic division to divide the first polynomial by the second. 2x^4-8^3+14x^2-14x+4…

A: Given, Divident- 2x^4-8^3+14x^2-14x+4 = 2x^4+14x^2-14x-508 Coefficients of (x⁴,x³,x²,x,x⁰) is given…

Q: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True…

A:

Q: Which polynomial would have the following end behavior? x+ -00, f(x) - -00 x+ 0o, f(x) → -00 A y =…

A:

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: 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: We can apply Eisenstein criterion for irreducibility of the polynomial 4x10−9x3+24x−18 over Q. true…

A: Using Eisenstein Criterion for irreducibility of f(x) over Q,

Q: If a polynomial f(x) when divided by (x - a) gives a remainder r₁, and when divided by (x - b) gives…

A: Given that fx is divided by x-a, we get remainder r1, so there exist a polynomial qx such that…

Q: Solve the following polynomial: xª -10r3-78x = -40x2 - 63 Select all that apply. Ox = 3…

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Q: 23 2. If the result of a polynomial division is 2x3 – 4x2 – 5x + x + 2 make at least three…

A: The result of the polynomial division is, 2x3-4x2-5x+23x+2 Let, f(x)=2x3-4x2-5x+23x+2…

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: Perform the following division of polynomials by synthetic division. (xª – x³ – 9x² + 29x – 30) ÷…

A: Given information: x4-x3-9x2+29x-30÷(x2-3x+4) Therefore, can be written as, x4-x3-9x2+29x-30x2-3x+4…

Q: determine the degree of the given polynomials. -x2y + 2xy2 - xy

A: Given the polynomials  -x2y+2xy2-xy

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

Q: 17) Perform the following division of polynomials by synthetic division. (x* – x³ – 9x² + 29x – 30)…

A: Given (x4-x3-9x2+29x-30) ÷ x2-3x+4