Do the polynomials a – 2x2 +1, 4.x² – x+3, and 3x- 2 generate P3(R)? Justify your answer.

Q: Find the zeroes of the polynomial  P(x) = 4x2 - 12x + 9

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Q: In Z,[x] The quotient when 5x* + 3x² + 1 is divided by 3x² + 2x + 1 is 4x² + 3x + 6. a) True b)…

A: We decide whether given statement is true or false

Q: For the polynomial below, 2 is a zero. h(x)=x'+4x+ 6x- 36 Express h (x) as a product of linear…

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Q: prodult of (4x?_6X+ 2) and CX-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: Show that x−6 is a factor of the polynomial p(x)=(1/3)x^3 − (15/2)x^2 + 56x − 138. How many real…

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Q: For the polynomial below, 2 is a zero. g (x) =x + 2x2 – 11x + 6 Express g (x) as a product of linear…

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Q: xpress the polynomial in factored form p(x)=x^3-x^2-8x+12

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Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

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Q: 15. If the zeros of the polynomial x²+px +q are double in value to the zeros of 2x²- 5x -3, find p…

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Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: Verify the factorization using the FOIL method. (x + 3y)(x – 7y) = x? – 7xy + 3xy – 21y² = x² – 4xy…

A: The given expression is: x+3yx-7y=x2-7xy+3xy-21y2⇒x+3yx-7y=x2-4xy-21y2    -1 Thus, we have:…

Q: 10. Use the appropriate method to solve the following polynomials. a. y = x* + 35x² – 36 - b. y =…

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

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Q: Is (x + 2) a factor of the polynomial: x^4 + x^3 - 2x^2 + 3x + 7, and what was the remainder? * no,…

A: Solution

Q: Given that (x + 2) is a factor of the polynomial 2a – 5x2 + ax + a, the - value of the constant a is

A: If (x+2)  is factor of the polynomial 2x3-5x2+ax+a then remainder will be zero when we divide (x+2)…

Q: Find m so that x+5 is a factor of 5x3+29x2+mx+20

A: Let f(x)=5x^3 + 29x^2 +mx+20 , if (x+5) is a factor of f(x) then by factor theorem f(-5)=0

Q: The number of zeros of the polynomial x² + 3x + 2 in Zg is: None O 2

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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: determine the degree of the given polynomials. 5x3y2 - 6x3y3

A: The given polynomial is 5x3y2-6x3y3. Recall, "The degree of a polynomial is the degree of its terms…

Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

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: Q3//A/By using co- factor 1 -2- if AD find A1 =? %3D 3. 2-

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Q: Find the zeroes of the given polynomials  p(x)=x4-16

A: The polynomial is given as, Px:x4-16 The degree of the given polynomial is four. Therefore, it will…

Q: 3. What is the kvalue for the polynomial x - 7x + 17x – 15 if a factor is x – 3? A. k= -3 B. k= 3 C.…

A: We can use factorisation in order to solve the given problem.

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: Simplify the Polynomials – 2x (5x – 15) -10x2 + 30x 3x2 – 17x - o M&Ms 10x? + 30

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Q: For the polynomial below, – 3 is a zero. h (x) = x³ + 9x² + 20x + 6 Express h (x) as a product of…

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

A: True

Q: For the polynomial below,  −3  is a zero. hx=x3 + 5x2 + 4x - 6 Express  hx  as a product of…

A: Given: -3 is a zero of h(x)=x3+5x2+4x-6. Express h(x) as a product of linear factors as follows.

Q: Find m so that x + 4 is a factor of 5x3 + 18x2 + mx+ 16

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Q: Used synthetic dIVision to find the other factors o 1. (2x + x³ + 7x² – 40), (x – 2) 2. (-9x² + 2x³+…

A: Use synthetic division to solve

Q: Factor out −1 from the polynomial. −t2 − 2t + 1

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Q: For the polynomial 8y4 – 3y + 1 1. Is it a monomial, binomial, or trinomial? 2. What is its degree?

A: Given: 8y4-3y2+1 Monomial contain only one term, binomial contain three terms and trinomial contain…

Q: Q1. Perform factorization of zero: Gy - 5) (3x³ – 81)(4x + 13)(v3x – 1)(12x + 12) = 0

A: (78y-5)(3x3-81)(4x+13)(3x-1)(12x+12)=0⇒(78y-5)=0 ⇒78y=5 ⇒y=8x57⇒y=407.Or 3x3-81=0⇒ 3x3=81…

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

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Q: By what polynomial must x3-4 x2y+5xy2-2y3 be divided to obtain a quotient of x-y?

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Q: Evaluate the polynomial for x = 5 and y= -4. Show your work. -3x°y 4xy² + 5

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Q: In Z,[x] The quotient when 5x* + 3x² + 1 is divided by 3x² + 2x + 1 is_ 4x² + 3x + 6 . a) True b)…

A: Note: We are allowed to solve only one question at a time kindly upload other questions as different…

Q: Find algebraically the zeros for .3 p(x) = x³ + x² – 4x – 4 %3D -

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Q: Consider the polynomial p(x)=45x3+69x2−24x−48 What are the zeros of 3p(x+1)?

A: Given,

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: Show that is a zero of the polynomial 2 P(x) = 2x* + æ – 5a2 +10x - 4

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Q: Consider the polynomial p (x) = 2 (x + 1) (x – 3)² (A) As х — —о y →? (B) As y →? (C) Find the zeros…

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Q: For the polynomial below, 3 is a zero. fx) =x' - 7x + 11x + 3 Express f (x) as a product of linear…

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