Find the greatest common divisor of p(x) = x^3 + x^2 − 4x + 4 and q(x) = x^3 + 3x − 2 in Z5[x].

Q: Find the zeros of f(X) = X^3– 5X^2– 4X + 20

A: Given function , fx=x3-5x2-4x+20

Q: Express as a polynomial.

A: Here given as 4z4-3z2+1-zz3+4z2-4

Q: Find the quotient and remainder of (x' + 8x² + 19x + 13) ÷ (x + 3). A (x² + 11x + 52) R 13 © (x² +…

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Q: Suppose that p(x) = x^3+ ax^2 + x + 1 has a zero at x = 1, where a is some constant. Determine a,…

A: given p(x)=x3+ax2+x+1 has zero at x=1 Therefore substitute x=1 and equate with 0…

Q: determine whether  the following numbers are roots of the polynomial equation P(x) = 0, P(x) =2x^3 -…

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Q: Show that x2 - 4 is a factor of x* – 5x3 + 2x2 + 20x – 24.

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Q: If f(x) is a 4th degree polynomial, and has 3 real numbers as roots, the other root is?

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Q: Find the gcd of (x^4+x^3+x^2+2x+3) and (x^3+4x^2+2x+3) in Z5.

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Q: Write an equation for the polynomial graphed below 5- 4 3 1 -5 /4 -3-2 -1 -1 1/2 3 4 5 -3 -4 -5+…

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Q: Find the x3 term in (x-1) (2x-2)4   4=n, 5 terms

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Q: Find the remainder when dividing the polynomial x^3-4x^2-7x+2 by x-5

A: detailed solution is given below

Q: Perform Crout's method on 2x₁5x₂ + x3 = 12 -X₁ + 3x₂x3 = -8 3x₁4x2 + 2x3 = 16

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Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: Express as a polynomial.

A: The given expression is as below:       (3x3-4x2+x-7)+(x4-2x3+3x2+5)

Q: Find a polynomial p(x) = ao + a1x + aza² + azx³ of degree < 3 (here ao, a1, a2, a3 are real numbers)…

A: In this question , use the given values and solve the equations and find the polynomial.

Q: 5/2 - 2x = x/2 - 5

A: Add 2x to both sides

Q: A polynomial which goes through the point (1,4) and has zeros at x=0,x=3 and x=-2

A: Given:A polynomial pass through the point (1,4) and has zeroes at x=0, x=3 and x=-2.

Q: Find a 5th degree polynomial with zeros x = 3 + 2i, 1 − squareroot2, and −1 with a co-efficient of 4…

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Q: Find all other zeros of P(x)=x^(3)+5x^(2)+9x+5, given that -2-i is a zero. (If there is more than…

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Q: Which is not a restriction  of 4x / 2x (x+4)

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