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

Q: Find  the value of the polynomial 5x-4x2 + 3 at x = 2 and  x = -1

A: Given, Polynomial  =  5x- 4x2 + 3  Finding the value of polynomial at x = 2  = 5*2 - 4(2)2 + 3 = 10…

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

A: Let f(x) and g(x) be two functions  then g(x) will be the factor of f(x) if remainder(f(x) / g(x))…

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

A:

Q: The number of zeros of the polynomial x² + 4x +1 in Z, is: 4 2 None

A:

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

A:

Q: Is x+2 a factor of x^5+8x^4−6x^3−3x^2−7x−146

A: To prove that x+2 is factor of given equation.

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

A:

Q: Express as a polynomial. (4x - 3y)(x - 5y)

A: Given: (4x - 3y)(x - 5y)

Q: Express the polynomial x5 + 3x3 + x2 + 2x as a product of its irreducible factors in Z5[x].

A: Given: [May be the question is wrong, otherwise the given solution is correct.] The given polynomial…

Q: The number of zeros of the polynomial x² + 3x + 2 in Z, is: 4 2 1 None

A: The polynomial is given as f(x)=x2+3x+2 Z6=0,1,2,3,4,5

Q: 9) Is x-2 a factor of x3 - 13x + 12?

A: To determine whether x-2 is a factor of x3-13x+12.

Q: Find the sum of the polynomials -3x +7x - 8 and 5x -7x+2.

A: As per the company guidelines given to us  I am allowed to  solve first question. I hope that the…

Q: What is the largest multiplicity in the factored polynomial y = (x2 – 1)(x + 2)(x + 4)?

A: Here function is :  y = (x2 - 1) (x +2 ) (x+4)  It can be written as  y = ( x - 1)( x + 1 )( x + 2)(…

Q: Show that (x-y) is a factor of (x2-7x2+14x-8) ,ccplete factors od expression

A:

Q: 9) Is x-2 a factor of x3 – 13x + 12?

A:

Q: Express as a polynomial.

A: We know the identity that, a-ba+b=a2-b2                  ⋯⋯1a-b2=a2+b2-2ab       ⋯⋯2 We have the…

Q: The value of r for which x2 - rx - 2 and x3 + x2 - x - 1 have a common factor is?

A: Given two equations x2-rx-2=0 and x3+x2-x-1=0

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

A:

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: Find factor of polynomial of  p(x) = x^2 - 6x + 8

A:

Q: Prove that 3x3+ 5x - 11 has a root between x=1 and x=2. Thanks!

A:

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

A:

Q: Show that x21 + 2x8 + 1 does not have multiple zeros in anyextensionof Z3.

A:

Q: 9. Use the Factor Theorem to explain if x + 3 is a factor of x³ + 2x² – 3x + 5.

A: To use the factor theorem to explain if x+3 is a factor of x^3+2x^2-3x+5

Q: The number of zeros of the polynomial x² + 2x + 3 in Z, is: 2 1 4 None

A: 2

Q: If x^3=3x^2, then what is x using the Zero-Product rule?

A: Given that x3 = 3x2.

Q: (d) Show that x^2 − 4 is a factor of x^4 − 5x^3 + 2x^2 + 20x − 24.

A:

Q: Examine whether x+ 2 is a factor of x3+3x2+5x+6 and of 2x+4

A:

Q: Is x+3 a factor of -x^3+3x-18. Yes or no.

A:

Q: The number of zeros of the polynomial x^2 +4x+1 in Z6 is:

A: See the detailed solution below.

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

A:

Q: Express as a polynomial. (5x + 7y)(3x - 2y)

A: Given that, the polynomial   (5x + 7y)(3x - 2y)   We need to  simplify the given polynomial.

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

A:

Q: What is the coefficient of x12 in (x+2)14?

A: Given expression is,

Q: (x - 2) is a factor for x2 - 5x + 6. صواب (خطأ

A: For   x-a to be a factor of a quadretic equation then x=a is a solution of the quadretic equation.

Q: Suppose three of the zeroes of the quintic polynomial 5x + 21x4 +74x³ + 191x² + 264x + 45 are -1/2,…

A: Given  three zeros

Q: 7. Find all the zeros of the polynomial: y = 2x* – 5x³ + 10x – 12. - -

A:

Q: The polynomial f(x)=(x−2)^3=(x−2)(x−2)(x−2) has x=2 as a zero four times. true or false?

A:

Q: Find the factor of x^2-7x+10

A: We have to find the factor of  x2 - 7x + 10  = x2 - 5x - 2x + 10

Q: What is the sum of the polynomials 1 - 2x + 3x^2 and 8x^2 + 30x - 6

A: sum of the polynomials 1 - 2x + 3x^2 and 8x^2 + 30x - 6 = 1 - 2x + 3x^2 + 8x^2 + 30x - 6

Q: The product of x* + x3 + 2x? and 2x² + 4x + 6 in z, [x]/ is:

A:

Q: Use the Factor Theorem to show that the statement in the exercise is true.

A:

Q: Show that x-1 is a factor of P(x)=x² − 6x² +11x-6 and hence, determine all factors.

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Q: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

A:

Q: State the discriminant of 6x2-2x+K

A: Quadratic equaton is  6x2-2x+K=0

Q: if the sum of the zeroes of the polynomial f(x) = 2x³ – 3kx² + 4x - 5 is 6, then the value of k is

A:

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

A:

Q: 1. Show that x + 4 is a factor of x* – x3 + 3x² – 3x + 356. -

A:

Q: show that x2-4 is a factor of x4-5x3+2x2+20x-24

A: