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

Q: 8. Which of the following is NOT a factor of x4- 4x2 ?

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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: FIND THE DOMAIN OF 1. ffx)= X²+5x+6 X² 5x+6

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Q: x^2+5x+6/ x^2 +10x+21divided by x^2+2x/x^24x-21

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Q: 8) Is (x+3) a factor of x4 + 2x2 + 17x – 48 Drop coefficients onto top line

A: Given,  x4+2x2+17x-48

Q: Show that the equation x4 + 4x + c = 0 has at most two real roots

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Q: The general solution to 3x" + 2y = 0 can be obtained using?

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Q: If y= (5x+1) (2x-1-1n7), then y’ will be (5X+1) 2/X2 +1/7

A: Given that  If y= (5x+1) (2x-1-1n7), then y’ will be (5X+1) 2/X2 +1/7

Q: If x - 2 is one of the factor of x^3 - 8, what is the other factor?

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Q: If x+2a is a factor of x5-4a2x3+2x+2a+3  find a

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Q: (a) Factor (fx)=x^3-4x^2+x-4 into factors of the form (x-c), given that 4 is a zero. (b)…

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Q: 3. If one of the factors of (x2 + 12x + 20)is (x + 10). Find the other factor

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Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5[x]/ is: 5x^2+ 5x +1 O None X^2+2 4x+1

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Q: Determine the value of 7A+7M if 2x4 + 3x3 + + 8x2 + 9x + 3 A За + М + (1+x²)² х — 3 x(1+x²)² 1+x² ||

A: Given: 2x4+3x3+8x2+9x+3x1+x22=Ax-x-31+x2+3x+M1+x22

Q: 3. Divide x+4x-3x-2 by X-2) then divide if CX-2) isa factor of x² t4x-3y-2 why?

A: We have to divide (x3 + 4x2 - 3x - 2) by (x - 2)  Then ,

Q: What is the completely factored form of xy – xn

A: Given : xy3 - x3y

Q: If x+2a is a factor of x5-4a2x3+2x+2a+3  Find a

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Q: Why is x-3 a factor of m(x) x^3-x^2-5x-3

A: It is  polynomial equation.

Q: If x- 4 is a factor of x + bx – 24 , what is the value of b? |

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Q: show that the equation 3x+2cosx+5=0 has exaclty one real root.

A: f(x)=3x+ 2 cos x +5

Q: One of the factors of 4x2-9 is 1) (x+3) 2) (2x +3) 3) (4x-3) 4) (x-3)

A: we have to find the one of the factor of 4x^2 -9

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

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Q: Find the general solution of the fifth-order DEQ. 2x(5) – 7x(4) + 12x" + 8x" = 0

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Q: Show all work to factor x4 - 5x2 + 4 completely.

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Q: If x=9 is a solution to a polynomial equation, then (x-9) will be a factor a that polynomial

A: The given statement is true.

Q: If (x + 3) is a factor of x3 - 13x – 12, what are the other factors. A. (x- 6) and (x + 2) B. (x –…

A: Given data is : If x+3 is a factor of x3-13x-12 What are the other factors.

Q: Find the linear factors of 2x²-y-x + xy + 2y - 1.

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Q: Is 5 a root of x* 5x' + 8x– 40? Is (x + 1) a factor of x- 1?

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Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5[x]/ is: 5x^2+ 5x +1 4x+1 O x^2+2 None

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Q: Find the discriminant of C(x)=3X^2-4X+3

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

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Q: Find the specific solution. Hint: factor by grouping in pairs first. x" + 2x" - 9x'- 18x = 0,…

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Q: Given that (3x2+4x)/(2x+9) = 45 Find x

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

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Q: Show that the equation 6x4 – 7x +1 = 0 does not have more than two distinct real roots.

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Q: 1(d) Show that x − 4 is a factor of x − 5x + 2x + 20x − 24

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Q: Which of the following is not a factor of x8 – 1?

A: We can use fellowing formula to solve the problem: (a+b)(a-b)=a²-b²

Q: what is the factored form of ax^2+bx+c where the roots are x1 and x2?

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Q: Solve this strictly by Factor Theorem.  3x3 + 7x2 + 2x - 4

A: use the definition of factor theorem .

Q: Show that for r=1x1 XER³, > A( 7 ) = 0 we have when 1x1=1 #0

A: Laplacian operator

Q: 1. What is the coefficient of x²y5 in (2x – 3y)7?

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Q: If x – 2 is a factor of x3- 4x2 + 8x + k then the value of k is

A: Given: x-2 is a factor of x3-4x2+8x+k.

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

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Q: Which of the following is not a factor of 45x-5? (1) 9x2-1 (3) x-5 (2) 5 (4) 3x+1 O 2 3

A: We have to check

Q: If (x + 3) is a factor of x3 – 13x – 12, what are the other factors. А. (х — 6) and (х + 2) В. (х —…

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Q: Find the value of x for which (8x+4) , (6x-2) and (2x+7) are in AP

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

A: