4. Find the product of (x +8)(x- 3) (X)

Q: if y3-3ax2+x3=0,then prove that y2+ 2a2x2y-5=0

A: Let dy/dx= y1 and d2/dx2=y2 And We will use the product rule of differentiation.

Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inverse in Z4[x].

A:

Q: Find the coefficient of x20 in (1 + x + x²+ ... +x)( x³ + x* +.. )* .

A: Use the expansion, 1+x+x2+x3+...n=1-x-1n=1-x-n=1+nx+nn+12!x2+nn+1n+23!x3+...     ...i

Q: 2. Find algebraically the zeros for 3 p(x) = x +x – 4x - 4

A:

Q: Find the quotient x + 4 x + 4 x² – 9 x2 + x – 12 | x - 4 x + -3, x + 3 x + 3 х — 4 x +3 x – 3 x +4 x…

A:

Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inversein Z4[x].

A:

Q: Find x, and x2- 4 29 -4 -3 - 23 X2

A:

Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

A:

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

A: Given,  x4+2x2+17x-48

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

A:

Q: аги аги + дх2 т дуг = 0 =

A: We have to solve given problem:

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

A:

Q: 1. Use the Product Rule to differentiate y = x³(2x + 1)*.

A:

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y -5=0

A: Our objective is to prove y2 + 2a2 x2 y -5=0 if  y3 -3ax2 +x3 =0. But note that when a=0 and x, y=3,…

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: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: Find the coefficient of x5 in (1 – 2x)-7 using generating function.

A: Given to find the coefficient of x5 in 1-2x-7 The generating function will be Gx=1-2x-7…

Q: 3. Find the coefficient of xy' in (2x + 3y)°.

A: The provided information is we find the coefficient of  x2y7    in (2x+3y)9 Then, (79)*(2x)2*(3y)7…

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

A:

Q: 5x + 3, xS -1 y = 32 - 3, x > -1 х> -1

A:

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: 22. Compute and completely simplify the difference quotient for g(x) = –3x² – 2x +1.

A:

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5=0

A:

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

A: Explanation of the answer is as follows

Q: The remainder upon the division of x98 +4 by x - 2 in z, is:

A: We have to use remainder theorem.

Q: Let ƒ(x) = (2x + 3)(3x2). Use the product rule to find ƒ′(x).

A: Consider the formula for product rule. Product rule: fg'=f'⋅g+f⋅g'

Q: Show that the polynomial x5 - 6x + 3 over Q is not solvable byradicals.

A:

Q: Find x, and x2.· - 5 - 4 X1 - 55 4 - 5 X2 3 X1 = %3D II

A: To find x1, x2

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5 =0

A: Given : y^3 - 3ax^2 + x^3 = 0

Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

Q: Prove that if 8x-5=-2x-15 then -x=1

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: Prove that x -2x+2>0 for value of x.

A:

Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - cis a factor of…

A:

Q: Find the coefficient of x16 in (x + x²+x³ +x4 + x³)(x² +x³ +xª + · . .)5.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A:

Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

A:

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

Q: 15. Determine the zeros for and the end behavior of Ax) =x(x – 4)(x + 2)*.

A: Recall: A polynomial function degree n ,f(x)=anxn+an-1xn-1+...+a0 has atmost n real zeros.⇒If a…

Q: Determine the value of k such that (x^3-2kx+1)/(x-k ) has a remainder of 0.

A: f(x)=(x^3-2kx+1)

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

A:

Q: 9. Use the graph of )-+3x-4 to identify the values of x for which - and to factor ). a. x- 2,x - c.…

A: Topic - functions Point at which graph cuts the x axis is zero of the polynomial or f(x)=0 at that…

Q: Which of the following is the product of (x + 1)(x + 1

A: (x+1)(x+1) than product of this  x^2+x+x+1 that is

Q: Is f(x) = x^2 + 1 a standard form or a vertex form or both? (I'm confused because it has 2 terms,…

A: Yes, fx=x2+1 is a standard form and a vertex form both. The standard form is given by fx=ax2+bx+c…

Q: 15. Show that (x+ 5) is a factor of f(x) =x3 -x² -21x + 45 then factor f (x) completely.

A:

Q: 3.) Find the der ivative of cosCx) (5x+) 니 (5x+1)

A: Given :           cosx1x25x+14

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

A:

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