4. Find the value of k for which x-3 is a factor of f(x) = 4x3 + 6x2 -9x + 2k. Hence, find the remainder when f(x) is divided by x + 2.

Q: Find the value of k such that x − 4 is a factor of x3 − kx2 + 2kx − 8.

A: Here we have to find the value of k,  It is given that,  x − 4 is a factor of f(x)= x3 − kx2 + 2kx −…

Q: 47. For what value of k will the polynomial function f(x)=x²+6x² +kx -4 have the same remainder when…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 6. Use the factor theorem to determine if r – 1 is a factor of f(r) = 2x* + 3x2 – 5x + 7.

A: Given- fx=2x4+3x2-5x+7 To determine- x-1 is a factor of function fx or not. Concept used- In factor…

Q: if sum of the squarew zeroes of the quadratic polynomials  f(x) =x2-8x+k is 40.Find K

A:

Q: 3. Given that f(x) = x³ + px? + qx – 3 is exactly divisible by (x – 1) and leaves a remainder of 3…

A:

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

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is

A: 1)  The statement is true  Now to see  ho the given polynomial is irreducible or not

Q: If a polynomial f(x) when divided by (x – a) gives a remainder r1, and when divided by ( – b) gives…

A:

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

A:

Q: 4. x-2x+1= 3

A:

Q: When p (x)=x+ kx2 +8 is divided by x +3, the remainder is the same as when q(x)%3D2%³+ kx -21 is…

A:

Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x)=x3-px2+qx-r,…

A: we know for cubic equation,  ax^3+bx^2+cx + d having roots α,β and γ  Sum of roots,α+β+γ=−b/a, Sum…

Q: Upon factoring L(x)=(x^4)−16 as far as possible, which one is true?   A. L(x) has three linear…

A: Question is solved.

Q: Find the value of k so that x-2 is a factor of P(x) = 2x3 – x2 + kx + 2

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is O 5 4 O 2 None of the choices о

A:

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: If the remainder on dividing the polynomial 2x* – kx +5x-3k+3 by (x + 2) is 4, then find the value…

A: Use the given information.

Q: - Given that ( x + 1) is factor of the polynomial P(x) = x³ – x² – x – m. The value of m is A 1 B в…

A: Using polynomial and its factor properties

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

A:

Q: I. Find the value of k so that the remainder in each division problem is (a) 23. (x³ + kx² - 4x + 2)…

A:

Q: For f(x)=2x4 +2x3-1 and g(x)=2x3 +2x+3 in Z4[x], the degree of fg is 7. True or false

A:

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: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: To show that x = -3 is a solution of the given equation, divide f(x) = x -37x - 84 by (x + 3) using…

A:

Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

Q: (b) Find the nested form Q(x) of the polynomial /(x) = x³ + 2x2-5x + 3 and hence evaluate Q(2.6)…

A:

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

A:

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A)…

A:

Q: Determine the values of m and n for f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero,…

A: Given that f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero, and when divided by (x-2)…

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: When f(x) is divided by (x - 2), the answer is 2x3 - 4x² + 3x + 1 with a remainder of k + 7, and if…

A:

Q: The remainder upon the division of x75+ 6 by x- 3 in z, is: 1 5 6.

A: I am solving it in step 2

Q: 47. a) If (x – 2) is a factor of 2x – 3x + k, find k. - b) When ax – 4x² + 5x – 3 is divided by (x +…

A:

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. b. P(x) =2x³ –…

A: Solution is given below:

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: If sun of the Squares zeroes of the quadratic Polynomials f(x)=x2-8x+k is 40.Find K.

A: Given- fx=x2-8x+k and sum of squares of zeros is equal to 40. To find-  The value of k. Concept…

Q: The remainder upon the division of x75 + 6 by x-3 in z, is: 1.

A: concept : when f(x) is divided by x-a then  Remainder is f(a).

Q: When px3 3 32x 2 − 10x + r is divided by (x x 2), the remainder is exactly the same as when it is…

A:

Q: 22. Find the quotient and the remainder for each of the followir x3-4x2+2x+5 1) x-2 4x3-2x2-3 2)…

A:

Q: Find the value of c so that x+2 is a factor of the polynomial p(x). p(x)=4x3+cx2+x+2

A: Here we find the value of c so that x+2 is a factor of the polynomial p(x)where p(x)=4x3+cx2+x+2

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: 1. What must be multiplied to (x2 + 2x + 1) to get (x + x + x2 + 3x + 2)? С. -ха- х - 2 D. x2 - x +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: - Which of the following is NOT factor of x4- 4x ? A C T+ 2 T 2 E (z-2) 2)

A:

Q: 2. Determine whether x−4 is a factor of f(x)=3x4−48x2+8x+32.

A: Use factor theorem. It states that a polynomial f(x) has a factor (x – a) if and only if f(a) = 0.

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

A:

Q: E Given that x = 3 is a solution of f(x), factor f(x) =x'-10x² +33x-36 completely using long…

A:

Q: It is known that (x + 2) is a factor of the polynomial P(x) and that P(x)= (xtxt )X Q(x)+ (2xt3).…

A: We will find out the required value.

Q: For the polynomial s2+2s+p=0, if the value of p is equal to 1, then the roots will be

A: Putting p=1, to find the roots of s.