. The polynomial 3x3 + mx2 - nx – 10 has a factor of x - 1. When divided by  x + 2, the remainder is 36. What are the values of m and n?

Q: Which of the following is the correct complete factorization of x4 - 1?…

A: To find the complete factorization of x4-1. Solution: We know that, a2-b2=a+ba-b Factorizing the…

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: Suppose we factor the polynomial f(x)=(x² – 6x + 9)² · (x² – 4x + 5)³ as much as possible. Choose…

A:

Q: For the polynomial s²+25+p=0, if the value of p is less than 1, then the roots will be

A: s2+2s+p=0, p<1

Q: 12. When the polynomial 2a3 – 11x - 5 is divided by æ – 5, the quotient is of the form ax? +bx +c.…

A:

Q: The polynomial 3x4 - 2x3 + 13x2 - 5 is of degree . The leading coefficient is _______ .

A: The degree of the polynomial is the highest power appearing for the variable presented in the…

Q: ,37 19 Polynomial P(x)=6x200+7x-2x19+10 is divided by (x+1). Find the remainder. |

A: P(x)=6x200+7x37-2x19+10 Divisor =x-1

Q: 1. When the polynomial f(x)= px' +5x +qx-2 where p and q are constants is divided by 2x +3x-2 the…

A:

Q: Given that (2x - 1) and (r + 3)are factors of the polynomial,2a + 13x2 + 17x 12, what is the third…

A:

Q: Find m so that x + 5 is a factor of - 3x - 10x + 20x - 22x + m.

A: Given: x+5 is a factor of   -3x4-10x3+20x2-22x+m. To find: The value of m.

Q: If the sum of the zeroes of the polynomial p(x) = (k2 -14) x2 - 2x -12 is 1 . Then find the value of…

A:

Q: 12) Find a polynomial for the sum of the shaded areas of the figure. A) 4x2 - 8x + 4 B) 4x2 - 8x C)…

A:

Q: 15. If the zeros of the polynomial x²+px +q are double in value to the zeros of 2x²- 5x -3, find p…

A:

Q: Find the roots of the following polynomial:  6x3- 7x2 - 28x + 20

A:

Q: If x = -1 is a root of the polynomial 0 = x3 + 4x? + 2x – 1, what are the remaining roots? -3+V13 x…

A:

Q: If the remainder after dividing the polynomial (5x³ - 3.x* + k) by (x+ 1) is 4, which of the…

A:

Q: A. Determine the factors of the given polynomial. 1. х3 + 2х2 -5х-6 2. х3 + x2- х-1 3. x3- x2- 10x-8

A:

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: Consider the polynomial P (x)=kx' + 3x + 4x + 2. 3. 2. %3D Find the value of k such that the…

A: The solution of the problem is given in the next step.

Q: 10. Determine whether the first polynomial in P3(R) can be expressed as a linear combination of the…

A:

Q: Is (x + 2) a factor of the polynomial: x^4 + x^3 - 2x^2 + 3x + 7, and what was the remainder? * no,…

A: Solution

Q: 2. For what values of b will the polynomial ƒ (x) =-2x + bx² – 5x +2 have the same remainder when…

A:

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: When dividing the polynomial p(t)=4t3−17t2+14t−3p(t)=4t3−17t2+14t−3 by t−3,t−3, the remainder can be…

A: Consider the following polynomial: Pt=4t3-17t2+14t-3 Divisor is t-3. Substitute t=3 in the above…

Q: Find m so that x+5 is a factor of 5x3+29x2+mx+20

A: Let f(x)=5x^3 + 29x^2 +mx+20 , if (x+5) is a factor of f(x) then by factor theorem f(-5)=0

Q: By what polynomial of lowest degree must (x2 – 64)(x² + 5x – 24) be multiplied to make it a perfect…

A: Givem polynomial is (x2-64)(x2+5x-24)To find lowest degree multiplier to make it perfect square.

Q: A polynomial P ( x ) with real coefficients has 5 + 9 i as a zero. What other number must be a zero…

A: Comples zeroes of polynomial always come with conjugate pair. For example if a + b i is zero then a-…

Q: Which of the following is the correct complete factorization of x4 - 1? (x-1)^{2}(x+1)^{2}

A: Given, x4-1

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. Is (x – 3) a factor of the polynomial p(x) = x' – 11x + 6? Why or why not? 2. What is the…

A:

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

A:

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: 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: 2) Write the factored form of the equation for the given polynomial. y (-1, 4) 4 -5 -2 -4

A:

Q: Suppose we factor the polynomial f(x)=(x² + 2x + 3)² · (x² – 6x + 10)³ as much as possible. Choose…

A:

Q: Q7. When the polynomial g(x) = x* + kx³ – k²x² + 5x – 12k (where k is a real number) is divided by…

A: remainder theorem

Q: If a polynomial P(x) has (x-7) as a factor, then what number must be a zero of P(x)?

A:

Q: If we divide the polynomial P by the factor x - c and we obtain the equation P(x) = (x – c)Q(x) +…

A: we know that if we divide the polynomial px by the factor x-c and we obtain the equation…

Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: If t = -3 then find the value of the given polynomial  3t2+5t+6

A:

Q: Find the LCM of the given polynomial. x2 + 4x + 4,  x3 + 2x2 , (x + 2) 3

A:

Q: The polynomial P is graphed. 5- 4+ 3- 24 -3 -2 -1 1 -2+ -3+ -4 What is the remainder when P(z) is…

A:

Q: . If the remainder dividing the polynomial P(x) = 2x + by x-4 is 114, find the quotient and the…

A:

Q: In the polynomial P(x)=(x-1)4(x+3)(2x+3)3(x-6)2 the multiplicity of the zero 6 is?

A: Given:

Q: Suppose we factor the polynomial f(x)=(x² + 2x + 3)² · (x² – 6x + 10)³ as much as possible. Choose…

A: To check whether a given quadratic equation can be factorized, we first need to check the…

Q: Consider the polynomial p(x)=4x3+16x2−25x−100. What is the sum of the zeros of p(x)?

A: The given polynomial is,

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.

Q: Given the polynomial P(z) = -9z - 9z² – 5z – 20 and divisor d(z) = -3z + 2, find the quotient Q(z)…

A: