Which of the following has a remainder of 16 when divided by (x + 2)?  a 3x3 − 7x2 − x + 1 b 3x3 + 7x2 − 5x − 1 c x3 + 4x2 − 3x + 2 d x3 + 2x2 − 3x + 6

Q: 4. Find the remainder when P(x) = - 2x³ + 5x²-3x - 7 is divided by x - 3. 5. Find the remainder when…

A:

Q: What is the result when 2x +14x² + 19x is divided by x + 2? If there is a r(x) remainder, express…

A: Given information: 2x3+14x2+19xx+2

Q: 2. Determine the quotient and remainder. (3x* – 5x' +x² -x-1) + (x² – 2x)

A: Given: Using long division,

Q: 3. Find the quotient and the remainder for (x4 + 8x² − 6x − 3 ) ÷ (x+2).

A: 3. A polynomial p(x) can be written as p(x)=q(x)d(x)+r(x)⇒p(x)d(x)=q(x)+r(x)d(x) Where, d(x) is…

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: The polynomial 2x^3 + ax^2 - 10x + b has a factor of ( x-1 ) and has a remainder of 15 when divided…

A:

Q: What is the value of k so that (x3 +4x 2+x + k)÷(x+2) give a remainder of 3?

A: To find the value of k so that x3+4x2+x+k÷(x+2) gives a remainder 3.

Q: .When a polynomial x4+x3-10x2-1 is divided by another polynomial, the quotient is x3-3x2+2x-8 and…

A: use the relation between dividend and divisor for finding the polynomial.

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

A:

Q: 6. Which of the following could be used to perform the synthetic division for ( 3 + x3 + 6x4 - 7x)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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: 6. What is the remainder when P(x) = 15x100-10x0 +5x'- is divided by x+1 %3D a) -1 b) 1 c) 0 d) 9 e)…

A:

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: I. Find the value of k so that the remainder in each division problem is (a) 21. (2x³ + 3x² + kx-2)…

A:

Q: What is the result when 2x4 + 2x - 8x2 3x + 14 is divided by x + 2? If there is a remainder, express…

A: We will divide 2x4+2x3-8x2-3x+14 is divided by x+2. So, we need to evaluate 2x4+2x3-8x2-3x+14x+2.…

Q: 11 Based on the Remainder Theorem, what is the remainder when 2x - 3x- 4xr+7 is divided by X-1? A. 0…

A:

Q: When a polynomial x4+x3-10x2-1 is divided by another polynomial, the quotient is x3-3x2+2x-8 and the…

A: Polynomial (dividend) x4+x3-10x2-1 Remainder is 31 Polynomial (quotient) is x3 -3x2 +2x -8 To find…

Q: What is the correct factorization of 2t2 -t-3? O (2t + 3)(t – 1) O (2t – 3)(t + 1) O (2t – 1)(t+3).…

A: From the given polynomial; 2t2-t-3

Q: If p(x) = 2x- 3x+ 5, what is the remainder of p(x)+ (x- 5)? 1)-230 2) 0 3) 40 4) 240 %3D

A: From the Remainder Theorem

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

A:

Q: Find the remainder if 3x3 – 4x2y + 5xy2 + 6y3 is divided by x2 – 2xy + 3y2.   A. 2   B. 1   C.…

A: Topic = Algebra Remainder = 0

Q: 8. The polynomial 3x³ + mx² - nx – 10 has a factor of x - 1. When divided by x + 2, the remainder is…

A: P(x) = 3x3 + mx2 - nx - 10                (i) It is given that (x - 1) is a factor of the above…

Q: #9. USE SYNTHETIC DIVISION TO FIND THE QUOTIENT AND REMAINDER а. x – 8x – 5; x + 3 - 3x + 1; - 8 -…

A:

Q: Which statement about 6x + 7x – 10 is true? O One of the factors is (x + 2). O One of the factors is…

A: To factorise ax2+bx+cwe have to break 'b' in such a waythat sum is 'b' & the product is ac.

Q: 7. f6x4 – 2x3 – 21x² + 7x + 8 is divided by 3x – 1 to give a quotient of 2x3 – 7x and a remainder of…

A:

Q: 1 What is the remainder when x²- 38x + 361 is divided by x- 19? А. х-19 В. х+ 19 С. 0 D. 19

A: We need to find the remainder when we divide  x2-38x+361    by     x-19

Q: 1. [K2] Without dividing, determine the remainder when P(x) = 10x3 – 9x2 – 8x + 11 is divided by 5x…

A: We use remainder theorem for calculating the remainder.

Q: What is the remainder when (5x^100 + 5) is divided by (x – 1)? * - 10 5 10 - 5 Factor:…

A:

Q: Find the value of k so that the remainder is 4 when x – kx² + 2x – 8 | is divided by x + 3.

A: According to reminder theorem, if a polynomial p(x) is divided by the binomial (x—a) then the…

Q: (a) . Let x E Z. List all possible remainders of 7x² when divided by 3. Justify your answer. (b) [ ]…

A:

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

A:

Q: 1. What is the remainder when a. − 3x^3+ 2x^2 − 5x + 8 is divided by x − 4 b. 4x^4 − x^3+ 12x^2 + 24…

A:

Q: When p (x)=x3 +kx2 +8 is divided by x +3, the remainder is the same as when q (x)=2x3+ kx -21 is…

A: Remainder Theorem  When a polynomial f(x) divides by x-a then its remainder is f(a)    So by…

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

A:

Q: Which of the following is the correct first row of the synthetic division when 3x-2x³-4 is divided…

A: We are going to solve

Q: The polynomial 6x^3 + mx^2 + nx - 5 has a factor of x + 1. When divided by x - 1, the remainder is…

A:

Q: Which of the following is the correct factorization of 27x3 - 1? O (3x - 1)(3x² + x + 1) O (3x +…

A:

Q: What is the result when 2x- 13x2 - 5x - 14 is divided by x- 7? If r(x) there is a remainder, express…

A:

Q: If 2x³ 2x² - 9x² + 4x 7 is divided by x - 3 to give a quotient of 3x - 5 and a remainder of -22,…

A:

Q: if p(x)=x4+2x3-7x2-8x+12. what is the remainder of p(x) divide (x-4

A: Given that: p(x)=x4+2x3-7x2-8x+12 divided by (x-4)

Q: what is the remainder when g(x)=x^{3}-3x^{2}+4x-12 is divided by (x-1)/

A:

Q: The ac product of 6x^2 + 13x + 6 is ____x^2.    The middle term can be rewritten as ___ x + ____ x…

A: Here I am attaching image so that you understand each and every step.

Q: Which polynomial gives a quotient of (3x^2 + 2x + 4) and a remainder of 19 when divided by (2x – 3)?…

A: We have to find polynomial on the basis of given information.

Q: _3. Which polynomial gives a quotient of (3x² + 2x + 4) and a remainder of 19 when divided by 2x -…

A: Division algorithm

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

A: Remainder Theorem :      If f(x) is divided by x-a then remainder is f(a).

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.