Give the vale of the remainder when p(x)=x3-4x+12 is divided by x+3.

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

A: Let f(x) and g(x) be two functions  then g(x) will be the factor of f(x) if remainder(f(x) / g(x))…

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

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Q: If  x3 + 7x - a has a remainder of 1 when divided by x+1 then a has a value of __?

A: Please refer the attached image for complete solution.

Q: 2x4 + 5x3 – 2x – 8 is divided by x + 3

A: In the given problem, Dividend, D=2x4+5x3-2x-8Divisor, d=x+3 Equate the divisor to zero, x+3=0⇒x=-3…

Q: How can you determine whether a linear binomial is a factor of a polynomial without using the…

A: to find : How can you determine whether a linear binomial is a factor of a polynomial without using…

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

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

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Q: Is the given binomial a factor of the given polynomial? If so, write the polynomial as a product of…

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Q: Find the remainder when the first polynomial is divided by the second polynomial.   x3 – 5x2 + 17x…

A: (1) Remainder theorem states that if a polynomial px is divided by x-a then remainder is pa. Given…

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

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Q: 2. Use long division to divide P(x) 3x'+ 7x - 2x- 11 by the binomial (x-2). Express your answer in…

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Q: What is the x-intercept of the fraction 9-x over x-5

A: To find the x- intercept put y=0

Q: By factorising x3+1, show that (for suitable values of x) 1/(x2-x+1) = ∑∞n=0 (-1)n x3n+ ∑∞n=0 (-1)n…

A: The given question is solved below.

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

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Q: We begin the process of factoring a polynomial by first factoring out the assuming that there is one…

A: Consider the given statement. Let's explain it by an example. Example. 3x2+6x Now, find the factor…

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

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Q: The remainder upon the division of x8 + 4 by x – 4 in Z, is= None

A: Given: The given polynomial is x98+4 by x-4

Q: 2. If the result of a polynomial division is 2x³ – 4x² – 5x + - ,make at least three x + 2…

A: Given the result of a polynomial division f(x)=2x3-4x2-5x+23x+2. Remainder theorem: The remainder of…

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

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Q: Find the remainder when x^2021 is divided by x-1 in Z_7 [x]

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Q: If a polynomial f(x) has a remainder of -9 when divided by a 3, what is f(3)?

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

A: We have to use remainder theorem.

Q: The remainder upon the division of x98 +4 by x - 2 in z, is: 6. None

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Q: 1. Is (x – 3) a factor of the polynomial p(x) = x' – 11x + 6? Why or why not? 2. What is the…

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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…

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

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Q: Find the sum of the polynomials: 8x3 - 2x2 + 6x - 2 and 3x4 - 2x3 + x2 + x

A: To find the sum of polynomials: 8x3-2x2+6x-2 and 3x4-2x3+x2+x Solution: (8x3-2x2+6x-2 )+…

Q: find the quotient and remainder 3x^3-12x^2-9x+2 over x+3

A: Given query is to find quotient and remaineder using synthetic division.

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: What is the result when 16x + 4x° - 14x2 - 23x - 3 is divided by 4x2 1? If there is a remainder,…

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

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Q: If a polynomial p(x) is divided with a polynomial (x + 3) using long division and the quotient is…

A: Let the remainder is Zero Given pxx+3=2x2-x+1 px=x+32x2-x+1=2x3-x2+x+6x2-3x+3        =2x3+5x2-2x+3

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

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

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Q: Use the Remainder Theorem to find the remainder when divided by the corresponding binomial. 1. x3 +…

A: As per our guidelines we are supposed to solve only one question

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: Find the conditions that the zeroes of the polynomials Ax) =x – px+ qx – r may be in arthametic…

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Q: 9. What is the possible equation of the following polynomial in factored form?

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Q: 4. Use what you have learned about the Remainder Theorem to show that X +1 is a factor of 19x42 +…

A: We will use the remainder theorem that states that the remainder is zero when we decide the function…

Q: 1. Use the Product Rule to find for y=(4x'-3x)(2x* +5).

A: Given          y=(4x3-3x5)(2x-6+5)          find dydxx=1Product rule :- Product rule states…

Q: 2. If the result of a polynomial division is 2x3 – 4x? – 5x + 23 ,make at least three x+ 2…

A: The given result of a polynomial division is 2x3-4x2-5x+23x+2. Observe the following. Quotient,…

Q: Beth claims that if a graph of a polynomial has zeros at (-5,0) and (3, 0), then the factored form…

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Q: 5. If the remainder dividing the polynomial P(x) = 2x³ + kx? + 7x +6 by x- 4 is 114, find the…

A: Quotient Remainder theorem  The answer after we divide one number by another. dividend ÷ divisor =…

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: Use the Remainder Theorem to find the remainder when each polynomial is divided by the correspond…

A: Remainder theorem: We know, the remainder theorem states that if a polynomial f(x) is divided by…

Q: 10.Determine if the given binomial is a factor of the polynomial, yes or no P(x) = x 3 +8x² +11x -…

A: Consider a polynomial p(x). If, At x=a, value of p(x) =0, then (x-a) is a factor of polynomial p(x).

Q: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

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Q: 15) Find the remainder of the polynomial 5x4 – 3x3 + 9x – 1 when divided by x + 3

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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.