Let f(x) = 3x4 +4x3 −6x2 +21x−7. Let g(x) = x2 −x+2. Since the degree of g is 2, the basic fact about long division of polynomials ensures that it is possible to find polynomials q(x) and r(x) such that f(x) = g(x)q(x) + r(x), with the degree of r(x) less than 2. Find such q(x) and r(x).

Q: The remainder theorem indicates that if a polynomial flx) is divided by x - c, then the remainder is

A: We have to fill in the blanks: The remainder theorem indicates that if a polynomial fx is divided by…

Q: Find the third degree polynomial function that has an output of 16 when x=2, and has zeros 1 and -2i

A: We have to find  a third degree polynomial function that has an output of 16 when x=2, and has zeros…

Q: Find a polynomial f (x) of degree 3 that has the indicated zeros and satisfies the given condition.

A: Since the zeros of the polynomial are -1, 2, 3, therefore the factors of fx are, x+1,  x-2  &…

Q: The general polynomial of degree n has the form P(x) = an xn + an-1 xn-1 + ........ + a2 x2 + a1 x +…

A: Consider the general form polynomial of degree n which is shown below,

Q: If f(x) is a polynomial with real coefficients and zeros of 5 (multiplicity 2), –1 (multiplicity 1),…

A: The number of zeroes are 4. But one zero has a multiplicity of 2 that is the zero is repeated.

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

A:

Q: Find a polynomial of degree 3 that has zeros x = 5 and x = 3i .

A:

Q: Use the remainder theorem to find f (c).

A: Given function is fx=x4-6x2+4x-8.

Q: Find the upper and lower bounds of the zeroes of each polynomial function. 1. f(x) = x^3 + 4x^2 + 8x…

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Q: 4. Use the Intermediate Value Theorem to show that the polynomial function f(x) = x" +8x' – x´ +2…

A:

Q: If a third degree polynomial has a lone x-intercept at x=a what does this imply about the linear and…

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Q: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23 x + 2 , make at least three…

A:

Q: What is the leading coefficient of athird degree polynomial function that has an output of 1,272…

A:

Q: If 3 + 4i is a zero of a polynomial function of degree 5 withreal coefficients, then so is_________

A: Given: 3+4i is zero of a polynomial fuction

Q: Find all rational zeros of the polynomial function.  P(x)=x^4+4x^3+6x^2+4x+1

A:

Q: The Remainder Theorem states that if the polynomial f(x) is divided by x - c, then the remainder is…

A: Given Data :  The polynomial fxis divided by x-c        To Find : Remainder The polynomial  fx is…

Q: Find a polynomial of degree 3 that has zeros of 3,-4, and 5, and where the coefficient of x2 is 8. O…

A: Given that the zeros are 3, -4 and 5. So the factors of the polynomial is (x-3), (x+4) and (x-5)…

Q: 6. Use the Remainder Theorem to evaluate f(x) = 10x* - x3 + 13x2 – 9x + 17 at x =-.

A: Since the student has mentioned to solve question number (6), so we are solving only question number…

Q: 2. Find the Zeros of a Polynomial Function: x3 + 2x2 + 25x + 50 Process: x3 + 2x² + 25x + 50 →…

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Q: 10 h(x) = x³ + 5x² - 4x- 20 %D

A:

Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

A: We need to find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of…

Q: 2. D- f(x) = -is not a polynomial function because %3D 2x

A: A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving…

Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. a. P(x) =x'-4x²…

A:

Q: Let f (x) = x4 –- 6x3 + 6x2 4x + 1. The coefficient of x7 in the 7th Taylor polynomial p7 is

A: Solve the following

Q: Consider the polynomial h with h'(x) = (x – 5)³(x– 3)². %3D Use the definition of an inflection…

A: we know that a point of inflection is found where the graph of a function changes concavity. To find…

Q: Determine the third Taylor polynomial of the function at x = 0. f(x) = e -4x 1- 16x + 128x2 1024 3…

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Q: Find a degree 4 polynomial having zeros −7, −3, 1 and 6 and the coefficient of x4 equal 1

A:

Q: Evalute the polynomial at x= -2    5x^4-3x^2 - x + 1 + 5x^3

A:

Q: Find a polynomial function of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of x…

A: We need to find the a polynomial function of degree 3 that has zeros 1, -2, and 3 and in which the…

Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 5; zeros:…

A: We know that whenever a complex number is a zero of a polynomial with real coefficients, its complex…

Q: The number of zeros of the polynomial x^2 +4x+1 in Z6 is:

A: See the detailed solution below.

Q: Write a polynomial function f of least degree that has rational coefficients, a leading coefficient…

A: Given zeros are 2and (3+i)which means all the zeros of polynomialare+2,-2,  3+i,…

Q: 4. How should the polynomial function f(x) = -x + 2x³ + 3x5 – 6 be written in standard form? A. f(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: f(x) = x + 5x3 - 7x2-29x + 30 %3D

A:

Q: If f is a polynomial function and f(a) and f(b) have opposite signs, then there must be at least one…

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Q: Find the polynomial f(x) of lowest degree with only real coefficients and having the zeros 3+ V2, 3-…

A:

Q: 4. Now consider the polynomial function g(x) = (x - 5)(x + 3)(x - 1). %3D Identify the zeros of this…

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Q: Find a 5th degree polynomial with zeros x = 3 + 2i, 1 − squareroot2, and −1 with a co-efficient of 4…

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Q: The polynomial f(x)=x3+x2+1 has a linear factor in Z3[x]. true or false?

A: Solve the following

Q: The Remainder Theorem states that if the polynomial f(x) is divided by x - c, then the remainder…

A:

Q: Use the factor theorem to find the polynomial of degree 3 having zeroes x = -4, x = 1 - i, and X = 1…

A: A zero of a function is a value in its domain for which the function takes the value 0. A polynomial…

Q: Find the critical points, A and B, of the following polynomial (with A<B) f(x) = 6x3 - 45x2 - 432x…

A: A = -3.04 B = 8.04

Q: Find a polynomial of degree 3 with real coefficients and zeros of −​3,−​1, and​ 4, for which…

A: Given data:     The first zero of the polynomial is: x1=-3. The second zero of the polynomial is:…

Q: The value of f(3) for the polynomial f(x)=x3+x2-5x+3 is 24. What does this mean in terms of…

A: Given:  f(x) = x3+x2-5x+3 Now we have f(3) = 24

Q: Use synthetic division to show that c is a zero of f (x) .

A: Given polynomial function is: fx=4x3-6x2+8x-3 ; at c=12 We have to prove that c=12 is a zero of…

Q: Q1. How many bends are there in the roller coaster? Q2. In the given domain, how many times does…

A:

Q: Use synthetic division to show that c is a zero of f (x) .

A: Given: fx=4x3-9x2-8x-3;     c=3 Write the problem in a division-like format. To do this: Take the…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: