The sum of coefficients of the polynomial f(x) is equal to 2 and the sum of coefficients in even places is equal to the sum of coefficieñts in odd places. Find the remainder of dividing f(x) by g(x) = x² – 1.

Q: Find the zeros of the polynomial f(x) = 3 its two zeros are equal in magnitude but opposite in sign…

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Q: For the polynomial function ​f(x)=5x4−4x3+44x2−36x−9​,   ​a) Find the rational zeros of​ f(x), and…

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Q: Find the rational zeros of the function f(x) = 3x3 − 19x2 + 33x − 9.

A: f(x)=3x3-19x2+33x-9

Q: Find the roots of the quadratic polynomials: f (x) = x2 − 2x − 1

A: We know that, for an standard equation fx=ax2+bx+c, roots are calculated by using quadratic formula…

Q: Find all zeros of the polynomial function f(x) = -(x - 2)2(x + 1)2.Then graph the function.

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Q: What will be the difference of the two polynomial function p(x) and q(x) at x= 9 where p(x)=6x2…

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Q: Given the function f(x) = 2 + 6x, then what is f(x – 2) simplified as a polynomial?

A: The given function is f(x)=2+6x

Q: f(x) = x4 – 1Ox2 + 9

A: Solution of polynomial function is given by x=-1,1,-3,3  Clearly each zero has multiplicity one…

Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x                    ...(1)…

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

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Q: Find a polynomial f(x) of degree 4 that has the following zeros. 1,-7,0,2 Leave your answer in…

A: The objective is to find the polynomial of degree 4. If a is the zero of any polynomial f(x), then…

Q: Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when…

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Q: Find an equation of polynomial function with real coefficients having zeros at 3,-1,4+2i

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Q: Find the equation of a 4th degree polynomial that has zeros at x=-7x=−7,  x=2x=2,  x=3x=3  and…

A: Given that, Polynomial has zeros at x = -7, x = 2, x = 3, x = 4 and we have to find the polynomial…

Q: If f(x) is a 4th degree polynomial, and has 3 real numbers as roots, the other root is?

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Q: Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve…

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Q: 6. Suppose the polynomial function has the given root. Find the other roots (a) f(x) = 2r3 – 4x2 –…

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Q: Find an equation of a polynomial function with real coefficients having zeros 4 and 2+3i

A: We have to find the equation

Q: If one of the zeroes of the quadratic polynomial f(x) = 4x2 - 8kx - 9 is equal in magnitude but…

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Q: Find the roots of the functionf(x) = (2x−1)·(x2+ 2x−3) withx∈R

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Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions, n =…

A: n=4, zeroes are -4, 13, 2+3i and f1=100. Since 2+3i is the zero of the polynomial function,…

Q: Find the zeros of the polynomial f (x)=x3-5x2-16x+80  ,if it's two zeros are equals tin magnitude…

A: The no. of roots of a polynomial is depend on the degree of polynomial Since, degree of this…

Q: One factor of f(x) = x^3 –8x^2 – 15x+54 is x - 2. What are the zeros of f(x)?

A: Solution of the equation

Q: Find the zero/s of the given polynomial function f(x) = x* + x³ – 29x2 – 9x + 180

A: The factors of a quadratic form of equation ax2+bx+c can be calculated using integer factorization .…

Q: Given the function b(x)=evcosx+x, what is the approximated value of b(0.20)? Solve by utilizing the…

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Q: Find a polynomial function of degree 3 with real coefficients that has the given zeros. -1, 2,-9 The…

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Q: - The of a polynomial f(x) are the solutions (or roots) of the equation f(x) = 0.

A: Suppose, f(x)= x2-3x+2 is a polynomial. So, to find the solutions or roots or zeroes of this…

Q: Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and…

A: NOTE: Refresh your page if you can't see any equations. . the first zero is x=2 so the first factor…

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

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Q: The term containing the highest power of x in the polynomial f (x) is 6x. One of the roots of the…

A: Given the quadratic polynomial x2-2x+3 is a factor of f(x) and the highest power of f(x) = 3 Let…

Q: (a) Find the rational zeros and then the other zeros of the polynomial function f(x) = 3x +7x +147x…

A: givenf(x)=3x3+7x2+147x+343a.(3x3+7x2)+(147x+343)=0x2(3x+7)+72(3x+7)=0

Q: Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization…

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Q: Given the function f(x) = ;x – x², then what is f(x - 2) as a simplified | | polynomial?

A: Given polynomial f(x)=52x-x2.

Q: For the function f(x) = ex , find a first-degree polynomial function               P1(x) = a0 + a1x…

A: Given  fx=ex To find a first degree polynomial P1x=a0+a1x whose value and slope agree with the value…

Q: Find a third-degree polynomial p(x) that is tangent to the line y = 14x − 13 at the point (1, 1),…

A: Let px=ax3+bx2+cx+d   →1 be the required third-degree polynomial. Differentiating with respect to x,…

Q: Find an equation for a polynomial f(x) that satisfies the following: Degree 3 Zero at x=3 Zero at…

A: We have to find degree 3 polynomial fx having zero at x=3, x=2 and x=-1, and y intercept is 0,4.

Q: Find a polynomial f (x) of degree 3 that has the following zeros. 0, -2, 1 Leave your answer in…

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Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=3x=3 and a root of…

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Q: State the degree of the polynomial function.  (If an answer does not exist, enter DNE). f(x) = x2-1…

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Q: Find a degree 3 polynomial having zeros -1, 2 and 5 and the coefficient of x^3 equal 1. The…

A: Here we find the polynomial whose zeros are given.

Q: Find the formula for a third degree polynomial with a zero at x = -5, a double zero at x = 3, and y…

A: Given that the polynomial has a zero at x=-5 So (x+5) is a factor of polynomial. Given that the…

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

A: Solve the following

Q: Given that 5x - 2is a factor of polynomial functions f(x) kx- bx + 2k, %3D determine the ratio k: b…

A: Given that 5x-2 is a factor of polynomial functions f(x)=kx2-bx+2k.

Q: Find a degree 3 polynomial having zeros -5, 2 and 6 and the coefficient of x° equal 1. The…

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Q: One factor of f(x) = x³ – 7x2 - 20x + 96 is x - 3. What are the zeros of f(x)? (Enter your answers…

A: Given:The given function is f(x)=x3-7x2-20x+96and one factor is given i.e. (x-3) To…

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: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=1 and a root of multiplicity 1…

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Q: Find a polynomial f(x) of degree 4 that has the following zeros: 4,-9,-5,0. Leave your answer in…

A: Find a polynomial f(x) of degree 4 that has the following zeros: 4,-9,-5,0. Leave your answer in…

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: