1. Give one example of a polynomial of degree 4 that has a zero at x = 5 with multiplicity 2. (There is more than one correct answer).

Q: 1. Determine the number of degree and the end behaviours of the polynomial y = (x + 5)(x − 1)(x +…

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Q: The polynomial of degree 5, P(x)P(x), has leading coefficient 1, has roots of multiplicity 2 at…

A: Definition used -             A polynomial with the given degree, roots, and multiplicity of roots…

Q: 2. Determine the polynomial of degree 4 whose graph is shown in the figure. SLO 2 5 4 3

A: Given query is to find the polynomial for the graph.

Q: Find a degree 4 polynomial that approximates the solution of y'=y+x², if y=1 when x=0. a.y=1+x+ b.…

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Q: i. Suppose p is an irreducible polynomial of degree n with coefficients in Q. Then p has

A: Determine whether p(x) = x3+x+1 is irreducible over  Sol: we know that , let f(x) be a polynomial in…

Q: 5. Find a polynomial of degree 4 with the zeros 3i and-v6j

A: Explanation of the solution is given below...

Q: Find a polynomial of degree 4 with 9 as a zero of multiplicity 1 and 4 as a zero of multiplicity 3

A: A polynomial of degree n has a zero  a  of multiplicity k iff (x-a)k is a factor of polynomial

Q: The polynomial of degree 5, P(r) has leading coefficient 1, has roots of multiplicity 2 at z = 4 and…

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Q: Give an expression for f(x) of degree 3 with roots z = -4 and r = -2, where the root at r = -2 has…

A: Zeroes are x=-4 and x=-2and x=-2 has multiplicity 2

Q: 1. If the leading coefficient of an odd-degree polynomial function is negative, then the function…

A: Check the end behaviour of the function as x tending to minus infinity and infinity.

Q: Find a polynomial of degree n=3 that has the given zero(s) x = −2, 6

A: A polynomial is an expression comprised of variables, their coefficients, constant, and exponents,…

Q: Which of the following is a polynomial f(x) of degree 3 with real coefficients which

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Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplic 2 at x = 2 and x…

A: roots : x=2,2,0,0, -5 Factors are given by:x-2,x-2,x-0.x-0,x+5hence P(x)=Product of factors…

Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at r = 4…

A: Given that the polynomial is of order 5. Root of multiplicity is 2 at x=4, x=0. Root of multiplicity…

Q: Find a polynomial of a degree n that has only the given zero(s). x=-8,5,3; n=3

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Q: Suppose T4(x) = 2 – 4(x – 2) + 5(x – 2)² - 8(x – 2)3 + 5(x – 2)4 is the degree 4 Taylor polynomial…

A: We use Taylor's formula

Q: Show that the nth Maclaurin polynomial for f(x) = e* is Tn (x) = 1+ 2! n!

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Q: 9. Find a fourth-degree polynomial with integer coefficients that has zeros 3i and –1, with -1 a…

A: 3i and -1, with -1 a zero of multiplicity 2

Q: 20. The function e* outgrows any polynomial faster as x→ oo than any polynomial Show that e grows…

A: Here we have to show that exponential function grows faster than any polynomial as x goes to…

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −3

A: Let us find a polynomial with a degree of 2 and a zero x=-3 A factored polynomial with a zero -3 has…

Q: A polynomial of degree n  1 has exactly zeros ifa zero of multiplicity m is counted m times

A: A polynomial of degree n≥1 has exactly  ___________  zeros if a zero of multiplicity m is counted m…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Follow the procedure given below.

Q: Find a formula for the polynomial P(x) with • degree 3 • a root of multiplicity 2 at z = 1 • a root…

A: Result used: If a polynomial function has zeros or roots of r1,r2,r3,…, then the polynomial function…

Q: A polynomial of degree n 2 1 has exactly zero(s) if a zero of multiplicity m is counted m times.

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Q: If f(1) = 2 and 3 <f'(x)<5, what is the largest f(4) can be? Be sure to fully justify your work. In…

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Q: 11. Find the quadratic polynomial y = ar +br+c whose graph passes through the points (-2,-16),…

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Q: 1. Determine the equation for a polynomial given a degree of 1 with zeros at o, 2 (multiplicity 3),…

A: To find the equation in factor form

Q: 8. The graph that could represent a fifth degree polynomial of the form y = ax+ bx + cx + dx² + ex +…

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Q: I Example 6.10. Assuming that the following values of y belong to a polynomial of degree 4, compute…

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Q: Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1

A: Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1

Q: Example 6.10. Assuming that the following values of y belong to a polynomial of degree 4, compute…

A: Given values of y are x 0 1 2 3 4 5 6 7 y 1 -1 1 -1 1                Let the value for x=5,…

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: 7. Find a fourth-degree polynomial with integer coefficients that has zeros x=3i and x=-1. The root…

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Q: A polynomial function of degree n(n 2 3) can have at most (n - 2) inflection points.

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Q: Express p(x)= x3 as a Taylor polynomial about a = -1.

A: The Taylor polynomial of degree n about  is given by:f(x) = f(a) + f'(a)(x-a) + f''(a)2!(x-a)2…

Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=4 and…

A: Topic - polynomials

Q: Within the interval 2 0 has a minimum value of and a maximum value of 3.

A: Find the values of a and b

Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x = 3…

A: We want to find required polynomial.

Q: - Find The polynomial of degree 7 which has only the following zeros: 2( multiplicity 4), 4(…

A: Given: Degree of polynomial is 7. The given zeros of the polynomial are, 2 with multiplicity 4 can…

Q: Find the polynomial f(x) of degree 6, 1/x which satisfies lim{1+ f(x)] =e? x3 X-0 and has local…

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Q: Find a formula for the polynomial P(x) with • degree 10 • leading coefficient 1 • root of…

A: Solution is given below:

Q: the polynomial of degree 4, p(x) has leading coefficient 1 had a zero of multiplicity 2 at x=2, a…

A: We are given that the polynomial p(x) has a zero of multiplicity 2 at x=2, i.e.; the polynomial has…

Q: Determine the smallest degree of the Maclaurin polynomial required for the error in the…

A: The solution is given below in the next step:

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: 3. A polynomial of degree n 21 has exactly a zero of multiplicity m is counted m times. zeros if

A: To fill in the blanks where statement is A polynomial of degree n≥1 has exactly ......... zeros if a…

Q: In Problems 19–22, construct a polynomial function f that has the given properties. There is no…

A: 19.f is of degree 4, its graph is symmetric with respect to the y-axis, y-intercept is (0,-6)

Q: Find a formula for the polynomial P(x) with degree 3 leading coefficient 1 zeros at 8, 5, and 0…

A: polynomial P(x) with degree 3 leading coefficient 1 zeros at 8, 5, and 0

Q: is a polynomial O has repeated roots at x = 0 O has a slope equal to zero at x = 0 O is always…

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Q: The polynomial of degree 5, P(r), has leading coefficient 1, has roots of multiplicity 2 at z = 1…

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