All Questions ⁺⁰237754 Questions

0

23

0

+1761

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - i \sqrt[3]{3}$. Give your answer in expanded form.

parmen Feb 21, 2025

0

1

25

1

+1761

Algebra

Let f(x) = x^3 + bx + c, where b and c are integers. If f(\sqrt{5}) = 0, determine b + c.

parmen Feb 21, 2025

0

1

22

1

+1761

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 - \sqrt{2} and x = 2 and x = 7. Give your answer in expanded form.

parmen Feb 21, 2025

0

3

23

1

+1761

Algebra

Find all roots of the polynomial
f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5.

parmen Feb 21, 2025

Feb 20, 2025

0

1

20

1

+1761

Algebra

Let p(x) be a cubic polynomial. If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then compute p(4).

parmen Feb 20, 2025

0

2

18

0

+1761

Algebra

Let p(x) be a polynomial with integer coefficients. Suppose p(4) = 5 and p(-2) = 3. If p(x) has an integer root r, then find all possible values of r.

parmen Feb 20, 2025

0

10

1

+1761

Algebra

Let f(x) = x^3 + ax^2 + bx + c be a polynomial. All the roots of f(x) are negative integers. If a + b + c = 10, then find the roots of f(x).

parmen Feb 20, 2025

0

1

30

0

+1761

Algebra

Let f(x) = x^3 + ax^2 + bx + c be a polynomial. All the roots are negative integers. If a + b + c = 10, then find c.

parmen Feb 20, 2025

0

1

8

1

+1761

Algebra

Find all positive integers n for which n^2 - 19n + 59 + n^2 + 4n - 31 is a perfect square.

parmen Feb 20, 2025

0

25

0

+1761

Algebra

Let f(x) be a polynomial with integer coefficients. There exist distinct integers p, q, r, s, t such that
f(p) = f(q) = f(r) = f(s) = 18
and f(t) > 18. What is the smallest possible value of f(t)?

parmen Feb 20, 2025

0

1

23

0

+1761

Algebra

If f is a polynomial of degree 4 such that
f(0) = 1, f(1) = 2, f(2) = -7, f(3) = 0, f(4) = 3,
then determine f(5).

parmen Feb 20, 2025

0

26

1

+1761

Algebra

The polynomial
g(x) = x^3 - 14x^2 - 67x - 90 + 5x^3 - 20x^2 + 7x - 135
has one integer root. What is it?

parmen Feb 20, 2025

0

39

0

+1761

Algebra

What is the remainder when the polynomial
g(x) = x^3 - 14x^2 - 67x - 90 + 5x^3 - 20x^2 + 7x - 135
is divided by x - 1?

parmen Feb 20, 2025

0

42

0

+1761

Algebra

Find all integers x for which x^3 = (x - 1)^3 + (x - 2)^3 + (x - 3)^3 + (x - 4)^3 + (x - 5)^3 + (x - 6)^3 + (x - 7)^3.

parmen Feb 20, 2025

0

1

24

0

+987

Algebra

Find all roots of the polynomial f(x) = 12x^3 - 28x^2 - 9x + 10 + 4x^3 - 40x^2 + 16x + 15.

booboo44 Feb 20, 2025

0

1

18

1

+987

Algebra

Find all roots of the polynomial f(x) = 3x^3 - 7x^2 - 10x + 4 + 4x^3 - 5x^2 + 18x + 28.

booboo44 Feb 20, 2025

0

1

27

0

+987

Algebra

Find all roots of the polynomial p(x) = 12x^3 - 28x^2 - 9x + 10 + 4x^3 - 40x^2 + 16x + 15.

booboo44 Feb 20, 2025

0

1

26

0

+987

Algebra

Find all roots of the polynomial p(x) = 3x^3 - 7x^2 - 10x + 4 + 4x^3 - 5x^2 + 18x + 28.

booboo44 Feb 20, 2025

0

1

34

0

+987

Algebra

Find all roots of the polynomial p(x) = 2x^3 - 5x^2 - 2x + 2 - 8x^3 + 11x^2 - 17x + 8.

booboo44 Feb 20, 2025

0

1

16

0

+987

Algebra

The polynomial
f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66
has one integer root. What is it?

booboo44 Feb 20, 2025

0

44

0

+483

Algebra

Find a polynomial f(x) of degree 5 such that both of these properties hold:
* f(x) is divisible by x^3.
* f(x) is divisible by (x+1)^3.
Write your answer in expanded form. read more ..

bIueb3rry Feb 20, 2025

0

40

0

+483

Algebra

Suppose the polynomial f(x) is of degree 3 and satisfies f(3) = 2, f(4) = -4, f(5) = 6, and f(8) = 8.
Determine the value of f(0).

bIueb3rry Feb 20, 2025

0

2

16

1

+294

Algebra

Find the range of the function
h(x) = \frac{5x^2 + 20x + 33}{x^2 + 4x - 7}.
Enter your answer in interval notation.

AUnVerifedTaxPayer Feb 20, 2025

0

48

0

+294

Algebra

Find all integers n for which \frac{n^2 + n + 1}{n - 2 + n^3} is an integer.

AUnVerifedTaxPayer Feb 20, 2025

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