ivative of f**5/40 + f**4/8 - 3*f**3/4 + 2*f**2. Solve v(n) = 0 for n.
-3, 1
Suppose m + 2*m = -2*i, -5*i = 5*m. Let l(k) be the second derivative of 2*k + 0*k**3 + 1/70*k**5 + i*k**2 + 0 - 1/42*k**4. Factor l(z).
2*z**2*(z - 1)/7
Suppose 5*a + 18 = -57. Let p be -1 + -1 - 40/a. Factor 2*x**2 - 2*x + p - 2/3*x**3.
-2*(x - 1)**3/3
Determine f so that -1/9*f + 0*f**3 - 2/9*f**4 + 2/9*f**2 + 0 + 1/9*f**5 = 0.
-1, 0, 1
Factor -p**2 + 1/2*p + 0 + 1/2*p**3.
p*(p - 1)**2/2
Suppose -2*v + 54 = 5*a, 5*v - 27 = -3*a + 2*v. Suppose -14 = -o - a. Suppose -12/5*u**3 - 18/5*u - 3/5 - 27/5*u**o = 0. Calculate u.
-1, -1/4
Factor -5*m**5 - 20*m**2 + 14*m**3 - 14*m**2 + 54*m**2 + 30*m**4 - 59*m**3.
-5*m**2*(m - 4)*(m - 1)**2
Let v(x) = -x**4 - 1. Let p(n) = 12*n**4 - 8*n**3 + n**2 + 2*n + 7. Let h(m) = -4*p(m) - 28*v(m). Factor h(r).
-4*r*(r - 1)**2*(5*r + 2)
Let s(y) = y + 3. Let m be s(-1). Factor -7*w**m + 7*w**4 + 0*w**3 + 0*w**3 + 2*w**3 - 2*w.
w*(w - 1)*(w + 1)*(7*w + 2)
Suppose -i = -5*q - 1, 2*q + 2*i - 2 = -0. Determine s, given that -3 + 5 + q*s - 3*s + 2*s**2 - s**2 = 0.
1, 2
Suppose -4*o - 12 = 0, 5*r - 11 = 5*o + 14. Factor -22/3*u - 32/3*u**3 - 24*u**r - 2/3 + 128/3*u**4.
2*(u - 1)*(4*u + 1)**3/3
Let u(y) be the second derivative of -y**5/30 - y**4/6 - y**3/3 + y**2 - y. Let f(r) be the first derivative of u(r). Factor f(p).
-2*(p + 1)**2
Let p(o) be the first derivative of 6 + 0*o + 0*o**2 + 1/3*o**3 + 1/4*o**4 - 1/5*o**5 - 1/6*o**6. What is h in p(h) = 0?
-1, 0, 1
Let c(s) be the first derivative of -7*s**4/6 + 32*s**3/9 + 17*s**2/3 - 4*s - 1. Factor c(j).
-2*(j - 3)*(j + 1)*(7*j - 2)/3
Let o(t) = 2*t**5 - t**4 - 6*t**3 - 8*t**2 + 3*t - 5. Let v = 4 + 1. Let d(z) = -z**5 + 3*z**3 + 4*z**2 - 2*z + 2. Let b(u) = v*d(u) + 2*o(u). Solve b(k) = 0.
-2, 0, 1
Let a(x) = -x**2 - x. Let j(b) = -2*b**2 + 2*b - 2. Let p(f) = -f + 4. Let i be p(5). Let w(d) = i*a(d) + j(d). Factor w(r).
-(r - 2)*(r - 1)
Let m(x) be the first derivative of -108*x**3 + 18*x**2 - x + 45. Find b, given that m(b) = 0.
1/18
Let k(w) be the second derivative of w**6/135 + w**5/15 + 13*w**4/54 + 4*w**3/9 + 4*w**2/9 + 23*w. Find y such that k(y) = 0.
-2, -1
Let f be (-1 - -2)*(2 - 0). Suppose -f*a - a = -18. Determine y, given that 7*y**2 + 6*y + 4 + a*y**3 + 8*y + 9*y**2 = 0.
-1, -2/3
Let f(n) be the first derivative of -1/11*n**2 - 1/22*n**4 + 0*n - 4/33*n**3 - 1. Find a such that f(a) = 0.
-1, 0
Let o(g) be the first derivative of -g**5/15 - g**4/2 - 8*g**3/9 + g**2 + 3*g + 15. Find z such that o(z) = 0.
-3, -1, 1
Let x be 0 - -1 - (-2)/(-3). Solve 2/3*z**2 + 0 - x*z**3 - 1/3*z = 0.
0, 1
Let s(i) be the second derivative of i**5/30 - i**4/2 + 3*i**3 - 9*i**2 - 9*i. Factor s(a).
2*(a - 3)**3/3
Let n be (1/((-2)/12))/(-2). Factor -1 + 0 + n + 2*b**2 + 3*b + b.
2*(b + 1)**2
Let j(r) be the first derivative of -3*r**5/20 + 15*r**4/16 - 2*r**3 + 3*r**2/2 + 23. Factor j(m).
-3*m*(m - 2)**2*(m - 1)/4
Factor -3*b**3 + 8*b**3 + 36*b - 16*b**2 - 4*b**2 - 16*b.
5*b*(b - 2)**2
Factor 5*v**3 - 1 - 73*v**4 - 5*v + 35*v**4 - 3*v**2 + 42*v**4.
(v - 1)*(v + 1)**2*(4*v + 1)
Find j such that 1/3*j**2 - 2/3 + 1/3*j = 0.
-2, 1
Let y(n) be the second derivative of n**7/168 - n**6/60 + n**5/80 + 26*n. Factor y(s).
s**3*(s - 1)**2/4
Let w = -19 + 22. Let o(f) be the third derivative of -1/105*f**7 - 1/20*f**6 + 2*f**2 - 1/12*f**4 + 0*f**w + 0 - 1/10*f**5 + 0*f. Solve o(t) = 0 for t.
-1, 0
Let d(f) be the second derivative of -f**6/30 - f**5/5 - 5*f**4/12 - f**3/3 - 11*f. Find o, given that d(o) = 0.
-2, -1, 0
Let p = -163/42 - -25/6. Let -6/7*q**2 + 4/7 + p*q = 0. Calculate q.
-2/3, 1
Let d = -56 - -56. Let n(j) be the first derivative of -1/15*j**3 + 3 + d*j + 1/10*j**2. Let n(x) = 0. Calculate x.
0, 1
Let s(m) be the first derivative of m**5/240 + m**4/24 + m**3/6 - m**2 + 1. Let t(o) be the second derivative of s(o). Suppose t(z) = 0. What is z?
-2
Let p(b) be the second derivative of b**4/6 - b**3/2 + 7*b. Let o be p(2). Determine i so that -1/4*i**o + 0*i + 1/4 = 0.
-1, 1
Let -3/5*c**2 + 0*c**3 + 0 + 2/5*c + 1/5*c**4 = 0. What is c?
-2, 0, 1
Let h(a) = -a**2 - 6*a - 2. Let m = 4 + -9. Let c be h(m). Factor 19*p + 25*p**4 + 7*p + 4 + 2*p + 70*p**c + 69*p**2.
(p + 1)**2*(5*p + 2)**2
Let l(v) = v**4 + v**3 + 2*v. Let z(c) = 5*c**4 + 4*c**3 + 9*c. Let k(r) = 18*l(r) - 4*z(r). Solve k(p) = 0 for p.
0, 1
Let b(i) be the third derivative of 0*i**5 + 0*i**3 + 0*i + 1/420*i**6 + 0 + 0*i**4 - 3*i**2. Let b(s) = 0. What is s?
0
Factor -2/3*z**2 + 2*z + 8/3.
-2*(z - 4)*(z + 1)/3
Let k = -22 - -24. Let x be (k - -2) + (-32)/9. Suppose 8/9*h**3 + 14/9*h**5 - x + 32/9*h**4 - 22/9*h - 28/9*h**2 = 0. Calculate h.
-1, -2/7, 1
Suppose -16/3*r**3 - 2/3*r**4 - 8 - 56/3*r - 46/3*r**2 = 0. What is r?
-3, -2, -1
Let v be ((-1)/(-2) - 0) + (-3)/18. Let x(q) be the first derivative of v*q**3 + 1/2*q**2 - q + 2 - 1/4*q**4. Find t, given that x(t) = 0.
-1, 1
Suppose -30 = -5*l - 10. Let w(a) be the second derivative of 0*a**5 - 1/165*a**6 + 1/33*a**l + 0*a**3 - 1/11*a**2 + 0 + 2*a. Factor w(g).
-2*(g - 1)**2*(g + 1)**2/11
Let m(y) be the third derivative of y**7/30 + y**6/60 - 7*y**5/60 - y**4/12 + 8*y**2. Factor m(a).
a*(a - 1)*(a + 1)*(7*a + 2)
Suppose -d + 5*d + 3*n - 12 = 0, 0 = -5*n. Let t(w) be the second derivative of -2*w + 2/7*w**2 - 5/42*w**4 + 0 + 1/7*w**d. Factor t(r).
-2*(r - 1)*(5*r + 2)/7
Suppose -5*y - 2 = -7. Let z(n) be the first derivative of 1/3*n**3 + y + 1/2*n**2 + 0*n. Suppose z(s) = 0. What is s?
-1, 0
Let p(n) be the first derivative of -n**4/6 - 4*n**3/3 - 4*n**2 + 4*n + 3. Let t(j) be the first derivative of p(j). Factor t(w).
-2*(w + 2)**2
Suppose v = 3*b - 4*b + 7, -4*b - 3*v + 24 = 0. Let i(c) be the second derivative of -1/4*c**2 + 2*c + 0 + 1/24*c**4 + 0*c**b. Factor i(l).
(l - 1)*(l + 1)/2
Factor -9/5*a**3 - 12/5 + 3*a**2 + 12/5*a.
-3*(a - 2)*(a + 1)*(3*a - 2)/5
Let y(u) be the second derivative of u**7/189 - 2*u**6/135 + u**4/27 - u**3/27 - 13*u. Solve y(g) = 0 for g.
-1, 0, 1
Find o such that -8/3*o + 0 - 7/3*o**3 - 10*o**2 = 0.
-4, -2/7, 0
Let u(g) be the first derivative of -g**6/2 - 3*g**5/5 + 3*g**4/2 + 2*g**3 - 3*g**2/2 - 3*g + 5. Suppose u(f) = 0. Calculate f.
-1, 1
Let o(a) be the first derivative of 2*a**3 - 3 - 3*a**2 - 1/2*a**4 + 2*a. Let o(m) = 0. What is m?
1
Let h = -9 + 21. Suppose 3*a**5 + a + 2*a + 18*a**3 + 25 + h*a**4 + 12*a**2 - 25 = 0. Calculate a.
-1, 0
Let r(s) = -4*s**4 - 3*s**3 + 8*s**2 - 6*s + 5. Let t(u) = -3*u**4 - 3*u**3 + 7*u**2 - 5*u + 4. Let p = 30 - 35. Let d(v) = p*t(v) + 4*r(v). Factor d(b).
-b*(b - 1)**3
Let p(n) = -2*n**3 + 2*n**2 + 8*n + 4. Let x(t) = -t**3 - t**2 + t + 1. Let z(y) = -p(y) + 4*x(y). Factor z(o).
-2*o*(o + 1)*(o + 2)
Let y(b) = b**4 - b**2. Let u(h) = 3*h**4 - 4*h**3 + 3*h**2 - 2*h. Suppose 3 = -2*z - 1. Let r(k) = z*y(k) + u(k). Factor r(j).
j*(j - 2)*(j - 1)**2
Suppose -2*n + 6 = z, z - 3*z - n = -9. Factor 1/3*c**z + 0 + 0*c + 2/3*c**3 + 1/3*c**2.
c**2*(c + 1)**2/3
Suppose 4*y = 5*y, y = 3*p. Suppose d - 4 = -p*d. Factor 6*b - 2 + d + 2*b**3 + 0*b**3 + 6*b**2.
2*(b + 1)**3
Suppose 0 = -4*j - j. Find s such that -4*s**2 + 4*s**3 - 4*s**2 + j*s**3 + 2*s**5 - 2*s + 4 + 4*s**4 - 4*s**5 = 0.
-1, 1, 2
Let u(v) be the third derivative of 0 - 1/24*v**4 + 3/20*v**5 - 2*v**2 + 0*v - 1/6*v**3 + 2/105*v**7 - 11/120*v**6. Find a such that u(a) = 0.
-1/4, 1
Let h(l) = 6*l - 1. Let i be h(1). Suppose -i*x = -3*c + 4, 0 = 2*c - 0*x - 4*x - 2. Determine a, given that 2*a + 2 - 1 + 3*a**2 - 5*a - a**c = 0.
1
Let q(b) = 13*b**3 + 51*b**2 + 112*b + 69. Let l(f) = 6*f**3 + 26*f**2 + 56*f + 34. Let k(h) = -5*l(h) + 2*q(h). Find w, given that k(w) = 0.
-4, -2, -1
Let i(f) = -8*f**3 + 4*f**3 + 2*f**2 - 3*f**2 + 2*f**3. Let h be i(-1). Solve 9/2*x**3 + 8*x**2 + 5/2*x - h = 0.
-1, 2/9
Let u = 4 - 4. Let c(x) be the third derivative of 0*x**6 + 1/315*x**7 - 1/90*x**5 + 0 + 0*x**3 - x**2 + 0*x**4 + u*x. Factor c(r).
2*r**2*(r - 1)*(r + 1)/3
Suppose 0 = -2*u + 6*u - 4*c, 0 = -u + 2*c. Let 6*n**2 - 3*n**3 + 2*n - 2*n + u*n - 3*n = 0. What is n?
0, 1
Let s(g) be the second derivative of 2*g**6/15 + 3*g**5/5 + g**4/3 - 2*g**3 - 4*g**2 - 4*g. Suppose s(u) = 0. What is u?
-2, -1, 1
Let n(k) = -3*k**3 - 2*k**2 + 3*k - 2. Suppose 4*u = -33 - 11. Let w(c) = 16*c**3 + 1