
2/3, 1
Let l = -20/87 + 118/261. Suppose -4/9*n**3 + 2/9*n**4 + 4/9*n + 0*n**2 - l = 0. Calculate n.
-1, 1
Suppose -3*w + 2*w - 9 = 0. Let g be (1/(-3))/(1/w). Factor -r**3 - 2*r**5 + g*r**5 + 0*r**5.
r**3*(r - 1)*(r + 1)
Let j(y) = y**3 + 3*y**2 + 3*y + 5. Let r be j(-2). Find k, given that 1/3*k**5 - 1/3*k**r + 0 + 0*k**4 + 0*k**2 + 0*k = 0.
-1, 0, 1
Let f be 22*1/2 + -3. Let q be f/(-14) - (-234)/91. Solve -2/11 + 0*t + 2/11*t**q = 0.
-1, 1
Let d(j) be the third derivative of -j**10/756000 + j**5/20 - 7*j**2. Let u(v) be the third derivative of d(v). What is x in u(x) = 0?
0
Find n such that n**5 - 17*n**3 + 15*n**3 + n - 1 + 1 = 0.
-1, 0, 1
Let d = -2/229 - -1384/1145. Let o be ((-12)/75)/(4/(-10)). Factor -o*p**2 + 0*p + 0 + 0*p**3 - 4/5*p**5 + d*p**4.
-2*p**2*(p - 1)**2*(2*p + 1)/5
Let r be -8*(14/5 + -3). Let x(z) be the first derivative of 2 - 16/5*z**2 - 14/15*z**3 - r*z. Find j such that x(j) = 0.
-2, -2/7
Let g(r) = -12*r + 3. Let p(m) = -m**2 + 11*m - 4. Let c(d) = 2*g(d) + 3*p(d). Factor c(l).
-3*(l - 2)*(l - 1)
Let -4/3*v**4 - 8*v**2 + 6*v + 0 - 22/3*v**3 = 0. Calculate v.
-3, 0, 1/2
Factor -2*a**2 - a**2 + 0 + 6*a - 5 + 2.
-3*(a - 1)**2
Suppose -b + 3 - 13 = 2*g, 0 = 2*g + 4*b + 10. Let c = -1 - g. Find z such that 10/9*z**3 + 0*z - 8/9*z**c + 0 - 2/9*z**2 = 0.
0, 1/4, 1
Let u be 4 - (-2 - (-7)/((-308)/(-232))). Find x such that 4/11 - 10/11*x + 8/11*x**3 - u*x**4 + 2/11*x**5 + 4/11*x**2 = 0.
-1, 1, 2
Find a, given that -6/11*a**4 + 0 + 6/11*a**3 + 0*a - 2/11*a**2 + 2/11*a**5 = 0.
0, 1
Suppose -300 = 3*k + 5*a, 139 = 4*k + 2*a + 539. Let u be (140/k)/(2/(-15)). Factor -u*i**2 + 3*i + 0.
-3*i*(7*i - 2)/2
Factor -4*d**4 - d**4 + 6*d**2 + 2*d**4 + 3*d**3.
-3*d**2*(d - 2)*(d + 1)
Factor -2*j - 35/2*j**3 + 0 + 12*j**2.
-j*(5*j - 2)*(7*j - 2)/2
Suppose -z + 4*z + 7 = 5*o, 0 = 2*z - 2. Let x be (-36)/(-27)*3/18. Suppose 0 + 2/9*k**o + x*k = 0. Calculate k.
-1, 0
Suppose 0*l - l + 3 = 0. Suppose -4*j + 0 = 3*b - 2, -8 = -j + l*b. Factor -4/3*o**j - 2/3 - 2*o.
-2*(o + 1)*(2*o + 1)/3
Solve -2*t**3 + 2*t - 2*t**2 + 2 - 6*t**2 + 2*t**2 + 4*t**2 = 0 for t.
-1, 1
Let c be (44/(-10))/(-2) - 1. Suppose 0 = 10*u + 412 - 432. Let 3/5*s**u + c*s + 0 = 0. Calculate s.
-2, 0
Factor 0 + 44/7*k**3 + 2/7*k + 16/7*k**2 + 18/7*k**5 + 48/7*k**4.
2*k*(k + 1)**2*(3*k + 1)**2/7
Let p(l) = 5*l**3 - 20*l**2 + 29*l - 10. Let q(i) = 5*i**3 - 20*i**2 + 28*i - 10. Let g(w) = -3*p(w) + 4*q(w). Solve g(n) = 0.
1, 2
Let a = 5 + -2. Let t be 2 + -1 + -2 + a. Factor -2/7*b**4 + 4/7*b + 2/7 - 4/7*b**3 + 0*b**t.
-2*(b - 1)*(b + 1)**3/7
Let p(q) be the first derivative of 3*q**4/4 - 5*q**3 + 13*q**2/2 + 23*q + 2. Let m(s) = 6*s**3 - 30*s**2 + 27*s + 45. Let o(w) = -4*m(w) + 9*p(w). Factor o(f).
3*(f - 3)**2*(f + 1)
Let c be 5/(30/9)*-6. Let r(q) = q + 9. Let n be r(c). Factor -1/5*i**4 + 1/5*i**3 + 1/5*i**2 + n - 1/5*i.
-i*(i - 1)**2*(i + 1)/5
Suppose -8*b - 8 = -4*b + 5*k, -4*b = k - 8. Determine a, given that -8*a**4 - b*a**4 + 19*a**2 - 4*a**2 - 6*a + 6*a**3 - 4*a**4 = 0.
-1, 0, 2/5, 1
Let y = -14/45 - -211/765. Let j = y - -4/17. Find x, given that 0*x - j*x**2 + 4/5 = 0.
-2, 2
Let q(c) = c**3 + c - 1. Let w(y) = -y**4 + 4*y**4 - 5 + 3*y**2 - y**3 + 0*y**4 + 5*y + 0*y. Let m(o) = -5*q(o) + w(o). Find p, given that m(p) = 0.
0, 1
Factor -16/3 + 16/3*y**2 - 4/3*y**3 - y**4 + 1/3*y**5 + 0*y.
(y - 2)**3*(y + 1)*(y + 2)/3
Find c, given that 0 + 1/6*c**2 + 2/3*c = 0.
-4, 0
Suppose 54 + 2/3*d**4 - 24*d**3 - 12*d**2 + 4/3*d**5 + 108*d = 0. What is d?
-3, -1/2, 3
Let q(x) = x**3 - 5*x**2 + 4*x + 2. Let t be q(4). Suppose 0 = -2*j - z - 0*z + 2, -2*z - 8 = -t*j. Solve 7*v - 2 + 0*v**3 - j*v**3 + 0*v**3 + 2*v**2 - 5*v = 0.
-1, 1
Let t be 2/4*6/(-153)*-17. Factor -1/3 - t*a + 2/3*a**2.
(a - 1)*(2*a + 1)/3
Let s(x) = x**2. Let g(j) = -3*j**2 + 12 + j**2 + j**2. Let u(n) = -g(n) + 2*s(n). Factor u(o).
3*(o - 2)*(o + 2)
Let r(l) be the first derivative of 2*l**6/5 + 4*l**5/25 - l**4 - 4*l**3/15 + 4*l**2/5 + 54. Determine s so that r(s) = 0.
-1, 0, 2/3, 1
Suppose -b + 12 = 10. Let u(o) be the first derivative of 3/2*o**4 + o**2 - b + 2*o**3 + 0*o + 2/5*o**5. Factor u(j).
2*j*(j + 1)**3
Let d(k) = 4*k**3 - 4*k**3 + k**2 + k**3. Let b be d(-1). Determine n, given that -8/7*n**2 - 12/7*n**3 + b - 2/7*n**5 - 8/7*n**4 - 2/7*n = 0.
-1, 0
Factor -2/5*b**2 - 2*b - 8/5.
-2*(b + 1)*(b + 4)/5
Let m(v) be the first derivative of -2*v**3/3 - 3*v**2 + 8*v + 4. Solve m(f) = 0.
-4, 1
What is z in z**2 + 90*z + z**3 + 90*z - 3 + 2 - 181*z = 0?
-1, 1
Let n(k) be the second derivative of k**4/12 + 5*k**3/6 + 2*k**2 + k. Let q be n(-4). Factor -2*p**3 + q*p - 2/3*p**5 + 2*p**4 + 0 + 2/3*p**2.
-2*p**2*(p - 1)**3/3
Let x = 2/10281 + 3247/925290. Let v(t) be the third derivative of 0*t**3 + 0*t - 2*t**2 + 1/270*t**5 + 0 + 0*t**4 - x*t**6 + 1/945*t**7. Factor v(c).
2*c**2*(c - 1)**2/9
Let o(d) be the first derivative of -2*d**3/39 - 3*d**2/13 + 8*d/13 + 2. Factor o(l).
-2*(l - 1)*(l + 4)/13
Let o(s) be the first derivative of -s**2 + 4 + 0*s + 4/3*s**3 - 1/2*s**4. Let o(d) = 0. What is d?
0, 1
Let m(y) be the first derivative of -y**3/18 - y**2/3 - 10. Determine p, given that m(p) = 0.
-4, 0
Let s = 12 - 8. What is v in -4*v**3 + 2*v - 6*v**2 - 3*v**s + 9*v**4 + 5*v - 3*v = 0?
-1, 0, 2/3, 1
Let h(r) be the second derivative of -r**7/420 + r**6/120 - r**5/120 - 3*r**2/2 + 3*r. Let x(t) be the first derivative of h(t). Factor x(o).
-o**2*(o - 1)**2/2
Let w(j) be the second derivative of -j**7/126 + j**5/15 - j**4/18 - j**3/6 + j**2/3 - 7*j. Solve w(p) = 0.
-2, -1, 1
Let x(g) be the third derivative of 5*g**2 + 0 + 0*g**3 - 1/90*g**5 - 1/54*g**4 + 0*g. Find o such that x(o) = 0.
-2/3, 0
Let q = -33 + 33. Let p be 3/4 + q/5. Let -r + p*r**3 + 1/4*r**4 + 0*r**2 + 0 = 0. Calculate r.
-2, 0, 1
Let p(y) = -1 + y**3 + 0*y**2 + y**2 - 2*y**2 + y - y**5. Let g(h) = -h**5 - 4*h**4 + 8*h**3 - 6*h**2 + 3*h - 2. Let j(t) = -g(t) + 2*p(t). Factor j(v).
-v*(v - 1)**4
Let s(j) be the third derivative of -j**5/36 - 5*j**4/72 + 5*j**3/9 - 6*j**2. Factor s(f).
-5*(f - 1)*(f + 2)/3
Let c(v) = -v**5 - v**3 + v**2 + v + 1. Let g(s) = 50*s**5 - 104*s**4 - 11*s**3 + 46*s**2 + 17*s. Let a(f) = -10*c(f) - 5*g(f). Let a(r) = 0. Calculate r.
-1/3, -1/4, 1, 2
Factor -1/8*c**3 - 1/2*c + 0 + 1/2*c**2.
-c*(c - 2)**2/8
Suppose -k - 5*y = 2*k + 19, -4*k = 3*y + 7. Suppose -3*s + 34 - k + 2*s**2 - 13*s = 0. What is s?
4
Factor 19*i**2 + 4*i**3 - 19 + 4*i - 5 + 5*i**2 - 8*i**2.
4*(i - 1)*(i + 2)*(i + 3)
Let l(g) = 32*g**4 - 5*g**3 - 19*g**2 + 16*g - 2. Let s(i) = -16*i**4 + 2*i**3 + 9*i**2 - 8*i + 1. Let n(w) = -6*l(w) - 11*s(w). Solve n(o) = 0.
-1, 1/4, 1
Let l(c) = -c**2 + 1. Let t(b) = -b**2 + 6*b + 7. Let s(k) = 2*l(k) - t(k). Let p be s(-4). Factor -18*v**2 + 21*v**4 + 9 - 9*v**2 - p + 15*v**3 - 15*v.
3*(v - 1)*(v + 1)**2*(7*v - 2)
Let l(k) = k**2 - 3*k + 3. Let f be l(3). Let h**3 + 3*h + 0*h - f*h = 0. What is h?
0
Let s(a) = -a + 9. Let f be s(7). Suppose -2*d - 1 + d**f + 2*d + 0*d**2 = 0. What is d?
-1, 1
Let m be (0 + -1 + 0)*-5. Find p, given that 0 + 0*p + 0*p**2 + 0*p**3 + 2/11*p**m + 2/11*p**4 = 0.
-1, 0
Let h(z) = z**3 + 5*z**2 + 4*z + 4. Let l be h(-4). Let f = 6 - l. Find v, given that -2/7*v - 2/7 + 2/7*v**f + 2/7*v**3 = 0.
-1, 1
Let r(a) be the second derivative of a**6/1620 + a**5/270 + a**4/108 + a**3 - 4*a. Let p(g) be the second derivative of r(g). Factor p(q).
2*(q + 1)**2/9
Let z(j) be the third derivative of 7*j**5/30 - j**4 - 4*j**3/3 - 2*j**2. Solve z(r) = 0 for r.
-2/7, 2
Let h = -55 - -91. Let p be (-4)/18 - (-8)/h. Determine n so that -1/3*n**2 + p + 0*n = 0.
0
Find c, given that 3/7*c**3 + 10/7*c**2 - 4/7 - 9/7*c = 0.
-4, -1/3, 1
Let u(q) be the second derivative of q**6/240 + q**5/160 - q**4/24 - q**3/12 - 52*q - 1. What is g in u(g) = 0?
-2, -1, 0, 2
Let r = -1 - -5. Let u(n) = 2*n**3 - 4*n**2 - 6*n + 8. Let f(o) = 2*o**3 - 4*o**2 - 5*o + 7. Let q(i) = r*f(i) - 3*u(i). Solve q(l) = 0.
-1, 1, 2
Let q(b) be the first derivative of -b**3 - 6 - 3/4*b**4 + 0*b + 0*b**2. Find p, given that q(p) = 0.
-1, 0
Let b = 389/4 - 97. Let m = 3 - 3. Factor -1/2*x**3 + m + 1/4*x**2 + b*x**4 + 0*x.
x**2*(x - 1)**2/4
Let o(g) be the second derivative of -98/15*g**6 - 8*g**2 + 0 + g**4 + 14*g**5 - 40/3*g**3 - 5*g. Let o(r) 