 - 5*n**3 + 4*n**3 - 12 - 15*n**2 + q*n**3 = 0. What is n?
1, 2
Let s(i) be the first derivative of i**3/3 - i**2/2 - 2*i - 20. Determine q, given that s(q) = 0.
-1, 2
Suppose -30/19*k - 18/19 - 2/19*k**3 - 14/19*k**2 = 0. What is k?
-3, -1
Let x be 1 - 1/((-120)/(-102)). Let y(a) be the first derivative of -2 + 0*a + 3/10*a**2 + x*a**4 - 2/5*a**3. Suppose y(l) = 0. What is l?
0, 1
Let i(a) be the second derivative of 1/110*a**5 + 1/33*a**3 - 1/22*a**4 + 1/55*a**6 + 0*a**2 - 2/231*a**7 - 3*a + 0. Determine l, given that i(l) = 0.
-1, 0, 1/2, 1
Let -2*c**4 + 0*c**4 + 8*c**3 - 3*c**4 + c**4 - 4*c**2 = 0. Calculate c.
0, 1
Suppose -5*v + z + 12 = 0, v = -3*v - 2*z + 4. Let o**2 - 29*o**v + o**3 + 8*o + 4 - 3*o**3 + 18*o**3 = 0. What is o?
-1/4, 1
What is l in -5 + 2*l - 10*l**2 + 6*l**3 + 6 + 1 = 0?
-1/3, 1
Factor -r**2 - 4*r**4 + 7*r**4 - 2*r**2.
3*r**2*(r - 1)*(r + 1)
Let g(v) be the first derivative of 3*v**5/100 + v**4/20 - v**3/5 + 3*v - 6. Let i(j) be the first derivative of g(j). Suppose i(r) = 0. Calculate r.
-2, 0, 1
Suppose -10 = -5*d + 10. Suppose -d*s = -6*s. Factor -8/5*n - 10*n**5 + 22/5*n**3 + 24/5*n**2 + s - 12*n**4.
-2*n*(n + 1)**2*(5*n - 2)**2/5
Solve 2/17*a**2 + 0 - 2/17*a**3 + 2/17*a - 2/17*a**4 = 0 for a.
-1, 0, 1
Factor -i**4 + 8*i**4 + 0 + 4*i**3 + 2 - 9*i**4 - 4*i.
-2*(i - 1)**3*(i + 1)
Suppose 4*j = 2*b + 8, b = -j + 2*j - 3. Let i be (0/(-4))/(j + 1). Factor 0 + i*o**2 - 1/4*o**3 - 1/4*o**5 - 1/2*o**4 + 0*o.
-o**3*(o + 1)**2/4
Determine h, given that 0 + 4/11*h + 6/11*h**4 - 4/11*h**3 - 6/11*h**2 = 0.
-1, 0, 2/3, 1
Let d(v) be the first derivative of v**4/10 - 22*v**3/45 + 8*v**2/15 + 8*v/15 + 20. Suppose d(p) = 0. Calculate p.
-1/3, 2
Let j = 2/973 - -11650/12649. Suppose -18/13 + j*i - 2/13*i**2 = 0. What is i?
3
Let w(y) be the second derivative of -y**4/4 - 9*y**3 - 243*y**2/2 - 36*y. Factor w(h).
-3*(h + 9)**2
Let r(i) be the third derivative of i**8/336 + i**7/210 - i**6/60 + 23*i**2. Factor r(q).
q**3*(q - 1)*(q + 2)
Let r(i) be the first derivative of 2/39*i**3 + 1/260*i**6 + 0*i - 1/195*i**5 + 2*i**2 - 1/52*i**4 - 4. Let n(t) be the second derivative of r(t). Factor n(q).
2*(q - 1)*(q + 1)*(3*q - 2)/13
Let h(i) be the second derivative of -i**5/12 + 10*i**4/9 - 85*i**3/18 + 25*i**2/3 + 9*i + 1. Find m such that h(m) = 0.
1, 2, 5
Find m such that 2/3 + 2/3*m**2 - 4/3*m = 0.
1
Let y(j) be the third derivative of -j**8/560 - j**7/280 + j**6/120 + j**5/40 - j**3/6 - j**2. Let i(m) be the first derivative of y(m). Factor i(r).
-3*r*(r - 1)*(r + 1)**2
Factor 0 - 24/5*r**2 + 2/5*r.
-2*r*(12*r - 1)/5
Let l = 18 - 18. Let g(r) be the third derivative of 2/945*r**7 - 1/540*r**6 + l*r**4 + 0*r**5 + 0 + 0*r**3 - 1/1512*r**8 + 0*r + r**2. Factor g(m).
-2*m**3*(m - 1)**2/9
Let j(s) be the second derivative of s**4 + 2*s + 0 + 1/10*s**6 + 0*s**3 + 0*s**2 - 3/5*s**5. Factor j(o).
3*o**2*(o - 2)**2
Let w = 2 + -2. Let u = 132 - 394/3. Factor w*v + 2/3*v**2 - u.
2*(v - 1)*(v + 1)/3
Let -2/7*p**3 - 16/7*p + 2*p**2 - 32/7 = 0. What is p?
-1, 4
Let u(r) = r**3 + 11*r**2 + 10*r + 5. Let y be u(-10). Let q(t) be the second derivative of 0 + 0*t**2 - 3*t + 1/6*t**4 + 1/6*t**3 + 1/20*t**y. Factor q(p).
p*(p + 1)**2
Let p(m) = -m**2 + 3*m - 2. Let f(u) = -3*u + u + 0 + 4*u - 1 - u**2. Let o(k) = -6*f(k) + 4*p(k). Determine l so that o(l) = 0.
-1, 1
Let p(i) be the third derivative of -i**8/60480 + i**7/15120 + i**5/20 + i**2. Let u(j) be the third derivative of p(j). Factor u(t).
-t*(t - 1)/3
Let q(c) be the second derivative of -c**6/90 - c**5/30 - c**4/36 - 5*c. Factor q(p).
-p**2*(p + 1)**2/3
Let a = 1 - -1. Let t(b) = -b**3 + b**2 + b + 8. Let m be t(0). Factor -2*r**a - 4*r**2 - m + r**3 + 12*r + 0*r**2.
(r - 2)**3
Let r(f) = 3*f - 4*f**3 - f**3 - 2*f**4 + 3*f**2 + 8*f**5 + 3*f**3. Let j(x) = x**5 + x**4 - x**3 + x. Let c(o) = 5*j(o) - r(o). Suppose c(g) = 0. What is g?
-2/3, 0, 1
Let n(o) = 9*o**4 - 3*o**3 - 9*o**2 - 9*o + 6. Let j(f) = 8*f**4 - 2*f**3 - 9*f**2 - 8*f + 6. Let u(z) = 6*j(z) - 5*n(z). Factor u(d).
3*(d - 1)**2*(d + 1)*(d + 2)
Let l = -6 + 1. Let u = -5 - l. Find o such that 0*o + 0 - 2/7*o**4 - 2/7*o**5 + u*o**3 + 0*o**2 = 0.
-1, 0
Let n(a) be the third derivative of a**6/120 + a**5/30 + a**4/24 - 9*a**2. Factor n(u).
u*(u + 1)**2
Let u be (0 + 0)/(-9 + (-35)/(-5)). Let m(x) be the first derivative of u*x**2 + 0*x + 3/4*x**4 - x**3 - 4. Factor m(v).
3*v**2*(v - 1)
Let m(q) = -4*q**2 - 7*q + 6. Let k = -12 + -3. Let t(s) = s**2 + s - 1. Let d(p) = k*t(p) - 3*m(p). Factor d(y).
-3*(y - 1)**2
Let v(i) be the second derivative of i**5/80 + i**4/48 - i**3/12 - 4*i. Factor v(f).
f*(f - 1)*(f + 2)/4
Let j be -1 + ((-200)/28 - 0)/(-2). Factor j*w - 69/7*w**2 + 48/7*w**4 + 27/7 - 24/7*w**3.
3*(w - 1)**2*(4*w + 3)**2/7
Factor 0*o**3 + 1/4*o**5 + 0*o + 1/2*o**4 + 0 + 0*o**2.
o**4*(o + 2)/4
Let c = -11 + 15. Suppose c*t = 3*t + 2. What is b in b**2 + b**4 - 9*b**5 - t*b**2 - b**3 + 10*b**5 = 0?
-1, 0, 1
Let l(h) be the second derivative of -h**4/30 + h**3/15 + 2*h**2/5 - 5*h. Factor l(z).
-2*(z - 2)*(z + 1)/5
Find h, given that -2*h**4 + 0 + 6/7*h**5 + 16/7*h - 12/7*h**3 + 24/7*h**2 = 0.
-1, -2/3, 0, 2
Let q(k) be the third derivative of -1/150*k**6 + 0*k - 1/120*k**4 + 0 + 0*k**3 + 1/60*k**5 - 2*k**2. Suppose q(o) = 0. Calculate o.
0, 1/4, 1
Let t(i) be the first derivative of -1 + 0*i**2 + 0*i + 0*i**3 + 1/14*i**4 - 4/35*i**5 + 1/21*i**6. What is l in t(l) = 0?
0, 1
Let o be 64/126 - (-4)/(-18). Let p = -59 - -415/7. Let -4/7*t + o*t**2 + p = 0. Calculate t.
1
Let w(k) be the first derivative of 3/20*k**5 + k**4 - 3*k + 3 + 3*k**2 + 5/2*k**3. Let b(c) be the first derivative of w(c). Factor b(i).
3*(i + 1)**2*(i + 2)
Factor -81 + 60*p**2 + 17*p**3 + 32*p + 8*p**3 - 9*p**3 + 69.
4*(p + 1)*(p + 3)*(4*p - 1)
Let m(s) = s**3 - 6*s**2 + 2. Let c be m(6). Solve i**2 + i**c + 4*i + 2*i - 4*i = 0.
-1, 0
Let w(y) = 14*y**3 - 64*y**2 + 208*y - 8. Let q(d) = 5*d**3 - 21*d**2 + 69*d - 3. Let v(s) = -8*q(s) + 3*w(s). Factor v(o).
2*o*(o - 6)**2
Let k(s) be the first derivative of -3*s**5/20 - 3*s**4/8 - s**3/4 - 3. Let k(g) = 0. Calculate g.
-1, 0
Let q(m) be the first derivative of 9*m**4/10 - 4*m**3 + 9*m**2/5 - 6. Factor q(s).
6*s*(s - 3)*(3*s - 1)/5
Let s(t) = 5*t**4 - 12*t**3 - 18*t**2 + 55*t - 33. Let p(x) = -5*x**4 + 11*x**3 + 19*x**2 - 55*x + 34. Let j(h) = -3*p(h) - 4*s(h). Solve j(v) = 0 for v.
-2, 1, 3
Suppose -4*r + x = 3 + 137, 88 = -3*r + 5*x. Let s be (-3)/(r/50) - 4. Factor -1/6*n**3 + s*n + 0*n**2 + 0.
-n*(n - 1)*(n + 1)/6
Let m(h) be the first derivative of -1/2*h**3 - 9/2*h**2 - 27/2*h + 3. Factor m(z).
-3*(z + 3)**2/2
Let r(y) = -3*y**2 + 1. Let h be r(1). Let w be 0/(6 - 3) - h. Factor 0 + 2/7*q + 4/7*q**w.
2*q*(2*q + 1)/7
Factor 0*u + 0*u**2 + u**3 + 4/3*u**4 + 0 + 1/3*u**5.
u**3*(u + 1)*(u + 3)/3
Let x(a) be the first derivative of 2*a**3/3 - 2*a**2 + 2*a - 5. Factor x(v).
2*(v - 1)**2
Let j(w) be the third derivative of w**7/315 - 2*w**6/45 + w**5/6 + 2*w**4/9 - 16*w**3/9 - 16*w**2. Factor j(s).
2*(s - 4)**2*(s - 1)*(s + 1)/3
Let n(k) = -k**3 + k**2 + k + 1. Let y(f) = 12*f**3 - 28*f - 16. Let a(w) = 16*n(w) + y(w). Determine x, given that a(x) = 0.
0, 1, 3
Find w, given that 2/3*w**2 + 0 + 2/3*w**4 + 4/3*w**3 + 0*w = 0.
-1, 0
Suppose 5*o - 6 = 44. Suppose -4*u = 5*a + o, 2*a - 5*a + 21 = -3*u. Factor -8/3*c**4 + 2/3*c + 0 + 4*c**3 + 2/3*c**5 - 8/3*c**a.
2*c*(c - 1)**4/3
Let c(f) = -4*f**2 + 24*f - 12. Let k(v) = -3*v**2 + 16*v - 8. Let o(i) = -5*c(i) + 8*k(i). Suppose o(z) = 0. Calculate z.
1
Let c(g) = g + 10. Let h be c(-8). Determine s so that 1/4*s**5 + 0 + s**4 + s**3 + 0*s**h + 0*s = 0.
-2, 0
Factor -1/3*g**2 + 2/3 + 1/3*g.
-(g - 2)*(g + 1)/3
Let i(w) be the second derivative of -5*w**7/42 + 5*w**6/6 - 9*w**5/4 + 35*w**4/12 - 5*w**3/3 + 10*w. Factor i(n).
-5*n*(n - 2)*(n - 1)**3
Find c such that 25*c**3 - 75*c**5 - 95*c**4 - 2*c - 8*c + 14*c**2 + 14*c**2 + 7*c**2 = 0.
-1, 0, 1/3, 2/5
Determine h, given that 4/7*h**2 + 12/7*h + 0 = 0.
-3, 0
Suppose 98*u + 9 = 99*u. Suppose -2*f + 10 = r, -4*f = -2*r - 2*r - 8. Factor 0 + 9*a**5 + 0*a - u*a**4 - 1/3*a**r + 3*a**3.
a**2*(3*a - 1)**3/3
Factor 6/7 - 27/7*d + 36/7*d**2 - 15/7*d**3.
-3*(d - 1)**2*(5*d - 2)/7
Let y(m) be the third derivative of -m**5/390 + m**3/