0, 1
Let o(l) be the second derivative of -l**6/10 + 9*l**5/20 - 3*l**4/4 + l**3/2 - 3*l. Factor o(y).
-3*y*(y - 1)**3
Suppose 12 = -4*r + 24. Let v(m) be the first derivative of -1/4*m**3 + 3/8*m**4 - 3/20*m**5 + 0*m + 0*m**2 + r. Determine a so that v(a) = 0.
0, 1
Let a(g) be the first derivative of -g**6/24 - g**5/5 - 3*g**4/8 - g**3/3 - g**2/8 - 3. Let a(t) = 0. What is t?
-1, 0
Let h = -402 + 405. Factor 0 + 6*v**h - 9/2*v**2 - 3/2*v.
3*v*(v - 1)*(4*v + 1)/2
Let a(y) be the third derivative of -5*y**8/1008 - 4*y**7/315 + y**6/40 + 2*y**5/45 - y**4/18 + 47*y**2. Determine c, given that a(c) = 0.
-2, -1, 0, 2/5, 1
Let t(i) be the third derivative of i**8/13440 + i**7/560 + 3*i**6/160 + 9*i**5/80 + 7*i**4/24 + 6*i**2. Let l(o) be the second derivative of t(o). Factor l(j).
(j + 3)**3/2
Let v(j) be the third derivative of -j**6/60 - 2*j**5/45 + j**4/9 - 7*j**2. Factor v(t).
-2*t*(t + 2)*(3*t - 2)/3
Let f(h) = 3*h**5 + 18*h**4 + 9*h**3 - 6*h**2 + 18*h + 18. Let s(l) = l**4 + l**3 + l + 1. Let d(v) = -f(v) + 18*s(v). Determine o, given that d(o) = 0.
-1, 0, 2
Let 60 - 62*t + 3*t**3 + 194*t + 27*t**2 - 60*t = 0. What is t?
-5, -2
Let i = -2 + 4. Factor -v - i*v**3 - 3*v + 4*v**2 + v + v.
-2*v*(v - 1)**2
Let c(b) be the first derivative of b**4/5 - 8*b**3/15 - 11*b**2/10 - 3*b/5 - 29. Factor c(f).
(f - 3)*(2*f + 1)**2/5
Let i(s) be the third derivative of s**7/70 - 3*s**6/40 + 3*s**5/20 - s**4/8 + 5*s**2. Factor i(m).
3*m*(m - 1)**3
Suppose -2*z - g + 5 + 3 = 0, -5*g = -3*z - 14. Factor 3/4 + 0*f - 3/4*f**z.
-3*(f - 1)*(f + 1)/4
Suppose -3*q + 3 + 3 = 0. Let 4 + 2*n**4 + 11*n**3 - 6*n**q - 23*n**3 - 2*n + 14*n**3 = 0. What is n?
-2, -1, 1
Let f be (4 - 9/1) + 7. Solve 0*t + 0*t**f + 0 + 8/7*t**4 - 2/7*t**5 - 8/7*t**3 = 0 for t.
0, 2
Let d(z) be the third derivative of 0 + 1/50*z**5 + 2*z**2 + 0*z**3 - 1/40*z**4 + 0*z - 1/200*z**6. Find p, given that d(p) = 0.
0, 1
Let u be (20/60)/(((-110)/12)/(-11)). Let 8*w + 14/5*w**3 + 36/5*w**2 + u*w**4 + 16/5 = 0. What is w?
-2, -1
Let w = 1 + 2. Factor w*u**3 - 10*u**2 - 34*u - 3 + 3*u**4 + u**2 + 19*u - 3.
3*(u - 2)*(u + 1)**3
Let p be 6/15 - 0/2. Factor -2/5*r - p*r**3 - 4/5*r**2 + 0.
-2*r*(r + 1)**2/5
Let v(r) be the third derivative of -r**6/360 + r**5/90 + r**4/72 - r**3/9 - 4*r**2. What is y in v(y) = 0?
-1, 1, 2
Let q(n) be the first derivative of n**6/8 - 3*n**5/4 + 21*n**4/16 + n**3/4 - 3*n**2 + 3*n + 3. Let q(j) = 0. Calculate j.
-1, 1, 2
Let j be ((-6)/21)/((-20)/105). Solve j + 3/2*b**2 + 9*b - 36*b**3 + 24*b**4 = 0 for b.
-1/4, 1
Let c be 25/(-10)*30/(-45). Let r**4 + 2/3 + r - 5/3*r**2 + 2/3*r**5 - c*r**3 = 0. Calculate r.
-2, -1, -1/2, 1
Let v be 32/(-6)*(-117)/26. Let n be 4/(-10) + v/10. What is m in 4/9*m**n + 0 + 2/9*m**3 + 0*m - 4/9*m**4 - 2/9*m**5 = 0?
-2, -1, 0, 1
Let l(f) = -f**3 + 3*f**2 + 5*f + 1. Suppose 5*k = 3*k + 8. Let o be l(k). Factor -p**2 - p**4 - o*p**3 + 0*p**2 + 3*p**3.
-p**2*(p + 1)**2
Suppose 4*w = 20, 2*w - 5*w + 5 = -5*s. Factor -2*z**2 + 12*z + 3*z**s - 10*z + z**2.
2*z*(z + 1)
Let j(i) be the third derivative of 7*i**6/780 + i**5/195 - 7*i**4/156 - 2*i**3/39 - i**2. Let j(l) = 0. What is l?
-1, -2/7, 1
Suppose -7*o + 15 = -3*o + 3*j, 5*j + 1 = 2*o. Let h(p) be the second derivative of 2/21*p**o - p - 1/7*p**2 + 0 - 1/42*p**4. Let h(w) = 0. Calculate w.
1
Factor 0*n + 2/5*n**2 + 0.
2*n**2/5
Let c be (52/(-130))/(14/(-10)). Factor -c*r + 2/7*r**2 + 0.
2*r*(r - 1)/7
Let y(c) be the third derivative of -c**8/336 - 2*c**7/105 + c**5/6 + c**4/24 - c**3 + 36*c**2. Solve y(l) = 0 for l.
-3, -2, -1, 1
Let l(f) be the first derivative of -f**6/15 + 6*f**5/25 - f**4/10 - 2*f**3/5 + 2*f**2/5 + 12. Solve l(n) = 0.
-1, 0, 1, 2
Let r(p) be the third derivative of 1/9*p**3 - 2*p**2 + 0 + 1/180*p**5 - 1/24*p**4 + 0*p. Factor r(i).
(i - 2)*(i - 1)/3
Let z(n) = -n - 3*n + 2*n**2 - 2*n + 7. Let m(l) = -1. Let f(x) = 3*m(x) + z(x). Suppose f(i) = 0. What is i?
1, 2
Factor -1/3*c + 0 + 0*c**2 + 0*c**4 + 2/3*c**3 - 1/3*c**5.
-c*(c - 1)**2*(c + 1)**2/3
Let u be -8*(-5)/60 - 16/42. Factor -u*k**2 + 0 + 4/7*k - 2/7*k**3.
-2*k*(k - 1)*(k + 2)/7
Let o(k) be the third derivative of k**8/840 - 13*k**7/1575 + 13*k**6/900 + k**5/50 - 4*k**4/45 + 4*k**3/45 + 3*k**2. Suppose o(b) = 0. What is b?
-1, 1/3, 1, 2
Let z be 2 + (-20)/9 + (-20)/(-60). Let u(h) be the third derivative of -1/15*h**5 - 1/18*h**6 + z*h**3 + 0*h + 0 + h**2 + 1/24*h**4. Factor u(s).
-(2*s + 1)**2*(5*s - 2)/3
Let c(a) = -a**3 + a**2 - 1. Let z(o) = -o**2 + 12*o + 17. Let v(l) = 2*c(l) + 2*z(l). Factor v(f).
-2*(f - 4)*(f + 2)**2
Factor -8/5 + 8/5*c - 2/5*c**2.
-2*(c - 2)**2/5
Let y be 2*(-4)/8 - -3. Factor 4*q**2 + 3*q**4 + y*q + 4*q**5 - 2*q**5 - 2*q**3 - 2*q**3 - 5*q**4 - 2.
2*(q - 1)**3*(q + 1)**2
Let p(k) be the third derivative of -2/9*k**3 - 3/70*k**7 + 1/3*k**4 + 2*k**2 + 11/72*k**6 - 53/180*k**5 + 0 + 5/1008*k**8 + 0*k. Factor p(z).
(z - 2)*(z - 1)**3*(5*z - 2)/3
Let w(k) be the first derivative of -k**5/5 - 3*k**4/4 - k**3 - k**2/2 - 3. Determine y so that w(y) = 0.
-1, 0
Let h(u) be the third derivative of 3*u**6/80 - u**5/80 - 9*u**2. Solve h(a) = 0.
0, 1/6
Let f(o) = -o**2 - 6*o - 2. Let x be f(-5). Factor 1/2*n**x + 0 + 0*n - 1/2*n**4 + 1/2*n**2 - 1/2*n**5.
-n**2*(n - 1)*(n + 1)**2/2
Let j(m) be the third derivative of m**7/840 + m**6/160 + m**5/80 + m**4/96 + 15*m**2. Determine o, given that j(o) = 0.
-1, 0
Let g = -2 + 5. Factor 4*q**3 - 4*q**3 - 2*q**4 - 2*q + 2*q**2 + 2*q**g.
-2*q*(q - 1)**2*(q + 1)
Let q = -11 - -11. Suppose q*l + 5*l - 10 = 0. Factor 0*s**l + 0 - 2/7*s**3 + 2/7*s.
-2*s*(s - 1)*(s + 1)/7
Let l = -57037/14 - -4077. Let w = 18/7 + l. Find o such that 7/2*o**4 + 8*o**3 + o + 0 + w*o**2 = 0.
-1, -2/7, 0
Let z = 48 + -48. Solve 2/7*c**2 - 2/7*c + z = 0.
0, 1
Let o(i) be the second derivative of -i**7/8820 + i**6/1260 - i**5/420 + i**4/4 - 2*i. Let c(t) be the third derivative of o(t). Factor c(b).
-2*(b - 1)**2/7
Let o(i) be the second derivative of -i**8/1344 + i**6/480 + 3*i**2/2 - 3*i. Let t(s) be the first derivative of o(s). Find c such that t(c) = 0.
-1, 0, 1
Let z be (3 - 1)/(4/(-10)). Let u(a) = -a**2 + 31*a + 25. Let j(k) = -k**2 + 21*k + 17. Let n(f) = z*u(f) + 7*j(f). Factor n(c).
-2*(c + 1)*(c + 3)
Let w = 16/7 - 4313/1890. Let y(o) be the third derivative of 1/27*o**4 - 3*o**2 - 4/27*o**3 + 0*o - w*o**5 + 0. Let y(k) = 0. What is k?
2
Suppose u - 12*u = -33. Let g(q) be the first derivative of -4 - 1/6*q**2 - 2/3*q + 1/9*q**u. Suppose g(n) = 0. Calculate n.
-1, 2
Let j be (-21)/6 - (-4)/8. Let z = -1 - j. Let 2/7*u + 2/7*u**z + 0 = 0. What is u?
-1, 0
Let v be 0/(3 - -2 - 3). Suppose v = 7*u - 3*u. Factor 2/3*x**4 - 4/3*x**3 + u*x + 0 + 2/3*x**2.
2*x**2*(x - 1)**2/3
Let d(b) be the third derivative of -b**6/280 - b**5/28 - b**4/8 - 3*b**3/14 + 5*b**2. Solve d(t) = 0.
-3, -1
Let t(j) be the second derivative of -j**3/6 - 5*j**2/2 + j. Let g be t(-7). Suppose 2*k**2 - g*k**4 + 5*k - k**5 - 4*k + 0*k = 0. Calculate k.
-1, 0, 1
Let l be 345/25 + -7 + -2. Let l + 38*c**2 - 128/5*c - 10*c**3 = 0. Calculate c.
2/5, 3
Find q, given that -23/2*q**2 - 2/3 - 14/3*q - 35/3*q**3 - 25/6*q**4 = 0.
-1, -2/5
Let u(w) be the first derivative of -2*w**2 - 2 + 0*w - 4/3*w**3. Factor u(d).
-4*d*(d + 1)
Factor 1/3*d**2 - 4/3 + 0*d.
(d - 2)*(d + 2)/3
Let i(x) be the first derivative of 5*x**3/3 + 25*x**2 + 45*x - 42. Suppose i(t) = 0. Calculate t.
-9, -1
Determine m, given that 27*m + 66*m**3 + 20*m + 15*m**5 - 56*m + 6 - 24*m**2 - 54*m**4 = 0.
-2/5, 1
Let n(m) be the third derivative of m**5/60 + m**4/12 + 15*m**2. Factor n(u).
u*(u + 2)
Let f(q) = 9*q**3 + 11*q**2 - 2*q - 18. Let r(w) = 3*w**3 + 4*w**2 - w - 6. Let k(p) = -p - 3. Let o be k(-5). Let h(z) = o*f(z) - 7*r(z). Factor h(t).
-3*(t - 1)*(t + 1)*(t + 2)
Solve 0 + 4/7*n**3 + 2/7*n**4 + 0*n + 2/7*n**2 = 0.
-1, 0
Let w be 34 - 0*(-1)/(-4). Let v = -67/2 + w. Let 1/2*i + i**2 - i**3 + 1/2*i**5 - 1/2*i**4 - v = 0. Calculate i.
-1, 1
Let r(d) be the third derivative of d**8/98 + d**7/147 - 3*d**6/70 - 2*d**5/105 + d**4/14 - d**3/21 - 3*d**2. Let r(n) = 0. Calculate n.
-1, 1/4, 1/3, 1
Let y(c) be the third derivative of -5*c**2 + 1/336*c**8 - 1/60*c**6 - 1/30*c**5 + 0*c + 1/210*c**7 + 0 + 1/24*c**4 + 1/6*c**3. Factor y(x).
(x - 1)**2*(x + 1)**3
Let 