*2 - 2*t + 6*t = 0. What is t?
-2, 1
Let v(i) be the second derivative of i**8/5040 - i**6/1080 - i**3/3 - 2*i. Let a(j) be the second derivative of v(j). Suppose a(z) = 0. Calculate z.
-1, 0, 1
Let m(u) be the second derivative of u**6/50 - 3*u**5/50 - 3*u**4/20 + 2*u**3/5 + 6*u**2/5 - 16*u. Let m(w) = 0. Calculate w.
-1, 2
Let c(y) be the second derivative of 1/4*y**4 + 0 - 3/20*y**5 + 0*y**3 - 2*y + 0*y**2. Determine b, given that c(b) = 0.
0, 1
Let i(u) be the second derivative of -25*u**8/112 + 9*u**7/14 - 3*u**6/5 + u**5/5 - 3*u**2/2 + 9*u. Let x(z) be the first derivative of i(z). Factor x(m).
-3*m**2*(m - 1)*(5*m - 2)**2
Let s(i) be the first derivative of -2*i**5/45 + 2*i**3/27 - 3. Find h such that s(h) = 0.
-1, 0, 1
Suppose -8 = -4*q + 4. Let 0 - a**q + 0*a - 3/4*a**4 - 1/4*a**2 = 0. Calculate a.
-1, -1/3, 0
Let a be 2/40*5/20. Let n(o) be the second derivative of 0*o**3 + 0*o**2 + 3*o + 0*o**4 + a*o**5 + 0 + 1/60*o**6 + 1/168*o**7. Suppose n(j) = 0. What is j?
-1, 0
Factor 0 + 8/5*k**3 + 0*k + 4/5*k**4 + 4/5*k**2.
4*k**2*(k + 1)**2/5
Let r = 31/5 + -79/20. Factor 1/4*b**2 + r - 3/2*b.
(b - 3)**2/4
Let x(r) = r**2 - 5*r - 2. Let k be x(5). Let o = k + 4. Factor b**4 - 7*b - b**o + 7*b.
b**2*(b - 1)*(b + 1)
What is p in -2*p**3 - 2*p**5 - 6*p**2 - 3 - 23*p**4 + 4*p + 29*p**4 + 3 = 0?
-1, 0, 1, 2
Let f(x) = -9*x**2 - 11*x - 11. Let y(h) = -14*h**2 - 17*h - 17. Let z(o) = -8*f(o) + 5*y(o). Let k be z(-3). Factor -a - a**5 + 12*a**2 + 2*a**3 - k*a**2.
-a*(a - 1)**2*(a + 1)**2
Let k(j) = -8*j**2 - j + 14. Let x(q) = -1. Let d(v) = -k(v) - 2*x(v). Let m(s) = -4*s**2 + 6. Let c(y) = 2*d(y) + 5*m(y). Find w, given that c(w) = 0.
-1, 3/2
Let p(a) be the second derivative of a**4/90 + a**3/15 - 17*a. Factor p(s).
2*s*(s + 3)/15
Let b(c) = c - 7. Let m = 34 + -27. Let i be b(m). What is t in 0*t - 2/13*t**3 + 0*t**2 + i = 0?
0
Let y = -498 + 1495/3. Factor 1/3*g - 1/3*g**2 + y - 1/3*g**3.
-(g - 1)*(g + 1)**2/3
Suppose -c - 15 = 5*b, 4*c + 1 = -b - 2. Suppose 4*m + 3*u = c, -3*m + 13 = -2*u + u. Solve 2/9*z**m + 0*z**2 + 0 - 2/9*z = 0 for z.
-1, 0, 1
Let o(t) be the first derivative of t**3/9 + 2*t**2/3 + 6. Find y such that o(y) = 0.
-4, 0
Let l(b) be the first derivative of -b**5/5 + b**4/4 + 7*b**3/3 - b**2/2 - 6*b + 63. Find j such that l(j) = 0.
-2, -1, 1, 3
Let r(x) = 2*x**2 - 3*x + 1. Let i be r(3). Let n be -3*(i/(-3))/2. Find t such that 2*t - 2*t**4 + 0*t**4 - 4*t**3 + 2*t**n + 2*t**4 = 0.
-1, 0, 1
Suppose -10*x + 2*x + 32 = 0. Factor 0*p**x + 2/7*p + 2/7*p**5 + 0 + 0*p**2 - 4/7*p**3.
2*p*(p - 1)**2*(p + 1)**2/7
Let t(a) be the second derivative of 0*a**2 + 0 - 9/10*a**5 + 2*a**4 + 3*a - 4/3*a**3. Factor t(q).
-2*q*(3*q - 2)**2
Let w(r) be the third derivative of -r**7/420 + r**6/360 + 7*r**5/360 + r**4/72 - 3*r**2. Determine l so that w(l) = 0.
-1, -1/3, 0, 2
What is a in a + 8 + 2*a**2 + 6*a + a = 0?
-2
Let a(w) be the third derivative of -w**8/5040 + w**7/2520 + w**6/1080 - w**5/360 - w**3/3 + w**2. Let n(y) be the first derivative of a(y). Solve n(k) = 0.
-1, 0, 1
Suppose 4*m - 8 = 4*k, -2*m - 4*k - 13 = -17. Let 14/13*z + 18/13*z**m + 10/13*z**3 + 4/13 + 2/13*z**4 = 0. Calculate z.
-2, -1
Let k = 8 - 6. Factor 27 + 9*m**2 + m**k - 18*m - 7*m**2.
3*(m - 3)**2
Determine b, given that 6/5*b**2 + 0 - 2/5*b**3 - 4/5*b = 0.
0, 1, 2
Find z such that -15*z**2 + 4*z**4 + 11*z**2 - 2*z**3 + 4*z**5 - 2*z**3 = 0.
-1, 0, 1
Let t(n) be the first derivative of -n**6/840 - n**5/420 + n**4/168 + n**3/42 + 3*n**2/2 - 2. Let y(u) be the second derivative of t(u). Factor y(c).
-(c - 1)*(c + 1)**2/7
Let q be -4*-5*(-9)/(-90). Let -1/6*t**q + 1/6*t + 1/3 = 0. What is t?
-1, 2
Let l = -24652 + 122533/5. Let z = 146 + l. Factor -12/5*h**3 - z - 12/5*h - 18/5*h**2 - 3/5*h**4.
-3*(h + 1)**4/5
Let p be (-2)/9 + 20/9. Solve 3*s**4 + s**3 + 7*s**2 + 2*s**3 - 13*s**p = 0 for s.
-2, 0, 1
Suppose -8 = -2*x - 2*x. Let a be -14*(-2)/4 + x. Factor 7*w**2 + 2 + 9*w + w**5 + a*w**2 + 14*w**3 + 0 + 6*w**4.
(w + 1)**4*(w + 2)
Let f(a) be the third derivative of -a**6/60 + 7*a**5/30 - 5*a**4/4 + 3*a**3 + 2*a**2 - 50. What is u in f(u) = 0?
1, 3
Let t(x) be the second derivative of x**6/195 - x**5/130 - x**4/78 + x**3/39 + 5*x. Factor t(q).
2*q*(q - 1)**2*(q + 1)/13
Let u(k) = 29*k**2 - 17*k + 17. Let m(r) = -5*r**2 + 3*r - 3. Let f(o) = 34*m(o) + 6*u(o). Determine l, given that f(l) = 0.
0
Let w be 2 + 2*5/(-6). Let m be (1/(-6))/(1/(-4)). Let -w*p**2 - m*p - 1/3 = 0. Calculate p.
-1
Let y(s) be the third derivative of s**7/7 - 19*s**6/40 + 3*s**5/10 + 5*s**4/8 - s**3 - 6*s**2. Suppose y(i) = 0. Calculate i.
-1/2, 2/5, 1
Let p(t) be the third derivative of -t**7/105 + t**6/60 + t**5/30 - t**4/12 - 3*t**2. Solve p(c) = 0 for c.
-1, 0, 1
Let l(g) be the third derivative of g**5/105 - g**4/21 + 2*g**3/21 - 4*g**2. Factor l(b).
4*(b - 1)**2/7
Let s(b) be the second derivative of -b**6/120 + b**5/40 - b**4/48 + 11*b - 2. Factor s(j).
-j**2*(j - 1)**2/4
Let v(p) be the first derivative of p**4/48 + p**3/6 + p**2/2 - 2*p - 2. Let t(q) be the first derivative of v(q). Solve t(a) = 0.
-2
Let x(a) be the third derivative of 0 + 0*a - 1/36*a**4 + 1/60*a**6 + 2/45*a**5 + 4*a**2 - 2/9*a**3. Factor x(q).
2*(q + 1)**2*(3*q - 2)/3
Let x(b) be the third derivative of b**6/1020 + b**5/510 - b**4/102 - 3*b**2. Solve x(a) = 0 for a.
-2, 0, 1
Suppose 8 = 31*p - 27*p. Factor -1/4*x**p - 9/4 - 3/2*x.
-(x + 3)**2/4
Let d = -1169/9 - -130. Let s(k) be the third derivative of 0*k + 1/18*k**4 + d*k**3 + 1/90*k**5 + 2*k**2 + 0. Find g such that s(g) = 0.
-1
Let f(a) be the first derivative of -a**6/15 - 2*a**5/5 - a**4/2 + 2*a**3/3 + 6*a**2/5 + 33. Suppose f(b) = 0. What is b?
-3, -2, -1, 0, 1
Suppose -2*l + 26 = -5*p, l - 23 = 4*p - 4. Let x be (p/(-5))/((-2)/(-5)). Let -2*h**3 - 1 + 1 + 4*h**4 - x*h**5 = 0. Calculate h.
0, 1
Let x(a) be the first derivative of 15*a**5 - 90*a**4 + 184*a**3 - 144*a**2 + 48*a - 10. Factor x(w).
3*(w - 2)**2*(5*w - 2)**2
Let r(l) be the second derivative of -l**7/105 + l**6/150 + 7*l**5/100 - 7*l**4/60 - l**3/30 + l**2/5 - 5*l. Suppose r(g) = 0. Calculate g.
-2, -1/2, 1
Let g = -161/3 - -55. Let i(d) be the third derivative of -13/6*d**4 - g*d**3 + 0 - 3*d**2 + 0*d + 49/120*d**6 - 7/6*d**5. Solve i(w) = 0 for w.
-2/7, 2
Let q be ((-9)/6)/((-3)/6). Suppose 2*a + 12*a**2 + a**4 - 16 + 10*a**q + a**4 - 10*a = 0. What is a?
-2, 1
Determine a so that -24*a + 5*a**2 - 12*a**2 + 11*a**2 + 12 + 20 = 0.
2, 4
Let m(a) be the third derivative of -5*a**2 + 1/40*a**6 + 0 + 0*a + 0*a**5 + 0*a**4 - 1/112*a**8 + 0*a**3 + 0*a**7. Factor m(f).
-3*f**3*(f - 1)*(f + 1)
Let u(s) be the third derivative of 0*s**4 - 2/525*s**7 + 1/150*s**5 + 0*s + 0*s**3 + 3*s**2 - 1/300*s**6 + 0. Factor u(f).
-2*f**2*(f + 1)*(2*f - 1)/5
Let h be (-63)/(-18) + (-3)/(-3)*-3. Suppose -1/4 + 3/4*u - h*u**2 = 0. What is u?
1/2, 1
Let d(n) = -n**2 + 16*n. Let q be d(16). Suppose w = 3, 2*k + q*k + 3*w - 15 = 0. Let 3/2*x**k - 9/2*x - 3 + 0*x**2 = 0. What is x?
-1, 2
Let x(z) = -z**2 + 8*z - 10. Let m be x(6). Factor -1/2*a**m - 1/4 - 3/4*a.
-(a + 1)*(2*a + 1)/4
Let g(n) = n**3 + 4*n**2 + 5*n + 6. Let d be g(-3). Let h(b) be the first derivative of 3/5*b**5 - 3 - 4/3*b**3 - b**4 + 0*b + d*b**2. Factor h(i).
i**2*(i - 2)*(3*i + 2)
Let f(c) be the second derivative of 4*c**7/63 - 2*c**6/9 + 11*c**5/40 - 5*c**4/36 + c**3/36 - c. Factor f(l).
l*(l - 1)**2*(4*l - 1)**2/6
Let l(b) be the third derivative of b**7/630 + b**6/72 + 2*b**5/45 + b**4/18 + 7*b**2. Factor l(y).
y*(y + 1)*(y + 2)**2/3
Let y(l) = -l + 7. Let u be y(5). Factor -3*x - x**2 + 10 - 4 - 8*x**u.
-3*(x + 1)*(3*x - 2)
Let c(j) be the second derivative of j**9/15120 + j**8/2240 + j**7/1260 + 5*j**4/12 + 5*j. Let t(q) be the third derivative of c(q). Factor t(f).
f**2*(f + 1)*(f + 2)
Suppose 0 = -2*b - 3*b + 25. Let h(f) be the second derivative of -1/135*f**6 - 2/45*f**b - 2/27*f**4 + 0*f**3 + 0*f**2 + 0 + 2*f. Factor h(v).
-2*v**2*(v + 2)**2/9
Factor -24 + 8*c - 2/3*c**2.
-2*(c - 6)**2/3
Let l be 6/9 + (-100)/(-75). Factor 0*v - 1/3 + 1/3*v**l.
(v - 1)*(v + 1)/3
Let d be (-11)/4 + 1 + 2. Let g(c) be the second derivative of -1/6*c**3 + 0*c**2 - 3*c - 1/30*c**6 + 0 - 3/20*c**5 - d*c**4. Factor g(j).
-j*(j + 1)**3
Let f(q) be the second derivative