f -4/27*q**3 + 0 - 1/27*q**4 + 0*q - 1/270*q**w - q**2. Factor h(i).
-2*(i + 2)**2/9
Factor -6*v**3 - 3*v**3 - v**4 - 4*v**2 - 3*v**4 + 3*v**3 - v**5 - v.
-v*(v + 1)**4
Let c(z) be the second derivative of z**5/140 - 3*z**4/28 + 9*z**3/14 - 4*z**2 - 3*z. Let p(s) be the first derivative of c(s). Find o such that p(o) = 0.
3
Let m(p) be the first derivative of p**4 - 4*p**3 + 6*p**2 - 4*p + 5. What is o in m(o) = 0?
1
Let b = 2 + 0. What is y in 2/11*y**5 + 0*y + 0 + 2/11*y**3 + 0*y**b + 4/11*y**4 = 0?
-1, 0
Factor -6/11*j - 2/11*j**3 + 0 + 8/11*j**2.
-2*j*(j - 3)*(j - 1)/11
Suppose 0 = -3*u + 26 - 62. Let v be 2/12 - (-2)/u. Factor v - 3/4*t**3 - 1/4*t + 1/4*t**4 + 3/4*t**2.
t*(t - 1)**3/4
Let p be (-2)/30 - (-66)/90. Find k, given that k - p - 1/3*k**2 = 0.
1, 2
Let j(k) = -25*k**2 + 29*k - 4. Suppose 0*d = -2*d. Suppose q + 4*q + 20 = d. Let x(c) = -12*c**2 + 14*c - 2. Let p(m) = q*j(m) + 9*x(m). Solve p(t) = 0 for t.
1/4, 1
Suppose -8*a = c - 3*a - 32, -5*a = -20. Let k = c + -7. Suppose -k + 0*d**3 + d + 4 + d**2 - d**3 = 0. Calculate d.
-1, 1
Let z(q) = 3*q + 1. Let r be z(1). Factor -r*p - 3*p**5 - 4*p**3 + 6*p + 5*p**5.
2*p*(p - 1)**2*(p + 1)**2
Let z(b) be the third derivative of b**8/20160 - b**6/720 + b**5/10 - 4*b**2. Let p(a) be the third derivative of z(a). Factor p(g).
(g - 1)*(g + 1)
Factor 8*a**2 + 1/2*a**5 + 7*a**3 + 3*a**4 + 1 + 9/2*a.
(a + 1)**4*(a + 2)/2
Let f(c) be the first derivative of -3*c**5/20 + c**4/2 - c**3/2 - 2*c + 3. Let r(j) be the first derivative of f(j). Suppose r(d) = 0. Calculate d.
0, 1
Let f(k) = -k**2 - 4*k - 1. Let h be f(-3). Suppose -3*i**2 - i**h - 17*i**3 - 2*i + 15*i**3 = 0. What is i?
-1, 0
Let t(k) be the first derivative of -2*k**5/45 - k**4/3 - 2*k**3/3 - 4*k**2/9 + 2. Suppose t(h) = 0. Calculate h.
-4, -1, 0
Let a(n) be the second derivative of -n**5/5 - 5*n**4/3 + 2*n**3/3 + 10*n**2 - 16*n. Factor a(b).
-4*(b - 1)*(b + 1)*(b + 5)
Suppose -2*q - 2*v = -14, -2*q = 3*v - 7*v + 4. Suppose -4*j**q + j**2 - 2*j**2 - 3*j**3 - 2*j**2 + 10*j**4 = 0. What is j?
-1/2, 0, 1
Let r(s) be the third derivative of 1/40*s**5 + 0*s - s**3 - 4*s**2 + 0*s**4 + 0. Factor r(v).
3*(v - 2)*(v + 2)/2
Let i = 8 - 15/2. Factor 1/3*l**4 - 1/6*l**2 + 1/2*l**3 - 1/6 - i*l.
(l - 1)*(l + 1)**2*(2*l + 1)/6
Let x(o) be the second derivative of o**4/15 - 2*o**3/15 - 4*o**2/5 + 15*o. Factor x(y).
4*(y - 2)*(y + 1)/5
Let p(c) be the second derivative of -3*c**5/80 - c**4/8 + c**3/2 + 3*c**2 - 5*c. Factor p(a).
-3*(a - 2)*(a + 2)**2/4
What is v in 27 + v**3 - 73*v + 19*v + 36*v**2 + v**4 - 7*v**3 - 4*v**3 = 0?
1, 3
Let y(o) be the first derivative of 1/42*o**4 + 0*o**2 - 2 - 3/70*o**5 - o + 2/21*o**3. Let j(d) be the first derivative of y(d). Solve j(m) = 0 for m.
-2/3, 0, 1
Let f(a) be the second derivative of -5*a**4/4 + 5*a**3/6 + 5*a**2 - 6*a. Let f(g) = 0. Calculate g.
-2/3, 1
Let k(j) = -11*j**2 - 46*j - 80. Let g(p) = -p**2 - p. Let i(y) = -6*g(y) + k(y). Factor i(l).
-5*(l + 4)**2
Let j(p) be the first derivative of 1/2*p**4 + 2*p**3 - 2 + 0*p**2 - 8*p. Suppose j(h) = 0. Calculate h.
-2, 1
Let d = -12 + 14. Suppose -2*r**d + r**2 - 2*r + 0*r + 4 - r**2 = 0. What is r?
-2, 1
Let w(f) = 7*f**5 + 3*f**3 - 5*f**2 - 5*f + 5. Let q(g) = 3*g**5 + g**3 - 2*g**2 - 2*g + 2. Let b(r) = -5*q(r) + 2*w(r). Factor b(x).
-x**3*(x - 1)*(x + 1)
Let x(d) = 3*d - 15. Let t be x(5). Factor t + 1/3*k**2 + 0*k.
k**2/3
Factor 0*k - 1/2*k**2 + 0 - 1/2*k**3.
-k**2*(k + 1)/2
Let s be 3/(-8)*(-1 + -7). Let v(g) be the first derivative of 0*g - g**2 + 1/2*g**4 + 0*g**s - 2. Factor v(d).
2*d*(d - 1)*(d + 1)
Suppose 0 - 8 = -4*w. Let l(z) be the first derivative of 0*z - 1/2*z**w + 7/8*z**4 + 5/6*z**3 + 2. Factor l(s).
s*(s + 1)*(7*s - 2)/2
Let p(h) be the second derivative of -h**7/147 + h**6/105 + h**5/70 - h**4/42 + 15*h. Factor p(g).
-2*g**2*(g - 1)**2*(g + 1)/7
Suppose 0 = 3*y - 3 - 3. Suppose 0 = 3*h + y*l - 1 - 13, h + l = 5. Factor -1/5*c**5 + 2/5*c**h + 1/5*c + 0 - 2/5*c**2 + 0*c**3.
-c*(c - 1)**3*(c + 1)/5
Let j(l) be the first derivative of 4*l**3/21 + 2*l**2/7 + 12. Suppose j(q) = 0. Calculate q.
-1, 0
Let i(a) be the third derivative of -a**8/504 - 2*a**7/315 + a**5/45 + a**4/36 + 8*a**2. Determine f so that i(f) = 0.
-1, 0, 1
Let o(c) be the second derivative of -4*c**7/21 + 7*c**6/15 + c**5/5 - 4*c**4/3 + 2*c**3/3 + c**2 - 12*c. Suppose o(x) = 0. What is x?
-1, -1/4, 1
Suppose 1/4*c + 1/2 - 1/4*c**2 = 0. Calculate c.
-1, 2
Let m(a) be the second derivative of a**6/45 + a**5/15 + a**4/18 - 18*a. Factor m(t).
2*t**2*(t + 1)**2/3
Factor 6/7*x + 4/7 + 2/7*x**2.
2*(x + 1)*(x + 2)/7
Suppose 0 = 2*i - 4, 4*d - 4*i = -2*i + 4. Factor 0 - 1/4*l**d - 1/2*l.
-l*(l + 2)/4
Let a be 8/(-110)*(0 - -2 - 7). Let g = 2 + 0. Let 2/11*d**4 - a*d**3 + 8/11*d + 8/11 - 6/11*d**g = 0. Calculate d.
-1, 2
Let r = 21 - 17. Factor 0*u**r + 5*u**4 + u**4 - 2*u**4.
4*u**4
Let y(d) be the second derivative of d**6/330 - 3*d**5/220 - d**4/132 + d**3/22 - 16*d. What is i in y(i) = 0?
-1, 0, 1, 3
Let a(n) be the third derivative of n**11/83160 + n**10/25200 - n**8/10080 - n**5/30 - 2*n**2. Let o(y) be the third derivative of a(y). What is b in o(b) = 0?
-1, 0, 1/2
Let l(x) be the third derivative of -x**8/140 - 3*x**7/350 + x**6/40 + 3*x**5/100 - x**4/40 + 2*x**2. Suppose l(o) = 0. What is o?
-1, 0, 1/4, 1
Suppose -13*b = b - 42. Let o = 109 - 543/5. Factor -o*m**b + 2/5*m + 7/5*m**4 - 7/5*m**2 + 0.
m*(m - 1)*(m + 1)*(7*m - 2)/5
Let c be 42/15 - (-3)/15. Factor 8*i**3 + 6*i**2 + 2 - 4*i + 16*i**c - 28*i**3 + i**4 - 1.
(i - 1)**4
Let l(o) be the second derivative of -1/2*o**3 + 0 - 1/2*o**4 + 0*o**2 - 3/20*o**5 - 4*o. Factor l(z).
-3*z*(z + 1)**2
Suppose 4*o = -o + 35. Factor -o*g**5 - 4*g**3 - 9*g + 16*g**3 - 6 + 6*g**2 + 4*g**5.
-3*(g - 2)*(g - 1)*(g + 1)**3
Suppose -10*s + 97 = 57. Let a = 6 + -4. Factor 0 - 2/3*y**s - a*y**3 - 2*y**2 - 2/3*y.
-2*y*(y + 1)**3/3
Let v(a) be the first derivative of 2/5*a**3 + 4/5*a - 2/5*a**5 - 1 + 7/10*a**4 - 7/5*a**2. Find x, given that v(x) = 0.
-1, 2/5, 1
Factor 5*c - 4*c**3 + 5*c**2 + 5*c**2 - c - 8 - 2*c**2.
-4*(c - 2)*(c - 1)*(c + 1)
Let s(p) be the third derivative of p**8/3360 + p**4/12 - 2*p**2. Let j(w) be the second derivative of s(w). Determine b so that j(b) = 0.
0
Let t(j) be the first derivative of -j**4/12 - j**3/3 - 4*j - 3. Let h(n) be the first derivative of t(n). Find a such that h(a) = 0.
-2, 0
Let o(z) be the first derivative of -z**3/6 + 3*z**2/4 + 3. Let o(l) = 0. What is l?
0, 3
Let y(t) = t - 6. Let k = 29 - 21. Let i be y(k). Let 2*x**2 - 3*x**i - 2*x + x = 0. Calculate x.
-1, 0
Suppose 2*p = -8, -5*p - 13 = -4*x + 23. Let y be (0 + -1)/(2/(-6)). Let 1/2*w**y + 0*w**2 - 1/2*w**x + 0*w + 0 = 0. Calculate w.
0, 1
Let m = -3/470 + 119/235. Find t such that 0 - m*t - 1/4*t**3 - 3/4*t**2 = 0.
-2, -1, 0
Let b(c) = 5*c - 48. Let n be b(10). Let o(u) = -u**3 + 3*u**2 - 3*u + 2. Let s be o(2). Factor s - 1/2*j**n - 1/2*j.
-j*(j + 1)/2
Factor 16/11*g + 2/11*g**2 + 32/11.
2*(g + 4)**2/11
Let q(w) be the second derivative of -4*w + 0 + 1/18*w**4 - 1/15*w**5 + 1/45*w**6 + 0*w**3 + 0*w**2. Factor q(s).
2*s**2*(s - 1)**2/3
Let z(s) = s + 0*s**2 + 1 + 0 + 7*s**2. Let x be z(-1). Let 0*k**4 + 2*k**4 - 6*k**5 - x*k**4 + 3*k**4 = 0. Calculate k.
-1/3, 0
Let j be (-4)/(-2) + -1 + 4/1. Let 3/2*d**j + 5/2*d**2 - d - 1/2*d**3 - 5/2*d**4 + 0 = 0. Calculate d.
-1, 0, 2/3, 1
Let f(o) be the second derivative of o**4/8 - o**3/4 - 9*o**2/2 + 9*o. Suppose f(w) = 0. Calculate w.
-2, 3
Let v(b) be the second derivative of -b**6/2 - b**5/2 + 3*b. Factor v(z).
-5*z**3*(3*z + 2)
Suppose 8*a = 12*a. Let v(r) be the second derivative of 0 - 3/110*r**5 + 1/66*r**4 + a*r**2 - 1/231*r**7 + 0*r**3 + 1/55*r**6 - 3*r. Let v(z) = 0. Calculate z.
0, 1
Let n(r) be the third derivative of r**8/11200 + r**7/3150 + r**6/3600 - r**4/24 + 6*r**2. Let s(b) be the second derivative of n(b). Factor s(m).
m*(m + 1)*(3*m + 1)/5
Let d = -943802/35 - -26964. Let y = d - -18/7. What is n in -y*n - 2/5 - 2/5*n**2 = 0?
-1
Suppose b + 25 = 6*b. Suppose b = -u, 0*q + 4*q = 3*u + 15. Suppose -4*n**3 + q*n**3 - 2*n**4 + 2*n**3 = 0. What is n?
-1, 0
Suppose -3*b**5 - 6*b**4 + 6*b**2 + 3*b**3 + 569*b - 569*b = 0. Calculate b.
-2, -1, 0, 1
Let d be (-3)/((-27)/24) - 2. L