0 + z**4/36 - z**3/36 - 4*z. Suppose i(t) = 0. What is t?
0, 1
Let p(j) be the first derivative of -12/5*j**5 - 2*j**4 - 2/3*j**6 + 0*j**2 + 0*j**3 - 6 + 0*j. Factor p(u).
-4*u**3*(u + 1)*(u + 2)
Let n = 32 - 29. Let m = n + -3. What is g in 3/4*g**2 + m + 9/4*g = 0?
-3, 0
Let f(q) be the second derivative of q**4/12 - 5*q**3/6 + 2*q**2 - 3*q. Let v be f(4). Factor u**2 + 1/2*u + 1/2*u**3 + v.
u*(u + 1)**2/2
Factor -4*r**4 + 4*r**3 + 6*r**2 + 2*r**4 - 2*r**2 - 6*r**3.
-2*r**2*(r - 1)*(r + 2)
Determine j, given that 6*j - 4/3 + 10/3*j**3 - 8*j**2 = 0.
2/5, 1
Let y(t) be the first derivative of -t**5/80 - 3*t**4/16 - 9*t**3/8 - 27*t**2/8 + 2*t + 2. Let s(b) be the first derivative of y(b). Let s(u) = 0. What is u?
-3
Let p(r) be the first derivative of -r**4/24 - r**3/3 - 3*r**2/4 - 2. Solve p(w) = 0 for w.
-3, 0
Suppose 4 = 5*u + 34. Let y be (4/(-5))/(u/15). Factor -8/7*b + 6/7*b**y + 2/7.
2*(b - 1)*(3*b - 1)/7
Let l(n) be the second derivative of -n**6/720 + n**5/180 - n**4/144 + 2*n**2 - 6*n. Let d(y) be the first derivative of l(y). Factor d(k).
-k*(k - 1)**2/6
Suppose 2*t = -2*j + 4*t + 10, 5*t - 25 = 0. Suppose l + 44 = 5*l. Factor p**2 + j - l + 3*p - 3*p.
(p - 1)*(p + 1)
Let q(s) be the first derivative of 2*s**4/11 - 10*s**3/33 - 7*s**2/11 + 4*s/11 - 37. Factor q(r).
2*(r - 2)*(r + 1)*(4*r - 1)/11
Let p = 105 - 105. Determine n, given that p - 2/5*n + 9/5*n**4 + 13/5*n**2 - 24/5*n**3 = 0.
0, 1/3, 2
Let y(o) = o**3 + 30*o**2 + 54*o - 51. Let l be y(-28). Find g such that 3/5*g**l + 0*g + 3/5*g**3 + 0 + 6/5*g**4 + 0*g**2 = 0.
-1, 0
Let t(k) = k**2 + 1. Let o(u) = 7*u**2 + 5. Let i(s) = o(s) - 6*t(s). Factor i(c).
(c - 1)*(c + 1)
Let i be (1503/8496)/(3/226). Let u = i + 3/472. Let 34/3*b**2 - 8/3*b**3 - u*b + 8/3 = 0. Calculate b.
1/4, 2
Let t(o) = -o - 6. Let i be t(-3). Let a be (-92)/(-224) + i/24. Let 0 + 2/7*y**3 - 2/7*y**4 - a*y + 2/7*y**2 = 0. What is y?
-1, 0, 1
Suppose -9*q = 3 - 3. Let k(z) be the first derivative of 1/6*z**3 - 1 - 1/2*z - 1/4*z**4 + 1/24*z**6 + 3/8*z**2 + q*z**5. Let k(b) = 0. Calculate b.
-2, -1, 1
Let p(d) be the third derivative of -d**6/1140 + 2*d**5/285 - 5*d**4/228 + 2*d**3/57 + 9*d**2. Factor p(t).
-2*(t - 2)*(t - 1)**2/19
Suppose 6*i - 2 = 22. Suppose -10 = -4*q + 6. Factor i*k**2 + k**2 - 2*k**2 - 2*k - q*k**2 + k**3.
k*(k - 2)*(k + 1)
Let d(h) be the first derivative of 0*h**2 + 2 + 1/15*h**5 + 4/9*h**3 + 0*h - 1/3*h**4. Factor d(z).
z**2*(z - 2)**2/3
Suppose -h - 10 = -12. Factor 0*a + 0 + 1/4*a**h.
a**2/4
Suppose -2*s + s - 9 = 2*n, 3*s - 4*n - 13 = 0. Let z = 3 - s. Determine m, given that 49/3*m**z + 4/3 + 20/3*m - m**2 - 70/3*m**3 = 0.
-2/7, 1
Let n(g) = 4*g**3 + 6*g**2 - 4*g - 8. Let f(y) = -y**2. Let h(w) = 2*f(w) - n(w). Factor h(d).
-4*(d - 1)*(d + 1)*(d + 2)
Let j = 35/86 + 4/43. Let f = 17 + -33/2. Solve 1/2*c**3 + j - f*c**2 - 1/2*c = 0.
-1, 1
Let a(q) = q**2 + 15*q + 4. Suppose n = 2*k - 5, 15 = 5*n + 3*k + 105. Let l be a(n). Factor -11/3*f**3 + 2*f**l - 1/3*f**5 + 2/3*f**2 - 8/3 + 4*f.
-(f - 2)**3*(f - 1)*(f + 1)/3
Let v(y) be the first derivative of 0*y - 2 - 1/96*y**4 + 0*y**3 + 1/240*y**5 - 1/2*y**2. Let g(j) be the second derivative of v(j). Find a such that g(a) = 0.
0, 1
Let q(u) be the third derivative of u**5/20 + 3*u**4/8 - 2*u**3 - 7*u**2. Factor q(n).
3*(n - 1)*(n + 4)
Factor -12*a**2 - 24*a**2 - 8 + 30*a**3 - 4*a**4 - 10*a**3 + 28*a.
-4*(a - 2)*(a - 1)**3
Find s, given that -6*s**2 - 7/3*s - 5/3*s**3 + 2 = 0.
-3, -1, 2/5
Determine b, given that 6/7*b**3 + 2/7*b + 8/7*b**2 - 8/7*b**4 + 0 - 8/7*b**5 = 0.
-1, -1/2, 0, 1
Let w(l) be the first derivative of -l**4/20 + l**3/15 + 11. Determine u so that w(u) = 0.
0, 1
Let o(y) = 2*y + 10. Let k be o(-4). What is n in 1/3*n**k + n**3 + 0 - 2/3*n = 0?
-1, 0, 2/3
Let n be 1/((-10)/(-24)) + -2. Let g(m) be the first derivative of 1/5*m**2 + 2 + 0*m + n*m**3. Factor g(u).
2*u*(3*u + 1)/5
Let h(b) = 4*b**5 - 36*b**3 - 16*b**2 + 16*b + 16. Let w(x) = -x**5 + 7*x**3 + 3*x**2 - 3*x - 3. Let a(g) = 3*h(g) + 16*w(g). Factor a(i).
-4*i**3*(i - 1)*(i + 1)
Let p be -3*((-4)/18)/1. Let w be 7/12*(-6)/21*-4. Let w*q - p*q**2 + 0 = 0. What is q?
0, 1
Let n(l) be the second derivative of -l**4/6 - l**3 + 5*l. Solve n(q) = 0 for q.
-3, 0
Suppose 5*y + 8 - 33 = 0. Let -16*f**2 + 0*f**4 - 10*f**3 - 6*f**4 - f**y - 2 - 9*f - 4*f**3 = 0. What is f?
-2, -1
Solve -3/2*x**2 + 0 - 3*x = 0.
-2, 0
Let n = 503 - 2506/5. Factor 3/5*m**3 + 21/5*m + n + 3*m**2.
3*(m + 1)**2*(m + 3)/5
Factor -2/9*w**5 + 2/9*w**4 + 0*w - 2/9*w**2 + 2/9*w**3 + 0.
-2*w**2*(w - 1)**2*(w + 1)/9
Let n(p) = -p**5 + p**4 + 1. Let r(d) = -d**5 + 3 - 1 - d**2 - d**4 - 3*d**3 + 5*d**3 + d**3. Let x(c) = -4*n(c) + 2*r(c). Solve x(z) = 0.
0, 1
Suppose -x + 4*x - 6 = 0. Suppose -3 = -k - x*k. Determine w, given that -5 + 4*w + 3 - 6*w**2 + 4*w**3 + k - w**4 = 0.
1
Let w = 1248 - 104831/84. Let u(l) be the third derivative of 4/735*l**7 + 0*l**3 + 2/105*l**5 + 1/1176*l**8 + w*l**4 + l**2 + 1/70*l**6 + 0 + 0*l. Factor u(n).
2*n*(n + 1)**4/7
Let b(d) = -d**2 - 13*d - 12. Let f = 12 - 24. Let y be b(f). Determine c so that -1/4*c**3 + 0*c**2 + y + 1/4*c = 0.
-1, 0, 1
Let m(g) = 260*g**4 - 820*g**3 + 930*g**2 - 470*g + 70. Let p(k) = 37*k**4 - 117*k**3 + 133*k**2 - 67*k + 10. Let c(n) = -2*m(n) + 15*p(n). Factor c(v).
5*(v - 1)**3*(7*v - 2)
Let k(p) be the first derivative of -4*p**5 + 15*p**4/4 + 20*p**3/3 - 15*p**2/2 - 29. Suppose k(b) = 0. Calculate b.
-1, 0, 3/4, 1
Let y(s) = 19*s - 209. Let h be y(11). Factor 14/13*m**2 + 6/13*m + 10/13*m**3 + 2/13*m**4 + h.
2*m*(m + 1)**2*(m + 3)/13
Let s(m) be the second derivative of 3/20*m**5 + 1/50*m**6 + 0 + 9/20*m**4 + 7/10*m**3 - 5*m + 3/5*m**2. Factor s(t).
3*(t + 1)**3*(t + 2)/5
Let q(o) be the first derivative of -1/10*o**2 + 1/20*o**4 + 0*o + 6 + 0*o**3. Factor q(t).
t*(t - 1)*(t + 1)/5
Let a = -122021 - -6345411/52. Let f = a + -18/13. Factor -1 + 7/4*u**3 + f*u**2 + 2*u.
(u + 1)*(u + 2)*(7*u - 2)/4
Let u = 29 + -23. Let s be (-2)/u + (-10)/(-12). Factor s - 5/4*m - 1/4*m**3 + m**2.
-(m - 2)*(m - 1)**2/4
Let d(g) be the second derivative of -g**4/16 + g**3/2 - 3*g**2/2 - 8*g. What is u in d(u) = 0?
2
Solve -1/2*b**2 - 1 - 3/2*b = 0.
-2, -1
Suppose -4*w + 3 = -w. Let n(a) = 5*a**2 - a. Let v be n(w). Determine p so that -3*p**2 - 4*p**v + p**2 + 3*p**4 - 3*p**3 + 0*p**4 = 0.
-2, -1, 0
Suppose 5*q - 2 = 2*b, -2*q - 2*b + 7*b - 16 = 0. Suppose -q*z + 4*v + 14 = 0, 7*v + 11 = z + 3*v. Factor 1/5*k**4 + 0*k**2 + 0*k + 1/5*k**z + 0.
k**3*(k + 1)/5
Let q = -85/2 + 1021/24. Let s(b) be the third derivative of 0*b + 1/48*b**4 + 1/240*b**5 + 0 + q*b**3 - b**2. Factor s(r).
(r + 1)**2/4
Let k(d) be the first derivative of -d**4/14 + 2*d**3/21 + d**2/7 - 2*d/7 + 21. Let k(p) = 0. Calculate p.
-1, 1
Let y = 15 + -12. Let g(m) be the first derivative of -2 - 4/5*m**2 + 21/10*m**4 + 0*m - 16/15*m**y. Let g(n) = 0. Calculate n.
-2/7, 0, 2/3
Let k(b) be the first derivative of -b**4/6 - b**3/3 + 2*b**2 + 3*b - 3. Let q(d) be the first derivative of k(d). Let q(v) = 0. What is v?
-2, 1
Factor -1/7*b**2 - 3/7*b + 4/7.
-(b - 1)*(b + 4)/7
Suppose -1 - 5 = -3*o. Let c = 8 + -5. Let -2*b + b - 3*b**c + 2*b**o + 2*b**3 = 0. What is b?
0, 1
Factor 5/4*x**2 + 1/2*x + 1/4*x**4 + 0 + x**3.
x*(x + 1)**2*(x + 2)/4
Let s(t) be the first derivative of -t**4/8 - t**3/2 + 2*t - 3. Solve s(r) = 0.
-2, 1
Let z(y) be the third derivative of 0*y**3 + 1/120*y**5 + 2*y**2 - 7/720*y**6 + 0*y**4 + 0*y + 0. Factor z(b).
-b**2*(7*b - 3)/6
Let q(a) be the first derivative of a**8/168 + a**7/35 + a**6/30 - a**5/15 - a**4/4 - a**3/3 + a**2 - 1. Let z(b) be the second derivative of q(b). Factor z(m).
2*(m - 1)*(m + 1)**4
Let n(h) be the first derivative of h**4/78 + 2*h**3/39 - 3*h**2/13 - 10*h - 6. Let p(a) be the first derivative of n(a). Factor p(b).
2*(b - 1)*(b + 3)/13
Let c(r) be the third derivative of -1/60*r**6 + 1/4*r**4 - 3*r**2 + 0 - 2/3*r**3 + 0*r + 0*r**5. Factor c(n).
-2*(n - 1)**2*(n + 2)
Let j(m) = -m**2 + 9*m - 8. Let n be j(8). Suppose n*c + c = -l + 4, -8 = -3*l + c. Factor 7/2*w**2 + 1/2 + 5/2*w + 3/2*w**l.
(w + 1)**2*(3*w + 1)/2
Let 0*w**3 - 3/7*w**2 + 0*w + 0 + 3/7*w**4 = 0. What is w?
-1, 0, 1
Determine p, given that 2*p**3 + 6*p - 6*p**5 + 3 - 6*p**3 + 4*p**2 - 1 - 