m**3 + 0*m**2 + 0 - o*m - 1/45*m**5 - 1/54*m**4. Factor n(a).
-2*a*(a + 1)*(2*a - 1)/9
Let r(l) be the first derivative of 2*l**3/3 - 10*l**2 + 50*l + 22. Let r(g) = 0. What is g?
5
Suppose 2*z - 19 = 3*z + a, 5*z + 103 = 3*a. Let y be 8/z + 28/45. Suppose 0*l + 0 - 2/9*l**4 - 4/9*l**3 - y*l**2 = 0. What is l?
-1, 0
Let w = 6 - 4. Suppose -14*n**5 - 13*n**2 - 6*n**3 + 5*n**4 + 9*n**w + 19*n**4 = 0. What is n?
-2/7, 0, 1
Let a(u) be the third derivative of -u**5/150 + 4*u**3/15 - 14*u**2. What is x in a(x) = 0?
-2, 2
Solve 0 + 1/2*t - 1/2*t**2 = 0.
0, 1
Let v(w) = w**3 + 11*w**2 - 28*w - 26. Let m be v(-13). Determine q so that m + 0*q - 1/2*q**3 - 1/4*q**2 - 1/4*q**4 = 0.
-1, 0
Factor 4*k + 0 + 12*k**2 + 0 + 13*k**3 - 8*k**3.
k*(k + 2)*(5*k + 2)
Factor 9/2 + 3/2*o**2 - 6*o.
3*(o - 3)*(o - 1)/2
Let n(v) be the second derivative of -1/9*v**3 + 0*v**2 + 0 - 2*v + 1/36*v**4. Factor n(l).
l*(l - 2)/3
Let h be 2*((-4)/6 - (-140)/192). Let f(w) be the first derivative of 1/16*w**4 - h*w**2 + 1/12*w**3 - 1 - 1/4*w. Factor f(p).
(p - 1)*(p + 1)**2/4
Let k(u) = u - 14. Let w be k(16). Let j(a) be the first derivative of -2*a - w - 3*a**3 + 11/2*a**2. Solve j(n) = 0.
2/9, 1
Let b = -2 - -11. Suppose -3*r + 0 + b = 0. Factor -1/2*f**r + 0 - 1/4*f**4 - 1/4*f**2 + 0*f.
-f**2*(f + 1)**2/4
Suppose -3*u = 3 - 9. Let i(t) be the third derivative of 0*t + 0*t**3 + 0 + 1/120*t**5 + 0*t**4 - u*t**2. Determine p so that i(p) = 0.
0
Let k(y) = -y**3 + y**2 + y + 1. Let u(w) = 20*w**3 - 15*w - 15. Let m(s) = -15*k(s) - u(s). Factor m(b).
-5*b**2*(b + 3)
Suppose 0 = 5*t + r + 4, 0*t - 16 = t + 4*r. Suppose 0 - 3/4*p + 3/2*p**3 + t*p**4 - 3/4*p**5 + 0*p**2 = 0. What is p?
-1, 0, 1
Let -4*k**2 - 4 + 2/3*k**3 + 22/3*k = 0. Calculate k.
1, 2, 3
Find k, given that 1 - 6*k + 12*k**2 - 1 - 15*k**2 = 0.
-2, 0
Let t(w) be the first derivative of w**3/3 - 5*w**2/2 - 6*w - 3. Factor t(g).
(g - 6)*(g + 1)
Let u(h) be the third derivative of h**9/4032 - h**7/560 + h**5/160 - h**3/6 - 4*h**2. Let c(r) be the first derivative of u(r). Let c(a) = 0. Calculate a.
-1, 0, 1
Let l(w) be the second derivative of -w**5/30 - w**4/12 - w**2 - w. Let o(b) be the first derivative of l(b). Factor o(f).
-2*f*(f + 1)
Let b = -8 + 13. Let u(g) = -g**3 + 5*g**2 + 4. Let m be u(b). Factor -2*k**m + k**3 - k + 1 + k**4 - 1 + k**2.
-k*(k - 1)**2*(k + 1)
Factor -1/4*h**2 + 1/4 + 1/4*h**3 - 1/4*h.
(h - 1)**2*(h + 1)/4
Suppose -v = 9 - 4. Let s = v + 8. What is l in 2/11*l**s + 4/11*l**2 + 0*l - 2/11*l**4 + 0 = 0?
-1, 0, 2
Suppose z = -3*g + 10, -20 = -0*z - 2*z + 3*g. Let l = z + -8. Factor -2/7 - 4/7*t + 6/7*t**l.
2*(t - 1)*(3*t + 1)/7
Let w be 14/40 - 8/(-20). Factor 15/4*j - 3*j**2 - w.
-3*(j - 1)*(4*j - 1)/4
Find m such that 15*m + 10*m - m - 4*m**2 + 8*m - 64 = 0.
4
Factor 0 + 1/9*i**2 + 0*i + 1/9*i**3.
i**2*(i + 1)/9
Let d(r) be the third derivative of r**10/680400 + r**9/90720 - r**7/5670 - r**5/30 - r**2. Let h(a) be the third derivative of d(a). Factor h(x).
2*x*(x - 1)*(x + 2)**2/9
Suppose 0 = -5*p, -3*s = -s - 5*p. Factor s*b**3 - 1/4*b - 1/2*b**2 + 1/4*b**5 + 0 + 1/2*b**4.
b*(b - 1)*(b + 1)**3/4
Let q(x) be the first derivative of x**5/5 + 5*x**4/4 + 8*x**3/3 + 2*x**2 - 17. Solve q(h) = 0 for h.
-2, -1, 0
Let q(u) be the first derivative of -3*u**5/5 - 21*u**4/4 - 18*u**3 - 30*u**2 - 24*u - 9. Factor q(l).
-3*(l + 1)*(l + 2)**3
Let i be (-2)/(-6) - 49/(-105). Let p(n) be the first derivative of 2/15*n**3 - 2/5*n + 1 - i*n**2 + 2/5*n**4. Factor p(s).
2*(s - 1)*(s + 1)*(4*s + 1)/5
Let k(t) = t**2 + 3*t - 1. Let a be k(-4). Suppose -a*y = y + l - 6, 4 = -3*y - 5*l. Factor 1/3*u**y + 0 - 1/3*u.
u*(u - 1)/3
Suppose 184 = -0*j - 2*j. Let c = j - -646/7. Factor 4/7*t + 2/7*t**2 + c.
2*(t + 1)**2/7
Let g = 19 + -15. Suppose 0*w = -g*w + 8. What is f in -f**w - 3/2*f**3 + 0*f + 0 = 0?
-2/3, 0
Let d(k) be the first derivative of -7*k**3/3 + 2*k**2 + 3*k - 10. Factor d(s).
-(s - 1)*(7*s + 3)
Factor 13*m**2 + 6*m**3 - 6*m**2 - 7*m**2 - 2*m**4.
-2*m**3*(m - 3)
Let f(s) be the second derivative of s**7/42 - 17*s**6/90 + 17*s**5/30 - 7*s**4/9 + 4*s**3/9 - 15*s. Solve f(m) = 0.
0, 2/3, 1, 2
Let n(p) = -p**3 - 9*p**2 - p - 7. Suppose 3*s = -3*t - 12, 2*s + 0 - 2 = -4*t. Let b be n(s). Factor 0 + y**b - 1/3*y.
y*(3*y - 1)/3
What is o in 15*o**3 + 49*o**3 + 1 - 1 + 44*o**2 + 8*o + 28*o**4 = 0?
-1, -2/7, 0
Let w(b) be the first derivative of b**5/420 - b**4/42 + 2*b**3/21 - 3*b**2/2 + 5. Let n(o) be the second derivative of w(o). Let n(q) = 0. What is q?
2
Let a(x) be the third derivative of x**9/68040 - x**7/11340 + x**4/4 + 6*x**2. Let f(k) be the second derivative of a(k). Factor f(h).
2*h**2*(h - 1)*(h + 1)/9
Suppose -4 = -v + b - 6*b, 2*v + b = 8. Determine w, given that 0*w**2 - 2*w**3 + 11*w**5 - 13*w**3 + 6*w**2 - 6*w**4 + v*w**5 = 0.
-1, 0, 2/5, 1
Let q(o) be the third derivative of o**7/105 + o**6/20 - 3*o**5/10 + 5*o**4/12 - 50*o**2. Let q(y) = 0. Calculate y.
-5, 0, 1
Let z(p) = -p**2 - 5*p + 8. Suppose 4*j - u = 7*j + 22, -4*j = 2*u + 32. Let h be z(j). Factor -3*l**2 + 5*l**h - 3 + 1.
2*(l - 1)*(l + 1)
Let l(j) = j**4 + j**3 + j**2. Let o(b) = -6*b**4 - 8*b**3 - 8*b**2 - b. Let c(d) = 5*l(d) + o(d). Solve c(m) = 0.
-1, 0
Let g(n) = -40*n - 78. Let x be g(-2). What is h in 4/5*h**4 + 0 - 1/5*h + 6/5*h**x - 9/5*h**3 = 0?
0, 1/4, 1
Let v(y) be the first derivative of -y**5/80 + y**4/32 + y**3/4 - 3*y**2 + 3. Let n(c) be the second derivative of v(c). Factor n(m).
-3*(m - 2)*(m + 1)/4
Let c = -3 - -4. Let n be (-16)/24*(-1)/c. Factor -10/3*w**3 - n*w**4 - 4/3 - 14/3*w - 6*w**2.
-2*(w + 1)**3*(w + 2)/3
Let r(q) be the first derivative of q**6/3 + q**5/5 - q**4/2 - q**3/3 + 38. Find y such that r(y) = 0.
-1, -1/2, 0, 1
Suppose -2 + 2/3*p + 2*p**2 - 2/3*p**3 = 0. Calculate p.
-1, 1, 3
Let y(d) be the first derivative of -35*d**4/4 - 25*d**3/3 + 40*d**2 - 20*d - 17. Suppose y(t) = 0. What is t?
-2, 2/7, 1
What is g in -500/3*g**2 + 0*g - 100*g**3 - 4/3*g**5 - 20*g**4 + 0 = 0?
-5, 0
Suppose 7 = 5*z - 18. Let v = -3 + z. Factor 4*f + f**2 - v - f + 4.
(f + 1)*(f + 2)
Let v(r) be the first derivative of -2*r**3/3 + 6*r**2 - 18*r + 5. What is y in v(y) = 0?
3
Let u(m) be the third derivative of m**8/210 + 2*m**7/105 - m**6/60 - m**5/12 + m**4/6 + m**3/3 - 3*m**2. Let n(r) be the first derivative of u(r). Factor n(t).
2*(t + 1)*(t + 2)*(2*t - 1)**2
Let j(a) be the third derivative of -2*a**2 + 0*a + 1/10*a**5 - 1/12*a**4 - 2/3*a**3 + 0. Determine f, given that j(f) = 0.
-2/3, 1
Let y be (-3)/9 + 23/33. Let u(j) be the first derivative of -y*j - 2 + 1/22*j**4 + 0*j**3 - 3/11*j**2. Factor u(l).
2*(l - 2)*(l + 1)**2/11
Let z(f) = 2*f**3 - f**2. Let h = -8 - -11. Let j(c) = -c**h + 3*c**3 + 2*c**3 - 3*c**2. Let w(v) = -2*j(v) + 5*z(v). Determine d, given that w(d) = 0.
-1/2, 0
Let j(a) be the second derivative of 0 - 1/5*a**2 + 6*a + 2/15*a**3 - 1/30*a**4. Suppose j(k) = 0. Calculate k.
1
Let i(u) be the second derivative of u**8/1512 - u**7/945 + 3*u**2/2 + 2*u. Let y(q) be the first derivative of i(q). Solve y(p) = 0 for p.
0, 1
Let z(y) be the first derivative of -y**5 + 5*y**3/3 + 9. Suppose z(n) = 0. What is n?
-1, 0, 1
Let n(z) be the first derivative of 1/6*z**4 - 6*z + z**2 - 6 + 10/9*z**3. Solve n(m) = 0 for m.
-3, 1
Let k(m) be the second derivative of 1/6*m**2 - 1/18*m**3 + 1/60*m**5 - 1/36*m**4 + 2*m + 0. Factor k(w).
(w - 1)**2*(w + 1)/3
Let t(r) = -r**2. Let x(l) = l**2 + 7*l + 1. Let a(v) = -v. Let q(o) = -2*a(o) - x(o). Let n(h) = -q(h) - 3*t(h). Factor n(y).
(y + 1)*(4*y + 1)
Suppose -5 = 2*s - 5. Let b(q) be the third derivative of 1/12*q**6 - 2*q**2 + q**4 + 3/5*q**5 + s - 8/3*q**3 + 0*q. Factor b(r).
2*(r + 2)**2*(5*r - 2)
Let m(p) be the first derivative of -4/7*p - 5/7*p**4 + 1/7*p**2 + 22/21*p**3 + 3. Let m(c) = 0. Calculate c.
-2/5, 1/2, 1
Determine h, given that 0 - 1/9*h**3 + 2/9*h**2 + 0*h = 0.
0, 2
Suppose -72 = -j - 2*j. Suppose -3*y = -y - j. Suppose -y*m**2 + m**3 + 11 + 15*m - 17 - 2*m**3 + 4*m**3 = 0. Calculate m.
1, 2
Let k = 9 + -6. Solve 2/9*h**k + 4/9*h**2 + 0 + 2/9*h = 0.
-1, 0
Determine p, given that -6/7*p**2 + 4/7*p + 2/7*p**4 + 0*p**3 + 0 = 0.
-2, 0, 1
Let z = -191 + 191. Let f(w) be the first derivative of z*w - 3/20*w**5 - 3/8*w**2 + 3 - 9/16*w**4 - 3/4*w**3. Suppos