20*l**5 + w*l + 2*l**2 + 0*l**4 + 1/120*l**6 + 1/420*l**7 + 0. Factor t(k).
k**2*(k + 1)**2/2
Let y be -5*(-2)/25*10. Let f(g) be the second derivative of 0 + 25/36*g**y - 10/9*g**3 + 2/3*g**2 + 3*g. Solve f(j) = 0.
2/5
Let m be (2/(-4))/(2/(-16)). Find j, given that m*j**3 - 4*j + 0*j + 2*j**2 + 2*j**3 = 0.
-1, 0, 2/3
Let n(p) be the first derivative of -2/55*p**5 - 3 + 4/33*p**3 + 0*p**4 + 0*p**2 - 2/11*p. Factor n(m).
-2*(m - 1)**2*(m + 1)**2/11
Suppose -2*a = 5*j + 26, -2*a - j = 14 - 4. Let l be a/(-2)*(-4)/(-3). Factor -1/6*y**3 - 1/6*y**4 + 0 + 1/6*y + 1/6*y**l.
-y*(y - 1)*(y + 1)**2/6
Let j = -129/2 - -65. Solve 0 - j*t**2 + 1/2*t = 0 for t.
0, 1
Let j(w) be the third derivative of -1/105*w**5 - 5/1176*w**8 - w**2 - 4/245*w**7 + 0*w + 0*w**4 + 0*w**3 + 0 - 3/140*w**6. Let j(s) = 0. What is s?
-1, -2/5, 0
Suppose -3 = -l, -5*y - 3*l + 23 + 1 = 0. Suppose -8*f + f**2 + 9*f**y + 2*f**2 + 4 - 1 - 6*f**4 - f = 0. What is f?
-1, 1/2, 1
Let i(a) be the first derivative of a**6/12 + 2*a**5/5 + a**4/2 - a**3/3 - 5*a**2/4 - a + 12. Solve i(x) = 0.
-2, -1, 1
Let z(m) be the first derivative of 2*m**3/15 + m**2/3 + 4*m/15 + 5. Let z(s) = 0. What is s?
-1, -2/3
Let l(v) be the first derivative of 7/60*v**5 - 1/12*v**4 - 2 + 0*v + 3/2*v**2 + 0*v**3. Let f(k) be the second derivative of l(k). Find q, given that f(q) = 0.
0, 2/7
Let s = 19 + -19. Let r be 3/(-12)*s*-1. Factor 0 + r*l**2 + 2/5*l - 2/5*l**3.
-2*l*(l - 1)*(l + 1)/5
Let u = 75 + -71. Let q(v) be the first derivative of 1/12*v**3 - 1/16*v**4 + 0*v + 0*v**2 + u. Solve q(r) = 0.
0, 1
Let p(s) be the first derivative of -s**4/4 + 10*s**3/3 - 5*s**2 + 12*s + 8. Let m be p(9). Let -2/3*y**m + 2*y**2 - 4/3 + 2/3*y - 2/3*y**4 = 0. Calculate y.
-2, -1, 1
Let o(v) be the first derivative of 4*v**5/5 + 2*v**4 - 4*v**3/3 - 4*v**2 + 2. Factor o(d).
4*d*(d - 1)*(d + 1)*(d + 2)
Let m(p) be the second derivative of 3*p + 1/7*p**2 - 1/42*p**4 + 0*p**3 + 0. Find j such that m(j) = 0.
-1, 1
Let i be ((-2)/(-6))/(34/(-153)). Let j = 11/6 + i. What is p in j*p**2 + 1/3*p - 2/3 = 0?
-2, 1
Let a(k) be the first derivative of k**6/33 + 2*k**5/55 - k**4/22 - 2*k**3/33 - 8. Factor a(b).
2*b**2*(b - 1)*(b + 1)**2/11
Let f = -141 - -567/4. Determine n, given that -1/4*n**5 + f*n**4 - 3/4*n**3 + 1/4*n**2 + 0*n + 0 = 0.
0, 1
Let s(w) = w**2 - w - 1. Let m = 10 - 13. Let j(k) = 5*k**2 - 4*k - 4. Let p(z) = m*s(z) + j(z). Determine b, given that p(b) = 0.
-1/2, 1
Let y(t) be the second derivative of -t**6/90 - 3*t**5/20 - 3*t**4/4 - 3*t**3/2 + 4*t. Factor y(c).
-c*(c + 3)**3/3
Let k(h) be the third derivative of h**8/672 - h**7/168 + h**6/120 - h**5/240 - 4*h**2. Factor k(i).
i**2*(i - 1)**2*(2*i - 1)/4
Let w be (3/(-5))/(234/(-520)). Factor -3*x - w*x**2 - 2/3.
-(x + 2)*(4*x + 1)/3
Let s(l) = 3*l**3 - 4*l**2 - 15*l + 8. Let z(k) = -k**3 + k**2 + 5*k - 3. Let m(c) = -3*s(c) - 8*z(c). Find j, given that m(j) = 0.
-1, 0, 5
Let l(s) = 4*s**2 + 15*s - 30. Let x(d) = -d**2 - d + 1. Let f(t) = -3*l(t) - 15*x(t). Determine q, given that f(q) = 0.
5
Let o be (-4)/(-18) + 0/(-13). Find c such that 2/9*c**4 + 2/9*c**3 - 2/9*c**2 - o*c + 0 = 0.
-1, 0, 1
Let u(d) be the third derivative of -d**5/60 - 5*d**4/24 - 2*d**3/3 - 3*d**2. Factor u(v).
-(v + 1)*(v + 4)
Factor 0 + 0*g - 4/5*g**2 - 2/5*g**3.
-2*g**2*(g + 2)/5
Let w = 5/16 + 17/48. Determine z so that 0 + 5/3*z**3 + w*z + 7/3*z**2 = 0.
-1, -2/5, 0
Let b(m) be the third derivative of 1/60*m**4 - 2*m**2 + 0 - 2/45*m**3 - 1/450*m**5 + 0*m. Let b(p) = 0. Calculate p.
1, 2
Let t(f) be the first derivative of -1/18*f**4 + 2/27*f**3 + 1/9*f**2 + 3 + 0*f - 2/45*f**5. Factor t(x).
-2*x*(x - 1)*(x + 1)**2/9
Let v be (-4)/8*0/(-2). Let f(m) be the first derivative of 1/6*m**2 - 1 + v*m + 2/9*m**3 + 1/12*m**4. Let f(r) = 0. Calculate r.
-1, 0
Let c(v) = -v**3 + 2*v**2 + 3*v + 3. Let d be c(3). Let o = 6 - 4. Factor -1 + 5*a + a**3 + 2 + d*a**o - 2*a.
(a + 1)**3
Let j(q) = -q**2 + 32. Let s be j(0). Let m = s - 32. Solve m + 1/2*y**4 + 1/2*y**3 - 1/2*y - 1/2*y**2 = 0 for y.
-1, 0, 1
Let u = -114 + 849/7. Let b = u + -125/21. Factor b - 2/3*m**2 + 2/3*m.
-2*(m - 2)*(m + 1)/3
Let l = -127/91 - -20/13. Let s(t) be the first derivative of -2 - l*t**2 + 0*t + 2/21*t**3. Factor s(o).
2*o*(o - 1)/7
Let b(h) be the first derivative of 4*h**3/9 - 2*h**2 + 8*h/3 - 6. Factor b(z).
4*(z - 2)*(z - 1)/3
Determine p so that -4/5*p + 0*p**2 + 0 + 4/5*p**3 = 0.
-1, 0, 1
Let v(w) be the third derivative of 8*w**7/315 + w**6/10 - 2*w**5/45 - w**4/2 - 4*w**3/9 + 39*w**2. Let v(d) = 0. What is d?
-2, -1, -1/4, 1
Factor 0 - 1/10*f**4 + 1/10*f**5 + 0*f - 1/10*f**3 + 1/10*f**2.
f**2*(f - 1)**2*(f + 1)/10
Factor -7*d**3 - 4*d + 12*d**2 + 4*d**3 - 13*d + 5*d.
-3*d*(d - 2)**2
Let b be (-2)/(-11) + 848/176. Let r(g) be the second derivative of -1/6*g**3 + 1/15*g**6 + 0*g**2 + 2*g + 1/20*g**b + 0 - 1/6*g**4. Factor r(j).
j*(j - 1)*(j + 1)*(2*j + 1)
Let o(j) be the first derivative of 3 + j**2 + j - 1/5*j**5 + 0*j**3 - 1/2*j**4. Factor o(r).
-(r - 1)*(r + 1)**3
Let 3/2*w - 1/4*w**2 + 0 = 0. Calculate w.
0, 6
Solve 33 - 33 + 14*q**5 - 15*q**5 + q**3 = 0.
-1, 0, 1
Let f = -1185 + 106651/90. Let s(x) be the second derivative of 0*x**3 + 0*x**4 + 2*x + 0*x**2 - 1/189*x**7 + 0 - 2/135*x**6 - f*x**5. Let s(v) = 0. What is v?
-1, 0
Suppose -4*v - 15 = -3*s, -5*v + 3 = 4*s - 17. Let c(h) = 7*h**2 + 2*h. Let i(w) = -8*w**2 - 2*w. Let k(x) = s*i(x) + 6*c(x). Factor k(f).
2*f*(f + 1)
Let n be ((-4)/(3 - 15))/((-8)/(-72)). Factor -2/9*a - 2/9*a**n + 0 - 4/9*a**2.
-2*a*(a + 1)**2/9
Let s = 1 + 2. Let -3*d**2 + s*d**2 + 2*d**2 = 0. What is d?
0
Let p(m) be the first derivative of m**4/10 - 2*m**3/3 + 8*m**2/5 - 8*m/5 + 17. Suppose p(u) = 0. What is u?
1, 2
Suppose 0 = -2*c + 11 + 5. Factor c*p - 2*p + 3 - 1 + 4*p**2.
2*(p + 1)*(2*p + 1)
Suppose -3*u + 13 = 2*i, 2*i - 6 = 5*u - 1. Let z(w) be the first derivative of 86/3*w**3 + 8*w - 2/3*w**6 - 73/4*w**4 + 28/5*w**i - 22*w**2 - 4. Factor z(d).
-(d - 2)**3*(2*d - 1)**2
Let z = 1 - -2. Suppose -4*g = -3*h + 1, 2*g - 2*h = -3 + 1. Determine c so that c**z + 0*c**g - 2*c**2 + 2 - 2*c + c**3 = 0.
-1, 1
Let a = -406/255 - 2/255. Let n = a + 34/15. Factor n*y**2 + 8/3 - 8/3*y.
2*(y - 2)**2/3
Let g(c) be the first derivative of c**7/140 + 2*c**6/45 + 7*c**5/60 + c**4/6 + 4*c**3/3 + 5. Let v(s) be the third derivative of g(s). Factor v(o).
2*(o + 1)**2*(3*o + 2)
Let o = -10 + 13. Let w(p) be the first derivative of 3 - 2/15*p**o + 2/25*p**5 + 1/30*p**6 - 1/10*p**2 + 0*p + 0*p**4. Determine b so that w(b) = 0.
-1, 0, 1
Let c(o) be the third derivative of o**8/1344 - o**6/160 - o**5/120 + 6*o**2. Factor c(q).
q**2*(q - 2)*(q + 1)**2/4
Let y be 1040/160 - (-4)/(-1 + -1). Find c, given that -3/2*c**4 + 15/2*c - 3/2*c**3 + 3 + y*c**2 = 0.
-1, 2
Factor 3/4*c**3 + 15/4*c + 3/2 + 3*c**2.
3*(c + 1)**2*(c + 2)/4
Let c(h) be the first derivative of h**3/3 + 5*h**2/2 + 4*h - 7. Factor c(r).
(r + 1)*(r + 4)
Suppose 3*a = 6 + 3. Suppose 10 = a*x + 2*x. Let -n + 0 + 0 + 2*n**2 - n**x = 0. What is n?
0, 1
Factor -12*g + 0 + 3*g**4 + 12*g**3 - 23 + 14 + 6*g**2.
3*(g - 1)*(g + 1)**2*(g + 3)
Let k be (246/280)/(36/10). Let y = k - -1/24. Factor 2/7 + y*i**4 + 0*i + 0*i**3 - 4/7*i**2.
2*(i - 1)**2*(i + 1)**2/7
Suppose 7*w - 9*w = -4. Factor -2/7*y + 4/7*y**3 + 0*y**w + 0*y**4 + 0 - 2/7*y**5.
-2*y*(y - 1)**2*(y + 1)**2/7
Suppose 1/2*k**4 - 1/2*k**2 + 3/2*k**3 - k + 0 - 1/2*k**5 = 0. What is k?
-1, 0, 1, 2
Suppose -5*d + 4*s = -7, 3*d - 5*s = d - 4. Solve -3/2*t**2 + 0 - 3/2*t**d - 1/2*t**4 - 1/2*t = 0.
-1, 0
Factor -3*o - 32*o**2 - 12 - 147*o**3 - 12*o + 87*o - 31*o**2.
-3*(o + 1)*(7*o - 2)**2
Let f(j) be the second derivative of j**5/10 + j**4/6 - 4*j**3/3 - 4*j**2 + 8*j. Factor f(o).
2*(o - 2)*(o + 1)*(o + 2)
Let q be -4 - (19/(-7) + -2). Determine t, given that 2/7*t**2 + 0 + 0*t - t**4 - q*t**3 = 0.
-1, 0, 2/7
Let g(q) be the second derivative of q**5/20 - q**4/12 - q**3/6 + q**2/2 - 2*q. Solve g(b) = 0 for b.
-1, 1
Let u = 22 + -22. Let l(i) be the third derivative of 0*i**3 - 3*i**2 + 0*i**4 + 1/240*i**5 + 0 + u*i. Find w such that l(w) = 0.
0
Let y be (-2)/(8/38) - -4. Let d = -5 - y. Determine v, given that 11/2*v**2 + d + 15/4*v = 0.
-1/2, -2/11
Let y(b) = -b**4 - b**3 + b**2 + b + 1. Let t(x) = -8*