
0
Let i(g) be the first derivative of g**4/18 - 4*g**3/27 + g**2/9 + 30. Let i(j) = 0. Calculate j.
0, 1
Let k be (-13)/(-4) - 8/((-8)/(-3)). Factor -1/4*s**2 + 1/2*s - k.
-(s - 1)**2/4
Let d(k) be the third derivative of -k**8/448 - k**7/280 + k**6/80 + k**5/40 - k**4/32 - k**3/8 - 7*k**2. Let d(h) = 0. What is h?
-1, 1
Factor 3*x**2 - 3*x**2 - 2*x + 4*x**2 + 4*x.
2*x*(2*x + 1)
Let b(p) = 10*p + 52. Let s be b(-5). Suppose -3/7*q**3 + 0 + 3/7*q**s + 3/7*q - 3/7*q**4 = 0. Calculate q.
-1, 0, 1
Factor -10*q - 3*q**2 + q**2 - 18 + 12*q + 10*q.
-2*(q - 3)**2
Let o(j) = -j**3 - 6*j**2 - 7*j + 8. Let x be o(-6). What is k in -10*k**2 - 4 - 6 - 32*k + 2 + x*k**3 = 0?
-2/5, 1
Let b(r) = -r**2 - 14*r + 12. Let z(i) = i**2 + 14*i - 13. Let o(t) = -2*b(t) - 3*z(t). Factor o(u).
-(u - 1)*(u + 15)
Let d = 1/22 + 85/66. Suppose 0*r**3 - 2/3*r + d*r**2 + 0 - 4/3*r**4 + 2/3*r**5 = 0. Calculate r.
-1, 0, 1
Let g(k) = -1 + 76*k + k**3 - 35*k + k**2 - 40*k. Let z(r) = 10*r**3 + 4*r**2 - 4*r - 20. Let v(x) = -22*g(x) + 2*z(x). Factor v(j).
-2*(j + 1)*(j + 3)**2
Find s, given that 3/4*s**5 + 6*s**4 + 6 + 57/2*s**2 + 21*s + 75/4*s**3 = 0.
-2, -1
Let k(b) be the third derivative of -b**9/40320 - b**8/3360 - b**7/840 + b**5/20 + 4*b**2. Let u(v) be the third derivative of k(v). Factor u(p).
-3*p*(p + 2)**2/2
Let q be 52/234 + 7/9 + 2. Let 0*t**q + 4/11*t**2 - 2/11*t - 4/11*t**4 + 2/11*t**5 + 0 = 0. Calculate t.
-1, 0, 1
Let f = -208/3 - -70. Let -f*y - 4/3 + 2/3*y**2 = 0. What is y?
-1, 2
Factor -9/2*t**2 + 4*t - 1/4*t**4 - 5/4 + 2*t**3.
-(t - 5)*(t - 1)**3/4
Let j(a) = a**2 - 1. Let b(y) = -2*y + 1 + 1 + 5*y**2 + 1. Let r(k) = -b(k) - 3*j(k). Determine d, given that r(d) = 0.
0, 1/4
Let w(s) be the second derivative of s**8/5040 - s**6/1080 - s**3/6 + 3*s. Let b(u) be the second derivative of w(u). Factor b(z).
z**2*(z - 1)*(z + 1)/3
Suppose 0*j**2 - 9*j**3 + 3*j**4 - 3*j + 0*j**4 + 9*j**2 = 0. Calculate j.
0, 1
Let v(u) be the third derivative of u**5/50 - u**3/5 - 5*u**2. Factor v(i).
6*(i - 1)*(i + 1)/5
Let h(v) be the third derivative of -v**7/280 - v**6/480 + v**5/48 + v**4/96 - v**3/12 - 32*v**2. Find t such that h(t) = 0.
-1, 2/3, 1
Let w(c) = 4*c**3 + 24*c**2 - 14. Let y(z) = z**3 + 5*z**2 - 3. Suppose -3*p - 13 = -64. Let n = p - 3. Let f(m) = n*y(m) - 3*w(m). Let f(b) = 0. Calculate b.
0, 1
Factor -4*m**3 + 4*m**5 + 34*m**4 - 34*m**4.
4*m**3*(m - 1)*(m + 1)
Let -3*k**4 - 7959*k**5 - k**4 + 7949*k**5 = 0. Calculate k.
-2/5, 0
Let c(j) be the first derivative of 36*j**5/5 - 111*j**4/4 + 39*j**3 - 45*j**2/2 + 3*j - 21. Suppose c(o) = 0. What is o?
1/12, 1
Suppose 7*m - 2*m = 4*q - 33, -3*q - 5*m = 19. Let -3*n + 0*n - 4*n**q - n = 0. Calculate n.
-1, 0
Let a be ((-8)/(-16))/((-1)/(-12)). Let c(j) be the second derivative of -2*j + 0*j**2 - 1/6*j**3 + 1/4*j**4 + 1/30*j**a + 0 - 3/20*j**5. Solve c(i) = 0 for i.
0, 1
Let z(s) be the first derivative of s**4/48 + s**3/18 - 13. Solve z(u) = 0 for u.
-2, 0
Let r(i) be the second derivative of i**6/75 + i**5/50 - i**4/30 - i**3/15 - 8*i. Suppose r(o) = 0. What is o?
-1, 0, 1
Determine p so that -1/8*p - 5/8*p**2 + 3/8*p**4 + 1/4 + 1/8*p**3 = 0.
-1, 2/3, 1
Suppose 1 + 6*l - 10 + 1 - 4*l**2 + 6*l = 0. Calculate l.
1, 2
Let t = 131/2 - 65. Factor 7/4*g - g**3 + t + g**2.
-(g - 2)*(2*g + 1)**2/4
Suppose 3*n = -2*n - 135. Let i be (-2)/(-10) + n/(-45). Determine o, given that -6/5*o**2 - i*o + 0 = 0.
-2/3, 0
Let 30/11*a - 14/11*a**2 + 2/11*a**3 - 18/11 = 0. What is a?
1, 3
Suppose 3*s = 0, 3*s = 2*c + 2*s - 8. Factor -3*a**2 - 3*a**5 - 11*a**c - 3*a**4 + 3*a**3 + 17*a**4.
-3*a**2*(a - 1)**2*(a + 1)
Let s = -239/5 - -48. Let v(h) be the first derivative of -4/5*h - s*h**2 + 1/10*h**4 + 4/15*h**3 + 1. Suppose v(c) = 0. Calculate c.
-2, -1, 1
Let j be 45/39 - (-2)/(-13). Let m(w) be the first derivative of 1/24*w**6 - w**2 + 1/12*w**3 + 7/16*w**4 + j - 1/4*w**5 + w. Suppose m(y) = 0. What is y?
-1, 1, 2
Let y be (-45)/(-24) - 1/(-8). Let c be -1 - y/3 - -2. Find k, given that k**2 + 1/3*k**3 + c + k = 0.
-1
Let r(i) be the second derivative of -5*i + 0 + 0*i**2 - 1/9*i**4 - 1/9*i**3 - 1/30*i**5. What is y in r(y) = 0?
-1, 0
Let k(t) = t + 6. Suppose 6*c = 4*c - 14. Let j be k(c). Let o(r) = r**2 + 2*r + 2. Let b(g) = -g. Let w(h) = j*o(h) - 5*b(h). Factor w(x).
-(x - 2)*(x - 1)
Factor 0 - 10/9*j**2 + 8/3*j**3 - 2/3*j.
2*j*(3*j + 1)*(4*j - 3)/9
Solve -24*c**2 + 12*c**3 - 129*c**4 + 16*c - 3 + 3 + 127*c**4 = 0.
0, 2
Let s be 4/1 + 1688/(-336). Let v = -5/14 - s. Determine k so that 0*k + 2/3*k**2 - v*k**4 + 0 + 0*k**3 = 0.
-1, 0, 1
Let d(n) be the third derivative of -n**8/84 + 2*n**7/35 - n**6/15 - 2*n**5/15 + n**4/2 - 2*n**3/3 + 5*n**2. Factor d(s).
-4*(s - 1)**4*(s + 1)
Let g(r) = -3*r - 4. Let f be g(-2). Let a(q) be the first derivative of 0*q**2 - 2/35*q**5 + 2/21*q**3 + 0*q**4 - f + 0*q. Find i, given that a(i) = 0.
-1, 0, 1
Let v(y) be the first derivative of -y**4/6 - 2*y**3/9 + 1. Solve v(b) = 0 for b.
-1, 0
Let j be (-113)/840 - 3/(-21). Let f(w) be the third derivative of 0*w + 1/3*w**3 - 1/30*w**5 + 0 + w**2 - j*w**6 + 1/24*w**4. Factor f(i).
-(i - 1)*(i + 1)*(i + 2)
Let z(n) = n**3 - n**2 - n. Let u be z(2). Suppose 3*o - 95 = -u*o. Factor o*d**2 + 3*d - d**2 + d.
2*d*(9*d + 2)
Let s(v) = -2*v**2 - 9*v - 4. Let a(o) = -3*o + 5*o**2 + 20*o + 8 - 2*o**2. Let n(g) = 6*a(g) + 14*s(g). Factor n(k).
-2*(k + 2)*(5*k + 2)
Let w(x) = 2*x + 0*x - 4 + x**2 - 1. Let i(n) be the third derivative of -n**5/60 - n**4/8 + n**3 + 5*n**2. Let g(z) = -3*i(z) - 4*w(z). Factor g(k).
-(k - 2)*(k + 1)
Factor 0 + 12/7*j**2 + 24/7*j**3 + 16/7*j**4 + 2/7*j.
2*j*(2*j + 1)**3/7
Let n(f) be the third derivative of f**8/1176 + f**7/735 - f**6/210 - f**5/105 + f**4/84 + f**3/21 + f**2. Let n(t) = 0. Calculate t.
-1, 1
Let a(h) be the first derivative of h**3/6 + h**2/2 - 3*h/2 - 9. Factor a(j).
(j - 1)*(j + 3)/2
Let z = 35 - -7. Let r be (-2)/(-7)*z/48. Let 1/4*k**5 - 1/2*k**3 + 1/4*k + 1/4 - 1/2*k**2 + r*k**4 = 0. Calculate k.
-1, 1
Let t(r) be the second derivative of -r**4/42 - r**3/7 + 4*r**2/7 - 9*r. Determine o, given that t(o) = 0.
-4, 1
Let w(m) = -m**2 - 12*m - 14. Let q be w(-10). Find c, given that -11*c**4 + 3*c**3 + q*c**4 - 3*c**2 + c + 4*c**4 = 0.
0, 1
Let j = 7 + 3. Solve -9*x**3 - j*x - 5*x - 2*x + 5*x - 24*x**2 = 0.
-2, -2/3, 0
Let v(b) be the third derivative of b**6/40 - b**5/5 + 5*b**4/8 - b**3 - 22*b**2. Factor v(f).
3*(f - 2)*(f - 1)**2
Suppose -5*r = -5*i + 5, -2*r + i + 10 = 2*i. Determine d, given that -1/3*d**2 + d**4 - 2/3 - 7/3*d**r + 7/3*d = 0.
-1, 1/3, 1, 2
Suppose 0 = 2*d + 502 - 512. Factor 1/2*t**4 + 0 - 1/3*t**d - 1/6*t**2 + 0*t**3 + 0*t.
-t**2*(t - 1)**2*(2*t + 1)/6
Suppose 0 = 5*k + 2*j + 3*j + 10, -5*k - 2*j = 10. Let m = 0 - k. Factor 4*t**4 + 2*t**5 - 3*t**5 - t + 4*t**2 + 2*t - m*t - 6*t**3.
-t*(t - 1)**4
Let a(r) be the third derivative of r**8/20160 - r**7/2520 + r**5/10 - 3*r**2. Let w(o) be the third derivative of a(o). Factor w(c).
c*(c - 2)
Let o(v) be the third derivative of -7*v**6/900 + 3*v**5/100 - v**4/30 - v**3/3 - v**2. Let f(i) be the first derivative of o(i). Factor f(q).
-2*(q - 1)*(7*q - 2)/5
Let a(i) be the first derivative of 2*i**3/3 + i**2 - 4*i - 8. Suppose a(u) = 0. Calculate u.
-2, 1
Let g = 49/612 + 1/306. Let n(b) be the third derivative of 1/90*b**5 + 2/9*b**3 - g*b**4 - 2*b**2 + 0*b + 0. Let n(q) = 0. Calculate q.
1, 2
Let x(w) be the third derivative of 3*w**8/56 - 11*w**7/70 + 3*w**6/20 - w**5/20 - 5*w**2. Determine q so that x(q) = 0.
0, 1/3, 1/2, 1
Let a(h) = h**3 - 10*h**2 + 8*h + 11. Let i be a(9). Let m(y) be the first derivative of -i + 0*y + 2/5*y**5 - 1/6*y**3 + 0*y**2 - 3/8*y**4. Factor m(c).
c**2*(c - 1)*(4*c + 1)/2
Let k(q) = -16*q**3 + 10*q**2 + 18*q + 12. Let o(s) = 5*s**3 - 3*s**2 - 6*s - 4. Let p(d) = -3*k(d) - 10*o(d). Let p(c) = 0. What is c?
-1, 2
Factor 8/9*q**3 - 2/3*q**2 - 2/9*q + 0.
2*q*(q - 1)*(4*q + 1)/9
Let m(j) = 19*j**2 + j - 4. Let r(u) = 265*u**2 + 15*u - 55. Let q(i) = -55*m(i) + 4*r(i). Factor q(a).
5*a*(3*a + 1)
Let m(a) be the first derivative of 5*a**6/4 + 3*a**5/5 - 15*a**4/8 - a**3 + 19. Solve m(x) = 0.
-1, -2/5, 0, 1
Let y(v) be the second derivative of 0 + 6/5*v**5 - v**2 - 2/3*v**3 + 5*v + 11/6*v**4. Factor y(o).
2*(o + 1)*(3*o 