 r = 12 + -10. Let g(q) be the third derivative of 0*q - q**r + 1/15*q**5 + 1/60*q**6 + 0*q**3 + 0 + 1/12*q**4. Let g(a) = 0. Calculate a.
-1, 0
Determine b, given that -1/5*b**4 - 1/5*b**3 + 0*b**2 + 0 + 0*b = 0.
-1, 0
Let x be (-12)/(-32) - (-41)/(-120). Let w(o) be the second derivative of 0*o**3 - 1/36*o**4 - 1/90*o**6 + 0 - x*o**5 + 0*o**2 - o. Let w(d) = 0. What is d?
-1, 0
Let t(k) be the first derivative of -3/4*k**2 + 3*k + 4 + 3/8*k**4 + 3/10*k**5 - 3/2*k**3. Suppose t(d) = 0. Calculate d.
-2, -1, 1
Let z be (-5 - -5)*2/4. Let m(t) be the first derivative of -2 + 6/5*t**5 + 0*t**3 - 1/2*t**4 + z*t**2 - 2/3*t**6 + 0*t. Solve m(d) = 0 for d.
0, 1/2, 1
Let p be (2/10 + (-8)/40)/1. Factor 3/2*f**3 + 1/4*f + f**2 + p + 1/4*f**5 + f**4.
f*(f + 1)**4/4
Let c(d) be the second derivative of -d**5/15 + 2*d**3/9 - 7*d. Suppose c(a) = 0. What is a?
-1, 0, 1
Let a(z) = z**2 - 13*z + 9. Let x(g) = -2*g**2 + 27*g - 18. Let s(c) = 7*a(c) + 3*x(c). Let u be s(9). Factor 0 - 2/5*p**5 + 2/5*p**4 + 0*p + u*p**2 + 0*p**3.
-2*p**4*(p - 1)/5
Let v be (-16)/(-4) - 64/18. Factor -v*q**4 + 0*q + 0*q**2 + 2/9*q**5 + 2/9*q**3 + 0.
2*q**3*(q - 1)**2/9
Let g(y) be the third derivative of -1/60*y**6 + 0*y**3 + 0 + 0*y + y**2 - 1/30*y**5 - 1/315*y**7 - 1/36*y**4. Suppose g(f) = 0. Calculate f.
-1, 0
Let k be (4/(-6))/((-16)/72). Let s = k - 0. Factor 1/4*v**s - 1/4*v**2 + 0 - 1/2*v.
v*(v - 2)*(v + 1)/4
Let t(l) = 2*l - 6. Let j be t(6). Let -j*w**4 + 3*w**4 + w**4 = 0. Calculate w.
0
Suppose -24 = -2*l + 110. Let n = -199/3 + l. Factor n + 3*w**2 - 11/3*w.
(w - 1)*(9*w - 2)/3
Suppose 9 = -b + 34. Let m = b + -25. Determine p so that 2/7 - 2/7*p**2 + m*p = 0.
-1, 1
Factor -3*a**4 + 7*a**4 + a**4 - 8*a**2 + 3*a**2 + 5*a**3 - 5*a.
5*a*(a - 1)*(a + 1)**2
Let -2 + 2/3*u**2 - 4/3*u = 0. Calculate u.
-1, 3
Suppose 13 = 4*f + 1. Factor -4*z**2 - 2*z**2 + 4*z**2 - 3*z**f - z**2.
-3*z**2*(z + 1)
Let d(t) = -t**2 - 7*t - 4. Suppose -3*f = 4*j + 14, 4*f + 23 = -j - 0*j. Let c be d(f). Factor -23*p**4 + 5*p**3 + 14*p**c - 4*p + 9*p**4 - p**3.
-2*p*(p - 1)*(p + 1)*(7*p - 2)
Let d(i) = -i**2 + 12*i + 16. Let b(v) = -2*v**2 + 12*v + 16. Let g(h) = 3*b(h) - 2*d(h). Factor g(n).
-4*(n - 4)*(n + 1)
Let r be -3 + 9/(-3) + 1. Let u be (8/r)/(6/(-15)). Factor 5*b**2 - 4*b**2 + 4 - u*b + 0*b.
(b - 2)**2
Let z = -11 - -3. Let w(u) = -u**3 - 5*u**2 - 2*u + 6. Let f be w(z). Solve -38*d**4 - 8 + 40*d - f*d**3 + 6*d**2 - 60*d**4 + 74*d**3 = 0.
-1, 2/7
Let v(p) be the third derivative of 0 + 1/4*p**4 - 1/30*p**6 + 0*p - 1/35*p**7 - 1/168*p**8 + 1/3*p**3 - 4*p**2 + 1/15*p**5. Factor v(w).
-2*(w - 1)*(w + 1)**4
Let z(b) be the third derivative of 0*b + 0 - 1/3*b**3 - 1/168*b**8 - 1/12*b**4 - 1/105*b**7 + 1/30*b**6 + 1/15*b**5 + 2*b**2. Factor z(q).
-2*(q - 1)**2*(q + 1)**3
Let z = 219 + -641/3. Let b = z + -8/3. Solve 0 + 0*c - 8/3*c**2 + b*c**3 - 2/3*c**4 = 0.
0, 2
Let v(f) be the third derivative of -f**6/200 + 3*f**5/100 - f**4/20 + 2*f**2 + 10*f. Let v(y) = 0. What is y?
0, 1, 2
Let j(q) = 6*q - 15. Let x be j(7). Suppose -x*t = -24*t. Factor t + 0*s - 4*s**3 - 2/3*s**2 - 6*s**4 - 8/3*s**5.
-2*s**2*(s + 1)**2*(4*s + 1)/3
Let x(l) be the second derivative of 0*l**2 + 0 - 1/25*l**6 - 3/50*l**5 + 0*l**3 - 1/30*l**4 - 1/105*l**7 - 3*l. Factor x(q).
-2*q**2*(q + 1)**3/5
Let o(h) be the first derivative of h - 1/3*h**3 + 1 + 0*h**2. Factor o(x).
-(x - 1)*(x + 1)
Let d(c) be the second derivative of 1/20*c**5 + 2*c + 0*c**2 + 0 - 1/6*c**3 + 0*c**4. Suppose d(j) = 0. What is j?
-1, 0, 1
Let v(h) = -h**3 + 8*h**2 - 8*h + 3. Let o be v(7). Let m = 4 + o. Determine n, given that -2/7*n**5 + 0*n**4 + 0*n**2 + m + 0*n + 2/7*n**3 = 0.
-1, 0, 1
Let p(r) be the first derivative of -4*r**5/5 + 4*r**3 + 4*r**2 - 13. Solve p(y) = 0 for y.
-1, 0, 2
Let j(p) = 5*p**2 + 26*p + 41. Let c(y) = -10*y**2 - 53*y - 83. Let l(q) = -4*c(q) - 7*j(q). Factor l(r).
5*(r + 3)**2
Suppose 24 = -3*a - 0*i + i, -3*i = 0. Let m = 8 + a. Factor 1/4*x**2 + m + 1/2*x.
x*(x + 2)/4
Let t(w) = w - 1. Let u be t(0). Let y = u - -6. Factor -3*s - 3*s**3 - 5*s**2 + 4 + 2*s + y*s.
-(s - 1)*(s + 2)*(3*s + 2)
Let r(h) be the first derivative of h**8/112 - h**6/40 + 5*h**2/2 + 2. Let x(b) be the second derivative of r(b). Let x(m) = 0. Calculate m.
-1, 0, 1
Let h(q) be the first derivative of -16/3*q**2 + 1 - 14/9*q**3 - 8/3*q. Let h(x) = 0. What is x?
-2, -2/7
Let w(g) be the second derivative of g**6/45 - 4*g**5/45 + 7*g**4/54 - 2*g**3/27 + 3*g. Factor w(m).
2*m*(m - 1)**2*(3*m - 2)/9
Let g(t) be the third derivative of -t**6/120 + t**5/60 + t**4/24 - t**3/6 + 9*t**2. Suppose g(n) = 0. What is n?
-1, 1
Suppose 1 + 1/4*o**2 - o = 0. What is o?
2
Factor -85/6*v - 13/6*v**4 - 29/3*v**3 - 25/6 - 1/6*v**5 - 53/3*v**2.
-(v + 1)**3*(v + 5)**2/6
Let c(m) be the first derivative of 0*m**2 + 0*m + 1/12*m**3 + 2. Factor c(a).
a**2/4
Let c(p) be the third derivative of p**6/420 + p**5/105 - p**4/84 - 2*p**3/21 - 10*p**2. Factor c(n).
2*(n - 1)*(n + 1)*(n + 2)/7
Let t(b) be the second derivative of 25*b**7/147 - 3*b**6/7 - b**5/70 + 41*b**4/42 - 8*b**3/7 + 4*b**2/7 + 2*b. Find z such that t(z) = 0.
-1, 2/5, 1
Let x(i) be the third derivative of 6*i**2 + i**3 - 1/20*i**5 + 1/8*i**4 + 0*i + 0. Factor x(n).
-3*(n - 2)*(n + 1)
Suppose y = -4*g + 5*y + 20, -2*y - 10 = g. Factor 4/11*c**2 - 2/11*c**3 - 2/11*c + g.
-2*c*(c - 1)**2/11
Suppose 4*m - 55 = -2*i + 5*i, -2*m = i - 15. Suppose -d + m = d. Factor -2*f**4 + f**4 - 2*f**d + 4*f**5.
f**4*(2*f - 1)
Let p(g) be the first derivative of 3*g + 4*g + 3 - 4*g**3 + 5*g**3 + 5*g - 6*g**2. Find b, given that p(b) = 0.
2
Let f(d) be the second derivative of d**5/80 - d**4/16 + d**3/8 - d**2/8 - 27*d. Let f(o) = 0. What is o?
1
Suppose 0 = -4*w + 4 + 16. Suppose -j = -5*x - 6*j, -w*j = 0. Factor -g**2 + x - 1/4*g**4 + 0*g - g**3.
-g**2*(g + 2)**2/4
Let y be 4/3*9/42. Let z = 17/35 - y. Let -1/5*q**5 + z*q**3 - 1/5*q**4 + 0*q + 0 + 1/5*q**2 = 0. What is q?
-1, 0, 1
Let g(m) be the second derivative of 0 + 1/2*m**2 + 5/6*m**4 - 7*m + 5/6*m**3 + 1/6*m**6 + 1/2*m**5 + 1/42*m**7. Factor g(y).
(y + 1)**5
Let x(j) be the third derivative of -j**7/1470 - j**6/280 - j**5/210 - 7*j**2. Find c, given that x(c) = 0.
-2, -1, 0
Let c be 1/(-2)*(-6 - 2). Determine z so that 8/7*z - 8/7*z**2 + 0 - 50/7*z**3 + 50/7*z**c = 0.
-2/5, 0, 2/5, 1
Let v(k) be the first derivative of -k**6/27 + k**4/18 + 8. Factor v(n).
-2*n**3*(n - 1)*(n + 1)/9
Factor 10/9*x**2 - 10/9 - 2/9*x + 2/9*x**3.
2*(x - 1)*(x + 1)*(x + 5)/9
Let k = 762217097/710 - 1073545. Let a = k + -1/142. Determine u, given that -1/5*u + 1/5*u**3 - 1/5*u**4 + a*u**2 + 0 = 0.
-1, 0, 1
Suppose 3*l = -l. Suppose 8 + l = 4*u. Find f, given that -3*f - 1 + 3*f**u + f - 4*f**2 + 0*f**2 = 0.
-1
Let k(g) be the first derivative of -g**5/20 + g**4/12 - 2*g**2 - 2. Let p(t) be the second derivative of k(t). Factor p(d).
-d*(3*d - 2)
Let t(c) = 21*c**2 + 15*c. Let a(y) = 10*y**2 + 7*y. Let d(o) = 9*a(o) - 4*t(o). Let z(g) = 25*g**2 + 13*g. Let m(s) = 9*d(s) - 2*z(s). Factor m(w).
w*(4*w + 1)
Suppose 12/5*m + 2 + 2/5*m**2 = 0. Calculate m.
-5, -1
Suppose 0 = -7*m - 3*m + 40. Let q(l) be the second derivative of 1/36*l**m + 0*l**2 + 0 + l + 1/60*l**5 - 1/90*l**6 - 1/18*l**3. Determine n so that q(n) = 0.
-1, 0, 1
Let f(h) = -h**2 + 3*h + 5. Let b be f(4). Suppose 2*j - 3*x = -6, -5*j - 3 - b = -2*x. Factor 8/5*u**3 + j + 2/5*u + 2*u**2.
2*u*(u + 1)*(4*u + 1)/5
Let c = -26 + 28. Let f(r) be the third derivative of 0*r**4 + 0*r**6 + 1/30*r**5 - r**c - 1/210*r**7 - 1/6*r**3 + 0 + 0*r. What is g in f(g) = 0?
-1, 1
Let j(u) be the first derivative of -2*u**3/3 - 2*u**2 + 4. Find s, given that j(s) = 0.
-2, 0
Factor 3/5*a**4 - 72/5*a + 66/5*a**2 + 27/5 - 24/5*a**3.
3*(a - 3)**2*(a - 1)**2/5
Let l(w) be the second derivative of -1/8*w**3 - 2*w + 0*w**2 + 0 + 1/16*w**4. Solve l(p) = 0 for p.
0, 1
Let o = -838/3 - -293. Let j = o + -13. Determine i so that 2/3 - j*i**2 - 2/3*i**3 + 2/3*i = 0.
-1, 1
Factor 0 + 2/11*d**2 + 2/11*d.
2*d*(d + 1)/11
What is o in 0*o**3 + 0 + 4/5*o**5 + 2/5*o**2 - 6/5*o**4 + 0*o = 0?
-1/2, 0, 1
Let y = 11 - 5. Let s be ((16/y)/4)/1. Let -s*m + 2/3*m**2 + 0 = 0. Calculate m.
0, 1
Let f(v) be the first derivative of v**5/25 - v**3/5 - v**2/5 + 13. Factor f(x).
x*(x - 2