) be the second derivative of s(j). Let r(d) = 0. What is d?
-1, 1
Let x(u) = -65*u**3 - 185*u**2 - 180*u. Let z(m) = 11*m**3 + 31*m**2 + 30*m. Let n(a) = 6*x(a) + 35*z(a). Solve n(i) = 0 for i.
-3, -2, 0
Let g(q) be the second derivative of 2*q**6/15 - 2*q**4/3 + 2*q**2 - 8*q. Find a such that g(a) = 0.
-1, 1
Let m be 4/(-10) - (8 + (-336)/40). Suppose m*b**3 + 0 - 1/2*b**2 - 1/4*b + 1/2*b**4 + 1/4*b**5 = 0. What is b?
-1, 0, 1
Let t(u) be the first derivative of 49*u**4/26 - 350*u**3/39 + 88*u**2/13 - 24*u/13 + 6. Let t(k) = 0. Calculate k.
2/7, 3
Factor 2/3*f**4 - 1/6*f**5 + 1/3*f**2 - 5/6*f**3 + 0 + 0*f.
-f**2*(f - 2)*(f - 1)**2/6
Factor 0*u + 1/4*u**5 + 0*u**2 - 1/4*u**4 - 1/2*u**3 + 0.
u**3*(u - 2)*(u + 1)/4
Suppose 59/4*t**2 - 5/2*t**3 - 45/2*t + 1/8*t**4 + 81/8 = 0. Calculate t.
1, 9
Factor 3*j + 2*j**3 + 1/2*j**4 - 11/2*j**2 + 0.
j*(j - 1)**2*(j + 6)/2
Let m(h) be the second derivative of -h**6/15 - h**5/20 + h**4/6 + h**3/6 - h. Factor m(x).
-x*(x - 1)*(x + 1)*(2*x + 1)
Let a = -13 - -13. Let z(f) be the second derivative of -1/24*f**4 + f - 1/12*f**3 + 0 + a*f**2. Let z(w) = 0. Calculate w.
-1, 0
Suppose -16*r - 6 = -19*r. Suppose -r*n**4 + 4/9*n**3 + 0*n + 0 + 0*n**2 = 0. What is n?
0, 2/9
Factor 0 + 2/15*f**4 - 2/15*f**2 + 2/15*f**3 - 2/15*f.
2*f*(f - 1)*(f + 1)**2/15
Find a such that 3/7*a + 3/7*a**5 + 0 + 12/7*a**4 + 12/7*a**2 + 18/7*a**3 = 0.
-1, 0
Let z(d) = d**2 + 5*d + 5. Let p be z(-5). Factor -12/5*n + 12/5*n**2 - 6/5*n**4 + 0 + 9/5*n**3 - 3/5*n**p.
-3*n*(n - 1)**2*(n + 2)**2/5
Suppose 0 = 3*u - 14 - 4. Let i(r) = r - 4. Let p be i(u). Solve -2 + 3*v - 3*v**2 - 6 - 11*v**p + 29*v = 0.
2/7, 2
Let q(x) be the third derivative of -x**8/1344 - x**7/280 - x**6/240 + x**5/120 + x**4/32 + x**3/24 - 5*x**2. Factor q(y).
-(y - 1)*(y + 1)**4/4
Suppose 7*o - 2*o = 15. Suppose 2 = o*d - 10. Let -1/3*z**2 - z**5 + 0*z - 1/3*z**3 + 5/3*z**d + 0 = 0. What is z?
-1/3, 0, 1
Let g = 22 - 20. Suppose 0 = -2*w - g*w + 8. Factor 2/3*q**4 + 4*q**w - 8/3*q - 8/3*q**3 + 2/3.
2*(q - 1)**4/3
Let g(p) = p**3 + 8*p**2 + p + 10. Let i be g(-8). Let b(s) be the first derivative of 0*s + 0*s**2 - 1/3*s**3 - i. Factor b(h).
-h**2
Suppose -8/7 + 10/7*t**2 - 2/7*t**4 - 6/7*t + 6/7*t**3 = 0. Calculate t.
-1, 1, 4
Let p(x) = -x**3 + 5*x**2 + 5. Let r be p(5). Factor 0*d + 1/4*d**r + 0 + 1/4*d**4 - 1/4*d**2 - 1/4*d**3.
d**2*(d - 1)*(d + 1)**2/4
Let o = 17 - 12. Suppose o*m + 8 = 53. Let 9*s**4 + 4*s**2 + 2*s + 2*s**5 + m*s**2 - 5*s**2 + 12*s**3 - s**4 = 0. What is s?
-1, 0
Factor 6/11*q**2 + 24/11 - 24/11*q.
6*(q - 2)**2/11
Let k(i) = 6*i**3 + 5*i + 5. Let d(u) = -5*u**3 - 4*u - 4. Let y(w) = -5*d(w) - 4*k(w). Suppose y(x) = 0. Calculate x.
0
Let d = -1625 + 14639/9. Factor -2*n**2 - 2/9*n**4 - d*n - 4/9 - 10/9*n**3.
-2*(n + 1)**3*(n + 2)/9
Suppose 4*o + 3*o**3 + 0*o + 0*o**3 - 3*o + 4*o**2 = 0. Calculate o.
-1, -1/3, 0
Let i(s) = -7*s + 14. Let m be i(2). Factor m + 2/3*d**5 + 0*d**4 + 0*d + 0*d**2 - 2/3*d**3.
2*d**3*(d - 1)*(d + 1)/3
Factor -2 - 8/3*h - 2/3*h**2.
-2*(h + 1)*(h + 3)/3
Let x = 319 - 1263/4. Factor p**3 + 11/4*p + x*p**2 + 1/2.
(p + 1)*(p + 2)*(4*p + 1)/4
Let r be (-6)/(-5) + 33/(-55). Determine t so that -t + 1/5*t**4 - r*t**2 - 2/5 + 1/5*t**3 = 0.
-1, 2
Let x(i) be the second derivative of i**5/330 - i**4/132 + 3*i**2/2 + i. Let u(k) be the first derivative of x(k). Factor u(j).
2*j*(j - 1)/11
Suppose 0 = 5*h + 4*r + 70, 0*h - 4*r = 3*h + 42. Let g be (-4)/h + 14/(-49). Determine f so that g + 0*f + 6/7*f**3 - 2/7*f**2 - 6/7*f**4 + 2/7*f**5 = 0.
0, 1
Suppose 11*p = 8*p + 15. Let x(y) be the second derivative of 0*y**4 + 3/20*y**p + 0*y**3 - 1/10*y**6 + 0 + 0*y**2 - 2*y. Factor x(s).
-3*s**3*(s - 1)
Let j(o) be the third derivative of -o**7/2520 + o**6/360 - o**5/120 - o**4/12 + o**2. Let x(f) be the second derivative of j(f). Let x(v) = 0. What is v?
1
Factor 2 + 2 - 4 + 4*r + 2*r**2.
2*r*(r + 2)
Let s(w) = w**2 + 7*w + 8. Let a be 9/2*(-24)/18. Let n be s(a). Factor -10/3*r - 2*r**n - 4/3.
-2*(r + 1)*(3*r + 2)/3
Let o(b) be the third derivative of b**8/126 - 8*b**7/945 - 13*b**6/540 + b**5/90 + 5*b**4/108 + b**3/27 + 6*b**2. What is k in o(k) = 0?
-1/2, -1/3, 1
Let s(t) be the third derivative of -49*t**8/60 - 14*t**7/15 + 469*t**6/75 + 1448*t**5/75 + 368*t**4/15 + 256*t**3/15 + 37*t**2. Find r, given that s(r) = 0.
-1, -4/7, 2
Let -1/3*j + 1/2*j**4 + 1/6*j**5 + 0 - 1/2*j**2 + 1/6*j**3 = 0. Calculate j.
-2, -1, 0, 1
Suppose 3*m = 38 + 22. Factor -9*f**3 + 3 + 21*f**2 - 25*f**4 + 1 - 11*f**3 + m*f.
-(f - 1)*(f + 1)*(5*f + 2)**2
Let y(c) be the third derivative of -c**5/105 - c**4/24 + c**3/21 - 6*c**2. Factor y(j).
-(j + 2)*(4*j - 1)/7
Let n = -6 + 5. Let g = 3 + n. Factor -1/3 + 2/3*v + 1/3*v**4 - 2/3*v**3 + 0*v**g.
(v - 1)**3*(v + 1)/3
Let l = 7 + -3. Suppose -29 = -5*d - l. Let -3*w**2 + 7*w**d + 7*w**4 + 18*w**3 - 29*w**4 + w**2 + w**5 - 2*w = 0. Calculate w.
-1/4, 0, 1
Let s(j) = 4*j**3 - 22*j**2 + 11*j + 1. Let l(y) = -3*y**3 + 23*y**2 - 12*y. Let k(z) = -3*l(z) - 4*s(z). Factor k(x).
-(x - 2)*(x - 1)*(7*x + 2)
Suppose 8*h + 36 = 2*h. Let o be (-129)/(-165) - h/(-10). Factor -o*y**2 - 6/11 - 8/11*y.
-2*(y + 1)*(y + 3)/11
Let t(u) be the first derivative of u**5 - 15*u**4/4 + 5*u**3/3 + 15*u**2/2 - 10*u - 12. Solve t(b) = 0 for b.
-1, 1, 2
Let n(w) = -w**5 - w**4 + w**3 - w**2. Let a(c) = 6*c**5 + 6*c**4 - 6*c**3 + 4*c**2. Let i = -4 + 9. Let m(u) = i*n(u) + a(u). Factor m(y).
y**2*(y - 1)*(y + 1)**2
Let m = -1027/2220 + -3/740. Let t = -1/15 - m. Let -t*y**2 + 0 - 2/5*y**3 + 4/5*y = 0. What is y?
-2, 0, 1
Suppose -y = -3*p + 1, -1 = p - 4*y - 5. Factor -2*t**3 - 2*t**2 + 7*t**3 + t**3 + p*t**3 + 8*t**4.
2*t**2*(t + 1)*(4*t - 1)
Suppose 2*k - 2*w = 0, 5*w = -5*k + 12 + 38. Determine m, given that 2*m**3 - 2 - k*m**3 + 9*m**2 + 2*m**3 - 7*m**4 + 5*m - 4*m**3 = 0.
-1, 2/7, 1
Solve 10*u**3 - 20*u**4 - 2*u**2 + 25*u**3 - 3*u**2 - 10*u**3 = 0.
0, 1/4, 1
Suppose 2*t + 24 = 5*t. Factor 6/5*h**5 + t*h**3 - 28/5*h**4 - 16/5*h**2 + 0*h + 0.
2*h**2*(h - 2)**2*(3*h - 2)/5
Let n be (0 - 0)/(-3*(2 - 3)). Suppose 1/2*x**4 + n - 3/2*x**3 - 1/2*x + 3/2*x**2 = 0. What is x?
0, 1
Find i such that -4/3 - 2/3*i**2 + 2*i = 0.
1, 2
Let i(k) be the first derivative of k**3/9 - k**2/6 + 4. Suppose i(q) = 0. Calculate q.
0, 1
Suppose 0 = 3*t + 3*u - 9, 2*t + t = 4*u + 30. Let n = -3 + t. Let 2/5*a**2 + 0*a**n + 0 + 0*a - 2/5*a**4 = 0. Calculate a.
-1, 0, 1
Suppose -50 = 2*w - f, 45 = -4*w - f - 67. Let n = w - -30. Factor 0 - 4/5*h - 6/5*h**2 - 2/5*h**n.
-2*h*(h + 1)*(h + 2)/5
Suppose 0*d + 0*d**3 - 1/4*d**4 + 1/4*d**2 + 0 = 0. Calculate d.
-1, 0, 1
Factor 5*m**3 - 11*m - 5*m**2 + 9*m - 3*m + 5.
5*(m - 1)**2*(m + 1)
Let d(c) = -4*c - 4. Let p = -11 + 16. Suppose 0 = 4*l - 15 + 7. Let n(t) = t**2 + 9*t + 8. Let z(k) = l*n(k) + p*d(k). Solve z(i) = 0.
-1, 2
Let w = -3709/5 + 746. Find f such that -21/5*f**3 + 6/5 - 6/5*f**2 + w*f = 0.
-1, -2/7, 1
Let t(i) be the third derivative of -i**6/660 + i**5/330 + i**4/132 - i**3/33 - 2*i**2. Factor t(y).
-2*(y - 1)**2*(y + 1)/11
Let r(a) = a + 12. Let q be r(-6). Let l = q - 4. Factor 0 + 0 + 1 - 3*d**l + 2*d.
-(d - 1)*(3*d + 1)
Suppose -2*l = -5*l + 27. Let p be 3/4*4/l. Find w, given that -2/3*w + 1/3*w**3 + 0 - p*w**2 = 0.
-1, 0, 2
Let v be (30/4 + -4)*-6. Let u be 6/v + (-524)/(-70). Determine c so that -5*c**3 + u*c + 8/5 + 6*c**2 = 0.
-2/5, 2
Let s(m) = -m**3 + 2. Let d be s(0). Suppose -k + d*k = 5. Suppose 2*w - w**3 - 2*w**3 - w**3 + 2*w**k = 0. What is w?
-1, 0, 1
Let i(b) be the second derivative of -b**4/12 + b**3/3 + 5*b. Factor i(h).
-h*(h - 2)
Suppose -3*w - 3 + 5 = -2*v, 5*v + 5 = 0. Factor 4*y**3 + y**5 + 2*y**5 + 4*y**2 - y**5 + w*y**5 - 6*y + 2 - 6*y**4.
2*(y - 1)**4*(y + 1)
Let q(s) be the first derivative of 2/3*s - 1/6*s**4 + 1/3*s**2 - 2/9*s**3 + 3. Factor q(v).
-2*(v - 1)*(v + 1)**2/3
Factor -16/5*g**3 + 0 + 0*g - 2/5*g**4 - 14/5*g**2.
-2*g**2*(g + 1)*(g + 7)/5
Let m(v) be the first derivative of -2*v**5/85 + v**4/17 - 2*v**2/17 + 2*v/17 - 2. Factor m(b).
-2*(b - 1)**3*(b + 1)/17
Let x be 2*-1*(3 + -4). Let -v - 3*v**2 - 2*v**x + 4*v**2 = 0. What is v?
-1, 0
Factor 0*c - 6/7*c**2 - 2/7*c**3 + 0.
-2*c**2*(c + 3)/7
Let m = 3944/5 - 788. Factor -m - 2*g - 4/5*g**2.
-2*(g + 2)*(2*g + 1)/5
Let j(i) 