 4*w**3/3 + 10*w. Let k(u) be the second derivative of p(u). Find a such that k(a) = 0.
-2, 1
Suppose -8 = -3*b - 2. Factor 4 - 2*s**3 + 2*s + 2*s**b - 5 - 1.
-2*(s - 1)**2*(s + 1)
Let h(k) = 24*k**4 - 15*k**3 - 23*k**2 - 7*k - 7. Let q(p) = 12*p**4 - 7*p**3 - 11*p**2 - 3*p - 3. Let r(x) = -3*h(x) + 7*q(x). Let r(o) = 0. Calculate o.
-2/3, 0, 1
Let i be 4*(0 + 6/8). Solve -10*v + 18*v - 8*v - 3*v**i = 0.
0
Let p(b) be the first derivative of -3*b**5/40 + 3*b**4/32 + b**3/2 - 3*b**2/4 - 4. Suppose p(y) = 0. Calculate y.
-2, 0, 1, 2
Let q(x) be the first derivative of x**5/15 - x**4/12 - x**3/9 + x**2/6 - 28. Determine a so that q(a) = 0.
-1, 0, 1
Let n(u) = 4*u**2 + 2*u - 9. Let g(w) = -w + 6. Let v be g(0). Let k(d) = 3*d**2 + d - 8. Let m(b) = v*n(b) - 7*k(b). Factor m(i).
(i + 1)*(3*i + 2)
Factor -2*s - 4/3 - 2/3*s**2.
-2*(s + 1)*(s + 2)/3
Suppose 0 = -5*s + i + 31, -2*s + 5*i + 15 = 2*i. Factor 75*w**2 + s*w**4 - 3*w**3 - 3*w**5 - 75*w**2.
-3*w**3*(w - 1)**2
Let u = 641/3 + -44869/210. Let k(t) be the third derivative of 0*t + u*t**5 + 0 - 2*t**2 + 0*t**3 + 1/84*t**4. What is l in k(l) = 0?
-1, 0
Let u(s) = 10*s**5 - 29*s**3 + 31*s**2 + 41*s - 9. Let f = -10 + 12. Let k(r) = -2*r**5 + 6*r**3 - 6*r**2 - 8*r + 2. Let g(n) = f*u(n) + 11*k(n). Factor g(a).
-2*(a - 1)**3*(a + 1)*(a + 2)
Let d = 20498 + -1541. Let v = 132999/7 - d. Suppose -120/7*s + 16/7 + v*s**2 - 250/7*s**3 = 0. Calculate s.
2/5
Suppose 5*p - 20 = 4*o, 3*p + 5*o + 8 = 5*p. Let -14/3*f - 10/3*f**p + 14/3*f**3 + 2*f**2 + 4/3 = 0. Calculate f.
-1, 2/5, 1
Let v = -769 - -771. Suppose -3/5*k**3 + 3/5*k - 3/5 + 3/5*k**v = 0. Calculate k.
-1, 1
Let y(r) be the third derivative of 3*r**6/40 - 11*r**5/20 + r**4 + 2*r**3 - 12*r**2. Factor y(t).
3*(t - 2)**2*(3*t + 1)
Suppose -4*w + 3*o + 8 = 0, 2*w + 0 - 4 = 2*o. Suppose -5*n + 3*x = -5, -12 + 2 = -5*n + w*x. Find r, given that 2*r + 0*r + 2*r**3 - n*r = 0.
-1, 0, 1
Let z(x) = 10*x**2 + 6*x - 12. Let a(y) be the first derivative of -y**3 - y**2 + 4*y - 4. Let q(h) = 8*a(h) + 3*z(h). Suppose q(c) = 0. What is c?
-1, 2/3
Suppose 5*a - 5*m = 9 - 4, -3*m = 3*a - 9. Factor 0*l**2 + a*l + 2 - l - l**2.
-(l - 2)*(l + 1)
Let q(l) be the first derivative of 2*l**5/35 - 2*l**4/7 + 8*l**3/21 + 26. Solve q(p) = 0.
0, 2
Let s = -27 - -30. Factor 0 + 2/9*k + 2/9*k**s - 4/9*k**2.
2*k*(k - 1)**2/9
Let a(o) be the second derivative of -o**7/1260 - o**4/12 + 2*o. Let h(g) be the third derivative of a(g). Let h(z) = 0. Calculate z.
0
Let q be 13/3*(-3)/(-1). Let b = -49 + 51. Factor -2*j**b - q*j + 10*j + 5*j.
-2*j*(j - 1)
Let w(d) be the second derivative of -d**5/60 + d**3/6 - d**2/3 - 18*d. Factor w(a).
-(a - 1)**2*(a + 2)/3
Let i(p) = p + 4. Let f be i(0). Suppose 5*g - 18 = 4*u, 20 - 2 = f*g - 5*u. Solve 3*q**4 - 7*q**4 + q**5 - 3*q**5 - g*q**3 = 0.
-1, 0
Let m(b) = b**2 - 2*b - 6. Let c(u) = u**2 + u - 1. Let q(n) = -n**3 + 1. Let o be q(0). Let d(j) = o*m(j) - 2*c(j). Factor d(s).
-(s + 2)**2
Let k(a) be the third derivative of a**2 + 0 - 1/4*a**4 + 1/10*a**5 - 1/60*a**6 + 0*a + 1/3*a**3. Factor k(x).
-2*(x - 1)**3
Suppose -14 - 18 = 2*v. Let q be (-3*v/(-60))/(-2). Factor q*p**3 + 2/5*p**4 + 0 + 0*p**2 + 0*p.
2*p**3*(p + 1)/5
Let l(n) be the first derivative of -1/12*n**4 - 2/9*n**3 - 1/6*n**2 - 2 + 0*n. Factor l(j).
-j*(j + 1)**2/3
Suppose 0 = -17*l + 16*l. Let k(g) = g + 8. Let f be k(-6). What is n in l + 2*n - n**f - 2 + 1 = 0?
1
Suppose 0 = -2*s - 6 + 16. Suppose 0 = 3*a + 5*q - 19, -14 + s = -5*a + 3*q. Factor 1/3 - 1/3*d - d**a - 5/3*d**2.
-(d + 1)**2*(3*d - 1)/3
Let a(k) be the second derivative of -k**7/252 + k**5/60 - k**3/36 - k. Factor a(x).
-x*(x - 1)**2*(x + 1)**2/6
Let x(m) = -m**3 + 12*m**2 + 13*m + 6. Let z be x(13). Suppose 3*v - 15 = -z. Factor -9/2*i + 15/2*i**v + 4*i**2 - 1.
(i + 1)*(3*i - 2)*(5*i + 1)/2
Let o be 1530/(-56) - 6/14. Let d = 28 + o. Factor -1/4*p + 0 - d*p**3 + 1/2*p**2.
-p*(p - 1)**2/4
Factor 3*t + 3/2 + 6*t**3 - 21/2*t**2.
3*(t - 1)**2*(4*t + 1)/2
Let f(k) = -k**2 + 9*k. Let u be f(9). Let r(n) be the second derivative of -1/9*n**3 - 1/9*n**2 - 1/18*n**4 - 1/90*n**5 + u + 2*n. Find y, given that r(y) = 0.
-1
Suppose 16 = -56*q + 60*q. Let f(u) be the third derivative of 1/84*u**q + 1/735*u**7 + u**2 + 0 - 1/420*u**6 + 0*u**3 - 1/210*u**5 + 0*u. Factor f(o).
2*o*(o - 1)**2*(o + 1)/7
Determine t so that 0*t + 0*t**2 + 0 - 1/5*t**4 + 1/5*t**3 = 0.
0, 1
Factor 22/5*i + 4/5 - 18/5*i**3 + 24/5*i**2.
-2*(i - 2)*(3*i + 1)**2/5
Let j = 416 - 414. Determine v, given that 0 + 0*v + 6/5*v**j + 3/5*v**4 + 9/5*v**3 = 0.
-2, -1, 0
Let g = -18 + 6. Let i be 10/4*g/(-75). Let -2/5*c**3 + 0 + 2/5*c**4 + 2/5*c**5 + 0*c - i*c**2 = 0. Calculate c.
-1, 0, 1
Let x be 6/30 - 3/(-60). Determine t, given that 7/2*t**2 - 5/4*t**4 - 3/4*t + x*t**5 - 9/4 + 1/2*t**3 = 0.
-1, 1, 3
Solve -1/3 - 1/3*p**4 - 4/3*p**3 - 2*p**2 - 4/3*p = 0 for p.
-1
Let j(c) be the second derivative of 0 + 1/60*c**5 + 1/18*c**4 + 3*c - 1/90*c**6 + 0*c**3 + 0*c**2. Factor j(q).
-q**2*(q - 2)*(q + 1)/3
Let y(b) be the third derivative of -5*b**9/1512 - b**8/420 + b**3/2 - b**2. Let n(w) be the first derivative of y(w). Find f, given that n(f) = 0.
-2/5, 0
Let f(x) be the second derivative of -x**4/18 - 2*x**3/9 - 9*x - 1. Factor f(c).
-2*c*(c + 2)/3
Factor -90*d + 21 - 24*d**2 - 121 + 32*d**3 - 4*d**4 - 70*d.
-4*(d - 5)**2*(d + 1)**2
Factor 15/2*b**3 - 10/3 + 40/3*b - 35/2*b**2.
5*(b - 1)*(3*b - 2)**2/6
Let d(i) be the first derivative of -i**3/24 + 3*i**2/4 - 9*i/2 + 15. Solve d(k) = 0.
6
Let v(k) be the second derivative of -k**6/35 - 11*k**5/210 - k**4/63 + k. Factor v(t).
-2*t**2*(t + 1)*(9*t + 2)/21
Let g(l) be the first derivative of l**8/1680 + l**7/840 - l**6/180 + l**3 + 1. Let j(u) be the third derivative of g(u). Factor j(y).
y**2*(y - 1)*(y + 2)
Let g be (40/(-75))/(-3 + (-21)/(-9)). Factor g - 1/5*y**2 - 3/5*y.
-(y - 1)*(y + 4)/5
Let p(k) = -k + 11. Let s be p(9). Suppose s*z - 2 = 2*i, 0 = i - 5*z + 1 + 12. Factor -1/3*x**i - 1/3*x + 0.
-x*(x + 1)/3
Suppose -2*w + 4 = -0. Factor -14*n**3 - 3*n**w - 7*n**3 - 16*n**2 - 6*n - 8*n**2.
-3*n*(n + 1)*(7*n + 2)
Suppose 3*t + 10 = 7*s - 2*s, 5*s = 5*t + 10. Let l = -9 + 15. Let 7*i**s - 2*i**4 + 4*i**3 - i**2 - 8*i - 2 - l = 0. Calculate i.
-1, 2
Let a = 1730/3 + -575. Suppose -4/3*s + 0 + 8/3*s**2 + 1/3*s**4 - a*s**3 = 0. Calculate s.
0, 1, 2
Factor 0*f + 0 + 0*f**3 + 0*f**2 - 2/5*f**4.
-2*f**4/5
Suppose 13 = 4*u + 5. Factor b**2 - 4*b - b**2 + 2*b**2 + u*b**2.
4*b*(b - 1)
Factor 0*v + 4/13*v**3 + 0 - 2/13*v**4 - 2/13*v**2.
-2*v**2*(v - 1)**2/13
Let f(b) be the third derivative of b**6/600 + b**5/100 + b**4/40 + b**3/30 + 36*b**2. Factor f(x).
(x + 1)**3/5
Let t(z) be the third derivative of 0*z**3 + 0*z + 1/36*z**4 - 1/90*z**5 + 2*z**2 + 0. Factor t(q).
-2*q*(q - 1)/3
Let i = -1 - -3. Solve 8*x - 4 + 2*x**4 + x**4 - 2*x - 6*x**3 - x**4 + 2*x**i = 0.
-1, 1, 2
Suppose 2*i = i + 3. Let p(j) be the third derivative of -1/4*j**4 + 0*j + 0 + j**2 - 1/30*j**5 - 2/3*j**i. Factor p(t).
-2*(t + 1)*(t + 2)
Let 0*t - 9/4*t**4 + 0*t**2 + 0 - 3/4*t**5 - 3/2*t**3 = 0. Calculate t.
-2, -1, 0
Let y(l) be the third derivative of l**8/24 + 19*l**7/105 + 2*l**6/15 - 2*l**5/15 - 7*l**2. Solve y(k) = 0.
-2, -1, 0, 2/7
Let z(q) be the third derivative of -q**5/270 + 5*q**4/108 + 2*q**3/9 - 3*q**2 - 2. Factor z(c).
-2*(c - 6)*(c + 1)/9
Let p(n) be the second derivative of -2*n + 0 + 0*n**5 - 2/15*n**6 + 1/21*n**7 + 0*n**3 + 0*n**4 + 0*n**2. Factor p(b).
2*b**4*(b - 2)
Suppose -4*b = -4 - 0. Suppose 5*s + 3*t = 19, 2*s - 6*s - b = -3*t. Factor -2 + q**4 - q**s + 2.
q**2*(q - 1)*(q + 1)
Factor 0 + 34/9*o**4 + 10/3*o**5 + 0*o + 4/9*o**3 + 0*o**2.
2*o**3*(o + 1)*(15*o + 2)/9
Let l(r) be the third derivative of -r**6/120 - r**5/30 + r**4/6 + 4*r**3/3 - 17*r**2. Let l(v) = 0. Calculate v.
-2, 2
Let h = -2/419 + 1289/6704. Let s = h - -1/16. What is f in s*f**2 + 1/4 - 1/2*f = 0?
1
Let v(s) be the second derivative of 1/4*s**5 - 3*s + 1/10*s**6 + 0*s**3 + 0*s**2 + 1/6*s**4 + 0. Determine l, given that v(l) = 0.
-1, -2/3, 0
Solve 1/2*o**3 - 7/2*o + 0*o**2 - 3 = 0.
-2, -1, 3
Let v(s) = 3*s**5 - 12*s**3 + 3*s**2 + 9*s. Let i(h) = h**4 - h**3 + h. Let g(x) = -3*i(x) + v(x). Determine r so that g(r) = 0.
-1, 0, 1, 2
Suppose -n = 6*n - 28.