1, 1
Let i(a) be the first derivative of -a + 1/6*a**4 + 0*a**3 - 2 + 0*a**2 + 1/10*a**5. Let u(z) be the first derivative of i(z). Factor u(h).
2*h**2*(h + 1)
Let h(f) be the second derivative of -f**8/2800 + f**7/4200 + f**3/6 + 3*f. Let d(a) be the second derivative of h(a). Suppose d(p) = 0. What is p?
0, 1/3
Let b(t) be the third derivative of t**7/42 - 5*t**6/24 + t**5/4 + 25*t**4/24 - 10*t**3/3 + 41*t**2. Factor b(x).
5*(x - 4)*(x - 1)**2*(x + 1)
Let s(d) = -3*d + d + 11*d**2 - 5*d**2. Let n(b) = b**2 - b. Suppose g - 4*a = 5*g + 24, -5*g + 10 = -3*a. Let u(t) = g*s(t) + 4*n(t). Factor u(l).
-2*l*(l + 1)
Let w = -52 - -55. Factor 0 + 0*t + 2/7*t**w + 2/7*t**2.
2*t**2*(t + 1)/7
Let m(n) = n**2 - 6*n + 9. Let r be m(3). Factor 0 + r*w - 2/7*w**2.
-2*w**2/7
Let c(a) be the first derivative of a**6/90 - a**5/30 - a**4/36 + a**3/9 + 9*a + 8. Let y(q) be the first derivative of c(q). Let y(t) = 0. Calculate t.
-1, 0, 1, 2
Let v be 30*-1*(-3)/9. Let r be (v/(-6))/((-2)/6). Factor 0 - 1/2*o + 7/2*o**4 - 9/2*o**3 - o**r + 5/2*o**2.
-o*(o - 1)**3*(2*o - 1)/2
Let a(z) be the second derivative of z**7/147 - 2*z**6/105 + z**4/21 - z**3/21 + 8*z. Factor a(f).
2*f*(f - 1)**3*(f + 1)/7
Let r = -14 - -27. Suppose -2*w = 5 - r. Let 0*s**w - 4*s**3 - 1 - 1 + 2*s**4 + 4*s = 0. Calculate s.
-1, 1
Find j, given that -3/4*j + 5/4*j**2 - 9/4 - 1/4*j**3 = 0.
-1, 3
Let c(z) be the first derivative of 0*z + 2/3*z**2 - 2*z**4 + 3 + 14/15*z**5 + 2/3*z**3. Let c(h) = 0. Calculate h.
-2/7, 0, 1
Let s(y) be the second derivative of -y**7/168 - y**6/120 + y**5/80 + y**4/48 + 7*y. Determine a, given that s(a) = 0.
-1, 0, 1
Let c(m) = -11*m**3 + 6*m**2 + 11*m - 11. Let n(h) = -5*h**3 + 3*h**2 + 5*h - 5. Let w(i) = -2*c(i) + 5*n(i). Factor w(b).
-3*(b - 1)**2*(b + 1)
Let g be -6 - (-3)/((-60)/(-125)). Factor -1/4*y**2 + 0 + g*y.
-y*(y - 1)/4
Let g(x) be the third derivative of x**7/231 + 7*x**6/660 + x**5/165 - x**2. Factor g(u).
2*u**2*(u + 1)*(5*u + 2)/11
Suppose 2*a = -7*a. Factor a*x + 1/2*x**2 + 0 - 7/4*x**3.
-x**2*(7*x - 2)/4
Let t(f) be the third derivative of 0*f**4 - 1/105*f**5 + 0*f + f**2 + 0*f**3 + 1/420*f**6 + 0 + 1/735*f**7. Let t(p) = 0. What is p?
-2, 0, 1
Let s = 3/26 + 11/130. Solve 1/5*j**3 + 0 - s*j + 0*j**2 = 0 for j.
-1, 0, 1
Let w(g) = 64*g - 1. Let k be w(1). Suppose -3 = 5*q - k. Find s such that 4 + s**5 - 4 + 2*s**2 - 8*s**5 - 3*s**3 - q*s**4 = 0.
-1, 0, 2/7
Factor 0 + 27/2*h**3 + 0*h - 3*h**2.
3*h**2*(9*h - 2)/2
Let o(p) be the first derivative of 5*p**6/3 + 16*p**5/5 + p**4/2 - 4*p**3/3 - 1. Factor o(l).
2*l**2*(l + 1)**2*(5*l - 2)
Let u = -15 - -16. Let z(v) be the first derivative of 0*v - 3/20*v**5 + 1/2*v**4 - 7/12*v**3 + 1/4*v**2 - u. Factor z(w).
-w*(w - 1)**2*(3*w - 2)/4
Let w(q) = -q**3 - 5*q**2 + 10*q - 4. Let x(s) = -3*s**3 - 21*s**2 + 40*s - 16. Let m(p) = -22*w(p) + 6*x(p). Suppose m(h) = 0. What is h?
1, 2
Let q(k) = k**5 + 5*k**4 + 3*k**3 - 4*k. Let a(f) = 2*f**5 + 6*f**4 + 2*f**3 - 4*f. Let m(x) = -5*a(x) + 6*q(x). Factor m(j).
-4*j*(j - 1)**2*(j + 1)**2
Let z(g) be the third derivative of -g**10/680400 + g**9/272160 + g**5/60 - 4*g**2. Let a(n) be the third derivative of z(n). Factor a(y).
-2*y**3*(y - 1)/9
Let g = -13/28 + 5/7. Find u, given that 0 + g*u - 1/4*u**2 = 0.
0, 1
Let u be 8/12 + 14/6. Let p be ((-6)/9)/(2/(-4)). Find c, given that 1/3*c + 0 - p*c**u - c**2 = 0.
-1, 0, 1/4
Factor 0 + 2/21*l**2 + 0*l.
2*l**2/21
Find r such that -1/3 + 2/3*r**3 + 5/6*r + 11/6*r**2 = 0.
-2, -1, 1/4
Let w = 86 - 84. Suppose -3/7 - 1/7*t**3 + 1/7*t + 3/7*t**w = 0. What is t?
-1, 1, 3
Factor -2/3*q**4 - 2/3*q**5 + 4/3*q**2 + 4/3*q**3 - 2/3 - 2/3*q.
-2*(q - 1)**2*(q + 1)**3/3
Let b be (0/(4 + -3))/1. Let z(o) be the second derivative of b*o**3 - 1/12*o**4 + 0 - 4*o + 1/2*o**2. Let z(k) = 0. Calculate k.
-1, 1
Let m = -1475/2 + 738. Factor -1/4*o**3 + 1/4*o**5 + 0 + 0*o + m*o**4 - 1/2*o**2.
o**2*(o - 1)*(o + 1)*(o + 2)/4
Let i(h) = h**3 + 8*h**2 + 13*h + 8. Let o be i(-6). Let m(d) be the second derivative of 1/12*d**4 + 0*d**o - 1/40*d**5 + 0 + 0*d**3 + 4*d. Solve m(j) = 0.
0, 2
Let b(y) be the third derivative of y**5/90 + 4*y**4/9 + 64*y**3/9 - 25*y**2. What is k in b(k) = 0?
-8
Suppose -18*j + 12*j = -12*j. Let -6/5*k + j + 3/5*k**2 = 0. Calculate k.
0, 2
Let r be (18 + -20)/(10/(-4)). Let j be ((-6)/(-10))/((-3)/(-2)). Factor 2/5 - r*w + j*w**2.
2*(w - 1)**2/5
Determine x so that -1/2*x**2 - 1/6 - 1/2*x - 1/6*x**3 = 0.
-1
Let y(z) be the second derivative of z**8/120 - z**7/210 + z**3 - 6*z. Let v(s) be the second derivative of y(s). Let v(j) = 0. Calculate j.
0, 2/7
Let c = 251/854 + -1/122. Solve 0 + c*r**2 + 2/7*r = 0.
-1, 0
Let j(k) = 5*k**2 - 9*k + 4. Let w(t) = 3*t**2 - 5*t + 2. Let o(i) = 4*j(i) - 7*w(i). Factor o(v).
-(v - 1)*(v + 2)
Let f(i) = -i**2 - 4*i + 10. Let s be f(-5). Let 24*v**4 + 99/5*v**3 + 3/5*v + 0 + 6*v**2 + 48/5*v**s = 0. What is v?
-1, -1/4, 0
Factor -1/3*x + 0 - 1/3*x**2.
-x*(x + 1)/3
Let c(t) = 1 - t + 1 - 5*t**2 - t**3 - 5. Let r be c(-5). Factor -k**3 + 2 - k**3 + r*k - 2*k**2 + 0*k**3.
-2*(k - 1)*(k + 1)**2
Suppose -3/7*d**3 - 1/7*d**2 - 1/7*d**5 + 0 + 0*d - 3/7*d**4 = 0. Calculate d.
-1, 0
Let i(f) = -f**3 - f**2 - f - 1. Let l(t) = -6*t**3 - 5*t**2 - 4*t - 5. Let g(d) = -5*i(d) + l(d). Factor g(v).
-v*(v - 1)*(v + 1)
Let n(w) be the first derivative of -1/3*w**3 + 1 + w**2 + 0*w. Let n(a) = 0. Calculate a.
0, 2
Factor 2*d**5 + 4*d**2 - 41*d**3 + 53*d**3 - 15*d**4 + 2*d**5.
d**2*(d - 2)**2*(4*d + 1)
Let w(l) be the first derivative of 3*l**4 + 1/3*l**6 + 0*l + 8/3*l**3 + 8/5*l**5 + 2 + l**2. Factor w(b).
2*b*(b + 1)**4
Suppose -a = -a + 5*a. Let -27/5*c + 3*c**3 + 3/5*c**4 + a + 9/5*c**2 = 0. What is c?
-3, 0, 1
Suppose 0 = 3*o - 5 - 7. Determine d, given that -4*d**3 + 2*d**2 + 3*d - 2*d - 3*d**3 - 4*d**o - 4*d**2 = 0.
-1, 0, 1/4
Let w(j) be the first derivative of j**6/300 + j**5/150 - 5*j**2/2 + 1. Let a(o) be the second derivative of w(o). Factor a(c).
2*c**2*(c + 1)/5
Let g = 301/6 + -50. Let u(j) be the second derivative of 0*j**2 - g*j**3 + 3*j + 0 + 1/20*j**5 + 1/30*j**6 - 1/12*j**4. Factor u(r).
r*(r - 1)*(r + 1)**2
Let v(m) = -4*m**3 + 4*m**2 - 3*m - 3. Let x(h) = 20*h**3 - 20*h**2 + 14*h + 14. Let j(p) = 14*v(p) + 3*x(p). Find a, given that j(a) = 0.
0, 1
Let m(t) be the third derivative of t**7/105 - t**6/15 + 2*t**5/15 - 6*t**2. Let m(p) = 0. What is p?
0, 2
Let g be -3 + 0 + ((-5)/(-2) - -1). Factor 0 + c**4 + g*c**2 - 9/4*c**3 + 0*c.
c**2*(c - 2)*(4*c - 1)/4
Let m(x) be the third derivative of -x**5/270 + 2*x**4/27 - 16*x**3/27 + 3*x**2. Determine q so that m(q) = 0.
4
Let g be -2*3*(-5)/(-20)*-2. What is a in -28/5*a + 8/5*a**4 - 1/5*a**5 + 8/5 - 5*a**g + 38/5*a**2 = 0?
1, 2
Let d(v) be the first derivative of -v**7/3360 + v**6/480 - v**5/160 + v**4/96 - v**3/3 - 2. Let j(f) be the third derivative of d(f). What is k in j(k) = 0?
1
Let r(b) = 4*b**2 - 7*b. Let u(v) = 4*v + 4. Let o be u(4). Let m(a) = 28*a**2 - 48*a. Let l(j) = o*r(j) - 3*m(j). Factor l(x).
-4*x*(x - 1)
Factor 9*a**4 + 2*a**3 - 13*a**5 - 5*a**4 + 15*a**5.
2*a**3*(a + 1)**2
Let h be 2/5 + (-16)/(-180)*-2. Let k(m) be the second derivative of 1/63*m**7 + 0 - h*m**4 + 0*m**2 + 0*m**3 - 1/9*m**6 + 4/15*m**5 + 3*m. Factor k(j).
2*j**2*(j - 2)**2*(j - 1)/3
Let s(o) be the first derivative of 0*o + 0*o**2 + 1 - 1/12*o**4 + 1/9*o**3. Factor s(c).
-c**2*(c - 1)/3
Suppose -2*u + 6 = -6. Suppose -x = 2*x - u. Let s**2 - s**3 + 3*s**2 - 3*s**x = 0. Calculate s.
0, 1
Let i(o) be the first derivative of -2*o**5/15 - o**4/6 + 2*o**3/3 + 5*o**2/3 + 4*o/3 - 50. Factor i(m).
-2*(m - 2)*(m + 1)**3/3
Let l(c) = -c**3 - 2*c**2 - 4*c - 17. Let f be l(-3). Factor 16/3*x - 4/3*x**3 + 0 - 2/3*x**f + 8/3*x**2.
-2*x*(x - 2)*(x + 2)**2/3
Let o = -248/9 - -28. Factor -2/9*b**2 - o + 2/3*b.
-2*(b - 2)*(b - 1)/9
Factor -2*y - y - 4*y**2 + 7*y**2 - 3 - 3.
3*(y - 2)*(y + 1)
Let q(g) = g**2 + g - 2. Let v = -4 + 6. Let u be q(v). Determine b, given that b**4 - b**2 + 5*b**2 + 4*b**3 - 4*b**u = 0.
-2/3, 0, 2
Let k(b) be the first derivative of 0*b**3 + 3*b + 1 + 1/6*b**4 - 2/15*b**6 + 1/10*b**5 + 0*b**2. Let s(y) be the first derivative of k(y). Factor s(q).
-2*q**2*(q - 1)*(2*q + 1)
Let v(p) be the second derivative of p**4/42 + 2*p**3/21 + 5*p. Fact