*m + 1/240*m**5. Solve c(r) = 0.
0, 1/4, 1
Let h(r) be the third derivative of r**6/45 - r**5/45 - 7*r**4/144 - r**3/36 + 7*r**2. Suppose h(s) = 0. What is s?
-1/4, 1
Let a(p) = -p**2 + p - 1. Let s(r) = -5*r**2 + 2*r - 3. Let h(t) = -6*a(t) + s(t). Let h(q) = 0. What is q?
1, 3
Let o(h) = -3*h + 1 + 3 + 2*h. Let v be o(2). Factor 5*x**3 - 8*x**4 - x**v - 2*x**5 + 6*x**5 + 0*x**3.
x**2*(x - 1)*(2*x - 1)**2
Let i(h) be the first derivative of 0*h + 3/10*h**4 + 0*h**2 + 3 + 2/25*h**5 + 4/15*h**3. Factor i(k).
2*k**2*(k + 1)*(k + 2)/5
Factor -1/2*c**2 + 0 + 1/2*c.
-c*(c - 1)/2
Let y be ((-2737)/(-147))/17 + 3/(-7). Factor y*r**3 + 0*r**2 + 0 - 2/3*r.
2*r*(r - 1)*(r + 1)/3
Let m(n) be the second derivative of 9*n**6/80 + 3*n**5/20 + n**4/16 - 3*n**2 - 4*n. Let k(y) be the first derivative of m(y). Factor k(z).
3*z*(3*z + 1)**2/2
Suppose -3*u = 4*x - 117, -2*x - 5*u + 25 = -16. Let n = -30 + x. Suppose -24/7*g**n - 4/7*g - 10/7*g**4 + 0 - 18/7*g**2 = 0. Calculate g.
-1, -2/5, 0
Let n = -160/3 + 54. Let m(d) be the second derivative of -1/3*d**3 + 1/18*d**4 + 0 + n*d**2 + 3*d. What is k in m(k) = 0?
1, 2
Let w(k) be the second derivative of -k**4/16 - k**3/4 - 3*k**2/8 - 15*k. What is v in w(v) = 0?
-1
Let n(u) = -4*u - 2. Let i be n(-1). Suppose -19 = 3*c - 5*c + 3*f, -i*c - 4*f = 16. What is q in -2/7*q**c + 6/7*q - 4/7 = 0?
1, 2
Let q(l) be the third derivative of -l**5/630 + l**4/84 - 2*l**3/63 + 15*l**2. Factor q(o).
-2*(o - 2)*(o - 1)/21
Suppose -2*z = -3*n - 2*n + 22, 17 = 4*n - z. Factor -3*k**3 - 3*k**2 + k**n + 2*k**2 + 2*k + k**3.
k*(k - 2)*(k - 1)*(k + 1)
Factor 2*k**2 + k**3 + 4/3*k + 1/6*k**4 + 0.
k*(k + 2)**3/6
Let x(n) be the second derivative of 3*n**7/700 + n**6/600 - n**5/200 + n**3/2 + 4*n. Let v(c) be the second derivative of x(c). Suppose v(a) = 0. What is a?
-1/2, 0, 1/3
Let t(o) be the third derivative of 0*o + 0*o**6 + 1/30*o**5 + 0 - 1/210*o**7 + 3*o**2 - 1/6*o**3 + 0*o**4. Suppose t(w) = 0. What is w?
-1, 1
Let n(j) be the first derivative of -j**6/2 + j**5/5 + 5*j**4/4 - j**3/3 - j**2 - 61. Solve n(x) = 0 for x.
-1, -2/3, 0, 1
Let z = -7 + 8. Let j be (-1 + z)/(1/1). Factor -8/3*m**5 + j - 5/3*m**2 + 1/3*m + 2*m**3 + 4/3*m**4.
-m*(m + 1)*(2*m - 1)**3/3
Let v(m) = -4*m**3 - 6*m**2 - 6*m. Let r be 2*((-15)/(-6) - 2). Let p = r + -5. Let l(t) = -4*t**3 - 7*t**2 - 5*t + 1. Let x(j) = p*l(j) + 3*v(j). Factor x(c).
2*(c + 1)*(c + 2)*(2*c - 1)
Let h(i) be the third derivative of -i**6/420 - 2*i**5/105 - i**4/84 + 2*i**3/7 + 49*i**2. Determine f, given that h(f) = 0.
-3, -2, 1
Determine c, given that 2/3 - 1/3*c**3 + 1/3*c - 2/3*c**2 = 0.
-2, -1, 1
Let w(t) = -t**3 - t**2 + t + 1. Let m(i) = 2*i - 2. Let h(k) = -m(k) - 2*w(k). Determine p, given that h(p) = 0.
-2, 0, 1
Let f(h) be the third derivative of h**8/672 - h**7/420 - h**6/240 + h**5/120 + 9*h**2. Determine s so that f(s) = 0.
-1, 0, 1
Let w = -5 - -3. Let v be (-66)/(-72) + w/3. Factor 1/2*o**3 - v*o**2 - 1/4*o**4 + 0 + 0*o.
-o**2*(o - 1)**2/4
Suppose -2*z + 2*r + 2 = 0, -2*r - 2 = -0*z + 5*z. Suppose 3 + 0*a**2 + 9*a + z*a**3 + 9*a**2 + 3*a**3 = 0. What is a?
-1
Let s(l) = -l**2 - l - 1. Let z(j) = j**3 - 9*j**2 - 6*j - 2. Let x(n) = 6*s(n) - z(n). Solve x(y) = 0.
-1, 2
Let q(m) be the first derivative of -35*m**6/18 + 3*m**5 - 5*m**4/6 + 11. Factor q(l).
-5*l**3*(l - 1)*(7*l - 2)/3
Let v(z) be the third derivative of z**6/60 - z**5/30 - 13*z**2. Suppose v(d) = 0. What is d?
0, 1
Let k(d) be the second derivative of d**6/6 - d**5 + 5*d**4/3 + 9*d + 1. Factor k(y).
5*y**2*(y - 2)**2
Suppose 3*h = 12 + 3. Let a(v) be the second derivative of 2*v - 2/5*v**2 + 3/5*v**3 - 9/50*v**h - 7/30*v**4 + 3/25*v**6 + 0. Solve a(m) = 0.
-1, 1/3, 2/3, 1
Suppose -3*i + d + 29 = 5*d, -2*d = 4*i - 22. Find v, given that -2/9*v**i - 2/9*v**4 + 0 + 2/9*v**2 + 2/9*v = 0.
-1, 0, 1
Suppose 4*q - 2*q = 6. Suppose q*k - 6 = -0. Let 2*n**k - 4*n - 4*n**2 + 4*n = 0. What is n?
0
Let 27 + p**2 - 5*p - 13 - 10 = 0. What is p?
1, 4
Suppose 3 = -m + 7. Factor -1/3 + 2/3*y**3 - 1/3*y**m - 1/3*y - 1/3*y**5 + 2/3*y**2.
-(y - 1)**2*(y + 1)**3/3
Let 2/3*b**2 + 6 - 4*b = 0. What is b?
3
Let z(f) = f + 1. Let j be z(3). Factor -2*s**3 - 3*s**4 - 3*s**3 - 2*s - 15*s**2 - j*s - 7*s**3.
-3*s*(s + 1)**2*(s + 2)
Factor -24/11*s**2 - 26/11*s**3 - 12/11*s**4 - 8/11*s + 0 - 2/11*s**5.
-2*s*(s + 1)**2*(s + 2)**2/11
Let h be ((-2)/(-28))/(8/192). Factor h*r - 8/7 - 4/7*r**2.
-4*(r - 2)*(r - 1)/7
Factor -8/7*x**2 + 2/7*x**3 + 0 + 6/7*x.
2*x*(x - 3)*(x - 1)/7
Let v = -3 - -5. Factor -4*l**4 + 2*l**4 - 6*l**3 - 6*l**2 + 4*l**v - 2*l**4.
-2*l**2*(l + 1)*(2*l + 1)
Let p = -1211 - -4845/4. Let -p*o**2 - 3/4 + o = 0. Calculate o.
1, 3
Suppose 0*i = 4*i - 36. Let q be 8/12 + (-3)/i. What is s in -2/3*s - 1/3 - q*s**2 = 0?
-1
Let t(c) = 2*c**2 - 3*c - 1. Let w(n) = n**3 + n**2 - n + 1. Let y(r) = 2*t(r) + 2*w(r). Determine j, given that y(j) = 0.
-4, 0, 1
Let d(u) be the first derivative of 2*u**6/5 - 3*u**5/5 - 33*u**4/20 + 7*u**3/5 + 21*u**2/10 - 6*u/5 - 8. Let d(q) = 0. What is q?
-1, 1/4, 1, 2
Let l(j) be the third derivative of -j**9/90720 + j**8/6720 - j**7/1680 + 5*j**4/24 - 8*j**2. Let b(t) be the second derivative of l(t). Factor b(u).
-u**2*(u - 3)**2/6
Let q(l) = l**2 + 3*l. Let j be q(-3). Let f be (1/2)/(0 + 1). Suppose j - 1/2*x**4 - f*x + 1/2*x**2 + 1/2*x**3 = 0. What is x?
-1, 0, 1
Suppose 5*n - 36 = p, 3*n = -n - 3*p + 44. Suppose -3*g = -n + 2. Find x, given that x + 2*x**2 + 5*x**g - 6*x**2 = 0.
-1, 0
Let z(u) be the first derivative of -u**5/10 + u**3/6 + 5. Factor z(d).
-d**2*(d - 1)*(d + 1)/2
Factor -2/5*b**3 + 0 + 0*b - 2/5*b**4 + 4/5*b**2.
-2*b**2*(b - 1)*(b + 2)/5
Let i be 10/(-1) + (-150)/(-15). Factor 0 + i*n + 3/4*n**2.
3*n**2/4
Suppose 0 = 3*w + 2*z - 0*z + 13, -5*z = 2*w + 5. Let u be 0*(-2 - w/2). Factor 1 + 2*t**3 - 2*t - 2*t**4 + u + t**4.
-(t - 1)**3*(t + 1)
Let g(w) = 5*w**2 + 2*w - 4. Let k be g(2). Let l be k/8 + (-7 - -5). Find v such that 3/4*v + l + 1/4*v**2 = 0.
-2, -1
Let m = -2/369 + 1486/1845. Factor -m*f**2 - 12/5*f - 8/5.
-4*(f + 1)*(f + 2)/5
Let v(t) = -9*t**3 + 15*t**2 - t - 7. Let u be -9 + 1 - (-4 - -3). Let p(a) = 8*a**3 - 14*a**2 + 2*a + 6. Let x(w) = u*p(w) - 6*v(w). Factor x(i).
-2*i*(i - 2)**2
Suppose d + 17 = 18. Let x(t) be the first derivative of 9/10*t**2 + 1/5*t**3 - d + 6/5*t. Factor x(y).
3*(y + 1)*(y + 2)/5
Let c(m) be the first derivative of -338*m**3/21 - 52*m**2/7 - 8*m/7 + 6. Factor c(i).
-2*(13*i + 2)**2/7
Let g(y) be the third derivative of -1/200*y**6 + 0*y**3 + 0*y + 0*y**5 + 1/40*y**4 + 4*y**2 + 0. Let g(p) = 0. What is p?
-1, 0, 1
Let v(d) be the second derivative of d**6/75 + d**5/25 - d**4/30 - 2*d**3/15 + 25*d. Factor v(x).
2*x*(x - 1)*(x + 1)*(x + 2)/5
Let l(k) be the second derivative of 3*k**5/80 + 5*k. Determine x, given that l(x) = 0.
0
Let m(c) be the first derivative of -1/5*c**5 + 1/4*c**2 + 0*c - 1/12*c**6 - 2 + 1/3*c**3 + 0*c**4. Factor m(l).
-l*(l - 1)*(l + 1)**3/2
Suppose -12*c + 3*c = -45. Let -2/7 - 2/7*a**4 - 4/7*a**c + 4/7*a**2 - 4/7*a + 8/7*a**3 = 0. What is a?
-1, -1/2, 1
Let g(n) = n**2 - 2*n - 1. Let h = 6 + -3. Let f be g(h). Factor -1/3*x**f + 1/3*x + 0.
-x*(x - 1)/3
Let k be 2 + -2 + 1*-2. Let l = k - -6. Let 42*w**5 - 4*w**3 + l*w**4 + 0*w**3 - 2*w**4 = 0. Calculate w.
-1/3, 0, 2/7
Factor 3*o**3 + 43*o**4 - 51*o**4 - 2*o**5 - 11*o**3.
-2*o**3*(o + 2)**2
Let z(x) = x**4 + 2*x**2 - 2*x + 2. Let s(l) = 1 + 6 - 4*l - 3*l + l**3 + 7*l**2 + 3*l**4. Let r(f) = 2*s(f) - 7*z(f). Suppose r(t) = 0. Calculate t.
0, 2
Let x(t) = t**2 - 5*t + 6. Let m(s) = -4*s**2 + 20*s - 25. Let f(p) = -4*m(p) - 18*x(p). Factor f(y).
-2*(y - 4)*(y - 1)
Let f = -113 - -115. Find v, given that -10*v + 9/2*v**3 - 4 - 3*v**f = 0.
-2/3, 2
Let o be ((-30)/5 + 4)*(-1)/8. Let -1/4 + p - 3/2*p**2 + p**3 - o*p**4 = 0. What is p?
1
Let t(g) = g**4 + g - 1. Let u(o) = 4*o**4 + 4*o**3 - 6*o**2 - 14*o - 10. Let q(s) = 4*t(s) - 2*u(s). Determine b so that q(b) = 0.
-2, -1, 2
Let x(c) = -3*c**2 - 8*c - 3. Let q(i) = 2*i**2 + 8*i + 2. Let d(a) = 7*q(a) + 6*x(a). Suppose d(r) = 0. Calculate r.
1
Let p = 0 - -6. Suppose -2*g - 3*g**2 - p - 11 - 31 - 22*g = 0. Calculate g.
-4
Let a(z) be the second derivative of -z**5/15 - z**4/6 + 8*z**3/9 - z**2 - 2*z. Factor a(d).
-2*(d