+ 1/2*c**2.
c**2/2
Let s(o) be the first derivative of 1/3*o**4 - 1/15*o**6 + 0*o**5 - 4 + 0*o**3 - o**2 - 2*o. Let l(n) be the first derivative of s(n). Factor l(t).
-2*(t - 1)**2*(t + 1)**2
Let t(q) = 5*q + 6. Let y(i) = i + 1. Let j(h) = -t(h) + 6*y(h). Let n be j(2). Solve -n + 3*o - 6*o - o - 2*o**2 = 0.
-1
Let a = 21 + -18. Let -66 + 3*q**2 + 66 - 6*q + 3*q**a = 0. Calculate q.
-2, 0, 1
Let u(f) be the first derivative of -f**4/12 - f**3/3 - f**2/2 - 7*f + 6. Let h(i) be the first derivative of u(i). Factor h(b).
-(b + 1)**2
Let u(q) be the second derivative of -q**5/50 + 3*q**4/10 - 9*q**3/5 + 27*q**2/5 - 4*q. Factor u(o).
-2*(o - 3)**3/5
Suppose -240*t + 134*t**3 - 49*t**3 + 75*t**3 + 120*t**2 - 75*t**4 - 45*t**5 + 80 = 0. Calculate t.
-2, 2/3, 1
Let c be 7 + 24/10 + -9. Find y such that -c*y**5 + y**4 + 0 + 0*y - 2/5*y**2 - 1/5*y**3 = 0.
-1/2, 0, 1, 2
Let g(q) = q**3 - 13*q**2 - q + 18. Let m be g(13). Suppose m*v - r = 20, 3*v - 6*r = -r + 34. Suppose 2/7*u**4 + 0*u**v + 2/7 + 0*u - 4/7*u**2 = 0. What is u?
-1, 1
Suppose -1 = 3*x + 2, -3 = -n - x. Suppose -3*g + g = -n. Factor -g*w**3 + 2*w - w + w**3.
-w*(w - 1)*(w + 1)
Factor 0*n**2 + 9/7*n**4 + 3/7*n**5 + 6/7*n**3 + 0*n + 0.
3*n**3*(n + 1)*(n + 2)/7
Suppose 3*n + 8 = 7*n. Suppose -2*w**3 - 1/2*w**4 + n*w - 3/2*w**2 + 2 = 0. What is w?
-2, -1, 1
Let g be (-13)/1*8/(-52). Factor 0*x - 1/3*x**g - x**3 - 1/3*x**5 - x**4 + 0.
-x**2*(x + 1)**3/3
Factor 0*d - 1/4*d**2 + 0*d**3 + 1/4*d**4 + 0.
d**2*(d - 1)*(d + 1)/4
Suppose 0 = 5*u + 7 - 27. Let j(p) = -p - 5*p**4 + 4*p**4 - 3*p**2 - 6*p**u + 6. Let l(s) = s**4 + s**3 - 1. Let z(x) = j(x) + 5*l(x). Let z(n) = 0. What is n?
-1/2, 1
Let w = 20 + -17. Factor 1/2*v**w - 1/4*v**5 + 0*v**2 + 0*v**4 - 1/4*v + 0.
-v*(v - 1)**2*(v + 1)**2/4
Suppose 18*c - 65 = 5*c. Let a be 2 - -4*(-2)/4. Suppose -9/4*q**3 - 5/4*q**c - 1/2*q**2 + a + 0*q - 3*q**4 = 0. Calculate q.
-1, -2/5, 0
Factor 2*c + 41*c**2 - 23*c**2 - 17*c**2 + 0*c.
c*(c + 2)
Let d = 7 - 4. Solve d - 3 + g + 3*g + 4*g**2 = 0.
-1, 0
Suppose -5*k - 11*k = -32. Factor 4/3 + 49/3*b**k + 28/3*b.
(7*b + 2)**2/3
Let v = -6 - -6. Let d be (3 - v) + 1 + 4. Let 0*t - 3*t + t - 18*t**3 + d*t**4 + 12*t**2 = 0. Calculate t.
0, 1/4, 1
Suppose i = -2*p + 3 + 4, -5*p + i = -7. Let a(o) be the second derivative of -1/20*o**5 + 1/36*o**4 + 0*o**p + 0 + 1/9*o**3 + o. Factor a(u).
-u*(u - 1)*(3*u + 2)/3
Let b(j) be the first derivative of 3*j**4 - 44*j**3/3 + 10*j**2 + 12*j + 7. Factor b(p).
4*(p - 3)*(p - 1)*(3*p + 1)
Let y(p) be the third derivative of -p**6/60 + 3*p**5/40 - p**4/8 + p**3/6 - 9*p**2. Let s(a) be the first derivative of y(a). Solve s(f) = 0.
1/2, 1
Let p be (0 - -8) + (4 - 6). Suppose -2*q + q + t = -p, 5*q = 4*t + 29. Let 1/4*j**3 + 0*j**4 - 1/4*j**q + 0 + 0*j**2 + 0*j = 0. Calculate j.
-1, 0, 1
Let b(m) be the third derivative of 0 + 0*m**4 + 0*m - 1/60*m**5 + 0*m**3 + 2*m**2 + 1/30*m**6. Factor b(t).
t**2*(4*t - 1)
Let a(w) be the second derivative of -w**7/105 - w**6/30 - w**5/30 + 3*w**2/2 + 2*w. Let g(i) be the first derivative of a(i). Let g(o) = 0. What is o?
-1, 0
Let l(g) = -6*g**4 - 8*g**3 + 8*g**2 + 12*g + 6. Let w(y) = -6*y**4 - 9*y**3 + 9*y**2 + 11*y + 5. Let i(p) = -5*l(p) + 6*w(p). Factor i(r).
-2*r*(r - 1)*(r + 3)*(3*r + 1)
Let y be (-11 + (-40)/(-4))*(-1)/4. Let b = 6 + -4. Solve 1/2*n + 1/4 + y*n**b = 0.
-1
Let v(a) = 18*a**5 + 12*a**4 - 3*a**3 - 12*a**2 - 15*a - 15. Let z(p) = p**5 + p**4 - p**2 - p - 1. Let b(w) = v(w) - 15*z(w). Suppose b(x) = 0. Calculate x.
-1, 0, 1
Let v(i) be the third derivative of i**9/22680 + i**4/24 + 4*i**2. Let d(o) be the second derivative of v(o). Let d(u) = 0. What is u?
0
Let o = -159 - -161. Determine z so that -1/4*z + 0 - 1/4*z**3 + 1/2*z**o = 0.
0, 1
Let x = -9 + 16. Let b = x + -4. Suppose 3*q**4 + 2*q**3 - 2*q + 2*q**2 - 2*q**4 - b*q**4 = 0. Calculate q.
-1, 0, 1
Let l(y) be the second derivative of y**4/30 - y**3/15 + 7*y. Factor l(h).
2*h*(h - 1)/5
Let k(l) = -2*l**3 + 14*l**2 - 20*l + 6. Let y be 16/6 + 12/(-18). Let m(x) = -x**3 + 13*x**2 - 20*x + 5. Let h(i) = y*m(i) - 3*k(i). Factor h(b).
4*(b - 2)*(b - 1)**2
Let g = -2 + 14. Factor -3*c**2 + 16*c**3 - 10*c**3 + g*c**2 + c**4.
c**2*(c + 3)**2
Let u(h) = h - 4. Let v be u(-4). Let w(i) be the second derivative of 17*i**5/20 - 2*i. Let j(t) = 11*t**3. Let f(z) = v*j(z) + 5*w(z). Factor f(d).
-3*d**3
Suppose 3*r - 2*t = 2*r + 2, 3*r = t + 11. Determine v, given that 25*v**3 - 5*v + 0*v**4 - 24*v**3 + 3*v**2 - v**r + 2 = 0.
-2, 1
Let y(w) = -2*w - 2. Let x be y(-4). Let q(g) be the first derivative of 1/15*g**x - 2/15*g**3 + 0*g + 2/25*g**5 + 0*g**2 - 1/10*g**4 + 2. Solve q(i) = 0 for i.
-1, 0, 1
Let b(o) be the third derivative of o**6/8 - 2*o**5/3 - 5*o**4/8 - 3*o**2. Let b(h) = 0. What is h?
-1/3, 0, 3
Let a(x) be the second derivative of -x**4/28 + x**3/14 - 7*x. Let a(l) = 0. What is l?
0, 1
Let q(c) be the first derivative of -c**4/14 - 2*c**3/21 - 5. Factor q(t).
-2*t**2*(t + 1)/7
Let c(i) be the third derivative of i**5/270 - i**4/36 + 3*i**2. Find t such that c(t) = 0.
0, 3
Let f(q) be the first derivative of -1/12*q**4 - 2 + 1/6*q**3 + q**2 + 2*q. Let b(k) be the first derivative of f(k). Factor b(z).
-(z - 2)*(z + 1)
Suppose -16/15*c**3 - 16/5*c**2 - 2/15*c**4 - 32/15 - 64/15*c = 0. Calculate c.
-2
Factor -1/7*h**4 + 0 - 4/7*h**3 - 3/7*h**2 + 0*h.
-h**2*(h + 1)*(h + 3)/7
Let z(g) be the third derivative of -g**9/15120 + g**8/5040 + g**5/15 - 5*g**2. Let k(m) be the third derivative of z(m). Factor k(f).
-4*f**2*(f - 1)
Let l(c) = 5*c**4 - 5*c**3 + 3*c + 3. Let i(a) = 3 - 42*a**3 + 3*a**4 + a**4 + 38*a**3 + 2*a - 1. Let y(u) = 3*i(u) - 2*l(u). Let y(h) = 0. Calculate h.
0, 1
Let m = 13 + -11. Determine t, given that 6*t + 11*t**2 + t - 3 - m*t + 3*t**3 = 0.
-3, -1, 1/3
Let z(h) be the first derivative of 2*h**3/3 - h**2 + 13. Factor z(u).
2*u*(u - 1)
Let w(c) be the second derivative of 0 + 0*c**3 + 0*c**2 + 1/12*c**4 - 2*c. Solve w(g) = 0.
0
Let c(k) be the first derivative of -k**3/5 - 6*k**2/5 - 4. Solve c(b) = 0 for b.
-4, 0
Let q(p) = -p**3 - 8*p**2 - 7*p + 10. Let f be q(-7). Let u be 14/(-35) + 34/f. Let 2*z**u - z**2 + 0*z**5 - 3*z**5 + z**4 + z**3 = 0. What is z?
-1, 0, 1/3, 1
Let h be -2*((-18)/(-3))/(-3). Factor -2*c - 1 + 2*c + h*c - c**2 - 2*c.
-(c - 1)**2
Let a = 33/20 - 7/5. Factor 1/2*f**3 - 1/2*f - a*f**4 + 1/4 + 0*f**2.
-(f - 1)**3*(f + 1)/4
Let v(k) be the first derivative of -k**6/24 + k**5/20 + 3*k**4/16 - 5*k**3/12 + k**2/4 + 4. Suppose v(b) = 0. What is b?
-2, 0, 1
Let c(v) = -9*v**3 + 2*v**2 - 2*v + 1. Let x be c(1). Let l be x/(-6)*(-6)/(-28). Solve l*p**4 + 0*p - 4/7*p**2 + 2/7 + 0*p**3 = 0 for p.
-1, 1
Let 0*k**3 - 4/3*k**4 + 2*k**5 + 0*k + 0 + 0*k**2 = 0. What is k?
0, 2/3
Let d(q) = -q + 3. Let z be d(0). Suppose 3*n + 3 = v - z*v, -v - n - 1 = 0. Factor -1/2*j**3 + 0*j - 1/2*j**2 + v.
-j**2*(j + 1)/2
Let j(c) = 7*c + 49. Let v be j(-7). Determine x, given that 6/7*x**2 + 4/7*x + v + 2/7*x**3 = 0.
-2, -1, 0
Let l(v) be the first derivative of v**5/60 + v**4/24 + 3*v**2/2 + 3. Let s(y) be the second derivative of l(y). Factor s(n).
n*(n + 1)
Let d = -1 + 4. Let y = -34 + 34. Factor 6/7*g**4 - 4/7*g**d + y*g**2 + 0*g + 0.
2*g**3*(3*g - 2)/7
Let h(k) be the first derivative of 2/3*k**3 + 2 - 8/15*k**5 + 5/3*k**2 - 5/6*k**4 + 2/3*k. Suppose h(n) = 0. Calculate n.
-1, -1/4, 1
Let y be (-225)/276 + (-2)/(-1). Let i = y + -10/23. Factor -3/2*a**3 - i*a**2 + 0*a - 3/4*a**4 + 0.
-3*a**2*(a + 1)**2/4
Let c be 36826/9*(-12)/(-2680). Let o = c - -4/335. Solve 23/3*k**2 + 25/3*k**5 - 4/3 + 19/3*k**3 - 8/3*k - o*k**4 = 0.
-2/5, 1
Let j be -4 - 1/(7/(-30)). Let w = 12 + -9. Factor -2/7*u**w + 0 + 0*u**2 + j*u.
-2*u*(u - 1)*(u + 1)/7
Let r(h) be the first derivative of h**4/6 - 10*h**3/9 + 8*h**2/3 - 8*h/3 - 7. Factor r(p).
2*(p - 2)**2*(p - 1)/3
Let k(x) = 4*x**2 + 6*x - 1. Let u(t) = -5*t**2 - 7*t. Let h(j) = -4*k(j) - 3*u(j). Let h(i) = 0. What is i?
-4, 1
Let h(t) be the second derivative of t**5/10 - 4*t**3/3 - 8*t. Determine q so that h(q) = 0.
-2, 0, 2
Suppose 4*y - 3 = 5. Factor 3*j**2 + 0 - 1 - 5*j - 2*j**y - 5*j**2.
-(j + 1)*(4*j + 1)
Suppose -2*f = -3*j - 21, 3*f - j - 29 = 3*j. Factor 0*u + 1/2*u**f - 1/4*u**2 + 0 - 1/4*u**4.
-u**2*(u - 1)**2/