first derivative of -21/4*n**4 + 3*n - 1/4*n**6 + 9/5*n**5 - 27/4*n**2 + 8*n**3 + 1. Factor i(b).
-3*(b - 2)*(b - 1)**4/2
Factor 9/8*i**2 + 0 - 3/4*i - 3/8*i**3.
-3*i*(i - 2)*(i - 1)/8
Factor 3*t**2 + 12*t - 12*t**3 + 12 - 12*t**2 - 13*t**4 + 10*t**4.
-3*(t - 1)*(t + 1)*(t + 2)**2
Let i(w) = -8*w**2 + 15. Let x(j) = -3*j**2 + 5. Let n(l) = 2*i(l) - 7*x(l). Factor n(p).
5*(p - 1)*(p + 1)
Let j(g) be the third derivative of g**6/150 - g**5/150 - g**4/30 + g**3/15 + 6*g**2. Factor j(n).
2*(n - 1)*(n + 1)*(2*n - 1)/5
Let a(x) be the second derivative of 0*x**2 + 1/60*x**5 - x + 0 + 1/270*x**6 + 1/6*x**3 - 1/18*x**4. Let c(w) be the second derivative of a(w). Factor c(m).
2*(m + 2)*(2*m - 1)/3
Let s(y) be the first derivative of y**4/8 - 3*y**2/4 + y + 7. Solve s(t) = 0.
-2, 1
Factor -3/5*d**3 + 9/5*d**2 + 0 + 0*d.
-3*d**2*(d - 3)/5
Let q be ((-32)/(-12) - 0)/2. Find i such that -10/3*i**5 + 0 - 2*i**2 - q*i + 14/3*i**3 + 2*i**4 = 0.
-1, -2/5, 0, 1
Let h(o) be the third derivative of -o**9/30240 + o**8/10080 + 2*o**5/15 + 3*o**2. Let k(g) be the third derivative of h(g). Suppose k(c) = 0. What is c?
0, 1
Let b(i) = -i + 3. Let w be b(1). Let j(o) be the second derivative of 1/48*o**4 - 2*o + 1/24*o**3 + 0 - 1/4*o**w. Factor j(y).
(y - 1)*(y + 2)/4
Let s be ((-1)/(-2) - (-305)/120) + -3. Let g(r) be the third derivative of 0*r + 0 - r**2 + 1/240*r**5 + 1/48*r**4 + s*r**3. Factor g(f).
(f + 1)**2/4
Let s(n) be the second derivative of 9/80*n**5 + 0 - n - 3/4*n**2 - 1/2*n**4 + 7/8*n**3. Factor s(g).
3*(g - 1)**2*(3*g - 2)/4
Let j be (-2)/(-3) - 4/6. Factor -2*c + j*c + 4*c**3 + 0*c - 2*c**5.
-2*c*(c - 1)**2*(c + 1)**2
Let h be ((-4977)/56)/(3/(-2)). Let a = h - 59. Factor 0*r**4 + 0*r**2 - 1/4*r + 0 - a*r**5 + 1/2*r**3.
-r*(r - 1)**2*(r + 1)**2/4
Let i(z) be the first derivative of 2*z**3/33 + 2*z**2/11 + 2*z/11 - 9. Find h such that i(h) = 0.
-1
Find s, given that -24/7*s + 60/7*s**2 - 27/7*s**4 + 0 - 18/7*s**3 = 0.
-2, 0, 2/3
Let n(g) be the first derivative of g**6/180 - g**5/30 + 4*g**3/9 + 9*g**2/2 + 4. Let s(u) be the second derivative of n(u). Factor s(y).
2*(y - 2)**2*(y + 1)/3
Let k be (3*(0 + 2))/(-2). Let t be (k/2)/(2/(-4)). Factor 0 + 4/3*c - 2/3*c**2 - 2/3*c**t.
-2*c*(c - 1)*(c + 2)/3
Let o(d) be the second derivative of -d**5/120 + d**3/12 + d**2/2 + 5*d. Let z(y) be the first derivative of o(y). Factor z(f).
-(f - 1)*(f + 1)/2
Solve 7/2*k**4 + 13/2*k + 23/2*k**3 + 27/2*k**2 + 1 = 0 for k.
-1, -2/7
Let x(i) be the first derivative of -i**5 + 5*i**4 - 20*i**3/3 - 13. Solve x(y) = 0 for y.
0, 2
Let l(o) be the second derivative of -o**5/20 + o**4/12 + o**3/6 - o**2/2 + 9*o. Let w(r) = r**2 - 2*r + 1. Let q(v) = -l(v) - w(v). Factor q(a).
a*(a - 1)**2
Let d(q) = -2*q - 2*q - 3*q**2 - 4*q - 5 + q**2. Let w(s) = s**2 + s + 1. Let g(k) = -d(k) + w(k). Factor g(m).
3*(m + 1)*(m + 2)
Let r(n) = -2*n + 1. Let u be r(-1). Let q be (-1 - (-2 + u)) + 6. Suppose 2*c**q - c**5 - 3*c + 3*c + c - 2*c**2 = 0. What is c?
-1, 0, 1
Let f(v) be the first derivative of -v**5/20 + v**4/4 - v**3/2 - 3*v**2 + 6. Let n(z) be the second derivative of f(z). Factor n(b).
-3*(b - 1)**2
Let n = -1101 - -14319/13. Suppose -4/13*q**2 - n*q**3 + 0*q + 2/13*q**5 + 0*q**4 + 0 = 0. Calculate q.
-1, 0, 2
Let n(h) be the third derivative of -h**6/540 - 2*h**5/135 - h**4/27 - 2*h**2. Factor n(o).
-2*o*(o + 2)**2/9
Let f(u) be the first derivative of u**6/3 - 8*u**5/15 - 2*u**4/3 + 45. Factor f(v).
2*v**3*(v - 2)*(3*v + 2)/3
Let 22*n**2 - 2*n**2 - 10*n - 4*n**3 - 25*n + 3*n + 16 = 0. What is n?
1, 2
Let l = -139 + 141. Factor 1/2 - 1/2*a**l + 0*a.
-(a - 1)*(a + 1)/2
Let d(c) = 6*c**4 - 2*c**3 - 6*c**2 + 2*c. Let z(i) = 25*i**4 - 9*i**3 - 25*i**2 + 9*i. Let q(m) = -9*d(m) + 2*z(m). Find u, given that q(u) = 0.
-1, 0, 1
Let k be ((-36)/8)/((-6)/85). Let u = 64 - k. Find s, given that -1/4*s + 0 + 1/4*s**3 + 1/4*s**4 - u*s**2 = 0.
-1, 0, 1
Let n(j) be the third derivative of -j**8/1680 + j**7/525 - j**5/150 + j**4/120 + 12*j**2. Factor n(d).
-d*(d - 1)**3*(d + 1)/5
Solve -4/5*x**4 + 16*x**2 - 88/5*x + 2/5*x**5 + 32/5 - 22/5*x**3 = 0.
-4, 1, 2
Let m be (2/7)/((-1)/(-7)). Suppose -4*c + 18 = -0*c - m*d, 3*d = 2*c - 7. Factor -b**4 + 0*b**5 - b**5 + 0*b**c + b**3 + b**2.
-b**2*(b - 1)*(b + 1)**2
Let v(m) be the first derivative of m**2 - 1/90*m**5 - 1/9*m**3 + 1 + 0*m - 1/18*m**4. Let c(h) be the second derivative of v(h). Find l such that c(l) = 0.
-1
Let h be (4 - (-68)/(-10))/((-136)/40). Determine n, given that -4/17*n**2 + h*n**5 - 14/17*n**3 + 0*n + 0 + 4/17*n**4 = 0.
-1, -2/7, 0, 1
Let i(u) be the first derivative of u**9/7560 - u**8/4200 - u**7/2100 + u**6/900 - u**3/3 + 2. Let t(c) be the third derivative of i(c). What is w in t(w) = 0?
-1, 0, 1
Suppose 0 = -3*q + o + 262, -4*o - 256 = -4*q + q. Factor -87*z**2 - 12 - 4 - 50*z**3 - 53*z**2 - q*z.
-2*(z + 2)*(5*z + 2)**2
Let u(x) = -7*x**3 - 17 + 1 - 13*x**3 - 3*x**5 - 9*x**5. Let g(c) = c**5 + c**3 + 1. Let l(i) = 16*g(i) + u(i). Factor l(p).
4*p**3*(p - 1)*(p + 1)
Let s(g) = -19*g**4 - 195*g**3 - 619*g**2 - 729*g - 164. Let l(f) = 132*f**4 + 1365*f**3 + 4332*f**2 + 5103*f + 1149. Let y(m) = 2*l(m) + 15*s(m). Factor y(k).
-3*(k + 3)**3*(7*k + 2)
Let z(k) = -5*k**2 + 5*k + 16. Let o(u) = 2*u**2 - 3*u - 8. Let c(s) = 14*o(s) + 6*z(s). Find m such that c(m) = 0.
-4, -2
Let h(x) = x**2 - 3*x - 4. Let y(u) = u**2 - u - 2. Let o(p) = -3*h(p) + 5*y(p). Find b such that o(b) = 0.
-1
Find t such that 4/7*t**2 - 2/7*t**3 - 4/7 + 2/7*t = 0.
-1, 1, 2
Let m be (-1*2)/((-1)/96). Suppose -5*r + m = -r. Suppose -r*a**3 + 24*a**2 + 7*a - 11*a + 25*a**4 + 3*a**3 = 0. What is a?
0, 2/5, 1
Let c = -15 - -21. Solve -c - 4*l + l**2 - 4*l**2 + 13*l = 0 for l.
1, 2
Let b(x) be the first derivative of x - 1/2*x**4 + 3*x**2 - 2/3*x**6 + 8/3*x**3 - 9/5*x**5 + 2. Let b(n) = 0. What is n?
-1, -1/4, 1
Let r be 3*1/(-6)*0. Let i(l) be the third derivative of -l**2 + 0 + 0*l**4 + 1/60*l**5 + 0*l**3 + r*l. Factor i(b).
b**2
Let y(l) be the first derivative of 1/8*l**2 + 1/12*l**3 + 1 - 1/2*l. Factor y(p).
(p - 1)*(p + 2)/4
Let k(t) be the second derivative of t**6/1440 - t**5/480 + t**3/2 - 3*t. Let f(b) be the second derivative of k(b). Determine n so that f(n) = 0.
0, 1
Let b(n) be the first derivative of -n**5/4 - 5*n**4/8 + 5*n**3/12 + 5*n**2/4 + 26. Suppose b(c) = 0. Calculate c.
-2, -1, 0, 1
Let v(u) be the third derivative of 0 + 1/504*u**8 + 4/9*u**3 + 4*u**2 - 1/63*u**7 + 1/90*u**5 + 0*u - 2/9*u**4 + 7/180*u**6. What is o in v(o) = 0?
-1, 1, 2
Let z(i) be the third derivative of -i**5/5 - 3*i**4/8 + i**3/2 - 6*i**2. Factor z(p).
-3*(p + 1)*(4*p - 1)
Let u = -240/13 + 1213/65. Factor 4/5*i + 4/5 + u*i**2.
(i + 2)**2/5
Suppose 0*r = r - 3. Factor -5*l**4 - r*l**3 + 2*l + 3*l**4 + l**2 + l**4 + l**5.
l*(l - 2)*(l - 1)*(l + 1)**2
Let g(j) be the second derivative of j**4/24 - j**2/4 - 14*j. Factor g(l).
(l - 1)*(l + 1)/2
Let t(x) = -x**3 + 9*x**2 + 2*x - 77. Let y be t(8). Let r be (-3)/(-4) - 2/4. Determine k so that k**2 + 5/4*k + 1/2 + r*k**y = 0.
-2, -1
Let b be -10*1/(-10)*2. Factor -9/5*w**b + 9/5*w - 3/5 + 3/5*w**3.
3*(w - 1)**3/5
Suppose -3*k = -2*k - 4*r + 1, 0 = -r + 2. Factor k*f**3 - 7*f**3 + 3*f**4 - 3*f**2.
3*f**2*(f - 1)*(f + 1)
Let l(v) = v + 10. Let o be l(-7). Let c be (-1)/6 - (-14)/21. Suppose 0*w**2 + c*w**o + 0 - 1/2*w = 0. What is w?
-1, 0, 1
Let c(m) = m**5 + m**2 - m. Let r(h) = 4*h**3 - 1 + 2*h**4 - 7*h**2 - 8*h**5 - 3*h**2 + 1 + 4*h + 2. Let o(p) = 6*c(p) + r(p). Factor o(d).
-2*(d - 1)**3*(d + 1)**2
Let u(b) be the third derivative of b**7/210 - 7*b**6/120 + 4*b**5/15 - b**4/2 - 50*b**2. Factor u(w).
w*(w - 3)*(w - 2)**2
Let c(o) be the first derivative of 4*o**5/5 - o**4 - 4*o**3 + 10*o**2 - 8*o - 5. Factor c(u).
4*(u - 1)**3*(u + 2)
Factor -1/10*p**2 + 4/5 + 1/5*p.
-(p - 4)*(p + 2)/10
Let b(v) be the second derivative of -4/3*v**3 + 0 - 4*v**2 + 4*v - 1/6*v**4. Factor b(g).
-2*(g + 2)**2
Let x be (-64 - -71) + (-66)/10. Let -4/5*g**3 + 4/5*g + 2/5*g**2 - x = 0. What is g?
-1, 1/2, 1
Let l = -1732/3 - -579. Solve 10/3*g**2 + 1/3 + 10/3*g**3 + 5/3*g + l*g**4 + 1/3*g**5 = 0.
-1
Let g = -12 + 15. Let i be 33/12 - g - -1. Suppose i*r**2 - 3/4*r**4 + 0 + 1/4*r**3 - 1/4*r = 0. Calculate r.
-1, 0, 1/3, 1
Let u(k) be the seco