2*z*(z - 1)*(z + 1)**2/7
Let i(m) be the second derivative of -m**5/110 - m**4/33 + 7*m. Factor i(h).
-2*h**2*(h + 2)/11
Let j(t) = t**3 - 6*t**2 - t + 4. Let r be j(6). Let o be -2*(r - (-10)/(-4)). Suppose -9*s**2 + 6*s - 4 + o*s**2 - 2*s**3 = 0. Calculate s.
-2, 1
Factor 1/3 + 0*p - 1/3*p**2.
-(p - 1)*(p + 1)/3
Let a(u) be the third derivative of -u**5/330 - u**4/66 + u**3/11 - 15*u**2. Solve a(c) = 0 for c.
-3, 1
Let o be (-3 - (-26)/8)*8. Solve 3*p**2 + p**3 + 6*p**2 - p**4 - 7*p**o = 0 for p.
-1, 0, 2
Let b be (3 - 7)*3/(-6). Factor -b*v + 2*v - 10*v**2 - 14*v**3 + 4*v.
-2*v*(v + 1)*(7*v - 2)
Suppose -9 + 4 = -4*g - 3*f, 5 = 2*g + f. Let c(j) be the first derivative of 1/20*j**g + 0*j + 0*j**2 + 1/12*j**3 + 1/8*j**4 - 2. Factor c(s).
s**2*(s + 1)**2/4
Suppose 0*o = 5*o - 25. Let h be -16*(-1)/o - 3. Factor -1/5*n**2 + 0 + 1/5*n - 1/5*n**3 + h*n**4.
n*(n - 1)**2*(n + 1)/5
Let b = 11 + -9. Factor 28*m - 2*m**4 - m**4 + 32*m - 24 - 54*m**b + 21*m**3.
-3*(m - 2)**3*(m - 1)
Let q(g) be the first derivative of 4/15*g**5 + 0*g**2 - 5/12*g**4 + 0*g + 3 + 1/9*g**3. Factor q(m).
m**2*(m - 1)*(4*m - 1)/3
Let i(n) = -5*n**5 - n**4 + 14*n**3 + n**2 + n + 5. Let g(c) = 3*c**5 + c**4 - 7*c**3 - c**2 - 2. Let v(m) = 5*g(m) + 2*i(m). Let v(l) = 0. Calculate l.
-1, 0, 2/5, 1
Let l(b) = -b**2 - 1. Let a be l(-2). Let j(h) = 4*h**2 - 3*h - 6. Let z = -4 + 3. Let s(f) = -f**2 + f + 1. Let p(o) = a*s(o) + z*j(o). What is u in p(u) = 0?
1
Let q(b) be the second derivative of 1/10*b**5 + 0 + 2*b + 0*b**4 + 1/15*b**6 + 0*b**2 + 0*b**3. Factor q(p).
2*p**3*(p + 1)
Determine l so that -2/3*l**2 + 2/3*l**4 - 4/3*l + 2*l**3 + 0 - 2/3*l**5 = 0.
-1, 0, 1, 2
Let o(x) be the first derivative of 2*x**5/11 - 9*x**4/11 - 26*x**3/33 + 18*x**2/11 + 16*x/11 + 1. Find w such that o(w) = 0.
-1, -2/5, 1, 4
Let l(n) = -n**3 - 11*n**2 + 2. Let p be l(-11). What is f in -3/5*f**p - 2/5*f + 7/5*f**3 + 3/5*f**4 + 0 - f**5 = 0?
-1, -2/5, 0, 1
Let l = -59/24 + 25/8. What is v in 8/3 + l*v**2 + 8/3*v = 0?
-2
Let o(l) be the second derivative of -l**7/84 + l**6/60 + l**5/20 - l**4/12 - l**3/12 + l**2/4 - 13*l. Factor o(q).
-(q - 1)**3*(q + 1)**2/2
Let k(n) = -154*n**3 - 324*n**2 - 208*n - 56. Let u(h) = 103*h**3 + 216*h**2 + 139*h + 37. Let c(x) = -5*k(x) - 8*u(x). Determine r, given that c(r) = 0.
-2/3
Let a(g) = 3*g**5 + 8*g**4 + 21*g**3 - 3*g**2 - 17*g - 5. Let b(v) = 2*v**5 + 9*v**4 + 22*v**3 - 4*v**2 - 18*v - 5. Let f(o) = 6*a(o) - 7*b(o). Solve f(w) = 0.
-1, -1/4, 1, 5
Let n = -414 - -831/2. Factor n + 1/2*w**2 - 2*w.
(w - 3)*(w - 1)/2
Let u(x) be the first derivative of -x**3/4 + 3*x**2 - 12*x - 13. Factor u(q).
-3*(q - 4)**2/4
Suppose 2*c - p - 263 + 56 = 0, 0 = -c + p + 103. Let s be (-2)/(-5) + c/65. Find j, given that s*j**2 + 10/3*j**3 - 4/3*j + 0 = 0.
-1, 0, 2/5
Let f(u) be the third derivative of u**5/15 + 4*u**4/9 - 2*u**3/3 - 31*u**2. Factor f(z).
4*(z + 3)*(3*z - 1)/3
Let s(n) be the first derivative of -n**7/42 - n**6/15 - n**5/20 + 4*n + 3. Let k(o) be the first derivative of s(o). Factor k(m).
-m**3*(m + 1)**2
Let q(s) be the second derivative of -s**7/42 - s**6/15 + s**4/6 + s**3/6 + 5*s. Factor q(p).
-p*(p - 1)*(p + 1)**3
Let s(a) = 3*a + 2. Let b be s(0). Factor 0 - 3/4*r**b + 1/4*r**4 + 0*r**3 + 1/2*r.
r*(r - 1)**2*(r + 2)/4
Let w(x) = x**2 + 5*x. Let y be w(-5). Let b be (y + -2 + -2)/(-2). Let -4 - 6*j + 0 + b + 2*j**2 + 6 = 0. Calculate j.
1, 2
Suppose 2*k - g - 9 = -2*g, 0 = 4*k + 5*g - 3. Find v, given that 117*v - 20*v**3 - 162*v**4 - 81*v**5 - k*v**3 + 8*v**2 + 130*v**2 + 24 - 9*v = 0.
-1, -2/3, 1
Let g(j) be the first derivative of j**3/12 + 3*j**2/2 + 9*j - 40. Factor g(s).
(s + 6)**2/4
Factor -m**2 + 152*m - 156*m + 5*m**2.
4*m*(m - 1)
Suppose -144 + 128*o - 48*o**2 + 50*o**3 + 20*o**2 - 8*o - 48*o**3 = 0. What is o?
2, 6
Find x such that -x**4 - 5*x + 3*x**3 + 5*x - x**5 - 2*x + x**2 = 0.
-2, -1, 0, 1
Let i(h) = -3 + 8*h + 6*h**2 + 0 + 2 - 1. Let s(m) = -m**2 - m + 1. Let u(y) = -i(y) - 4*s(y). Find f such that u(f) = 0.
-1
Let y(k) = -k**3 - 12*k**2 - 9*k + 25. Let x be y(-11). Factor -6*g + 9/2*g**x + 6 - 15/2*g**2.
3*(g - 2)*(g + 1)*(3*g - 2)/2
Suppose -32 = 40*d - 36*d. Let n be (-18)/135 - d/10. Factor 0*p + 0*p**2 + 0 - 2/3*p**5 + n*p**4 + 0*p**3.
-2*p**4*(p - 1)/3
Let r = 519 + -54494/105. Let d(u) be the second derivative of r*u**7 + 1/75*u**6 + 1/5*u**2 + 0 - 1/25*u**5 - 1/15*u**4 + 1/15*u**3 + 2*u. Factor d(v).
2*(v - 1)**2*(v + 1)**3/5
Let w(k) be the second derivative of k**9/3780 - k**8/672 + k**7/315 - k**6/360 + k**4/6 + 5*k. Let x(q) be the third derivative of w(q). Factor x(r).
2*r*(r - 1)**2*(2*r - 1)
Let g = 12 - 2. Suppose -g = 5*m, -2*m = 2*q + m + 2. Factor 5*j**3 + 3*j - j - 6*j**3 + j**q.
-j*(j - 2)*(j + 1)
Let q = 111/1100 - 1/100. Let d = q - -15/77. Factor d*i**2 - 4/7*i - 2/7 + 4/7*i**3.
2*(i - 1)*(i + 1)*(2*i + 1)/7
Suppose 4*k = -5*g, -g - 3*k = -4*k. Suppose -2*r - 4*s = g, 5*s = -0*r + 2*r - 9. Find d such that 2/7*d + 4/7*d**r + 0 + 2/7*d**3 = 0.
-1, 0
Let i(n) be the third derivative of 0*n**3 + 0 + 0*n + 2*n**2 + 1/60*n**4 - 1/150*n**5. Factor i(t).
-2*t*(t - 1)/5
Let z(t) be the first derivative of -t**6/360 + t**5/180 + t**4/72 - t**3/18 + 3*t**2/2 + 5. Let p(l) be the second derivative of z(l). Factor p(b).
-(b - 1)**2*(b + 1)/3
Let s(u) be the first derivative of u**5/4 - 85*u**4/8 + 165*u**3 - 4235*u**2/4 + 6655*u/4 + 62. Determine x, given that s(x) = 0.
1, 11
Solve -a**2 + 0*a**2 - 5 + 2 - 4*a = 0 for a.
-3, -1
Let b(p) be the second derivative of p**7/105 + p**6/30 - p**5/30 - p**4/6 - 3*p**2/2 + 3*p. Let f(c) be the first derivative of b(c). What is v in f(v) = 0?
-2, -1, 0, 1
Let h(d) be the second derivative of d**4/4 - 3*d**3 + 27*d**2/2 + 2*d. Suppose h(n) = 0. Calculate n.
3
Let n(x) be the second derivative of 0*x**2 - 9/14*x**7 + 9/10*x**6 + 4/3*x**3 + x - 7/3*x**4 + 9/10*x**5 + 0. Factor n(c).
-c*(c + 1)*(3*c - 2)**3
Let l(o) be the third derivative of o**8/224 + 13*o**7/420 + 37*o**6/720 + o**5/360 - o**4/24 + 7*o**2. Solve l(g) = 0.
-3, -1, -2/3, 0, 1/3
Let b = -1725/7 - -247. Find p such that b + 2/7*p**2 + 6/7*p = 0.
-2, -1
Let o(t) be the second derivative of t**6/10 - 3*t**5/10 + t**3 - 3*t**2/2 - t. Factor o(i).
3*(i - 1)**3*(i + 1)
Determine r so that 0 - 1/4*r + 1/4*r**2 = 0.
0, 1
Determine q so that 1 - 11 - 3*q**3 + 9*q**2 - 2 = 0.
-1, 2
Let r = -29/2 - -15. Factor r*u**2 + u + 1/2.
(u + 1)**2/2
Let g(p) be the second derivative of -p**5/5 - p**4/3 + 4*p**3/3 + p. Let g(a) = 0. What is a?
-2, 0, 1
Let p(w) be the second derivative of -3/2*w**2 + 3*w + 1/4*w**4 + 0 - 1/20*w**5 + 1/6*w**3. Factor p(x).
-(x - 3)*(x - 1)*(x + 1)
Find u, given that u + 3/4*u**4 - 1/2*u**2 - u**3 - 1/4 = 0.
-1, 1/3, 1
Let p(j) be the third derivative of -j**6/60 + j**5/15 + j**4/12 - 2*j**3/3 + 27*j**2. What is q in p(q) = 0?
-1, 1, 2
Let j(i) be the first derivative of 1/8*i**2 + 1/24*i**6 + 1 + 0*i + 0*i**3 + 0*i**5 - 1/8*i**4. What is l in j(l) = 0?
-1, 0, 1
Let o(n) be the second derivative of -1/36*n**4 + 1/18*n**3 - 2*n + 0 + 1/3*n**2. Solve o(m) = 0.
-1, 2
Let r = 19 - 14. Let c(i) be the first derivative of 32/5*i**r + 0*i**2 - 1 + 0*i + 11/2*i**4 + 4/3*i**3 + 7/3*i**6. What is f in c(f) = 0?
-1, -2/7, 0
Let h(r) = r - 5. Let w be h(7). Determine d, given that -2*d**4 + 4/3*d**w + 2/3*d**5 - 2*d + 2/3 + 4/3*d**3 = 0.
-1, 1
Find a such that -21*a**4 - 4*a**3 - 6*a**3 + 40*a + 29*a**4 + 0*a**3 - 30*a**2 - 8 = 0.
-2, 1/4, 1, 2
Let b be (-5)/(-6)*(-24)/(-80). Factor -1/2 - b*k + 1/4*k**2.
(k - 2)*(k + 1)/4
Let c be 1/5*(0 + 1). Suppose -u = -3*g + 12, -4*u + 7*u - 4 = -g. Factor -c*j + u - 1/5*j**2 + 1/5*j**4 + 1/5*j**3.
j*(j - 1)*(j + 1)**2/5
Let m(d) be the first derivative of 4 + d + 1/5*d**5 - 2/3*d**3 + 0*d**2 + 0*d**4. Factor m(c).
(c - 1)**2*(c + 1)**2
Let u = -26 - -29. Suppose 5 = -2*r + 3*q - u, -4*q = r - 18. Solve 2/9 + 2/9*w + 2/9*w**4 + 2/9*w**5 - 4/9*w**3 - 4/9*w**r = 0 for w.
-1, 1
Factor 1/5*c**5 + 0*c + 0*c**4 + 0 - 1/5*c**3 + 0*c**2.
c**3*(c - 1)*(c + 1)/5
Determine m, given that 59*m**3 - 63*m**3 - 3*m + 16*m**2 + 23*m = 0.
-1, 0, 5
Suppose 0 = g - 5*g + 4. Let u(w) = w + 2. Let q be u(g). Solve -1/2*a**q - 1/4 + a - a**2 + 5/4*a**4 - 1/2*a**5 = 0.
-1, 1/2, 1
Factor 13*y**3 - 1391 - 61