- i*l**2 - 12*l**3 + 6.
-3*(l + 1)*(2*l - 1)*(2*l + 1)
Let t(i) be the first derivative of -i**7/126 - i**6/45 + i**4/18 + i**3/18 + i - 3. Let p(w) be the first derivative of t(w). What is j in p(j) = 0?
-1, 0, 1
Let r(w) be the first derivative of -w**6/33 - 6*w**5/55 - 3*w**4/22 - 2*w**3/33 + 68. What is y in r(y) = 0?
-1, 0
Let d = 29 - 29. Let w(a) be the second derivative of d*a**2 + 1/40*a**5 + 0*a**3 + 1/12*a**4 - 3*a + 0. Let w(b) = 0. Calculate b.
-2, 0
Let h(o) be the first derivative of -o**6/480 - o**5/240 + 7*o**2/2 + 3. Let q(j) be the second derivative of h(j). Factor q(f).
-f**2*(f + 1)/4
Factor 10*t**2 + 4 + 5*t - 3 - 1 - 5*t**5 - 10*t**4.
-5*t*(t - 1)*(t + 1)**3
Let p(u) be the second derivative of -u**4/28 - u**3/14 + 18*u. Factor p(x).
-3*x*(x + 1)/7
Factor 9/5 - 6/5*z - 12/5*z**2 + 3/5*z**4 + 6/5*z**3.
3*(z - 1)**2*(z + 1)*(z + 3)/5
Let t(o) be the second derivative of 0*o**2 + 1/2*o**3 + 1/10*o**6 + 9/20*o**5 + 3/4*o**4 - 4*o + 0. Let t(x) = 0. Calculate x.
-1, 0
Let h(d) = -d**2 - d + 92. Let b be h(-10). Factor 1/2*g**3 + 0*g + 0*g**b + 1/2*g**5 - g**4 + 0.
g**3*(g - 1)**2/2
Let r(d) = d. Let w be r(1). Let z be 3/(-6)*(1 - w). Factor -2*g + z*g**3 - 2*g**2 + g - 2*g**3 + 2 + 3*g**3.
(g - 2)*(g - 1)*(g + 1)
Let o(z) = -5*z**5 + 15*z**4 - 15*z**3 + 5*z**2 - 5. Let w(s) = -2*s**5 + 7*s**4 - 8*s**3 + 3*s**2 - 3. Let y(u) = -3*o(u) + 5*w(u). Factor y(p).
5*p**3*(p - 1)**2
Let d(q) be the second derivative of -2/21*q**3 - 1/7*q**2 - 3*q - 1/42*q**4 + 0. Factor d(z).
-2*(z + 1)**2/7
Suppose 16 = -0*m + 4*m. Let t = m + -2. Factor 0*g**4 - 2/3*g**5 + 0*g**t + 0*g + 2/3*g**3 + 0.
-2*g**3*(g - 1)*(g + 1)/3
Let q(m) be the second derivative of -m**7/7 - 2*m**6/15 + 2*m**5/5 + m**4/3 - m**3/3 - 5*m. Find x, given that q(x) = 0.
-1, 0, 1/3, 1
Let z = 41/66 + 1/22. Determine a, given that -z*a**3 - 2/3*a**5 + 0*a**2 + 0 + 0*a + 4/3*a**4 = 0.
0, 1
Let y(v) be the third derivative of v**9/7560 - v**7/630 + v**5/60 + v**4/12 - v**2. Let f(j) be the second derivative of y(j). Solve f(w) = 0.
-1, 1
Suppose 0 = -o + 4*o - 21. Let a(f) = f**3 - 7*f**2 + 3. Let t be a(o). Find k such that 0*k + 2/7*k**t + 2/7*k**2 + 0 = 0.
-1, 0
Factor 1/4*d**2 - 1/2 + 1/4*d.
(d - 1)*(d + 2)/4
Let j = 10 - -37. Find t such that 21*t + 18 - 20*t + j*t + 32*t**2 = 0.
-3/4
Let t be 6/33 + 698/(-3960). Let f(p) be the third derivative of 0*p + 0 + t*p**5 + 1/18*p**4 + 2/9*p**3 + p**2. Factor f(d).
(d + 2)**2/3
Let m(q) be the first derivative of q**6/2 - q**5 + 7*q**4/12 - q**3/9 + 7. Factor m(k).
k**2*(k - 1)*(3*k - 1)**2/3
Let k(p) = p**3 + p**2 + p. Let v(s) = 4*s**3 - 20*s**2 - 48*s - 32. Let z(r) = 8*k(r) - v(r). Factor z(w).
4*(w + 1)*(w + 2)*(w + 4)
Let v(m) = -3*m**3 - m**2 - 3*m - 1. Suppose 0*r - 8 = -4*r. Let f(b) = 13*b**3 + 3*b**2 + 12*b + 4. Let j(n) = r*f(n) + 9*v(n). Factor j(s).
-(s + 1)**3
Let f(u) = u**3 + 7*u**2 - 8*u. Let q be f(-8). Let y(v) be the third derivative of 3/10*v**5 + q*v + 0 + 9/40*v**6 + 3*v**2 - v**3 - 5/8*v**4. Factor y(h).
3*(h + 1)*(3*h - 2)*(3*h + 1)
Determine r so that -3 - 24*r - 12*r**2 + 1 - 3*r**3 - 4 + 9*r = 0.
-2, -1
Let w(s) = -s + 3. Suppose -15 = -5*l - 0*l. Let r be w(l). Let r + 0*g + 1/2*g**3 + 1/4*g**2 = 0. Calculate g.
-1/2, 0
Let u(s) be the third derivative of -s**5/75 - s**4/5 - 6*s**3/5 - 14*s**2. Factor u(c).
-4*(c + 3)**2/5
Let v = 11 + -6. Suppose -r - 16 = -v*r, -5*r + 4 = -4*z. Solve q**2 + 5*q**2 - z*q**2 = 0 for q.
0
Let k(g) be the first derivative of 3*g**4/20 - 3*g**2/10 + 14. Find f, given that k(f) = 0.
-1, 0, 1
Let p be (86/215)/((-44)/(-10)). Let x(o) be the first derivative of 0*o**3 - 1/11*o**4 + p*o**2 + 1/33*o**6 - 2 + 0*o + 0*o**5. Factor x(t).
2*t*(t - 1)**2*(t + 1)**2/11
Suppose 16 = 2*c - 0*c. Suppose 2*b - 3*y = 20, b - y + 0*y = c. Factor -2*n**2 + b*n - 4*n.
-2*n**2
Let a(j) be the second derivative of 35*j**5/4 + 5*j**4/3 - 10*j**3/3 - 20*j. Factor a(d).
5*d*(5*d + 2)*(7*d - 2)
Factor 3/7*t**2 - 3/7 + 0*t.
3*(t - 1)*(t + 1)/7
Let s(z) = -z**2 + 6*z - 4. Let l be s(4). Let y be -5*(12/(-5) + 2). Factor 0 - 1 - w**y + 4*w**3 + 2 - l*w.
(w - 1)*(w + 1)*(4*w - 1)
Find d such that -2*d**4 + d**2 - 2 - 6*d + 3*d**2 + 6*d = 0.
-1, 1
Let i(w) = 0*w - w**2 + 12*w**3 - 1 - 13*w**3 - w. Let o(f) = 9*f**4 + 18*f**3 + 7*f**2 - 4*f - 6. Let j(v) = -6*i(v) + o(v). Determine u, given that j(u) = 0.
-2, -1/3, 0
Let o(z) be the second derivative of 0*z**4 + 0*z**6 + 0*z**3 + 3*z + 0 - z**2 - 1/630*z**7 + 1/180*z**5. Let p(h) be the first derivative of o(h). Factor p(w).
-w**2*(w - 1)*(w + 1)/3
Let 38/3*h**4 - 32/3*h - 4/3*h**5 + 112/3*h**2 + 0 - 38*h**3 = 0. What is h?
0, 1/2, 1, 4
Suppose 4*n - 2*g + 1 = 15, 0 = -3*n - 5*g + 17. Suppose 0*d**2 - d**n - d**5 + d**2 - d**2 = 0. Calculate d.
-1, 0
Suppose 13 + 17 = 5*q - 5*r, -12 = 4*q + 5*r. Factor -8*p**3 + 2*p - 3*p + p - 4*p**q + p**4 + 2*p**5.
p**2*(p - 2)*(p + 2)*(2*p + 1)
Let c(a) = -a**3 + a**2 + a + 1. Let j(m) = m**3 - m**2 - 2*m - 2. Let u = 0 - -3. Suppose k = u*k - 2. Let v(l) = k*j(l) + 2*c(l). Suppose v(w) = 0. What is w?
0, 1
Let u(z) be the third derivative of -z**6/96 + z**5/48 + 2*z**2. What is x in u(x) = 0?
0, 1
Let c be (-252)/(-245) + (-6)/14. What is j in 0 - c*j**5 + 0*j**2 - 3/5*j + 6/5*j**3 + 0*j**4 = 0?
-1, 0, 1
Let i(q) = -q - 1. Let u be i(-3). What is g in -3*g + 2*g + 3*g + 5*g**u = 0?
-2/5, 0
Factor -3*l**3 - 3*l**3 - 2*l**4 + 2*l**3.
-2*l**3*(l + 2)
Let o(h) be the first derivative of 0*h**2 + 1/6*h**4 + 0*h - 2 + 1/18*h**3. Factor o(g).
g**2*(4*g + 1)/6
Let p be (-1)/(-2 + 7/3). Let n = p + 4. Factor 4*y - 6*y**2 + y**4 - y**4 - y**4 + 4*y**3 - n.
-(y - 1)**4
Factor 3*v + 6178 + 3*v**3 - 2*v**5 - 6178 - 7*v**2 + 3*v**4.
-v*(v - 1)**3*(2*v + 3)
Suppose v + 4 = -2*p + 10, 0 = -3*p - 2*v + 10. Let c(r) be the second derivative of 0*r**3 - 1/5*r**2 + 1/30*r**4 + 0 - p*r. Factor c(f).
2*(f - 1)*(f + 1)/5
Let a be 16 - 8 - (2 - 1). Let p = a - 3. Solve 0*u + 0 + 1/2*u**p + 1/2*u**5 - 1/2*u**2 - 1/2*u**3 = 0.
-1, 0, 1
Suppose 2*r = -4 - 8. Let u = r + 9. Determine v, given that -2*v + 2*v**3 - 2 - 2*v**2 + u + 1 = 0.
-1, 1
Let f(z) = 3*z**2 + z. Let t be f(3). Let d be 6*(-8)/t - -2. Factor 2/5*v**2 - d*v**3 + 0*v + 0.
-2*v**2*(v - 1)/5
Suppose -3*u + 11 = -4*k, -u + k = 2*u - 5. Let l = 2 + u. Suppose 12 + 12*z - 5*z**2 - 12*z**3 - l*z**4 - 9*z**2 + 5*z**2 = 0. Calculate z.
-2, -1, 1
Let u(n) = 16*n**4 + 24*n**3 + 25*n**2 - 7*n + 4. Let o(z) = 5*z**4 + 8*z**3 + 8*z**2 - 2*z + 1. Let b(d) = 21*o(d) - 6*u(d). Find y such that b(y) = 0.
-1, 1/3
Let l be (-43)/86 + 2 + -1. Factor 0 - l*d**3 - d**2 - 1/2*d.
-d*(d + 1)**2/2
Let w(a) = 3*a**3 - 6*a**2 - 3*a - 6. Suppose 5*n + t - 29 = 0, -n + t + 3 = 4*t. Let h(d) = 3*d**3 - 7*d**2 - 3*d - 7. Let m(q) = n*h(q) - 7*w(q). Factor m(g).
-3*g*(g - 1)*(g + 1)
Suppose -10*f + 13*f = 15. Suppose 2*y - f*y + 15 = 0. Factor -n**2 - 1/2*n + 0 + 1/2*n**y + n**4 + 0*n**3.
n*(n - 1)*(n + 1)**3/2
Let y(o) be the third derivative of -o**5/100 - o**4/40 + 6*o**3/5 - 14*o**2 + 2*o. Determine i so that y(i) = 0.
-4, 3
Factor 12/5*h + 1/5*h**3 - 8/5 - 6/5*h**2.
(h - 2)**3/5
Let n(l) be the second derivative of -1/108*l**4 - 2*l + 2/27*l**3 + 0 - 1/270*l**5 - l**2. Let a(f) be the first derivative of n(f). Factor a(s).
-2*(s - 1)*(s + 2)/9
Determine p so that 1/3*p**3 - 1/3*p**4 + 2/3*p**2 + 0 + 0*p = 0.
-1, 0, 2
Suppose -4*u + 9 + 7 = -2*m, -3*m + 3*u = 9. Let w = -51 - -54. Suppose -2/3*o**w + 0*o + 0 - 2/3*o**m = 0. What is o?
-1, 0
Let d(w) be the second derivative of -3*w**6/70 + 11*w**5/140 + 17*w**4/42 - 22*w**3/21 + 4*w**2/7 - 13*w. Find f, given that d(f) = 0.
-2, 2/9, 1, 2
Suppose -1 = -2*r + 3*o + 2, -4 = -4*o. Let g be r/4 + (-27)/(-12). Suppose -q**g + 2*q**3 - q - 1 + 0*q**3 + q**2 = 0. Calculate q.
-1, 1
Let g(h) = -9*h + 2. Let y be g(-2). Suppose -y + 0 = -5*i. What is s in -2/7 - 2/7*s**5 - 20/7*s**2 - 10/7*s - 10/7*s**i - 20/7*s**3 = 0?
-1
Let o = 11 + -9. Suppose 0 = 4*f - o*j - 10, -3*f - j + 5 + 5 = 0. Factor 0 + 3/4*x**5 + 3/4*x**2 + 0*x - 3/4*x**4 - 3/4*x**f.
3*x**2*(x - 1)**2*(x + 1)/4
Let a(l) = 4*l**4 - 3*l**3 + 1. Let c(z) be the first derivative of -z**6/6 - z**5/5 + z**3/3 - z + 5. Let n(p) = -3*a(p) - 3*c(p). What is i in n(i) = 0?
0, 1
Let a(m) be the first 