i**2 + 21*i - 10. Let c(k) = 2*l(k) - 3*u(k). Factor c(q).
2*(q - 1)**2*(q + 5)
Let k(z) be the first derivative of -z**6/75 + z**4/15 - z**2/5 - 2*z + 6. Let c(v) be the first derivative of k(v). Factor c(b).
-2*(b - 1)**2*(b + 1)**2/5
Let h(y) = -13*y + 28. Let c(n) = -6*n + 14. Let m(s) = -7*c(s) + 3*h(s). Let w be m(6). What is f in -f**3 + f + 1/2*f**w + 0*f**2 - 1/2 = 0?
-1, 1
Suppose -86 = -5*w - 76. Factor -3/4 + 0*k + 3/4*k**w.
3*(k - 1)*(k + 1)/4
Let j(n) be the third derivative of -n**6/540 + n**4/108 + 15*n**2. Factor j(h).
-2*h*(h - 1)*(h + 1)/9
Let h = -14 + 22. Solve 15*k**3 + 2*k**5 - h*k**2 - 3*k**3 + 2*k - 2*k**4 - 2*k**4 - 4*k**4 = 0 for k.
0, 1
Let n(f) be the third derivative of -f**6/300 - f**5/75 + f**4/20 + 3*f**2 + 7. Let n(q) = 0. Calculate q.
-3, 0, 1
Let p(i) be the second derivative of -i**4/24 + i**2/4 + 12*i. Let p(a) = 0. Calculate a.
-1, 1
Let a(k) be the first derivative of -k**4/4 - 4*k**3/3 - k**2/2 + 6*k - 8. Suppose a(n) = 0. What is n?
-3, -2, 1
Let o be 601/35 - (-18)/45. Let t = o + -1051/63. Factor 4/3*y**3 + 0 + 2/9*y + 2/9*y**5 + t*y**2 + 8/9*y**4.
2*y*(y + 1)**4/9
Let c(v) be the second derivative of -2/3*v**3 + 0*v**2 + 6/5*v**5 - 3*v + 1/2*v**4 + 0 + 7/15*v**6. Factor c(n).
2*n*(n + 1)**2*(7*n - 2)
Let j(f) be the first derivative of 0*f + 1/3*f**2 - 32/15*f**5 - 2*f**3 - 4 + 4*f**4. Suppose j(a) = 0. What is a?
0, 1/4, 1
Let y(z) = z**2 + 2. Let d be y(0). Suppose 14*a - 11*a - 6 = 0. Solve 12*j**d - 16*j + 0*j**3 + 8 - a*j**3 - 2*j**2 = 0.
1, 2
Let y(g) be the third derivative of 1/112*g**8 + 0*g - 2/35*g**7 + 1/10*g**6 + 0 + 0*g**3 + 0*g**5 + 6*g**2 + 0*g**4. Find z such that y(z) = 0.
0, 2
Let k be 9*-1*(5 + (-532)/105). Factor 3/5*v - k*v**3 + 0 + 0*v**2.
-3*v*(v - 1)*(v + 1)/5
Suppose 2/13*w**5 + 6/13*w**2 - 4/13*w + 0 + 2/13*w**3 - 6/13*w**4 = 0. What is w?
-1, 0, 1, 2
Let h(k) be the third derivative of -k**9/1512 + k**7/420 + k**3/6 + k**2. Let c(s) be the first derivative of h(s). Factor c(m).
-2*m**3*(m - 1)*(m + 1)
Suppose -5 + 15 = 2*h. Let j(s) be the second derivative of -1/63*s**7 + 0*s**2 + 2/45*s**6 + 0*s**h + 1/9*s**3 + 0 - 1/9*s**4 - s. Let j(u) = 0. Calculate u.
-1, 0, 1
Let b(y) be the second derivative of y**4/78 + 11*y**3/39 + 48*y. Suppose b(r) = 0. Calculate r.
-11, 0
Let b(h) be the second derivative of -1/8*h**4 + 1/20*h**5 + 0 + 0*h**3 + 3/2*h**2 + 3*h. Let i(p) be the first derivative of b(p). Factor i(r).
3*r*(r - 1)
Let s be (-24)/(-40) + 27/5. Let p be ((-3 + s)/9)/1. Suppose 0*u - p*u**3 + 0 + 0*u**4 + 1/3*u**5 + 0*u**2 = 0. Calculate u.
-1, 0, 1
Suppose -11 - 1 = 4*b. Let u be 2*(0 - b/36). Factor u*m**2 + 1/3*m + 1/6.
(m + 1)**2/6
Let y = -15 + 17. Let k(n) = -n**3 + 3*n**2 - 2*n + 3. Let t be k(y). What is j in 1/2*j**4 + t*j**2 + 2*j + 2*j**3 + 1/2 = 0?
-1
Let x(d) = 3*d**2 + d - 2. Let k(y) = -16*y**2 - 6*y + 11. Let c(i) = 6*k(i) + 33*x(i). Find n such that c(n) = 0.
0, 1
Let u(l) be the second derivative of -l**6/15 + l**5/10 + l**4/6 - l**3/3 - 23*l. Solve u(x) = 0.
-1, 0, 1
Let z(i) be the second derivative of -i**7/3 + 26*i**6/15 - 17*i**5/5 + 8*i**4/3 + i**3/3 - 2*i**2 - 2*i. Factor z(p).
-2*(p - 1)**4*(7*p + 2)
Let x(w) = -3*w**3 + 2*w**2 - 1. Let h(n) = n**3 + 1. Suppose -3*c = -0*c + 2*k - 3, 0 = -2*c - 4*k + 2. Let q(b) = c*h(b) + x(b). What is o in q(o) = 0?
0, 1
Let w = 161/2 + -79. Suppose 0 - w*c**2 + 0*c**3 + 3/2*c**4 + 0*c = 0. What is c?
-1, 0, 1
Let m(h) be the second derivative of h**6/45 + 7*h**5/30 + 17*h**4/18 + 17*h**3/9 + 2*h**2 + 15*h. What is i in m(i) = 0?
-3, -2, -1
Factor 0*u + 0 + 2/7*u**3 - 2/7*u**2.
2*u**2*(u - 1)/7
Let x(i) be the third derivative of -i**7/105 + i**6/30 - i**5/30 - 6*i**2. Factor x(m).
-2*m**2*(m - 1)**2
Let d be 6/9*(-1 + 4). Factor 5*r + 0*r - 8*r**d - 3*r.
-2*r*(4*r - 1)
Let l(d) be the first derivative of -d**4/8 - d**3/2 + d**2 - 20. Suppose l(k) = 0. What is k?
-4, 0, 1
Factor 6/7*h + 2/7*h**2 + 4/7.
2*(h + 1)*(h + 2)/7
Let m(v) be the second derivative of -5*v + 1/8*v**6 - 1/2*v**3 - 19/48*v**4 + 1/2*v**2 + 1/10*v**5 + 0 + 1/42*v**7. Find c such that m(c) = 0.
-2, -1, 1/4, 1
Let i = -33 + 35. Factor 2/9*a**4 + 0*a + 0 + 2/3*a**3 + 4/9*a**i.
2*a**2*(a + 1)*(a + 2)/9
Let y(u) = 24*u**3 - 30*u**2 + 5*u + 5. Let p(r) = -48*r**3 + 60*r**2 - 11*r - 11. Let i(q) = 2*p(q) + 5*y(q). Let i(v) = 0. What is v?
-1/4, 1/2, 1
Let m be (-2)/3 - (-6)/9. Let p be -3 - (m + 0) - -5. Solve 0 + 0*k - 7/3*k**5 - 2/3*k**3 + 0*k**p - 3*k**4 = 0.
-1, -2/7, 0
Let c be ((-4)/(-7))/(8/28). Suppose 1 - 11 = -5*l. Suppose j - l*j - 4*j**2 + j**3 - 3*j**4 - 2 + 9*j**c = 0. What is j?
-1, -2/3, 1
Let z = 22 - 31. Let h = z - -13. Factor -l**4 - l**3 + l**4 - l**h.
-l**3*(l + 1)
Suppose 12 + 0 = 4*l. Factor 6*a**5 - a**5 - 2*a**5 - 6*a**4 + l*a**3.
3*a**3*(a - 1)**2
Solve 8*y + 26*y**2 - 3*y + 4 - 31*y**2 + 6 = 0 for y.
-1, 2
Let x(c) = 2*c**2 + 3. Let y be x(3). Let f be y/(-7) - 14/(-4). Factor -l**2 - f*l - 1/2*l**3 + 0.
-l*(l + 1)**2/2
Factor 0 - 2/9*p**4 - 2/9*p**3 + 0*p + 4/9*p**2.
-2*p**2*(p - 1)*(p + 2)/9
Let g(k) = -3*k**4 + 8*k**3 - 2*k**2 - 4*k + 1. Let b(r) = -30*r**4 + 81*r**3 - 21*r**2 - 39*r + 9. Let f(p) = 2*b(p) - 21*g(p). Solve f(o) = 0 for o.
-1, 1
Let c(k) be the first derivative of 7*k**3/3 - 4*k**2 + k - 11. Suppose c(q) = 0. What is q?
1/7, 1
Let l(s) be the second derivative of -s**5/2 + 5*s**4/12 + 25*s**3/6 + 5*s**2 - 10*s. Solve l(j) = 0 for j.
-1, -1/2, 2
Factor -5*h + 16 - 5*h - h - 5*h + 4*h**2.
4*(h - 2)**2
Solve -25/8*q**2 + 1/8*q**3 - 18 + 21*q = 0.
1, 12
Solve 0*v - 2/5*v**4 + 0 + 2/5*v**3 + 4/5*v**2 = 0.
-1, 0, 2
Let c be -1 + 2 + 7 + 0. Suppose -t = t - c. What is u in 6*u**2 - 2*u + 0*u**3 + u**2 - 1 - t*u**3 = 0?
-1/4, 1
Let c = -2/39 + 47/156. Factor 1/4*x**2 + 1/2*x + c.
(x + 1)**2/4
Let f(l) be the second derivative of -l**7/3 + l**6/3 + l**5/5 + 6*l. Factor f(x).
-2*x**3*(x - 1)*(7*x + 2)
Let s(w) be the second derivative of -w**7/14 + 9*w**5/10 - 2*w**4 + 3*w**3/2 + 46*w. Factor s(j).
-3*j*(j - 1)**3*(j + 3)
Let y(b) be the first derivative of b**5/30 - b**4/3 + 4*b**3/3 + 5*b**2/2 - 1. Let l(m) be the second derivative of y(m). Factor l(q).
2*(q - 2)**2
Let l(v) = -20*v**3 + 248*v**2 - 972*v + 732. Let o(w) = -8*w**3 + 99*w**2 - 389*w + 293. Let n(q) = 5*l(q) - 12*o(q). Determine p so that n(p) = 0.
1, 6
Let j(f) be the third derivative of -f**6/420 - f**5/70 - f**4/42 + 7*f**2. Factor j(l).
-2*l*(l + 1)*(l + 2)/7
Let q(w) be the first derivative of 0*w - 5/9*w**6 - 3 - 2/3*w**2 - 34/15*w**5 - 7/2*w**4 - 22/9*w**3. Find d such that q(d) = 0.
-1, -2/5, 0
Let c be (-1)/5*29/(-3). Let z = c - 8/5. Factor 0*s**3 - 2/3*s**4 + 1/3*s**5 - z*s + 0 + 2/3*s**2.
s*(s - 1)**3*(s + 1)/3
Let m(i) be the second derivative of 0*i**4 + 0 - 1/15*i**3 + i + 0*i**2 + 1/50*i**5. Factor m(a).
2*a*(a - 1)*(a + 1)/5
Let v = 2/859 - -3418/7731. Suppose -2/9*b + v*b**2 + 0 - 2/9*b**3 = 0. Calculate b.
0, 1
Let b(w) = -w**3 - 6*w**2 + 7*w + 4. Let s be b(-7). Suppose -4*i**4 - 12*i**2 + 8 + 0*i**2 + 8*i**s + 4*i - 4*i**3 = 0. What is i?
-1, 1, 2
Let s(o) be the third derivative of o**6/40 - o**5/15 - 11*o**4/72 - o**3/9 + 9*o**2. Find x such that s(x) = 0.
-1/3, 2
Let w = -4 - -7. Suppose -w = m - 4*m. Factor m + 1 - 2*h**2 + 0.
-2*(h - 1)*(h + 1)
Factor -2/3*o - 2/9*o**2 - 4/9.
-2*(o + 1)*(o + 2)/9
Suppose 5*k - 4 = -4*v + 13, 6 = -3*v. Factor -4/9*u**3 + 0*u**2 + 0 + 2/9*u**k + 2/9*u + 0*u**4.
2*u*(u - 1)**2*(u + 1)**2/9
Let n(b) be the second derivative of -b**6/40 + b**5/20 - b**2 + 9*b. Let r(g) be the first derivative of n(g). Factor r(l).
-3*l**2*(l - 1)
Let o = 36/43 - 80/301. Find j, given that -4/7*j**3 - 2/7*j**4 + o*j + 0*j**2 + 2/7 = 0.
-1, 1
Factor 40 + 43 - 85 + 11*g - 16*g**2 + 7*g**3.
(g - 1)**2*(7*g - 2)
Let w(i) = i**3 + i**2 + 1. Let d(t) = -t**3 - 11*t**2 + 10*t - 7. Let z be 10/(-5)*2/(-4). Let x(c) = z*d(c) + 3*w(c). Let x(n) = 0. What is n?
1, 2
Let h(u) = u - 2. Let g be h(5). Suppose -4*p = -g*w - 1, 4*w + 3*p - 12 = 20. Factor -6*c**4 + 0*c**5 + c**w + 5*c**4.
c**4*(c - 1)
Suppose -47*w + 5*y = -43*w - 22, 0 = 3*w - 5*y - 19. Factor 1/7*a**2 + 0 + 1/7*a**w + 0*a.
a**2*(a + 1)/7
Let t(z) = 2*z**2 - 10*z. Suppose -2*j - 10 = -5*g + g, 4*j - 20 = 0. Let c be t(g). Factor c - 1/6*r**2 + 1/6*