*h - 5*h = 2. Let i(d) be the first derivative of -1 - 2/3*d**3 - 2*d - 2*d**j. Factor i(v).
-2*(v + 1)**2
Let z = 1267/7150 + 3/650. Suppose -2*o = -0*o - 8. Factor -2/11*l**5 + 0 - 4/11*l**o + 4/11*l**2 + z*l + 0*l**3.
-2*l*(l - 1)*(l + 1)**3/11
Suppose -20 = 4*l, -16*i + 15*i - 3*l = 13. Let 1/2*c - 1/2*c**i + 1 = 0. What is c?
-1, 2
What is n in -8/3*n**2 + 8/3*n**4 + 0*n**3 - 4/3*n**5 + 4/3*n + 0 = 0?
-1, 0, 1
Let g be (-2)/5 - 6/(-15). Suppose -3*s - 4*i = s - 20, -3*s + 3*i = 3. Determine c, given that s*c**2 + 5*c - 4*c + g*c**3 + c**3 = 0.
-1, 0
Let l(u) be the second derivative of -u**7/63 - u**6/15 - u**5/15 + u**4/9 + u**3/3 + u**2/3 + 6*u. Factor l(y).
-2*(y - 1)*(y + 1)**4/3
Let g(o) be the second derivative of o**7/21 - 4*o**6/15 + o**5/5 + 2*o**4/3 - o**3 - 14*o. Factor g(d).
2*d*(d - 3)*(d - 1)**2*(d + 1)
Let f(s) = -7*s**2 - 7*s + 6. Let l(o) = 20*o**2 + 20*o - 17. Let c(x) = -18*x**3 + x**2. Let i be c(1). Let v(b) = i*f(b) - 6*l(b). Let v(k) = 0. What is k?
-1, 0
Factor -3 - 1 - 2*j**2 + 6*j**2 - 4*j + 4*j**3.
4*(j - 1)*(j + 1)**2
Suppose 0 = -3*y - y + 12. Let 0*q**4 + 0*q**4 + 3*q**4 - 2*q + 8*q - y - 6*q**3 = 0. Calculate q.
-1, 1
Let j(d) = -47*d**2 + 14*d + 1. Let f(i) = -46*i**2 + 14*i + 2. Let u(n) = 2*f(n) - 3*j(n). Factor u(y).
(7*y - 1)**2
Let b(q) be the third derivative of -q**6/480 - q**5/240 - 7*q**2. Factor b(h).
-h**2*(h + 1)/4
Let t(q) be the third derivative of 4/105*q**6 + 0 + 4/105*q**5 - 1/12*q**4 + 0*q + q**2 + 1/21*q**3. Factor t(u).
2*(u + 1)*(4*u - 1)**2/7
Let x(y) be the second derivative of 0 - 1/12*y**4 + 0*y**2 + 1/40*y**5 + 0*y**3 - 4*y. Factor x(i).
i**2*(i - 2)/2
Suppose -10*k = -30*k + 60. Let -1/2*w + 1/4*w**2 + 1/4*w**k + 0 = 0. Calculate w.
-2, 0, 1
Let g(z) be the second derivative of z**5/30 + z**4/18 + 4*z. Determine a, given that g(a) = 0.
-1, 0
Let v(s) be the first derivative of -s**6/135 - 2*s**5/45 - 2*s**4/27 - 2*s - 2. Let y(n) be the first derivative of v(n). Factor y(b).
-2*b**2*(b + 2)**2/9
Let j(i) = 8*i**2 + 16*i + 4. Let u(p) = -15*p**2 - 31*p - 7. Let q(o) = 7*j(o) + 4*u(o). Factor q(a).
-4*a*(a + 3)
Let i(c) be the first derivative of c**8/3360 + c**7/420 + c**6/144 + c**5/120 + c**3/3 - 3. Let a(d) be the third derivative of i(d). Factor a(q).
q*(q + 1)**2*(q + 2)/2
Let w(a) be the first derivative of 2*a**5/15 + 2*a**4/3 + 8*a**3/9 - 38. Factor w(z).
2*z**2*(z + 2)**2/3
Let f(l) be the first derivative of -1 - 2/5*l + l**2 - 8/15*l**3. Factor f(q).
-2*(q - 1)*(4*q - 1)/5
Let z(g) be the first derivative of 5*g**4/12 + 7*g**3/9 + g**2/3 + 8. Factor z(j).
j*(j + 1)*(5*j + 2)/3
Let c = -404 + 2840/7. Determine d, given that c*d + 3/7*d**2 + 9/7 = 0.
-3, -1
Let p(b) be the third derivative of 1/60*b**6 - 1/105*b**7 + 1/10*b**5 - b**2 + 0 + 2/3*b**3 - 5/12*b**4 + 0*b. Factor p(n).
-2*(n - 1)**3*(n + 2)
Let u(k) be the third derivative of -k**5/30 + 2*k**4/3 - 5*k**3 - 2*k**2 - 3. Factor u(f).
-2*(f - 5)*(f - 3)
Factor -4/7*d**2 + 0*d - 2/7*d**3 + 0.
-2*d**2*(d + 2)/7
Let b be (51/17)/(6/8). Let c(n) be the second derivative of 0 - 3*n - 1/9*n**3 + 0*n**2 - 1/9*n**b - 1/30*n**5. Let c(p) = 0. What is p?
-1, 0
Let j(c) be the second derivative of 2/3*c**3 - 3*c**2 + c - 1/18*c**4 + 0. Factor j(m).
-2*(m - 3)**2/3
What is k in 4/7 + 4/7*k - 4/7*k**2 - 4/7*k**3 = 0?
-1, 1
Suppose -4*b + 3*b + 2*k = 2, 0 = 3*b - 3*k - 9. Let s(v) = -v**3 - 7*v**2 - v - 4. Let t be s(-7). Factor 4/3 - b*d**2 - 14/3*d**t - 2*d.
-2*(d + 1)**2*(7*d - 2)/3
Let v = -6 - -4. Let l be (3*30/(-9))/v. Determine x so that 3*x**5 + 4*x**5 - 5*x**l - 2*x**3 = 0.
-1, 0, 1
Let t = 61 + -56. Let v(c) be the first derivative of 2/5*c**t + 0*c - c**4 + 0*c**2 + 2 + 2/3*c**3. Determine p, given that v(p) = 0.
0, 1
Let c(f) be the second derivative of f**4/42 + f**3/21 - 2*f. Factor c(h).
2*h*(h + 1)/7
Let d be 428/260 - (-16)/104. Factor -3/5*g**3 - 6/5*g - d*g**2 + 0.
-3*g*(g + 1)*(g + 2)/5
Let y(o) be the second derivative of -o**5/30 - o**4/9 - o**3/9 + 9*o. Determine t, given that y(t) = 0.
-1, 0
Let s be (1/12)/(-1 + (-22)/(-16)). Factor 2/9*a**2 - 2/9*a + 2/9*a**3 - s.
2*(a - 1)*(a + 1)**2/9
Suppose 18*v - 19*v + 3 = 0. Let h(b) be the second derivative of 0 - 1/36*b**4 - 2/3*b**2 - 2/9*b**3 + v*b. Solve h(q) = 0 for q.
-2
Suppose 5*o - o - 60 = 0. Let -o*a**3 + 2 + 21*a**4 + 15*a + 12 - 10 - 27*a**2 + 2 = 0. What is a?
-1, -2/7, 1
What is p in 8/9*p**2 - 2/9*p**3 - 10/9*p + 4/9 = 0?
1, 2
Let a(l) be the first derivative of l**6/21 + 4*l**5/35 - 4*l**3/21 - l**2/7 + 3. Factor a(g).
2*g*(g - 1)*(g + 1)**3/7
Solve 2/13*p**4 - 4/13*p**3 + 4/13*p - 2/13 + 0*p**2 = 0.
-1, 1
Suppose 56 = 4*a + 40. Solve -2/3 + 20/3*u**3 - 20/3*u**2 + 10/3*u - 10/3*u**a + 2/3*u**5 = 0 for u.
1
Let z(q) = -2*q - 2. Let o be z(-3). Solve 3 + a - 2*a - a - a**2 - o = 0.
-1
Let w = 47 + -45. Let u(r) be the third derivative of -1/3*r**3 + 2*r**w + 0 - 1/6*r**4 - 1/40*r**5 + 0*r. Factor u(k).
-(k + 2)*(3*k + 2)/2
Let d(n) = 22*n**3 + 62*n**2 + 58*n + 18. Let v(p) = -9*p**3 - 25*p**2 - 23*p - 7. Let a(o) = 5*d(o) + 12*v(o). Determine s, given that a(s) = 0.
-3, -1
Let a(n) be the first derivative of -13*n**6/12 + 11*n**5/10 + n**4/4 + 19. Factor a(p).
-p**3*(p - 1)*(13*p + 2)/2
Let f(a) be the second derivative of -a**8/1512 + a**7/945 + a**6/540 - a**5/270 - a**2 - 4*a. Let g(q) be the first derivative of f(q). Factor g(k).
-2*k**2*(k - 1)**2*(k + 1)/9
Let a(i) be the third derivative of i**6/180 + i**5/60 - i**3/2 + 4*i**2. Let g(b) be the first derivative of a(b). Factor g(r).
2*r*(r + 1)
Solve 2 - 5/3*n**2 - 5/3*n**3 - 1/3*n**4 + 5/3*n = 0.
-3, -2, -1, 1
Let c(q) be the third derivative of q**7/168 + q**6/48 - q**5/12 - 5*q**4/12 + 10*q**2. Factor c(r).
5*r*(r - 2)*(r + 2)**2/4
Let f(w) be the first derivative of 30/7*w**2 + 1/7*w**4 + 7 + 4/3*w**3 + 36/7*w. Factor f(l).
4*(l + 1)*(l + 3)**2/7
Let z(v) be the second derivative of -v**7/13860 + v**5/165 + v**4/4 - 4*v. Let r(l) be the third derivative of z(l). Factor r(y).
-2*(y - 2)*(y + 2)/11
Let j(c) be the third derivative of c**9/20160 + c**8/3920 + c**7/3920 - c**6/840 - 7*c**5/60 + 7*c**2. Let r(v) be the third derivative of j(v). Factor r(u).
3*(u + 1)**2*(7*u - 2)/7
Let n = 3/4 - 2/3. Let u(x) be the third derivative of 1/60*x**6 - 1/105*x**7 + 0*x**3 + 0 + 1/30*x**5 + 3*x**2 + 0*x - n*x**4. Let u(i) = 0. Calculate i.
-1, 0, 1
Suppose 0 = -4*o + 2*o + 14. Let u(m) = -m**3 - m**2 - 2*m + 4. Let c(t) = -4*t**3 - 2*t**2 - 7*t + 12. Let p(n) = o*u(n) - 2*c(n). Let p(y) = 0. What is y?
-1, 2
Let 11 + 2012*w**2 + 5 - 12 + 160*w - 412*w**2 = 0. Calculate w.
-1/20
Let a(z) be the third derivative of z**6/180 - z**4/12 - z**3/6 - 2*z**2. Let n(p) be the first derivative of a(p). Solve n(g) = 0 for g.
-1, 1
Let g(q) be the first derivative of -q**3 + 3*q**2/4 - 5. Factor g(l).
-3*l*(2*l - 1)/2
Let u = 125/12 - 833/80. Let p(l) be the third derivative of u*l**5 + 0 + 1/96*l**4 + 0*l - 1/12*l**3 - l**2. Determine w so that p(w) = 0.
-2, 1
Let q(f) be the third derivative of -f**2 + 0*f + 0*f**3 + 1/80*f**6 + 1/48*f**4 - 1/40*f**5 - 1/420*f**7 + 0. Factor q(x).
-x*(x - 1)**3/2
Let g(q) be the third derivative of q**6/360 + q**5/60 + q**3 - q**2. Let r(w) be the first derivative of g(w). Find n, given that r(n) = 0.
-2, 0
Let i(a) = a**3 - 6*a**2 + 4*a + 7. Let f be i(5). Determine t so that 2/3*t**f - 2*t**3 + 2/9 + 10/9*t = 0.
-1/3, 1
Suppose 0 = -16*s - 53 + 53. What is z in -2/5*z**4 - 4/5*z**3 + 0 + 0*z + s*z**2 = 0?
-2, 0
Factor 2*d**5 - 3*d**3 - d**3 - d**4 + 3*d**4 - 4*d**2 + 0*d**4 + 2 + 2*d.
2*(d - 1)**2*(d + 1)**3
Let h(d) be the second derivative of d**6/120 - d**5/40 + d**4/48 + 10*d. Find v, given that h(v) = 0.
0, 1
Let c(k) be the second derivative of -2*k**7/105 + 7*k**6/150 - k**5/50 - k**4/60 - 34*k. Find q such that c(q) = 0.
-1/4, 0, 1
Let b(f) be the third derivative of -f**5/420 - f**4/56 + 2*f**3/21 - f**2. Determine a so that b(a) = 0.
-4, 1
Find p, given that 0*p + 0 - 1/3*p**4 + 0*p**3 + 4/3*p**2 = 0.
-2, 0, 2
Let y(k) be the first derivative of -16*k**3/9 + 10*k**2 + 16*k/3 - 49. Factor y(j).
-4*(j - 4)*(4*j + 1)/3
Let k(f) be the second derivative of f**7/168 + f**6/30 + f**5/20 - f**4/24 - 5*f**3/24 - f**2/4 - 37*f. Determine o, given that k(o) = 0.
-2, -