Suppose -6*q = -3*q. Find h, given that -4/7*h**2 + 0*h**4 - 6/7*h**3 + q + x*h**5 + 0*h = 0.
-1, 0, 2
Let k(n) be the second derivative of -n**7/210 + n**6/90 + n**5/15 - 7*n**3/3 - 12*n. Let l(u) be the second derivative of k(u). Factor l(v).
-4*v*(v - 2)*(v + 1)
Let -6534 - 132*f - 2/3*f**2 = 0. What is f?
-99
Suppose 0*v - 3/5*v**5 + 0 - 3*v**4 - 12/5*v**2 - 24/5*v**3 = 0. Calculate v.
-2, -1, 0
Let h = -2648 - -7946/3. Factor 0*u**3 - 2/3*u**4 + h*u**2 + 0 + 1/3*u - 1/3*u**5.
-u*(u - 1)*(u + 1)**3/3
Let p = -11 - -21. Let q = p - 14. Let h(t) = 3*t**3 + t**2 - 3*t - 9. Let s(r) = -r**3 + r**2. Let a(x) = q*s(x) - h(x). Factor a(j).
(j - 3)**2*(j + 1)
Factor -24/11 - 14/11*s**2 - 2/11*s**3 - 32/11*s.
-2*(s + 2)**2*(s + 3)/11
Let l = -91 - -98. Let c be l/6 - (-5 + 6). Factor 0 - 1/6*n + c*n**2.
n*(n - 1)/6
Let s(n) = n - 2. Let q(x) = x - 3. Let g(m) = -2*q(m) + 3*s(m). Let v(j) = -2*j**2 + 4*j. Let o(p) = 6*g(p) - v(p). Factor o(w).
2*w*(w + 1)
Let u(z) be the third derivative of -z**9/3024 - z**8/840 + z**7/120 - z**6/90 + z**3/6 - 21*z**2. Let s(y) be the first derivative of u(y). Factor s(p).
-p**2*(p - 1)**2*(p + 4)
Let h(q) be the second derivative of -q**4/18 + 59*q**3/9 - 58*q**2/3 + q - 34. Determine b, given that h(b) = 0.
1, 58
Let b(n) be the third derivative of -n**6/12 + 2*n**5/5 + 3*n**4/4 + n**2 + 1. Let b(y) = 0. Calculate y.
-3/5, 0, 3
Let y(g) be the second derivative of -g**4/96 - g**3/4 - 11*g**2/16 - 13*g - 23. Factor y(q).
-(q + 1)*(q + 11)/8
Let u(l) = 4*l**2 - 30*l + 8. Let y(q) = -9*q**2 + 62*q - 20. Let s(g) = -5*u(g) - 2*y(g). Let s(o) = 0. Calculate o.
0, 13
Let s = -240 + 88. Let f = s - -611/4. Factor 0 + 3*b**2 - f*b.
3*b*(4*b - 1)/4
Let p(v) be the third derivative of v**9/3780 - v**8/240 + v**7/42 - v**6/20 + v**4/24 + 9*v**2. Let n(f) be the second derivative of p(f). Factor n(j).
4*j*(j - 3)**2*(j - 1)
Let y(t) be the third derivative of 2/105*t**5 - 1/21*t**4 + 0*t**3 - 1/735*t**7 + 41*t**2 + 0*t + 1/420*t**6 + 0. Factor y(b).
-2*b*(b - 2)*(b - 1)*(b + 2)/7
Suppose 30*v + 69*v - 95 + v - 100*v**3 - 840*v**2 + 930*v**2 + 5*v**4 = 0. What is v?
-1, 1, 19
Factor 11/2*l - 21/4 - 1/4*l**2.
-(l - 21)*(l - 1)/4
Let m(t) be the first derivative of t**4/8 - 5*t**3/6 + t**2/2 + 4*t - 295. Suppose m(d) = 0. What is d?
-1, 2, 4
Let b be ((-1)/3)/((-749)/84 - (-1 + -7)). What is m in 6/11*m**2 - 10/11*m - b = 0?
-1/3, 2
Let b = -2381/28 - -597/7. What is u in 0*u + 0*u**3 + 0*u**2 - 1/8*u**4 + 0 + b*u**5 = 0?
0, 1/2
Let z(h) be the first derivative of 1/4*h**2 + 9/10*h**5 + 1 + 15/8*h**4 + 0*h + 7/6*h**3. What is m in z(m) = 0?
-1, -1/3, 0
Let c(o) = -2*o**4 - 12*o**3 - 12*o**2 + 24*o - 2. Let l(x) = -x**3 + 2*x**2 + 1. Let p(y) = 2*c(y) + 4*l(y). Suppose p(b) = 0. What is b?
-6, -2, 0, 1
Let q(d) be the first derivative of 5*d**7/84 - d**6/4 + d**5/4 + 9*d - 11. Let x(v) be the first derivative of q(v). Factor x(r).
5*r**3*(r - 2)*(r - 1)/2
Let w(h) be the first derivative of 0*h**3 + 0*h**5 + 2 - 1/96*h**4 - 5/2*h**2 + 0*h + 1/480*h**6. Let t(n) be the second derivative of w(n). Factor t(s).
s*(s - 1)*(s + 1)/4
Let f(j) be the second derivative of -j**6/180 + j**5/15 - j**4/3 + 9*j**3 - 3*j - 7. Let d(b) be the second derivative of f(b). Find t, given that d(t) = 0.
2
Let b(a) be the second derivative of a**5/60 + a**4/9 - 7*a**3/6 + 188*a - 2. Find j such that b(j) = 0.
-7, 0, 3
Suppose -56 = 21*d - 49*d. Factor -d*n + 3/2*n**2 + 1/2.
(n - 1)*(3*n - 1)/2
Let d(n) be the third derivative of -n**5/30 + 5*n**4/3 - 25*n**3 - 698*n**2. Factor d(f).
-2*(f - 15)*(f - 5)
Let r(i) be the second derivative of i**9/30240 - i**8/1680 + i**7/315 + i**4/12 + 7*i**2/2 - 43*i + 1. Let q(c) be the third derivative of r(c). Factor q(x).
x**2*(x - 4)**2/2
Let t(g) be the second derivative of -g**5/20 + g**4 - 86*g. Solve t(r) = 0 for r.
0, 12
Suppose -13/4*m**2 - 1/8*m**4 + 0 - 11/8*m**3 - 2*m = 0. What is m?
-8, -2, -1, 0
Suppose 4*a - 25 = -5. Factor 11*n**4 + 3*n**5 - 4*n**4 - 5*n**a + 9*n**4 - 32*n**3.
-2*n**3*(n - 4)**2
Let j = 3549 + -10642/3. Factor 1 + j*h - 1/3*h**3 + 1/3*h**2.
-(h - 3)*(h + 1)**2/3
Solve 46*c**3 + 3*c**4 - 50*c**3 + 33*c**2 + 40*c**3 = 0.
-11, -1, 0
Let s(f) be the third derivative of 0*f - 2*f**2 - 3/8*f**4 + 0 + f**3 + 1/20*f**5. Suppose s(q) = 0. Calculate q.
1, 2
Factor -462 + 29*n + 462 - 9*n**2 - 15*n.
-n*(9*n - 14)
Factor 22*a**2 + 16*a**2 + 2605*a - 8*a**2 - 2613*a.
2*a*(15*a - 4)
Let x(i) = i**2 + 8*i + 4. Let j be x(-8). Solve -4*d**3 - 2*d - j*d**2 + 4*d + 6*d = 0.
-2, 0, 1
Let r(p) be the first derivative of -5*p**4/48 + p**3/8 + p**2/4 + 3*p + 7. Let w(i) be the first derivative of r(i). Factor w(q).
-(q - 1)*(5*q + 2)/4
Suppose 0 = 2*c - 3*y - 31, 74*c - 71*c - 5*y - 51 = 0. Factor 0 + 3/2*u + 2*u**c + 1/2*u**3.
u*(u + 1)*(u + 3)/2
Let l(p) = -57*p + 800. Let y be l(14). Find j such that 0 + 5/2*j**y - 5/2*j**4 + 0*j - 5/2*j**5 + 5/2*j**3 = 0.
-1, 0, 1
Find w, given that -4*w - 2*w**2 + 22216 + 2*w**3 - 22216 = 0.
-1, 0, 2
Let d(w) be the second derivative of w**5/10 + 5*w**4/6 - 2*w**3/3 - 24*w**2 - 133*w. Determine o, given that d(o) = 0.
-4, -3, 2
Let u(i) be the third derivative of -11*i**2 + 0*i**3 + 1/96*i**4 + 1/240*i**5 + 0*i + 0. Factor u(r).
r*(r + 1)/4
Let j(m) be the first derivative of -4/9*m**3 - 2 + 0*m**2 + 0*m + 1/12*m**4. Factor j(t).
t**2*(t - 4)/3
Let i(w) be the first derivative of 1/180*w**5 + 7/2*w**2 - 1/36*w**4 + 1/120*w**6 + 0*w + 0*w**3 - 5. Let m(x) be the second derivative of i(x). Factor m(v).
v*(v + 1)*(3*v - 2)/3
Suppose 17 = -6*f + 47. Let p(t) be the third derivative of 0 + 0*t**3 - 1/30*t**f + 0*t + 5*t**2 + 1/210*t**7 + 1/120*t**6 + 0*t**4. Factor p(v).
v**2*(v - 1)*(v + 2)
Suppose -5/2*j - 5/2*j**3 + 5*j**5 + 1 + 23/2*j**4 - 25/2*j**2 = 0. What is j?
-2, -1, -1/2, 1/5, 1
Let n be 17 - (-7 - -13) - (-86)/(-8). Factor -5/4*v + 1/4*v**2 + 3/4 + n*v**3.
(v - 1)**2*(v + 3)/4
Suppose -2*t + 0*t - 40 = 0. Let r = t - -34. Find h such that -4*h**3 - 22*h**2 - 2*h - 2*h + r*h**2 = 0.
-1, 0
Let f(h) be the second derivative of 0*h**4 - 1/5*h**5 + 0 - 2*h + 0*h**3 + 2/15*h**6 + 0*h**2. What is k in f(k) = 0?
0, 1
Let q = 599 - 599. Let l(y) be the first derivative of 0*y**2 + 3/20*y**4 + 2 + 3/25*y**5 + 0*y + q*y**3. Factor l(i).
3*i**3*(i + 1)/5
Let h(a) be the first derivative of -a**4/30 - 8*a**3/45 - 4*a**2/15 - 187. Solve h(b) = 0.
-2, 0
Let v(n) be the second derivative of -n**4/4 - n**3/2 + 9*n**2 - n - 99. Solve v(z) = 0 for z.
-3, 2
Let u(z) be the third derivative of -2/15*z**7 + 7/216*z**8 + 8/27*z**3 + 11/540*z**6 - 5/9*z**4 + 0*z + 23*z**2 + 0 + 59/135*z**5. Solve u(y) = 0.
-1, 2/7, 1, 2
Suppose 4*z = 4*m - 4, 2*m = -7*z + 6*z + 2. Factor 0 - s**2 - 3*s**4 + z*s - 7/2*s**3.
-s**2*(2*s + 1)*(3*s + 2)/2
Let n(r) = 3*r**2 + 2. Let t(i) = 7*i**2 + 2*i + 4. Let h(v) = 2*n(v) - t(v). Solve h(l) = 0 for l.
-2, 0
Let s(l) be the first derivative of -7 - 4*l**2 + 12*l - 18*l**3 - 8*l**2 + 13*l**3. Find z, given that s(z) = 0.
-2, 2/5
Let z be (2/(-22))/((-32)/12 - -3). Let l = 37/55 + z. Factor -l - 36/5*y**2 - 26/5*y**4 + 44/5*y**3 + 14/5*y + 6/5*y**5.
2*(y - 1)**4*(3*y - 1)/5
Suppose 2*k + 2*v - 10 = -2*k, 0 = -4*k - 4*v + 12. Solve 6*n**3 - 5*n**3 + 40*n - 39*n**2 + k*n**3 - 4*n = 0 for n.
0, 1, 12
Suppose 20*c + 66*c = -28*c + 342. Solve -9/5*j**c - 7/5 - 43/5*j - 69/5*j**2 = 0 for j.
-7, -1/3
Suppose -24*m + m**2 + 4*m**2 - 11*m = 0. Calculate m.
0, 7
Factor -8/7*i + 0*i**2 + 0 + 2/7*i**4 + 6/7*i**3.
2*i*(i - 1)*(i + 2)**2/7
Suppose 26*s - 4 - 29 = 19. Suppose -d = -4*d. Find n such that 0 - 1/2*n**3 + 1/2*n + d*n**s = 0.
-1, 0, 1
Let h(d) = d**3 + 3*d**2 - 2*d + 2. Let b be h(-3). Factor -b*n**5 + 6*n**3 - 4*n**3 - 3*n**3 - n**4 + 9*n**5 + n**2.
n**2*(n - 1)**2*(n + 1)
Suppose -5*o = t - 0*t - 7, -3 = -2*t + o. Let c(r) be the second derivative of -2/7*r**t + 2*r - 1/7*r**3 + 0*r**4 + 1/70*r**5 + 0. Let c(g) = 0. What is g?
-1, 2
Suppose 0*i + 7*i - 42 = 0. Let g(a) be the third derivative of 0 - 1/1470*a**7 - 4*a**2 + 0*a + 1/420*a**5 - 1/168*a**4 + 1/840*a**i + 0*a**3. Factor g(l).
-l*(l - 1)**2*(l + 1)/7
Let g(v) be the first derivative of -v**4/2 + 21*v**3 - 91*v**2/2 + 30*v + 261. Factor g(a).
-(a - 30)*(a - 1)*(2*a - 1)
Suppose 35*b = 192 - 52. 