*j - 2/5*w = 0. What is w?
-1, 0
Let q(y) be the third derivative of -y**8/6720 + y**6/1440 + y**3/2 - 3*y**2. Let z(w) be the first derivative of q(w). What is u in z(u) = 0?
-1, 0, 1
Suppose 9/4*u**3 + 0*u + 0 + 3/4*u**5 + 27/4*u**2 - 15/4*u**4 = 0. What is u?
-1, 0, 3
Let v(y) be the first derivative of -5*y**4/4 + 20*y**3/3 - 10*y**2 - 4. Find m such that v(m) = 0.
0, 2
Let o(f) = 3*f - 1. Let q be o(2). Let g be (4/15)/(1/q). Find m such that 1/3*m + m**3 + 0 - g*m**2 = 0.
0, 1/3, 1
Let w(f) = -35*f**3 - 70*f**2 + 50*f + 70. Let k(t) = -5*t**3 - 10*t**2 + 7*t + 10. Let l(c) = 15*k(c) - 2*w(c). Factor l(u).
-5*(u - 1)*(u + 1)*(u + 2)
Find g, given that -5*g**2 + 5/2*g**3 + 0 + 0*g = 0.
0, 2
Suppose 20 = 3*t + 3*m + 2*m, 4*m - 16 = -t. Factor -1/2*v**2 + t*v + 1/2.
-(v - 1)*(v + 1)/2
Let j(o) = o**2 - 9*o + 4. Let r(h) = -9*h**2 + 90*h - 39. Let g(t) = -21*j(t) - 2*r(t). Factor g(v).
-3*(v - 2)*(v - 1)
Let a(t) = -4*t**2 - 22*t - 7. Let m be a(-5). Factor 1/4*r**2 + 0 - 1/4*r**4 + 0*r + 1/4*r**5 - 1/4*r**m.
r**2*(r - 1)**2*(r + 1)/4
Let q(k) be the first derivative of k**6/18 - k**4/12 - 4. Factor q(n).
n**3*(n - 1)*(n + 1)/3
Suppose -10 = -4*w + 2. Factor -2*g + g**2 - 3*g**2 + 3*g**2 + 2*g**2 - g**w.
-g*(g - 2)*(g - 1)
Let j(k) be the first derivative of 1/20*k**4 + 1/5*k - 1/10*k**2 + 4 - 1/15*k**3. What is z in j(z) = 0?
-1, 1
Let u(c) = -7*c + 35. Let g be u(5). Determine d so that -2/5*d**3 - 2/15*d + 2/15*d**4 + 2/5*d**2 + g = 0.
0, 1
Let w(h) be the third derivative of -h**5/27 + h**4/108 + 2*h**3/27 + 3*h**2. Factor w(v).
-2*(2*v - 1)*(5*v + 2)/9
Let g(x) be the third derivative of x**5/15 + x**4/2 + 4*x**3/3 - x**2 + 13. Suppose g(f) = 0. What is f?
-2, -1
Let v(s) = -s**3 - 9*s**2 - 3*s - 4. Let x be v(-9). Let w = -21 + x. Find l, given that 0 - 1/3*l**w + 1/3*l = 0.
0, 1
Let -18*r**2 + 5 + r**4 + 3*r**3 - 12*r + 19 + 2*r**4 = 0. Calculate r.
-2, 1, 2
Suppose -5*p = -l + 8, l - 4*p + 0 - 7 = 0. Suppose -8*x + 3*x = -10. Factor -b + 18 + b**x - b**l + 4*b - 2*b - 19.
-(b - 1)**2*(b + 1)
Let c be 80/198 - (-2)/(-9). Factor -4/11*r + c - 2/11*r**4 + 0*r**2 + 4/11*r**3.
-2*(r - 1)**3*(r + 1)/11
Let s(f) be the second derivative of f**6/9 + f**5/6 - 5*f**4/24 - 5*f**3/9 - 5*f**2/12 + 11*f. What is a in s(a) = 0?
-1, -1/2, 1
Let x(j) be the second derivative of j**8/672 - j**7/420 - j**2/2 + 3*j. Let d(n) be the first derivative of x(n). Factor d(w).
w**4*(w - 1)/2
Let l(k) be the first derivative of -1/10*k**5 - 1 - 1/2*k + 1/12*k**6 + 1/4*k**2 + 1/3*k**3 - 1/4*k**4. Factor l(q).
(q - 1)**3*(q + 1)**2/2
Let k be (8 - 12)/(-3 + -11). Solve 2/7*u + k*u**2 + 0 = 0 for u.
-1, 0
Let -17*z**3 + 31*z**2 + 3*z**4 - 19*z + 6 - 19*z + 15*z = 0. Calculate z.
2/3, 1, 3
Let i = -727/4 + 182. Let y(t) be the second derivative of t + 0 - 3/2*t**2 + i*t**4 + 0*t**3. Solve y(v) = 0.
-1, 1
Suppose -2*k - 4*k = -0*k. Let p(f) be the second derivative of -2*f**2 - f**3 + 1/10*f**5 + 0 + k*f**4 + f. Factor p(s).
2*(s - 2)*(s + 1)**2
Let h(x) = 49*x**2 + 5*x - 8. Let g(f) = 25*f**2 + 3*f - 4. Let j(a) = -7*g(a) + 3*h(a). Factor j(w).
-2*(2*w + 1)*(7*w - 2)
Let y(n) be the first derivative of -n**7/14 - 3*n**6/10 - 3*n**5/10 - 4*n - 2. Let b(x) be the first derivative of y(x). Suppose b(o) = 0. What is o?
-2, -1, 0
Let r be 6/10 - (-99)/(-15). Let g = -4 - r. Factor 0*a - 3*a**2 + a + 2*a**g.
-a*(a - 1)
Let v = -17251914/1093 - -15784. Let w = 8726/9837 - v. Determine i so that 2/9*i**2 + w - 8/9*i = 0.
2
Let n(l) = -l + 12. Let s be n(8). Let i be 56*((-15)/(-9))/5. Let -26/3*h - 26/3*h**s - i*h**5 + 82/3*h**3 + 4/3 + 22/3*h**2 = 0. Calculate h.
-1, 1/4, 2/7, 1
Let y = -93 + 96. Factor 2/3*h**5 + 4/3*h**4 - 4/3*h**2 - 2/3*h + 0*h**y + 0.
2*h*(h - 1)*(h + 1)**3/3
Factor -8*d - 19*d**3 - 37*d**3 - 33*d**3 - 72*d**2 - 73*d**3.
-2*d*(9*d + 2)**2
Factor -25*v**4 + 2*v - 2*v**3 - 35*v**2 - 12*v - 5*v**5 - 43*v**3.
-5*v*(v + 1)**3*(v + 2)
Let c(v) be the first derivative of -v**4/12 - v**3/9 + v**2/6 + v/3 + 10. Let c(q) = 0. What is q?
-1, 1
Let t(b) be the second derivative of -2*b**6/15 + 3*b**5/5 + 7*b**4/3 - 10*b**3 - 36*b**2 + 40*b. Factor t(a).
-4*(a - 3)**2*(a + 1)*(a + 2)
Let m be 9/(-2)*2/(-3). Factor 0 + 7/2*n**m - 9/2*n**2 + n.
n*(n - 1)*(7*n - 2)/2
Let u(z) = 2*z + 3. Let k be u(-2). Let i(p) = -2*p**3 + p**2 - 1. Let l be i(k). Solve h**2 + 0*h**2 - 8 - 2*h**2 - 8*h - h**l = 0.
-2
Solve 19 + 20*o - 9*o**2 - 26*o - 3*o**3 - 19 = 0 for o.
-2, -1, 0
Suppose -1/2 - 1/2*a**2 + a = 0. What is a?
1
Let z(r) be the second derivative of -2*r**7/189 - r**6/15 - r**5/30 + 2*r**4/27 - 8*r. Solve z(a) = 0 for a.
-4, -1, 0, 1/2
Let p(o) be the first derivative of o**6/24 - o**5/10 + o**3/6 - o**2/8 - 5. Solve p(z) = 0 for z.
-1, 0, 1
Let d(y) = -y**2 - 8*y - 10. Let q be d(-5). Factor q*k**3 - 7*k**3 + 5*k**3 - 3*k**2 + 3*k**3.
3*k**2*(2*k - 1)
Let r(p) = 5*p**2 + 23*p - 6. Suppose -2*x = 5*w - 18, w = -0*w + 4*x + 8. Let h(s) = 2*s**2 + 8*s - 2. Let v(y) = w*r(y) - 11*h(y). Factor v(b).
-2*(b - 1)**2
Suppose 4*w - 16 = 5*a, -4*a + 7*w = 4*w + 12. Suppose a = -5*t - 5*x + 35, -6 = -5*t + 2*x + 1. Factor g**2 + 3*g - 5*g**t - g - 4*g**2.
-g*(g + 1)*(5*g - 2)
Let l = -26 + 37. Factor 0*f**3 - l*f - 7*f**2 + 11*f**3 - 9*f - 4 - 2*f**3.
(f - 2)*(f + 1)*(9*f + 2)
Let y = -9 + 47/5. Find z such that y*z - 2/5*z**2 + 4/5 = 0.
-1, 2
Let s(u) be the third derivative of 0 + 1/210*u**5 + 1/84*u**4 + 0*u - 2*u**2 + 0*u**3. Factor s(f).
2*f*(f + 1)/7
Suppose 6 - 2 = 2*f. Let m(t) be the second derivative of 0*t**f + 0*t**6 + 1/12*t**3 + 0*t**4 + 1/84*t**7 - 1/20*t**5 + 0 + t. Let m(z) = 0. Calculate z.
-1, 0, 1
Suppose -2*m + j - 2 = 2*m, 3*m + 2 = j. Suppose -5*p + m + 20 = 0. Factor -1/2*b**p + 0 + 0*b + 1/2*b**3 + b**2.
-b**2*(b - 2)*(b + 1)/2
Factor -14*u**4 - 35*u**3 - 24*u**4 - 10*u**2 + 13*u**4.
-5*u**2*(u + 1)*(5*u + 2)
Let k = 6 - 10. Let a be ((-12)/(-84))/((-1)/k). Factor 4/7*l + 2/7 - 2/7*l**4 + 0*l**2 - a*l**3.
-2*(l - 1)*(l + 1)**3/7
Let y be 129 + -134 + 52/10. Factor 6/5*i**3 + 2*i - y*i**4 - 12/5*i**2 - 3/5.
-(i - 3)*(i - 1)**3/5
Let k = 26153/8 + -3263. Let a(l) be the first derivative of -8*l**2 - k*l**4 + 3 + 77/6*l**3 + 2*l. Solve a(m) = 0 for m.
2/7, 1
Suppose 81/2*b - 27/2*b**2 + 3/2*b**3 - 81/2 = 0. What is b?
3
Let o(g) be the first derivative of -g**3/7 - 3*g**2/14 + 6*g/7 + 6. Let o(z) = 0. Calculate z.
-2, 1
Let q = 18 + -16. Factor m**4 + 4 - m**3 - 7 + 1 + 5*m - 3*m**q.
(m - 1)**3*(m + 2)
Let w be 6/(-21) + 18/14. Let x(t) = -t**3 - t + 1. Let z(n) = 2*n**3 + 4*n**2 + 2*n - 4. Let g(l) = w*z(l) + 4*x(l). Let g(o) = 0. What is o?
0, 1
Let g(m) be the first derivative of -m**3/24 + m**2/16 + 7. Factor g(l).
-l*(l - 1)/8
Let y = 83 - 54. Let n be -2 - (-1 - -2 - 7). Factor -2*i**3 + 29 + 8*i**5 + 6*i**n - y.
2*i**3*(i + 1)*(4*i - 1)
Determine a so that 16/5*a**3 + 16/15*a**2 + 0 + 2/15*a + 32/15*a**5 + 64/15*a**4 = 0.
-1/2, 0
Factor 2/7*l**2 + 32/7*l**4 - 48/7*l**3 + 2/7 + 12/7*l.
2*(l - 1)**2*(4*l + 1)**2/7
Let x(k) = k**2 + 3*k + 2. Let t(u) = -u**2 - 1. Let v = 10 - 6. Suppose 2*w + 5*a - a = -v, -w - 4*a = 10. Let l(z) = w*t(z) + 2*x(z). Factor l(c).
-2*(c - 1)*(2*c - 1)
Factor 0*k**2 + 4 - k**2 + 1 + 5 + 3*k.
-(k - 5)*(k + 2)
Let r(u) be the first derivative of u**4/16 - 3*u**3/8 + 3*u**2/4 - 4*u + 6. Let w(g) be the first derivative of r(g). What is b in w(b) = 0?
1, 2
Let h(r) = -5*r**3 + 5*r**2 + 8*r - 8. Let c = -28 + 20. Let m(s) = 3*s**3 - 3*s**2 - 5*s + 5. Let d(f) = c*m(f) - 5*h(f). Factor d(g).
g**2*(g - 1)
Factor 4/13*b**2 + 2/13*b - 2/13*b**3 - 4/13.
-2*(b - 2)*(b - 1)*(b + 1)/13
Factor 39/7*p - 6/7 - 81/7*p**2 - 3*p**4 + 69/7*p**3.
-3*(p - 1)**3*(7*p - 2)/7
Let s(x) = x + 14. Let q be s(-12). Factor -1 + q + n - n**2 + n + 2*n**2.
(n + 1)**2
Let u(p) be the first derivative of p**4/22 - 2*p**3/11 + 3*p**2/11 - 2*p/11 + 9. Solve u(k) = 0 for k.
1
Let q(c) be the third derivative of c**5/60 - c**4/12 - c**3/2 + c**2. Determine k so that q(k) = 0.
-1, 3
Let m(h) be the third derivative of h**8/26880 - h**7/2520 + h**6/720 + h**4/12 + 3*h**2. Let c(b) be the second derivative of m(b). Factor c(q).
q*(q - 2)**2/4
Let y(q) = q**3 + 12*q**2 + 10*q - 7. Let l be y(-11). Factor 0*v - 1/2*v**2 + 7/4*v**3 + 3/4*v**5 + 0 - 2*v**l.
v**2*(v