 Let b(m) = 0. What is m?
-1, 0
Let a(h) be the second derivative of -h**7/1260 + h**6/180 - h**5/60 + h**4/12 - 4*h. Let i(b) be the third derivative of a(b). Factor i(j).
-2*(j - 1)**2
Let x(i) = -5*i**5 + 4*i**4 - 28*i**3 + 28*i**2 - 12*i - 4. Let p(c) = 11*c**5 - 7*c**4 + 57*c**3 - 55*c**2 + 23*c + 9. Let n(m) = 4*p(m) + 9*x(m). Factor n(z).
-z*(z - 2)**4
Let r(g) be the first derivative of g**4/12 + 2*g**3/9 + g**2/6 - 24. What is c in r(c) = 0?
-1, 0
Let s(h) be the first derivative of 3/8*h**4 + 3/20*h**5 - 3/2*h**2 - 4 + 3*h - 3/4*h**3. Factor s(k).
3*(k - 1)**2*(k + 2)**2/4
Let j(m) be the second derivative of -4*m + 0*m**4 + 1/5*m**5 + 0*m**3 + 0 + 0*m**2 + 2/21*m**7 - 4/15*m**6. Solve j(v) = 0.
0, 1
Let q(g) = 6*g**4 - 6*g**3 + 6*g**2 + 2*g. Let o(m) = -5*m**4 + 6*m**3 - 6*m**2 - m. Let k(j) = 4*o(j) + 3*q(j). Factor k(h).
-2*h*(h - 1)**3
Let s be -1*1 - (-4 - 0). Factor -t + 0*t**3 - 4*t**3 - 3*t**2 + t**s - t**4 + 0*t**2.
-t*(t + 1)**3
Let x(n) = -n + 11. Let s be x(11). Let 0*i**2 + 0*i - i**4 - 2/3*i**3 + s - 1/3*i**5 = 0. Calculate i.
-2, -1, 0
Let t(w) = w**2 - 7*w + 9. Let r be t(4). Let z be 9/6*(-4)/r. Suppose 2/7*a**z - 6/7*a + 4/7 = 0. Calculate a.
1, 2
Let x(s) be the first derivative of 0*s**4 - 2/27*s**6 + 2/15*s**5 + 0*s**2 + 0*s + 2 - 2/27*s**3. Factor x(c).
-2*c**2*(c - 1)**2*(2*c + 1)/9
Suppose 2*m - 2*v + 37 = -7*v, 5*m + 2*v = -40. Let a be 1/(((-4)/m)/2). Determine i, given that 2/5*i**a + 0*i**2 + 0*i - 2/5*i**4 + 0 = 0.
0, 1
Suppose -9 = -3*c - 3. Factor -2*u - 4*u**2 + 6 + 0*u**c - 2 + 2*u**2.
-2*(u - 1)*(u + 2)
Suppose 5*y - 18 = 17. Factor -2 - 7 - 8*h - y - h**2.
-(h + 4)**2
Factor -2/3*d**3 + 2/3*d - 5/3*d**2 + 0 + 5/3*d**4.
d*(d - 1)*(d + 1)*(5*d - 2)/3
Let u(b) be the first derivative of 2*b**3/21 - 3*b**2/7 + 4*b/7 + 1. Factor u(o).
2*(o - 2)*(o - 1)/7
Find g such that -10/7*g - 2/7*g**2 - 4/7 + 4/7*g**3 = 0.
-1, -1/2, 2
Let g(w) be the first derivative of w**6/40 - w**4/8 - 3*w**2/2 - 2. Let b(h) be the second derivative of g(h). Determine y so that b(y) = 0.
-1, 0, 1
Factor 10*g + 3*g**2 - 16*g + 18*g + 9.
3*(g + 1)*(g + 3)
Factor 2/3 - 16/3*u - 32/3*u**3 + 12*u**2 + 10/3*u**4.
2*(u - 1)**3*(5*u - 1)/3
Let j = 6 + -1. Let a(z) = 16*z**3 - 2*z**2 + 7. Let g(l) = 11*l**3 - l**2 + 5. Let u(i) = j*a(i) - 7*g(i). Factor u(v).
3*v**2*(v - 1)
Let k = -3 + 5. Find u such that 2*u + 0 + 0 - 2*u**k + 2*u = 0.
0, 2
Suppose 23*o = 20*o. Let t = -5 - -7. Determine a, given that -a + o*a - a**t + a = 0.
0
Let y = 14 + -20. Let v be 15/25*(-2)/y. Factor 1/5*i**2 + 0 - v*i.
i*(i - 1)/5
Let i(p) be the third derivative of 1/165*p**5 + 0*p**4 + 0*p - 1/33*p**3 - 1/1155*p**7 + 0 + 0*p**6 + p**2. Determine q so that i(q) = 0.
-1, 1
Suppose -4*c + 4*j + 28 = 0, 3*c + 3*j + 9 = -0*j. Factor 0*z - 4*z**2 - 2*z + 0*z**c.
-2*z*(2*z + 1)
Let v(d) be the third derivative of -d**5/120 + 5*d**4/48 + d**3/2 + 27*d**2. Let v(c) = 0. What is c?
-1, 6
Let u(s) be the third derivative of s**7/210 + s**6/40 + s**5/30 + 12*s**2. Factor u(a).
a**2*(a + 1)*(a + 2)
Let l(m) be the third derivative of m**8/2520 + m**7/2520 + m**5/20 + 3*m**2. Let o(f) be the third derivative of l(f). Find k, given that o(k) = 0.
-1/4, 0
Let x(d) be the second derivative of d**9/7560 + d**8/3360 - d**7/1260 - d**6/360 + d**4/12 + 2*d. Let p(t) be the third derivative of x(t). Factor p(v).
2*v*(v - 1)*(v + 1)**2
Factor 0 - 2/17*y**4 + 6/17*y**3 + 2/17*y - 6/17*y**2.
-2*y*(y - 1)**3/17
Determine x so that -54/7*x**5 + 12*x**2 - 201/7*x**4 + 0 + 24/7*x - 150/7*x**3 = 0.
-2, -2/9, 0, 1/2
Let n(p) be the second derivative of p**7/378 - p**5/90 + p**3/54 + 9*p. Factor n(i).
i*(i - 1)**2*(i + 1)**2/9
Suppose -4*l - 4 + 4 = 0. Find i, given that 2/5*i**3 - 2/5*i**2 + l - 4/5*i = 0.
-1, 0, 2
Let z be 20/(-25) + (-5)/(-5). Solve 2/5*f**3 - 1/5*f**5 + 1/5 - z*f + 1/5*f**4 - 2/5*f**2 = 0.
-1, 1
Let t(y) be the third derivative of 0*y + 1/60*y**4 - 1/150*y**5 + 0*y**3 - 2*y**2 + 0. Solve t(w) = 0.
0, 1
Let s(m) be the third derivative of m**8/1344 + m**7/280 - m**5/60 - 7*m**2. Solve s(q) = 0 for q.
-2, 0, 1
Suppose 0 = 9*x + 260 - 278. Let -2/5*w**3 + 0 + 0*w**x + 2/5*w = 0. What is w?
-1, 0, 1
Let a = -11 + 13. Let x(y) = -y**3 + 4*y**2 + 4*y + 7. Let o be x(5). Determine l, given that -2*l - o*l**a - 1/2 = 0.
-1/2
Let w(t) = -t**3 + 7*t**2 + 6*t + 16. Let l be w(8). Let p(v) be the third derivative of l*v - 3*v**2 - 1/30*v**4 + 1/15*v**3 + 1/150*v**5 + 0. Factor p(d).
2*(d - 1)**2/5
Let b be (-20)/(-8)*6/(-5). Let m(v) = 6*v**4 + 6*v**3 - 9*v + 3. Let p(s) = s**4 + s**2 - s + 1. Let t(y) = b*p(y) + m(y). Factor t(o).
3*o*(o - 1)*(o + 1)*(o + 2)
Suppose 0 = -d - 3 + 6. Let h(r) be the second derivative of 0*r**2 + 3*r - 1/30*r**d + 0 + 1/60*r**4. Factor h(p).
p*(p - 1)/5
Let m = 111 + -108. What is w in 0*w + 3*w**m - 3/5*w**2 - 12/5*w**4 + 0 = 0?
0, 1/4, 1
Suppose 9*q**3 - 24 - 18*q**3 + 25*q + 5*q**4 + 4 - 16*q**3 + 15*q**2 = 0. What is q?
-1, 1, 4
Factor -2*j**4 + j + j + 3*j**3 + j**2 - 5*j + 1.
-(j - 1)**2*(j + 1)*(2*j - 1)
Let 0*b + 8/15*b**5 + 8/3*b**3 + 2*b**4 + 4/3*b**2 - 2/15 = 0. What is b?
-1, 1/4
Let p(v) be the second derivative of v**7/14 - 2*v**6/15 - v**5/10 + v**4/3 - v**3/6 - 3*v. Factor p(f).
f*(f - 1)**2*(f + 1)*(3*f - 1)
Let f = 35 + -32. Let s(i) be the second derivative of -f*i + 0 + 1/20*i**4 + 0*i**3 - 3/10*i**2. Determine j, given that s(j) = 0.
-1, 1
Suppose -4*y + 0*y = 0. Let w(z) be the second derivative of y*z**2 - 4/105*z**7 - z - 3/25*z**6 - 3/25*z**5 + 0*z**3 + 0 - 1/30*z**4. Factor w(h).
-2*h**2*(h + 1)**2*(4*h + 1)/5
Let -2/5*d**4 + 0 - 2/5*d**2 + 0*d + 4/5*d**3 = 0. What is d?
0, 1
Suppose -16 = -4*k, -7 = -5*i + k - 1. Let -8*d**4 + 3*d**i - 3*d**2 - 10*d**3 - 2*d**2 = 0. Calculate d.
-1, -1/4, 0
Let c = 3 + 0. Factor -6*y**c - 4*y**3 - 2*y**4 + 62*y + 3*y**5 - 63*y - 2 + 12*y**2.
(y - 1)**3*(y + 2)*(3*y + 1)
Let f(h) be the second derivative of -5*h**4/12 + 5*h**3/6 + 5*h**2 - 8*h. Factor f(p).
-5*(p - 2)*(p + 1)
Let z(i) be the first derivative of 0*i**4 + 0*i**2 - i - 2 - 1/5*i**5 + 2/3*i**3. Suppose z(q) = 0. Calculate q.
-1, 1
Let n(k) be the first derivative of 0*k + k**4 - 2/5*k**5 - 1 + 0*k**2 - 2/3*k**3. Factor n(s).
-2*s**2*(s - 1)**2
Factor -r - r + 6 + 3*r**2 + 11*r.
3*(r + 1)*(r + 2)
Suppose 5*x - 9 = 2*j - 0, 15 = 2*j + 3*x. Factor 0 + 2/9*s**j + 2/3*s**2 + 4/9*s.
2*s*(s + 1)*(s + 2)/9
Let c(k) be the first derivative of k**6/30 + k**5/20 - 2*k + 4. Let u(y) be the first derivative of c(y). Factor u(d).
d**3*(d + 1)
Let j(t) be the third derivative of -t**8/168 - t**7/105 + t**6/30 + t**5/15 - t**4/12 - t**3/3 + 8*t**2. Solve j(d) = 0 for d.
-1, 1
Let a(q) be the second derivative of q**4/42 + 16*q**3/21 + 64*q**2/7 + 24*q. Factor a(l).
2*(l + 8)**2/7
Let b = -1858611/7 - -266102. Let a = -585 + b. Factor 2/7 + a*m**2 + 8/7*m.
2*(2*m + 1)**2/7
Find o, given that -8/3*o**2 + 16/9*o**4 - 4/9*o**3 + 0*o - 4/9*o**5 + 0 = 0.
-1, 0, 2, 3
Let f(s) be the first derivative of 98/25*s**5 - 7*s**4 - 104/15*s**3 + 0*s - 5 - 8/5*s**2. Factor f(y).
2*y*(y - 2)*(7*y + 2)**2/5
Let k be ((-2)/(-5))/(3/(-30)). Let o be 128/22 + k/(-22). Solve -o + 2 + 0 + 2*a + 2*a**2 = 0 for a.
-2, 1
Let y(s) = 6*s**4 + 4*s**3 - 2*s**2 + 2*s + 2. Let g(d) = -5*d**4 - 3*d**3 + 3*d**2 - d - 2. Let v(n) = -3*g(n) - 2*y(n). Determine a, given that v(a) = 0.
-1, 2/3, 1
Let x(a) be the first derivative of -a**3 - 4 + 15/16*a**4 - 3/8*a**2 + 0*a. Suppose x(w) = 0. Calculate w.
-1/5, 0, 1
Let w(r) be the second derivative of r**7/5460 + r**6/2340 + 4*r**3/3 + 5*r. Let f(h) be the second derivative of w(h). Let f(n) = 0. What is n?
-1, 0
Let d(s) = s**3 + s. Suppose 4*i + i + u = 1, -3*u = 2*i + 10. Let c(m) = -m**3 - 9*m**2 + 2*m. Let l(x) = i*c(x) - 2*d(x). Factor l(r).
-3*r**2*(r + 3)
Let q(o) be the third derivative of 1/90*o**5 + 2*o**2 + 1/180*o**6 - 1/315*o**7 - 1/504*o**8 + 0*o**3 + 0*o**4 + 0 + 0*o. Factor q(w).
-2*w**2*(w - 1)*(w + 1)**2/3
Let u(y) = -y**2 - y + 1. Let o(n) = 5*n**4 + 20*n**3 + 18*n**2 - 2*n + 2. Let l(q) = o(q) - 2*u(q). Factor l(w).
5*w**2*(w + 2)**2
Let g(h) = h**3 - 14*h**2 + 13*h + 2. Let k be g(13). Determine u, given that 2*u**2 + 0*u + 4 + 3*u**3 + 10*u + 6*u**k - u**3 = 0.
-2, -1
Let g be (12/(-16))/((-2)/(-16)). Let 