l + 1)**2/3
Let p be (2/32 + 0)/(6/24). Determine j so that 1/4*j - p*j**2 + 0 = 0.
0, 1
Factor -4/5 + 0*v**2 - 8/5*v + 8/5*v**3 + 4/5*v**4.
4*(v - 1)*(v + 1)**3/5
Let f(o) be the third derivative of 0*o + 1/210*o**7 + 0 + 0*o**4 - 5*o**2 + 0*o**5 + 1/336*o**8 + 0*o**6 + 0*o**3. Find c, given that f(c) = 0.
-1, 0
Suppose 3*p - 2*t - 4 = 0, 4*t - 7*t = -p - 1. Let r = -4/3 + 5/3. Solve 1/3 + s**3 + r*s - 5/3*s**p = 0 for s.
-1/3, 1
Factor 0 - 4*n**2 - 8/7*n - 20/7*n**3.
-4*n*(n + 1)*(5*n + 2)/7
Let z(p) be the third derivative of -1/20*p**5 - 7*p**2 + 0 + 0*p + 0*p**3 + 0*p**4. Factor z(w).
-3*w**2
Let r(x) be the second derivative of x**7/49 - 2*x**6/105 - x**5/70 + 9*x. Factor r(t).
2*t**3*(t - 1)*(3*t + 1)/7
Let y(l) be the third derivative of -2*l**2 + 7/10*l**5 - 1/4*l**4 + 0 + 0*l + 0*l**3 - 49/80*l**6. Factor y(n).
-3*n*(7*n - 2)**2/2
Suppose -8*p**2 + 3*p - 9*p**2 + 14*p**2 = 0. What is p?
0, 1
Let q(v) be the second derivative of -v**9/7560 + v**8/1120 - v**7/420 + v**6/360 + v**4/12 - 2*v. Let n(j) be the third derivative of q(j). Factor n(x).
-2*x*(x - 1)**3
Factor -8/5*l**2 + 2/5*l + 0 + 2*l**3 - 4/5*l**4.
-2*l*(l - 1)**2*(2*l - 1)/5
Let w be (19 - 13)*(-3)/(-6). Let -80/7*m**w + 32/7*m**4 + 66/7*m**2 + 2/7 - 20/7*m = 0. What is m?
1/4, 1
Let a(n) be the second derivative of -n**4/27 + 2*n**3/27 + 2*n. What is w in a(w) = 0?
0, 1
Let o(g) be the first derivative of g - g**2 + 1/3*g**3 + 3. Suppose o(x) = 0. What is x?
1
Let w(x) = x + 1. Let k be w(-1). Factor -5*p**4 - p**4 + k*p**4 - 13*p**3 - 12*p**2 - 2*p - 2*p - p**5.
-p*(p + 1)**2*(p + 2)**2
Let f(z) be the third derivative of -2*z**7/21 + 5*z**6/24 + z**5/2 - 11*z**2 + 3. Factor f(n).
-5*n**2*(n - 2)*(4*n + 3)
Let b(u) be the first derivative of -5*u**4/4 + 5*u**3 + 5*u**2/2 - 15*u - 19. Determine k, given that b(k) = 0.
-1, 1, 3
Let l(j) be the first derivative of -j**3/9 - j**2/2 - 2*j/3 + 3. Factor l(q).
-(q + 1)*(q + 2)/3
Factor 16*g**3 + 2*g**4 - 528*g**2 + 2*g**4 - 16 + 540*g**2 - 16*g.
4*(g - 1)*(g + 1)*(g + 2)**2
Factor 0*w - 12/5 + 3/5*w**3 + 9/5*w**2.
3*(w - 1)*(w + 2)**2/5
Let t(r) be the first derivative of -r**4/20 + 2*r + 1. Let w(o) be the first derivative of t(o). Determine f, given that w(f) = 0.
0
Let b(i) = 2*i**3 + 16*i**2 - 18*i - 4. Let y(m) = -5*m**3 - 47*m**2 + 54*m + 11. Let g(u) = 11*b(u) + 4*y(u). Factor g(r).
2*r*(r - 3)**2
Let r(a) be the third derivative of a**6/30 - 2*a**5/15 - 5*a**4/6 + 4*a**3 + 19*a**2. Suppose r(o) = 0. Calculate o.
-2, 1, 3
Factor 1/2*t**4 + 0 + 0*t + 0*t**2 + 1/2*t**3.
t**3*(t + 1)/2
Factor 1/3*w + 2/3 - 2/3*w**2 - 1/3*w**3.
-(w - 1)*(w + 1)*(w + 2)/3
Let n(z) be the second derivative of -z**7/168 - z**6/24 - 9*z**5/80 - 7*z**4/48 - z**3/12 + 18*z. Solve n(j) = 0.
-2, -1, 0
Let f(i) be the third derivative of -i**5/45 + i**4/9 - 2*i**3/9 + 10*i**2. Suppose f(l) = 0. Calculate l.
1
Let k(x) be the first derivative of 2*x**5/5 - x**4/5 - 2. Let k(o) = 0. Calculate o.
0, 2/5
Let l(m) = m**3 - 6*m**2 + 4*m - 5. Let c be l(5). Let i be (-16)/c - 6/(-15). Factor -d**3 + d**i - 2*d**4 + 1 - 3*d + 4*d**3 + 0*d**3.
-(d - 1)**2*(d + 1)*(2*d - 1)
Let n(i) = i**3 + 8*i**2 - 8*i + 3. Let c be n(-9). Let y be 3/c*(-1)/2. What is p in -y*p**3 + 0*p**2 + 1/4*p + 0 = 0?
-1, 0, 1
Let z = -323/21 - -47/3. Let m be (610/(-90) - -7)/(1/9). Factor 0 - 4/7*g**m + 0*g + z*g**3.
2*g**2*(g - 2)/7
Suppose 14*u = 11*u. Factor 2/7*g**4 - 4/7*g**2 + u*g + 0 + 2/7*g**3.
2*g**2*(g - 1)*(g + 2)/7
Let s(j) = -7*j**2 + 56*j - 45. Let w(r) = -27*r**2 + 222*r - 180. Let o(v) = 15*s(v) - 4*w(v). Solve o(p) = 0.
1, 15
Let j(z) be the third derivative of -z**5/12 - 5*z**4/8 + 10*z**3/3 + 12*z**2. Determine n, given that j(n) = 0.
-4, 1
Let k(c) be the third derivative of c**7/3360 + c**6/320 + c**5/80 + c**4/8 - 3*c**2. Let o(x) be the second derivative of k(x). Factor o(q).
3*(q + 1)*(q + 2)/4
Let j(x) be the second derivative of -x**8/448 + x**7/280 + x**6/160 - x**5/80 - x**2/2 + 2*x. Let h(p) be the first derivative of j(p). Factor h(n).
-3*n**2*(n - 1)**2*(n + 1)/4
Let s(z) be the third derivative of -z**6/120 - z**5/60 - 9*z**2 - 2*z. Factor s(j).
-j**2*(j + 1)
Let g = 13 - 1. Let t be (8/g)/((-2)/(-6)). Factor -5*o**2 + t - 6 + 3*o - o**3 - 11*o.
-(o + 1)*(o + 2)**2
Suppose -79*b + 70*b = -18. Factor 1/2 + 0*r - 1/2*r**b.
-(r - 1)*(r + 1)/2
Factor 0 + 0*a**2 + 0*a + 1/2*a**3.
a**3/2
Let q(v) = -4 + 2*v**2 - 5*v**2 - 9*v**2 - 6*v - 10*v**2. Let g(u) = 7*u**2 + 2*u + 1. Let y(n) = -16*g(n) - 5*q(n). Solve y(j) = 0.
-2, 1
Let s(l) be the first derivative of l**6/21 - 8*l**5/35 - 11*l**4/14 + 52*l**3/21 + 64*l**2/7 + 64*l/7 + 16. Let s(c) = 0. What is c?
-2, -1, 4
Let n be (-2)/4*(0/(-4))/(-2). Factor 2*q**2 + n + 14/9*q**3 + 4/9*q.
2*q*(q + 1)*(7*q + 2)/9
Let y(i) be the second derivative of i**8/960 + i**7/504 - i**6/360 + i**4/6 + 3*i. Let z(x) be the third derivative of y(x). Find t, given that z(t) = 0.
-1, 0, 2/7
Factor 3/8*q**4 + 0*q**3 - 3/4*q**2 + 0*q + 3/8.
3*(q - 1)**2*(q + 1)**2/8
Let q be (-1 + -2 - -10) + -4. Let y(h) be the second derivative of 0*h**q - 1/42*h**7 + 2*h + 0*h**2 - 3/20*h**5 - 1/12*h**4 + 0 - 1/10*h**6. Factor y(g).
-g**2*(g + 1)**3
Suppose 2*d - 3 = 3, 5*d = 4*i + 3. Suppose -h + 0*h + 2*l = -13, i*l + 32 = 4*h. Factor -n**2 + 3/2*n**4 - 3/2*n + n**3 + 1/2*n**h - 1/2.
(n - 1)*(n + 1)**4/2
Factor -1/4*i + 0 - 1/2*i**2 - 1/4*i**3.
-i*(i + 1)**2/4
Let y(n) be the third derivative of -1/150*n**5 + 0 - 2*n**2 + 0*n + 0*n**3 + 1/60*n**4. Let y(a) = 0. What is a?
0, 1
Let s(b) = -6*b**4 - b**3 - b**2 - 8. Let c(d) = -d**4 - 1. Let o(x) = -24*c(x) + 3*s(x). Determine h, given that o(h) = 0.
-1/2, 0, 1
Let c = -72 + 74. Let o(j) be the first derivative of -1/10*j**4 + 0*j**c + 0*j**3 - 1 + 0*j**5 + 0*j + 1/15*j**6. Factor o(l).
2*l**3*(l - 1)*(l + 1)/5
Let l = 3993/13 + -307. What is d in -2/13 - 4/13*d**2 - 4/13*d**3 + 6/13*d**4 - l*d**5 + 6/13*d = 0?
-1, 1
Let d(n) be the second derivative of -n**5/300 + n**4/120 - 3*n**2 - 6*n. Let c(b) be the first derivative of d(b). Find k such that c(k) = 0.
0, 1
Suppose 5*a - 4*l - 25 = 0, 2 = 2*a - 2*l - 8. Let s(b) be the second derivative of 0*b**2 + 1/10*b**a + 0 + 2*b - 1/6*b**4 + 0*b**3. Factor s(d).
2*d**2*(d - 1)
Let v(u) be the second derivative of 1/6*u**3 + 1/360*u**6 + 0*u**4 - 1/120*u**5 + 0 + 0*u**2 + u. Let w(p) be the second derivative of v(p). Factor w(q).
q*(q - 1)
Let j(b) be the second derivative of 2*b**7/147 + b**6/21 + 3*b**5/70 - b**4/42 - b**3/21 + 31*b. Determine w so that j(w) = 0.
-1, 0, 1/2
Let k(y) be the third derivative of -y**11/554400 + y**10/126000 - y**9/100800 + y**5/60 - 5*y**2. Let z(d) be the third derivative of k(d). Solve z(v) = 0.
0, 1
Let j(n) be the second derivative of -n**5/180 - n**4/72 - n**2 - n. Let x(t) be the first derivative of j(t). Factor x(g).
-g*(g + 1)/3
Let a(r) be the third derivative of r**6/24 + r**5 - 45*r**2. Solve a(z) = 0.
-12, 0
Let o(n) = -85*n**2 + 275*n - 360. Let h(y) = 7*y**2 - 23*y + 30. Let r(f) = 25*h(f) + 2*o(f). Factor r(j).
5*(j - 3)*(j - 2)
Let x = -17 - -32. Suppose -3*f = 2*f - x. Factor -w**3 + w - w**2 - 1 + 2 + 0*w**f.
-(w - 1)*(w + 1)**2
Let o(f) = f**2 - 1. Let a(u) = 8*u**2 - 18*u + 22. Let d(r) = a(r) - 5*o(r). Find t, given that d(t) = 0.
3
Let s(k) be the second derivative of -2*k**6/45 + 4*k**5/15 - 5*k**4/9 + 4*k**3/9 + 6*k. Factor s(l).
-4*l*(l - 2)*(l - 1)**2/3
Let p(d) = 2*d + 23. Let s be p(-10). Let n(r) be the second derivative of 0 - s*r + 0*r**3 - 1/54*r**4 + 0*r**2. Let n(u) = 0. Calculate u.
0
Suppose -11*n = 6*n - 10*n. Find o such that n*o + 3/2*o**2 - 6 = 0.
-2, 2
Let s(t) be the first derivative of t**6/1080 - t**5/360 - t**3/3 + 1. Let n(d) be the third derivative of s(d). Factor n(j).
j*(j - 1)/3
Let m(s) = -7*s**2 + 3*s + 10. Let v(b) be the third derivative of -b**5/10 + b**4/8 + 3*b**3/2 - 2*b**2. Let u(n) = 3*m(n) - 4*v(n). Factor u(p).
3*(p - 2)*(p + 1)
Let z(g) = 17*g**4 + 17*g**3 - 17*g**2 - 17*g. Let f(o) = 4*o**4 + 4*o**3 - 4*o**2 - 4*o. Let x(q) = -9*f(q) + 2*z(q). Determine a, given that x(a) = 0.
-1, 0, 1
Let -3/10*l**4 + 2/5*l**2 + 0*l**3 + 0*l + 0 + 1/10*l**5 = 0. What is l?
-1, 0, 2
Factor 2/11*k + 10/11*k**2 - 2/11*k**3 - 10/11.
-2*(k - 5)*(k - 1)*(k + 1)/11
Suppose 19