+ 0.
-g*(g + 1)/3
Suppose 2*a - 17 = -3. Let o = a + -3. Factor -2*t**3 + 2*t**4 + t**3 - t**o.
t**3*(t - 1)
Let z(p) be the third derivative of -p**8/5040 + p**7/630 - p**6/270 - p**4/8 - 2*p**2. Let q(r) be the second derivative of z(r). Determine u so that q(u) = 0.
0, 1, 2
Let h(b) be the third derivative of b**8/84 - b**7/70 - b**6/24 + b**5/20 + b**4/24 + 36*b**2. Suppose h(f) = 0. Calculate f.
-1, -1/4, 0, 1
Let s(z) be the third derivative of 0*z**3 + 0*z**4 + 0 - 7/40*z**6 + 4/35*z**7 + 0*z - 7*z**2 - 3/112*z**8 + 1/10*z**5. Factor s(k).
-3*k**2*(k - 1)**2*(3*k - 2)
Let o(m) = m + 10. Let c be o(-8). Let g(f) be the first derivative of 1 + 0*f - 1/3*f**3 + 1/6*f**c - 1/3*f**4. Factor g(b).
-b*(b + 1)*(4*b - 1)/3
Let d(o) be the third derivative of 1/80*o**6 + 1/420*o**7 + 0 + 0*o**3 + 7*o**2 + 1/60*o**5 + 0*o + 0*o**4. Factor d(q).
q**2*(q + 1)*(q + 2)/2
Let c = 917/614 - -2/307. Factor 3/4*h - c*h**2 - 3/4*h**3 + 3/2.
-3*(h - 1)*(h + 1)*(h + 2)/4
Factor 3*j**2 + j + 1/4*j**5 + 13/4*j**3 + 3/2*j**4 + 0.
j*(j + 1)**2*(j + 2)**2/4
Suppose -5*z + 56 = 4*i, -6*z + z - 5*i = -60. Factor 0 + 2/3*l**4 + z*l**2 + 16/3*l + 4*l**3.
2*l*(l + 2)**3/3
Let x(k) be the third derivative of -k**6/300 + k**5/150 + k**4/30 - 6*k**2. Suppose x(h) = 0. Calculate h.
-1, 0, 2
Find u such that -4/7*u**4 + 0 - 12/7*u**2 + 4/7*u + 12/7*u**3 = 0.
0, 1
Let f(v) = -3*v + 5. Let p be f(4). Let t = -4 - p. Factor -k**5 + k**3 - k**3 + k**t.
-k**3*(k - 1)*(k + 1)
Let r be (0/3)/3*-1. Let b = r - -4. Factor 5*k - b*k + 0*k**2 + k**2.
k*(k + 1)
Solve 0 + 1/7*y + 2/7*y**2 = 0 for y.
-1/2, 0
Let r(x) be the first derivative of -2*x**5/35 + 2*x**4/7 - 2*x**3/7 - 4*x**2/7 + 8*x/7 + 58. Suppose r(u) = 0. What is u?
-1, 1, 2
Let p(t) be the first derivative of 2*t**5/5 + t**4 - 2*t**2 - 2*t + 32. Factor p(s).
2*(s - 1)*(s + 1)**3
Let x(j) be the second derivative of j**7/5040 - j**6/1440 - j**4/12 + j. Let r(z) be the third derivative of x(z). What is n in r(n) = 0?
0, 1
Let j(b) be the second derivative of b**7/6300 - b**4/4 + 4*b. Let h(f) be the third derivative of j(f). Determine u, given that h(u) = 0.
0
Let b(g) be the first derivative of -g**6/120 + g**5/180 + g**3/3 - 4. Let l(o) be the third derivative of b(o). Let l(u) = 0. Calculate u.
0, 2/9
Let u(b) be the second derivative of b**5/10 - b**4/2 - 16*b**3/3 - 12*b**2 - 25*b. Factor u(l).
2*(l - 6)*(l + 1)*(l + 2)
Let g be 65/7 - (-14)/(-49). Let l be -2*2*(-1)/g. Factor 0*q**3 + 0*q - 2/9*q**4 - 2/9 + l*q**2.
-2*(q - 1)**2*(q + 1)**2/9
Let u(h) be the second derivative of 1/30*h**4 + 16/5*h**2 + 8/15*h**3 + 5*h + 0. What is s in u(s) = 0?
-4
Let f(t) be the third derivative of 27*t**8/154 + 117*t**7/385 + 9*t**6/55 - t**5/55 - 2*t**4/33 - t**3/33 - 6*t**2. Factor f(r).
2*(3*r + 1)**4*(4*r - 1)/11
Let j(z) be the third derivative of 1/70*z**7 + 0*z**3 + 1/24*z**4 + 0 + 1/12*z**5 + z**2 + 7/120*z**6 + 0*z. Suppose j(v) = 0. What is v?
-1, -1/3, 0
Determine d, given that 0*d + 81/7*d**4 + 120/7*d**3 + 0 + 36/7*d**2 + 15/7*d**5 = 0.
-3, -2, -2/5, 0
Let u(q) be the third derivative of 0*q**6 + 0 + 0*q**3 - 1/120*q**5 + 0*q + 1/420*q**7 + 0*q**4 - 6*q**2. Solve u(x) = 0 for x.
-1, 0, 1
Factor u - 1/2*u**2 - 1/2.
-(u - 1)**2/2
Let u(o) be the second derivative of -o**7/14 - 3*o**6/10 + 3*o**5/20 + 7*o**4/4 - 6*o**2 - 4*o. Let u(r) = 0. What is r?
-2, -1, 1
Suppose -3*o - 3*m + 25 = 7, 2 = -3*o + 2*m. Factor 12/11*n**3 + 24/11*n + 2/11*n**4 + 26/11*n**o + 8/11.
2*(n + 1)**2*(n + 2)**2/11
Let b(k) = -4*k**4 - 19*k**3 + 11*k**2 - 19*k - 4. Let o(x) = x**4 + 6*x**3 - 4*x**2 + 6*x + 1. Let h(d) = 4*b(d) + 14*o(d). Suppose h(z) = 0. What is z?
1
Let h be (6 + -2)/(6 + 4). Let z = 19 - 17. Factor -2/5*a**z + 2/5 - h*a + 2/5*a**3.
2*(a - 1)**2*(a + 1)/5
Find x such that x**2 - 6 + 2*x**5 + 4 - 4*x**3 + 4*x**4 - 3*x**5 - 3*x**2 + 5*x = 0.
-1, 1, 2
Let y = 9/106 + -5437/53. Let g = -95 - y. Factor -11/2*x**4 - g*x**5 + 0 + 0*x - x**3 + 0*x**2.
-x**3*(3*x + 1)*(5*x + 2)/2
Let i(g) be the third derivative of -g**7/126 - g**6/36 - g**5/36 - 15*g**2. Suppose i(n) = 0. Calculate n.
-1, 0
Suppose 0 = 4*p - 3 - 1. Let l be p/(-4) - (-117)/52. Solve 1/3*d + d**3 + 1/3*d**4 + 0 + d**l = 0 for d.
-1, 0
Let g(r) = 4*r - 3. Let q(i) = 3*i - 2. Let y(l) = 2*g(l) - 3*q(l). Let x(w) = -10*w**2 - 14*w. Let d(o) = -x(o) + 10*y(o). Factor d(s).
2*s*(5*s + 2)
Let g = 477/2 - 250. Let b = g - -12. Factor 0*n**3 + b*n**4 - n**2 + 1/2 + 0*n.
(n - 1)**2*(n + 1)**2/2
Determine r, given that 4/5*r**3 - 8/5*r + 2/5*r**4 - 6/5*r**2 + 8/5 = 0.
-2, 1
Factor 6/5*u**2 + 3/5*u - 6/5 - 3/5*u**3.
-3*(u - 2)*(u - 1)*(u + 1)/5
Let j = 54 + -22. Find r, given that -2*r**2 - j + 8*r - 3*r + 11*r = 0.
4
Let s(c) be the third derivative of 0*c + 0 + 1/210*c**5 - 5*c**2 + 1/42*c**4 + 0*c**3. Factor s(t).
2*t*(t + 2)/7
Suppose 0 = -2*l - 2*l - 4*k + 20, -22 = -5*l - 2*k. Let a = l - 2. Factor 0 + 2/3*d**a - 1/3*d - 1/3*d**3.
-d*(d - 1)**2/3
Let x be 96/(-704)*(-8)/6. Factor 6/11*v + x*v**3 + 2/11 + 6/11*v**2.
2*(v + 1)**3/11
Factor 2/17*l**4 - 8/17*l + 0 + 16/17*l**2 - 10/17*l**3.
2*l*(l - 2)**2*(l - 1)/17
Let g(m) be the second derivative of -3*m + 1/5*m**2 + 1/30*m**4 + 0 + 2/15*m**3. Factor g(o).
2*(o + 1)**2/5
Let g(h) be the third derivative of h**6/135 + 7*h**5/270 - h**4/54 - 8*h**2. What is p in g(p) = 0?
-2, 0, 1/4
Let z(g) be the second derivative of g**6/30 - g**5/20 + g**4/12 + g**2/2 + 7*g. Let u(s) = -s**4 - 3*s**2 + 2*s - 2. Let m(l) = -2*u(l) - 4*z(l). Factor m(p).
-2*p*(p - 2)*(p - 1)*(p + 1)
Factor -1/5*l**3 + 1/10*l**4 + 0*l + 0 + 1/10*l**2.
l**2*(l - 1)**2/10
Let w = -3 - -7. Factor 0*p**4 - 5*p**4 - p**4 + 6*p**3 + 4 - 2*p**2 + w*p**4 - 6*p.
-2*(p - 2)*(p - 1)**2*(p + 1)
Find z such that -1/7*z**2 - 9/7 + 6/7*z = 0.
3
Let m(d) be the first derivative of d**6/12 + 2. Factor m(a).
a**5/2
Factor 5/3*p + 2/3 + 1/3*p**3 + 4/3*p**2.
(p + 1)**2*(p + 2)/3
Let m be (2 - 60/32)*(-24)/(-22). Let f(s) be the first derivative of 2/55*s**5 - m*s**4 + 0*s + 2/11*s**3 - 1/11*s**2 + 1. Factor f(k).
2*k*(k - 1)**3/11
Suppose 8 = 3*r - r. Suppose 0 = -j + 5*j - 16. Solve 3*f**j + 0*f**r - 2*f**2 - f**4 = 0 for f.
-1, 0, 1
Let v be 2/(-4) - 2/(-4). Suppose 4*g + 0*o - 5*o - 25 = v, -2*o - 10 = 0. What is n in 1/5*n**2 + 1/5*n**3 - 1/5*n - 1/5*n**4 + g = 0?
-1, 0, 1
Let x(n) = -n**4 + 6*n**3 + 8*n**2 + 4*n + 3. Let y(t) = t**3 + t**2 + t + 1. Let o(m) = 2*x(m) - 10*y(m). Factor o(w).
-2*(w - 2)*(w - 1)*(w + 1)**2
Let w(m) = 3*m**2 + 12*m + 27. Let r(c) = -4*c**2 - 13*c - 28. Let d(l) = -2*r(l) - 3*w(l). Let d(p) = 0. Calculate p.
-5
Let s(t) be the third derivative of -t**7/70 + t**5/10 - t**3/2 + 5*t**2. Factor s(m).
-3*(m - 1)**2*(m + 1)**2
Factor -5*w + 4 - 4*w**2 + 4*w**3 + 7*w - 6*w.
4*(w - 1)**2*(w + 1)
Suppose r + 12*h = 10*h + 2, 3*h + 11 = 2*r. Suppose -38/11*d**2 + 26/11*d**3 - 8/11 - 40/11*d + 14/11*d**5 + 46/11*d**r = 0. Calculate d.
-2, -1, -2/7, 1
Let b(j) be the third derivative of j**6/96 + j**5/48 - 5*j**4/96 - 5*j**3/24 + 27*j**2. Factor b(g).
5*(g - 1)*(g + 1)**2/4
Let t(i) = 2*i**2 - 2*i + 4. Let g be t(5). Let l be 33/g - (-5)/(-12). Let -2/3 + c - l*c**2 = 0. What is c?
1, 2
Factor -12/5*q**3 + 32/5*q**2 - 8/5 - 12/5*q.
-4*(q - 2)*(q - 1)*(3*q + 1)/5
Let b(t) = -t**4 - t**3 + 1. Let g(y) = -20*y**4 + 130*y**3 - 30*y**2 - 15. Let n(c) = 15*b(c) + g(c). What is v in n(v) = 0?
0, 2/7, 3
Let g = 82 + -80. Factor 2/5*f**3 - 2/5*f**5 + 0 - 2/5*f**g + 0*f + 2/5*f**4.
-2*f**2*(f - 1)**2*(f + 1)/5
Let m(c) = 2*c**2 + 4*c + 3*c**2 - 7*c**3 - c. Let n(f) = f + 54*f**2 - 1 - 53*f**2 + 1. Let s(p) = -m(p) + 3*n(p). What is l in s(l) = 0?
0, 2/7
Suppose -18*p + 13*p + 10 = 0. What is i in 0*i + 0 + 0*i**p - 2/5*i**5 + 4/5*i**4 - 2/5*i**3 = 0?
0, 1
Let q(t) = -11*t**2 - t - 5*t**3 + 4*t**3 + 4*t + 14 - 2*t. Let f be q(-11). Solve 6/5*u**2 + 0 - 2/5*u**f - 4/5*u = 0 for u.
0, 1, 2
Let w(n) = -3*n**2 + 32*n - 77. Let b(a) = a - 1. Let i(f) = -2*b(f) + w(f). Suppose i(u) = 0. Calculate u.
5
Let j(t) = -t**3 + t**2 - t. Let a(u) = -2*u**3 + 3*u**2 - 4*u. Let b(p) = p**2 + 11*p + 3. Let n be b(-11). Let m(v) = n*j(v) - a(v). Factor m(q).
-q*(q - 1)*(q + 1)
Let c(j) = -j**3 - 5*j**2 + 2. Let b be c(-5). Factor -h**4 - 1 + 0*h**4 + 0*h**2 + 0 + 2*h**b.
-(h - 1)**2*(