-1, 1
Let a(g) be the third derivative of -g**7/70 + g**6/10 - 3*g**5/10 + g**4/2 - g**3/2 - 8*g**2. Factor a(l).
-3*(l - 1)**4
Suppose -16*n = 3*n. Factor -16/3*p**3 + 2/3*p**2 + 4/3*p + 10/3*p**4 + n.
2*p*(p - 1)**2*(5*p + 2)/3
Let h = 378 - 378. What is p in 0*p + 0*p**3 + 3/4*p**4 + h + 1/2*p**5 - 1/4*p**2 = 0?
-1, 0, 1/2
Suppose -8*z + 7*z + 4 = 0. Factor -5*m - z*m**3 + 3*m**3 + m - m**2 + 4 + 2*m**3.
(m - 2)*(m - 1)*(m + 2)
Let q(t) be the first derivative of -27*t**6/2 + 54*t**4 + 64*t**3 + 24*t**2 + 8. Solve q(m) = 0 for m.
-2/3, 0, 2
Suppose o - 4*o + 6 = 0. Let r = o + 1. Factor 0 - 4/7*i + 6/7*i**r - 2/7*i**2.
2*i*(i - 1)*(3*i + 2)/7
Let x(o) = -o**2 + 23*o - 74. Let s be x(19). Let 0 + 1/5*q**3 + 0*q + 1/5*q**s = 0. Calculate q.
-1, 0
Factor -4/13 + 2/13*n**2 - 2/13*n.
2*(n - 2)*(n + 1)/13
Let h(c) be the second derivative of 1/4*c**4 + 0 - 1/30*c**6 + 1/6*c**3 - 1/20*c**5 - c**2 + 3*c. Factor h(m).
-(m - 1)**2*(m + 1)*(m + 2)
Let d(z) = -5*z**5 + 3*z**4 + 5*z**3 + 3*z. Let k(v) = -11*v**5 + 7*v**4 + 11*v**3 + 7*v. Let t(o) = 7*d(o) - 3*k(o). What is y in t(y) = 0?
-1, 0, 1
Let b be (-2)/((3/(-18))/(1/4)). Suppose -1/4*m**4 + 1/4*m**2 + 1/4*m + 0 - 1/4*m**b = 0. What is m?
-1, 0, 1
Let q be (5/(-60))/(3/(-12)*1). Factor -q*i**5 + 2/3*i**3 - 1/3*i + 0 + 0*i**2 + 0*i**4.
-i*(i - 1)**2*(i + 1)**2/3
Let h = 40 + -38. Let p(x) be the third derivative of -h*x**2 + 1/120*x**6 + 0 + 0*x**3 + 0*x**4 - 1/60*x**5 + 0*x. Suppose p(g) = 0. Calculate g.
0, 1
Let i = 129 - 117. Factor i*n + 18/7 + 8/7*n**3 + 50/7*n**2.
2*(n + 3)**2*(4*n + 1)/7
Let w(i) = 5*i**5 + i**4 - 7*i**3 - 3*i**2 + 8*i - 2. Let x(v) = -6*v**5 + 6*v**3 + 3*v**2 - 9*v + 3. Let j(o) = 3*w(o) + 2*x(o). Factor j(n).
3*n*(n - 1)**2*(n + 1)*(n + 2)
Let b(r) = -r**3 + 4*r**2 + 3. Let i be b(4). Suppose 2*x = -5*g + 4*g - i, -9 = 2*x + 3*g. Suppose 0 + 0*k**3 - 2/7*k**2 + x*k + 2/7*k**4 = 0. What is k?
-1, 0, 1
Let a(x) be the second derivative of -x**8/23520 - x**7/8820 + x**6/1260 + 2*x**4/3 + 8*x. Let z(t) be the third derivative of a(t). Factor z(o).
-2*o*(o - 1)*(o + 2)/7
Factor 13/9*f + 7/9*f**3 + 1/9*f**4 + 5/3*f**2 + 4/9.
(f + 1)**3*(f + 4)/9
Let l = -3 + 2. Let u be (2 + -6)*l/(-1). Let j(r) = -10*r**2 - 15*r - 2. Let i(z) = 11*z**2 + 14*z + 2. Let h(d) = u*i(d) - 3*j(d). Let h(s) = 0. What is s?
-1/2, -2/7
Let q(o) be the second derivative of -o**9/15120 + o**7/2520 + 7*o**4/12 - 2*o. Let x(a) be the third derivative of q(a). Let x(u) = 0. What is u?
-1, 0, 1
Let j = 6 + -4. Suppose -d = 5*z - 49, 0*z + 2 = j*z - 4*d. Factor -3*f - 6*f**4 + 3 + z*f**2 - 3*f**2 + 3*f**5 - 3.
3*f*(f - 1)**3*(f + 1)
Let y(w) be the second derivative of w**6/60 - w**4/12 + w**2/4 + 14*w. Factor y(c).
(c - 1)**2*(c + 1)**2/2
Solve -5/4*g**4 + 0*g**2 + 0 + 0*g - 5/2*g**3 = 0 for g.
-2, 0
Factor -3/5 + 3*o**2 - 12/5*o.
3*(o - 1)*(5*o + 1)/5
Let z(y) = -8*y**2 - y + 1. Let k be z(1). Let c be (8/(-30))/(k/12). Let -2/5 - c*g**2 - 4/5*g = 0. What is g?
-1
Let f(t) = 5*t**3 - 5*t**2. Let q(k) = 5*k**3 - 4*k**2 - k. Suppose 0 = 2*l - 0*l + 12. Let g(v) = l*f(v) + 4*q(v). What is n in g(n) = 0?
0, 2/5, 1
Let d(h) = h**2 - 4*h + 2. Let n be d(3). Let m = n - -3. Find o such that -3*o**3 + 3*o**3 + 6*o**2 + m + 2*o**3 + 6*o = 0.
-1
Factor 2*x**2 + 9*x - 7*x - 8*x.
2*x*(x - 3)
Let g(x) = x**2. Let h(t) = -4*t**2 + 1. Let o(k) = 3*g(k) + h(k). Let o(c) = 0. Calculate c.
-1, 1
Let l(k) = -3*k - 12. Let m be l(-4). Solve m*t**2 + 0 + 1/4*t**3 + 0*t = 0.
0
Let i(y) be the third derivative of -y**6/24 - 5*y**5/4 - 125*y**4/8 - 625*y**3/6 - 11*y**2. Factor i(m).
-5*(m + 5)**3
Let n(g) be the first derivative of 3*g**3 + 0*g**2 - 12*g + 3/4*g**4 + 1. Find v, given that n(v) = 0.
-2, 1
Let d(i) be the third derivative of i**8/60480 + i**7/7560 - i**5/20 + 4*i**2. Let x(j) be the third derivative of d(j). Solve x(w) = 0 for w.
-2, 0
Find o such that -4*o + 4/3*o**2 + 0 = 0.
0, 3
Let b be (-2)/18*-3*0. Let f(s) be the third derivative of 0*s + 2*s**2 + 0*s**4 + b*s**5 + 0*s**3 + 0 + 1/120*s**6. Let f(k) = 0. What is k?
0
Let u(m) = m**2 + 131*m - 360. Let n(w) = w**2 + 66*w - 180. Let r(d) = -11*n(d) + 6*u(d). Factor r(h).
-5*(h - 6)**2
Let o = 44/13 - 106/39. Factor 8/9 - 16/9*d + o*d**2.
2*(d - 2)*(3*d - 2)/9
Let v be 4 - 2/(-12) - 4. Let o(s) be the third derivative of -3*s**2 + 0 - 1/60*s**5 + 0*s - v*s**3 + 1/12*s**4. Solve o(j) = 0.
1
Let v(t) = t**2 + 3*t + 4. Let o(z) = -2*z**2 - 4*z - 5. Let h(r) = -2*o(r) - 3*v(r). Factor h(f).
(f - 2)*(f + 1)
Let c(r) = 2*r - 5. Let d be c(4). Let p = -1 + d. Let -3*q + 16*q**4 - 24*q**3 + 6*q**2 + 0*q**4 + 9*q**p - 4*q**4 = 0. What is q?
0, 1/2, 1
Let i(k) be the third derivative of k**10/302400 - k**8/20160 + k**6/1440 + k**5/30 - 3*k**2. Let x(u) be the third derivative of i(u). What is m in x(m) = 0?
-1, 1
Let y(m) be the third derivative of m**7/3780 - m**3/2 + m**2. Let k(l) be the first derivative of y(l). Suppose k(u) = 0. What is u?
0
Let v(x) be the first derivative of -x**7/840 - x**6/160 - x**5/120 - x**2 - 4. Let z(i) be the second derivative of v(i). Suppose z(w) = 0. What is w?
-2, -1, 0
Let z(y) = -y**3 - 8*y**2 - 13*y - 4. Let u be z(-6). Factor -2/3 + l - 1/3*l**u.
-(l - 2)*(l - 1)/3
Let k = -52 + 52. Let g(a) be the third derivative of -1/10*a**5 + 2*a**2 + 0 + 4/3*a**3 + k*a + 0*a**4 - 1/60*a**6. Solve g(o) = 0 for o.
-2, 1
Let t(r) be the second derivative of r**7/2940 + r**6/1260 - r**5/210 - 2*r**3/3 - 2*r. Let v(n) be the second derivative of t(n). Solve v(p) = 0.
-2, 0, 1
Let c(f) = 3*f**2 + 7*f - 3 + 0*f**2 + f. Let b(m) = -m**2 - 4*m + 2. Let g(z) = 5*b(z) + 2*c(z). Find t such that g(t) = 0.
2
Let f(v) be the second derivative of v**6/135 + v**5/90 + 2*v. Factor f(a).
2*a**3*(a + 1)/9
Suppose -14 = -2*u - l, 5*u - 34 = -4*l + 4. Factor 6*c**3 - 2*c**3 + 15*c**4 - 3*c**2 + 3*c**3 + 2*c**3 + u*c**5 - 3*c.
3*c*(c + 1)**3*(2*c - 1)
Find g such that 12*g**3 + 167*g + 100*g**2 - 38*g**3 - 16 - 255*g = 0.
-2/13, 2
Suppose -3/5*i**4 - 9/5*i**3 + 9/5*i + 0 + 3/5*i**2 = 0. What is i?
-3, -1, 0, 1
Let t = -467/48 - -39/4. Let g(w) be the third derivative of -1/120*w**5 + w**2 - 1/240*w**6 + t*w**4 + 1/12*w**3 + 0 + 0*w. Determine p so that g(p) = 0.
-1, 1
Let x(j) be the third derivative of -1/4*j**4 + 0 - 1/2*j**3 + 1/20*j**6 + 0*j**5 + 4*j**2 + 1/70*j**7 + 0*j. Factor x(w).
3*(w - 1)*(w + 1)**3
Let j be (12598/(-2100) - -2) + 8/2. Let i(s) be the third derivative of 0*s**3 - s**2 + 0*s - 1/120*s**4 + 1/600*s**6 - 1/300*s**5 + 0 + j*s**7. Factor i(m).
m*(m - 1)*(m + 1)**2/5
Let t = -275 + 827/3. Solve 0 + 0*i + 2/9*i**3 + t*i**2 = 0 for i.
-3, 0
Factor -1/2*l**2 + 0 - 1/2*l.
-l*(l + 1)/2
Let h(l) be the first derivative of 1/4*l**4 + 0*l**3 + 3 + 0*l**5 + 0*l - 1/6*l**6 + 0*l**2. Determine i, given that h(i) = 0.
-1, 0, 1
Let g be ((-18)/8)/(-1) + 1 + -2. Find r such that r**3 - g*r**2 - 1/4*r**4 + 1/2*r + 0 = 0.
0, 1, 2
Let v(m) be the third derivative of 1/240*m**5 - 1/480*m**6 - 1/24*m**3 - m**2 + 1/96*m**4 + 0 + 0*m. Determine j, given that v(j) = 0.
-1, 1
Let q(i) be the first derivative of -2*i**5/65 + 3*i**4/26 + 2*i**3/39 - 3*i**2/13 - 21. Find d such that q(d) = 0.
-1, 0, 1, 3
Let h be -9*(32/(-36))/4. Let z be (1 - 0)/(1/h). Factor 2*v**4 - 16/9*v - 16/3*v**3 + 44/9*v**z + 2/9.
2*(v - 1)**2*(3*v - 1)**2/9
Let o(m) be the first derivative of -5*m**6/6 + 7*m**5/2 - 23*m**4/4 + 14*m**3/3 - 2*m**2 - m + 4. Let i(n) be the first derivative of o(n). Factor i(f).
-(f - 1)**2*(5*f - 2)**2
Suppose -19 = -u - 2. Suppose 22*t = u*t. Factor -1/2*r**2 + t + 1/2*r.
-r*(r - 1)/2
Let q(r) = 4 - 2*r**3 + 7*r**2 + 4*r - 2*r**2 + 3*r**3. Let x be q(-4). Find w, given that w**x - 41/5*w**3 - 4/5 + 5*w**5 + 16/5*w - 1/5*w**2 = 0.
-1, 2/5, 1
Let j(x) be the first derivative of 3*x**3 - 6 + 6*x**2 - 12*x - 3/5*x**5 - 3/2*x**4. Determine u, given that j(u) = 0.
-2, 1
Suppose 0 = -2*z - 0 - 10, 2*z = 2*s - 14. Let u be ((-4)/21)/(12/(-14)). Solve -u*f**5 + 0 + 0*f - 2/9*f**s + 2/9*f**3 + 2/9*f**4 = 0 for f.
-1, 0, 1
Let u(i) be the third derivative of 0 + 0*i**3 + 5*i**2 + 0*i**4 - 1/210*i**5 + 0*i. Factor u(n).
-2*n**2/7
Let x(z) = 2*z**3 - 2*z - 6. Let g(y) = 1. Let m = -16 + 15. Let n(f) = m*x(f) - 6*g(f). Factor n(j).
-2*j*(j - 1)*(j + 1)
Let n(r) be the th