g - 2*u - u. Let k be g/(-10)*(-4)/18. Factor -1/3*b**3 + 0*b**2 + k*b + 0.
-b*(b - 1)*(b + 1)/3
Let z(x) be the third derivative of x**5/300 - x**4/30 + x**3/10 - 5*x**2. Factor z(w).
(w - 3)*(w - 1)/5
Factor 28*p**3 - 3 - 13 - 100*p + 1 - 9 - 48*p**2.
4*(p - 3)*(p + 1)*(7*p + 2)
Let k(a) be the second derivative of -a**7/14 + a**6/10 + 3*a**5/20 - a**4/4 - 3*a. Suppose k(n) = 0. What is n?
-1, 0, 1
Let q be (-1*4)/(-2 - 0 - 0). Suppose -2/5*h**q - 1/5*h + 1/5*h**5 + 0*h**3 + 0 + 2/5*h**4 = 0. What is h?
-1, 0, 1
Suppose 0 = -l + 2*a + 13, 2*a = -3*l - l + 12. Suppose 8 - 2 = 3*o. Factor -2*b**2 - 2*b**4 - l*b**3 + 1 + o*b - b**2 - b.
-(b + 1)**3*(2*b - 1)
Let h(k) = -4*k**3. Let a(n) = -8*n**3 - n**2. Let v(f) = 4*a(f) - 7*h(f). Factor v(i).
-4*i**2*(i + 1)
Let c(y) = y + 12. Let m be c(-9). Suppose 0 - 3*l**2 - 16 - 14 + 18*l + m = 0. What is l?
3
Let j(l) be the first derivative of l**7/21 + 4*l**6/15 + 2*l**5/5 + l + 11. Let h(q) be the first derivative of j(q). What is z in h(z) = 0?
-2, 0
Let q(h) be the first derivative of -1 + 0*h - 1/2*h**2 + 1/6*h**3 - 1/12*h**4 + 1/60*h**5. Let z(r) be the second derivative of q(r). Factor z(m).
(m - 1)**2
Let a(q) = -3*q + q**2 + 2*q + 2*q**2 - q**3 - 6 + 7*q. Let k be a(4). Solve 3*z**3 - 5*z**k - 2*z**3 + 4*z**2 = 0 for z.
0, 1
Let g(y) be the third derivative of -y**6/30 + y**5/15 + 14*y**2. Determine d, given that g(d) = 0.
0, 1
Let j(a) be the first derivative of -a**4/12 - a**3/9 + 1. Suppose j(u) = 0. Calculate u.
-1, 0
Let m(t) be the second derivative of 1/54*t**4 - t + 0*t**3 + 0*t**2 - 1/90*t**5 + 0. Solve m(k) = 0.
0, 1
Let v(g) be the third derivative of g**9/13608 - g**8/3780 + g**6/810 - g**5/540 - 7*g**3/6 + 6*g**2. Let b(x) be the first derivative of v(x). Factor b(y).
2*y*(y - 1)**3*(y + 1)/9
Factor -1/3*f**4 - 4/3*f - 4/3*f**3 - 2*f**2 - 1/3.
-(f + 1)**4/3
Let v be (-176)/(-168) + (-2)/(-7). Let 6*w**3 + 14/3*w**2 + 0 + 10/3*w**4 + 2/3*w**5 + v*w = 0. What is w?
-2, -1, 0
Let a(w) be the first derivative of -w**4/4 + w**3/3 + 8*w**2 + 20*w + 13. Find j such that a(j) = 0.
-2, 5
Let a = -9 - -9. Let x be a/((-4*2)/4). What is o in 2/11*o**4 - 2/11*o**2 + x + 2/11*o**3 - 2/11*o = 0?
-1, 0, 1
Let l(u) be the first derivative of 0*u - 1/540*u**6 - 2 + 1/90*u**5 + u**3 + 0*u**2 - 1/36*u**4. Let n(d) be the third derivative of l(d). Factor n(v).
-2*(v - 1)**2/3
Let w = -7 - -9. Factor 2 + 0*o**2 - o**w - o**2.
-2*(o - 1)*(o + 1)
Let x(j) = -3*j**4 + 2*j**3 + 5*j**2 + 4. Let p(r) = r**4 - r**2 - 1. Let u(m) = -4*p(m) - x(m). Suppose u(k) = 0. What is k?
-1, 0
Let b = -125/34 - 2753/102. Let i = b - -33. Determine k so that -i*k**2 + 2/3 - 5/3*k = 0.
-1, 2/7
Factor 20 - 5*b**3 - 689*b**2 + 3*b**3 + 713*b**2 - 42*b.
-2*(b - 10)*(b - 1)**2
Factor 8*y**2 - 2*y**4 + 4*y**5 - 22*y**3 - 4 - y**4 + 14*y**3 - y**4 + 4*y.
4*(y - 1)**3*(y + 1)**2
Let n(f) be the second derivative of 0*f**3 + 1/5*f**5 + f + 1/6*f**4 + 0 - 7/15*f**6 + 0*f**2 + 4/21*f**7. Determine t so that n(t) = 0.
-1/4, 0, 1
Let k(v) be the third derivative of -1/40*v**6 - 5*v**2 + 1/8*v**4 + 0 + 0*v + 0*v**5 + 0*v**3. Solve k(f) = 0.
-1, 0, 1
Let g = 12 + -7. Let k(p) = p - 5. Let o be k(g). Factor -4*c**3 + o*c**5 + 1 + 6*c**4 + 4*c**5 - 8*c**2 + 1.
2*(c - 1)*(c + 1)**3*(2*c - 1)
Let f(d) = d**2 - 7*d + 8. Let g be f(6). Determine a, given that 3*a**2 + 0*a**g + 3*a**3 - 9*a**2 + 3*a = 0.
0, 1
Let j(z) = 3*z**3 + 71*z**2 - 379*z + 621. Let y(a) = -10*a**3 - 285*a**2 + 1515*a - 2485. Let r(g) = 15*j(g) + 4*y(g). Solve r(i) = 0 for i.
5
Let u(g) be the second derivative of g**7/315 + g**6/45 + 2*g**5/45 + g**2 - 4*g. Let v(z) be the first derivative of u(z). Solve v(p) = 0 for p.
-2, 0
Let r(c) = c**3 - 9*c**2 + 2*c + 6. Let i(l) = -3 - 9*l - 2 + 7*l + 8*l**2 - l**3. Let g(a) = 6*i(a) + 5*r(a). Factor g(h).
-h*(h - 2)*(h - 1)
Let k = -121 - -59. Let r = 808/13 + k. Let 0*l + 2/13 + 0*l**3 + r*l**4 - 4/13*l**2 = 0. Calculate l.
-1, 1
Let b(u) be the second derivative of u**4/12 + u**3/3 + 2*u. Factor b(s).
s*(s + 2)
Factor 4/7*g**2 + 0*g**3 + 0 + 0*g - 1/7*g**4.
-g**2*(g - 2)*(g + 2)/7
Factor 2/5*x**2 + 72/5 - 24/5*x.
2*(x - 6)**2/5
Let y(a) be the first derivative of 2*a**6/3 + 4*a**5 + 10*a**4 + 40*a**3/3 + 10*a**2 + 4*a - 6. Suppose y(r) = 0. Calculate r.
-1
Let j(f) be the second derivative of -5/3*f**3 + 2/3*f**4 + 2*f**2 - 6*f - 1/10*f**5 + 0. Factor j(n).
-2*(n - 2)*(n - 1)**2
Let z(q) be the third derivative of -q**5/300 + q**3/30 - 43*q**2. Suppose z(o) = 0. Calculate o.
-1, 1
Let f(k) be the second derivative of k**4/18 - 7*k**3/27 + 2*k**2/9 + k. Suppose f(n) = 0. Calculate n.
1/3, 2
Let q(a) be the first derivative of -6 - 23/7*a**4 - 22/35*a**5 - 81/7*a**2 - 60/7*a**3 - 54/7*a - 1/21*a**6. What is h in q(h) = 0?
-3, -1
Let c(k) be the second derivative of -4/3*k**2 + 1/6*k**4 + 7/3*k**5 + 0 + 3*k - 20/9*k**3 - 49/45*k**6. Determine h so that c(h) = 0.
-2/7, 1
Let n(r) = -r**2 - 7*r - 5. Let t be n(-7). Let d(i) = -i - 3. Let x be d(t). Factor 0*j + 1/2*j**4 + 1/2 + 0*j**3 - j**x.
(j - 1)**2*(j + 1)**2/2
Let n(m) = -5*m**2 - 9*m + 8. Let p(h) = 6*h**2 + 10*h - 9. Let c(b) = -7*n(b) - 6*p(b). Suppose c(j) = 0. What is j?
1, 2
Let g(y) = 2*y**4 - 5*y**3 - 30*y**2 - 3*y. Let u(d) = 15*d**4 - 35*d**3 - 210*d**2 - 20*d. Let w(m) = -20*g(m) + 3*u(m). Factor w(a).
5*a**2*(a - 3)*(a + 2)
Suppose 8*w = 3*w - 40. Let z = -6 - w. Factor 30*f**2 - 2 + 5*f - 112*f**3 - 4*f**2 + 4*f - z*f**2.
-(4*f - 1)**2*(7*f + 2)
Let d(o) = -8*o - 302. Let w be d(-38). What is b in 0 + 4/9*b**3 + 0*b + 2/9*b**4 + 0*b**w = 0?
-2, 0
Suppose -2*l + 4 + 2 = 0. Let s = -25/7 - -107/28. Factor 1/4*o**l + 1/4 - s*o - 1/4*o**2.
(o - 1)**2*(o + 1)/4
Let s(y) = 6*y**3 + y**2 + y. Let k be s(-1). Let w be (2/6)/((-1)/k). Factor -2*q**4 + 7*q - 12*q**2 - w + 0*q**4 - 5*q + 8*q**3 + 6*q.
-2*(q - 1)**4
Suppose 2*k - 6 = -k. Factor -k*b**4 - 2*b**3 + 8*b**3 - 4*b**4 + 8*b**2 - 8*b + 2*b**5 - 2*b**4.
2*b*(b - 2)**2*(b - 1)*(b + 1)
Let z(u) = -u**3 + u**2 + 9*u - 9. Let c(l) = l - 1. Let k(i) = 24*c(i) - 3*z(i). Factor k(j).
3*(j - 1)**2*(j + 1)
Find l, given that -30*l**3 + 18*l**3 - 2*l**5 + 5*l**4 - 3*l**4 - 16*l - 8 - 2*l**2 + 22*l**3 = 0.
-1, 2
Suppose 0*t + 3*t = -2*t. Let l(p) be the second derivative of 0*p**3 + 1/21*p**7 + 0*p**2 + 1/10*p**5 + 0 + t*p**4 - 2/15*p**6 - 3*p. Factor l(y).
2*y**3*(y - 1)**2
Suppose -u**2 + 2*u**4 + 25*u - 25*u - u**2 = 0. Calculate u.
-1, 0, 1
Let m(b) be the third derivative of -b**8/3360 - b**7/336 - b**6/90 - b**5/60 + 2*b**3/3 + 5*b**2. Let g(q) be the first derivative of m(q). Factor g(d).
-d*(d + 1)*(d + 2)**2/2
Let n(d) be the second derivative of -d**5/20 - d**4/12 - 7*d. Factor n(g).
-g**2*(g + 1)
Let d(m) be the second derivative of -3*m**2 + 7*m - m**3 - 1/8*m**4 + 0. Factor d(i).
-3*(i + 2)**2/2
Let b(f) be the third derivative of f**4/24 + f**3 + 3*f**2. Let a be b(-3). Factor -u**2 + a*u + 2*u - 3*u.
-u*(u - 2)
Let v(s) = 2*s**2 - 8*s - 2. Let y(t) = -t + 2. Let n(f) be the first derivative of f - 2. Let l(m) = 3*n(m) - y(m). Let r(x) = -4*l(x) - v(x). Factor r(w).
-2*(w - 1)**2
Factor 15*b**2 - 11 - 40*b - 8 - 7 + 6 + 45*b**3.
5*(b - 1)*(3*b + 2)**2
Let o = 40 - 119/3. Suppose 8*u = 15 + 17. Determine x, given that x**u + 0 - o*x**5 + 0*x - x**3 + 1/3*x**2 = 0.
0, 1
Let c be (-60)/(-18) + 2/3. Determine y so that -c*y**2 + 7*y**2 + 3*y**2 + 2 + 6*y + 2*y**3 = 0.
-1
Let p(k) be the third derivative of -k**9/5040 + k**8/560 - k**7/210 - k**4/8 + 2*k**2. Let v(c) be the second derivative of p(c). Determine f so that v(f) = 0.
0, 2
Let t(c) be the first derivative of -5*c**6/6 - 3*c**5 - 15*c**4/4 - 5*c**3/3 + 18. Factor t(p).
-5*p**2*(p + 1)**3
Let a(k) be the second derivative of k**9/1512 - k**7/210 + k**5/60 - k**3/6 - 3*k. Let z(n) be the second derivative of a(n). Factor z(v).
2*v*(v - 1)**2*(v + 1)**2
Let o be ((4 + -2)/(-18))/(4/(-24)). Factor 0*c + o*c**3 - 2*c**2 + 8/3.
2*(c - 2)**2*(c + 1)/3
Let t = 107/62 - 38/31. Factor t + 1/4*o - 3/4*o**3 - o**2.
-(o + 1)**2*(3*o - 2)/4
Factor -1/5 - 1/5*s**3 - 3/5*s - 3/5*s**2.
-(s + 1)**3/5
Factor 3/4*c**2 - 9/2*c**4 - 21/8*c**5 - 9/8*c**3 + 0*c + 0.
-3*c**2*(c + 1)**2*(7*c - 2)/8
Let b(l) = 220*l**3 - 850*l**2 - 730*l + 305. Let d(i) = 13*i**3 - 50*i**2 - 4