k + 18*k**3 - 59 + 59 = 0. Calculate k.
-2, 0, 2/9
Suppose -1 = -h + 2*j - 0, 0 = -5*j + 5. Find k such that -k - k**h - 6*k**2 + 0*k**2 + 4*k**2 = 0.
-1, 0
Factor 0*w + 0 - 1/3*w**4 - w**3 - 2/3*w**2.
-w**2*(w + 1)*(w + 2)/3
Let q(h) be the first derivative of h**6/540 - h**4/9 - h**3/3 + 4. Let i(d) be the third derivative of q(d). Factor i(m).
2*(m - 2)*(m + 2)/3
Let y(u) = -u - 1. Let g be y(-1). Let n(c) be the second derivative of 0*c**2 + 0*c**3 - 3*c - 1/12*c**4 - 1/5*c**5 + g. Factor n(v).
-v**2*(4*v + 1)
Let r(s) be the third derivative of s**7/7560 - s**6/540 + s**5/90 + s**4/6 - 2*s**2. Let u(p) be the second derivative of r(p). Solve u(w) = 0 for w.
2
Let d(j) = -j**2 + 14*j + 74. Let h be d(18). Determine a, given that 1/4 - 5/4*a + a**h = 0.
1/4, 1
Let a(m) be the first derivative of 1/2*m**2 + 2/5*m**5 + 0*m - 1/6*m**6 - 2/3*m**3 + 1 + 0*m**4. Solve a(x) = 0.
-1, 0, 1
Let l(c) be the second derivative of c**7/14 - 7*c**6/30 + c**5/6 + c**4/6 - c**3/6 - c**2/6 + 35*c. Factor l(w).
(w - 1)**3*(3*w + 1)**2/3
Let g(d) be the second derivative of -3*d**5/80 - 3*d**4/8 - 9*d**3/8 - 3*d**2/2 - d. Factor g(y).
-3*(y + 1)**2*(y + 4)/4
Let i = 24 + -16. Suppose 3*u + 2 = i. Factor -1 + 3 - 4 - u*m - 4*m**2 + 4.
-2*(m + 1)*(2*m - 1)
Let t(z) = 7*z**2 - 6*z + 9. Suppose -3*k = -4*g - 44, -2*k - 3*g = -8 - 27. Let y(o) = -22*o**2 + 18*o - 28. Let x(f) = k*t(f) + 5*y(f). Factor x(n).
2*(n - 2)*(n - 1)
Let z(j) be the third derivative of j**8/112 + j**7/70 - j**6/20 - j**2. Let z(a) = 0. Calculate a.
-2, 0, 1
Let j be 632/14 - (-24)/(-168). Let h be 40/j*6 - 4. Factor 2/3*q**2 + 2/3 - h*q.
2*(q - 1)**2/3
Let h(c) = -2*c. Let x be h(0). Suppose 0 + 2/3*o**3 + x*o - 4/9*o**2 + 14/9*o**5 + 8/3*o**4 = 0. What is o?
-1, 0, 2/7
Let a(z) be the first derivative of 3 + 1/18*z**3 + 1/6*z**2 + 1/6*z. Suppose a(c) = 0. What is c?
-1
Suppose -4*q + 5 = -11. Let t be (q/(-14))/(4/(-7)). Factor 3/4*c**2 - 1/2 + 3/4*c - t*c**3.
-(c - 2)*(c + 1)*(2*c - 1)/4
Let o(q) be the third derivative of -q**2 - 1/180*q**6 + 0*q**3 + 0*q**7 + 0*q**5 + 1/1008*q**8 + 1/72*q**4 + 0*q + 0. Factor o(p).
p*(p - 1)**2*(p + 1)**2/3
Let g(y) be the third derivative of -y**5/330 + y**4/44 - 2*y**3/33 - 25*y**2. Determine a so that g(a) = 0.
1, 2
Let b(p) be the second derivative of 0 - 1/30*p**5 - 2/9*p**4 - p - 5/9*p**3 - 2/3*p**2. Factor b(v).
-2*(v + 1)**2*(v + 2)/3
Let m = 9 + -7. Let w(i) be the third derivative of 0*i + 0*i**3 - 1/100*i**6 - 4/75*i**5 + 1/15*i**4 + 3/175*i**7 + i**m + 0. Factor w(g).
2*g*(g + 1)*(3*g - 2)**2/5
Factor -12/11*o + 18/11 + 2/11*o**2.
2*(o - 3)**2/11
Let c(y) = y**2 - 17*y + 16. Let n be c(16). Let f(d) be the third derivative of n - 1/540*d**6 - 3*d**2 - 1/135*d**5 + 0*d + 0*d**3 + 0*d**4. Factor f(r).
-2*r**2*(r + 2)/9
Factor -1/2*p - 5/4*p**2 + 0 + 7/4*p**3.
p*(p - 1)*(7*p + 2)/4
Let r(g) be the first derivative of g**3 - 3*g - 7. Factor r(u).
3*(u - 1)*(u + 1)
Let y(m) be the second derivative of -m**9/7560 - m**8/3360 - 5*m**4/12 - 9*m. Let x(r) be the third derivative of y(r). Let x(d) = 0. What is d?
-1, 0
Let g(b) be the third derivative of -b**5/30 - 5*b**4/12 - 4*b**3/3 - 14*b**2. Find s such that g(s) = 0.
-4, -1
Let f(v) = -9*v**3 + 18*v**2 - 9*v + 3. Let m(o) = -o**4 - 8*o**3 + 18*o**2 - 8*o + 3. Let n(h) = 4*f(h) - 3*m(h). Suppose n(i) = 0. What is i?
1
Determine w so that 8*w**3 - 3*w**5 + 2*w**5 + 10*w**3 - 16*w**3 - w = 0.
-1, 0, 1
Let g(o) = -o**2 - 17*o + 38. Let x be g(-19). Factor 0 + x*b + 1/2*b**4 + 1/2*b**2 + b**3.
b**2*(b + 1)**2/2
Let l(p) = p**4 + p**3 + p**2 + p - 1. Let n(c) = 3*c - 1 + 0*c + 2*c**4 + c**2 - c**3 - 1. Let t(h) = -2*l(h) + 2*n(h). Solve t(i) = 0 for i.
-1, 1
Let n(l) be the second derivative of l**5/80 + 17*l. Factor n(g).
g**3/4
Factor -2/5*u**3 + 4*u**2 + 0 - 10*u.
-2*u*(u - 5)**2/5
Suppose -g + 27 = 2*g. Suppose 14*s - 10 = g*s. Solve -2*p**3 + s*p**3 - 6 - p**3 - 3*p + 4*p**3 + 6*p**2 = 0.
-2, -1, 1
Suppose 0 = 5*u + 4 - 14, 5*u = -w + 13. Let t(f) be the first derivative of 0*f**2 - 1/4*f**4 + 0*f + 1/3*f**w - 3. Factor t(c).
-c**2*(c - 1)
Let m be 50/8 + (-2)/8. Suppose x - m = -2*x. What is n in -2/5*n**3 + 1/5*n + 1/5*n**5 - 1/5*n**4 + 2/5*n**x - 1/5 = 0?
-1, 1
Determine a, given that -5*a**3 + 16*a + 3*a**3 - 10*a - 4 = 0.
-2, 1
Let z = 73/24 - 3. Let o(g) be the second derivative of 0 + 0*g**2 - 2*g + z*g**3 - 1/48*g**4. Let o(y) = 0. Calculate y.
0, 1
Let c(j) be the second derivative of -17/40*j**5 + 1/4*j**2 + 1/24*j**3 + 3*j - 1/24*j**7 + 0 - 13/60*j**6 - 1/3*j**4. Solve c(u) = 0 for u.
-1, 2/7
Let x(y) be the first derivative of -4/7*y + 2/21*y**3 - 1/7*y**2 + 1. Suppose x(h) = 0. What is h?
-1, 2
Let l(i) be the first derivative of -i**3/3 + i**2 - i + 3. Factor l(j).
-(j - 1)**2
Let v be 4/(-10) - (306/60 - 6). Let i(m) be the first derivative of m + 2 - 17/8*m**4 - 11/4*m**2 + 7/2*m**3 + v*m**5. Solve i(u) = 0.
2/5, 1
Let n(z) = -2*z**3 + 4*z**2 + 3. Let b(c) = -c**3 - c + 1. Let s(d) = 6*b(d) - 2*n(d). Factor s(w).
-2*w*(w + 1)*(w + 3)
Let f(l) = l**4 + 3*l**3 + l**2 + l - 2. Let t(w) = -10*w**4 + w**3 - 4*w**3 - w + 9*w**4 + 3. Let c(d) = -3*f(d) - 2*t(d). Suppose c(g) = 0. Calculate g.
-1, 0
Let h(b) be the first derivative of -b**4/30 + 4*b**3/15 - 3*b**2/5 - 10. Find n, given that h(n) = 0.
0, 3
Let t = 28 - 23. Let b(n) be the second derivative of 0 + 2*n + 1/12*n**4 + 0*n**2 + 0*n**t - 1/30*n**6 + 0*n**3. Let b(p) = 0. What is p?
-1, 0, 1
Suppose 0 = 2*p + x - 12, -2*p - 2*x = p - 20. Suppose -p*u = -u - 3. Determine c, given that -u - c**3 - c + 0*c**3 - 3*c**2 - 2*c + 0*c**2 = 0.
-1
Solve 1/2 + 7*s**2 + s**3 - 15/2*s**4 - 9/2*s**5 + 7/2*s = 0 for s.
-1, -1/3, 1
Let b(a) = 2*a**3 - 2*a**2 - 3*a + 1. Let j be b(2). Let l(r) = r**3 - 3*r**2 + 2. Let u be l(j). Factor 0*m**u - 1/3*m + 1/3*m**3 + 0.
m*(m - 1)*(m + 1)/3
Let z(j) = 2*j**3 - 6*j**2 - 4. Let d be 4/6*(-5 - 1). Let a(t) = 3*t**3 - 7*t**2 + t - 5. Let w(m) = d*z(m) + 3*a(m). Factor w(r).
(r + 1)**3
Let d(t) be the third derivative of 3*t**7/385 + t**6/110 - 4*t**5/165 - t**4/22 - t**3/33 + 5*t**2. Suppose d(u) = 0. Calculate u.
-1, -1/3, 1
Let c(d) be the third derivative of -d**5/60 + d**3/3 + d**2. Let x be c(0). Factor -2 - 2*b**4 + 2*b**2 + x.
-2*b**2*(b - 1)*(b + 1)
Let y(s) be the third derivative of s**5/12 - 25*s**4/4 + 375*s**3/2 + 33*s**2 + s. Factor y(t).
5*(t - 15)**2
Let r(y) be the first derivative of -1/4*y**4 - 1/2*y**2 - 2/3*y**3 + 0*y + 1. Factor r(f).
-f*(f + 1)**2
Let l(n) be the third derivative of -1/840*n**8 + 0 + 1/300*n**6 + 0*n**3 + 0*n**4 + 0*n**5 + 0*n - 3*n**2 + 0*n**7. Factor l(h).
-2*h**3*(h - 1)*(h + 1)/5
Let s = 2443/2 - 1221. Factor -1/2*b**3 + 0 + s*b**2 + 1/8*b**4 + 0*b.
b**2*(b - 2)**2/8
Let k be 18/40 - 6/15. Let o(q) be the third derivative of k*q**5 - 1/4*q**4 + q**2 + 0*q + 1/2*q**3 + 0. Find j, given that o(j) = 0.
1
Let p(z) be the third derivative of -z**7/1050 - 11*z**6/600 - 3*z**5/25 - 2*z**4/15 + 32*z**3/15 - 6*z**2. Find v, given that p(v) = 0.
-4, 1
Let q(y) be the second derivative of -y**7/210 + y**6/50 + y**5/100 - y**4/20 + 14*y. Find s such that q(s) = 0.
-1, 0, 1, 3
Suppose 6 + 4 = 2*a. Solve -a - s**2 + 2*s + 5 = 0.
0, 2
Factor 3*f - 24/5*f**2 - 2/5 - 16/5*f**3.
-(f + 2)*(4*f - 1)**2/5
Let c(p) be the second derivative of 0 - 1/6*p**4 - 3*p**2 - 4/3*p**3 + p. Find a, given that c(a) = 0.
-3, -1
Let r(t) be the first derivative of -2*t**5/15 - 2*t**4/3 - 10*t**3/9 - 2*t**2/3 + 21. Determine y, given that r(y) = 0.
-2, -1, 0
Let q(w) be the third derivative of -w**8/1008 + 2*w**7/315 - w**6/72 + w**5/90 - 18*w**2. Factor q(z).
-z**2*(z - 2)*(z - 1)**2/3
Let q(d) be the first derivative of 0*d**3 + 1/15*d**4 + 8 - 2/15*d**2 + 2/75*d**5 - 2/15*d. Factor q(s).
2*(s - 1)*(s + 1)**3/15
Let z(d) be the first derivative of d**6/240 - d**5/60 - d**4/48 + d**3/6 - 2*d**2 + 2. Let o(i) be the second derivative of z(i). Solve o(g) = 0.
-1, 1, 2
What is z in -6*z**4 + z - z**3 - 5*z + 4*z**2 + 2*z**5 + 3*z**3 + 2*z**2 = 0?
-1, 0, 1, 2
Let h(i) = -i**2 - 8*i + 3. Let w be h(-8). Suppose 0 = -2*g + w + 5. Factor 2*x**2 + g*x**4 + 6*x**3 + x**5 - 2*x**2 + 4*x**2 + x.
x*(x + 1)**4
Suppose -84 = -4*x + 3*s, -4*x = 3*s - 44 - 40. Let i be 35/x + -1 + 0. Let -i*k**2 + 5/6*k + 1/