 5*g**2. Let h(n) be the third derivative of d(n). Find x such that h(x) = 0.
0, 1
Let z(k) be the third derivative of k**7/140 - k**6/40 - k**5/40 + k**4/8 + 20*k**2. Factor z(y).
3*y*(y - 2)*(y - 1)*(y + 1)/2
Suppose 2 = -2*g - 6. Let m = 5 + g. Factor -4*u - m + 5 + 2*u**2 - 2*u.
2*(u - 2)*(u - 1)
Let g = -18 - -20. Factor 1/5*j**4 - 1/5*j**g - 1/5*j**3 + 1/5*j + 0.
j*(j - 1)**2*(j + 1)/5
Let n(c) be the second derivative of -c**7/336 + c**6/240 + 10*c - 2. Determine m so that n(m) = 0.
0, 1
Let r(p) be the second derivative of p**4/12 + p**3 - 11*p. Let r(m) = 0. Calculate m.
-6, 0
Let -2*q**5 + 51 - q**5 + 57*q - 69 + 6*q**4 + 18*q**3 - 60*q**2 = 0. Calculate q.
-3, 1, 2
Let m(w) = -w**2 + 9*w - 10. Let y be m(7). Suppose 3*j - g - 4 = -0*g, y*j - g = 7. Factor 0*v**4 + 4/3*v**j - 2/3*v**5 - 2/3*v + 0*v**2 + 0.
-2*v*(v - 1)**2*(v + 1)**2/3
Let r = 103/594 - 2/297. Let a(q) be the second derivative of 0 - q + 1/24*q**4 + 1/4*q**2 - r*q**3. Factor a(k).
(k - 1)**2/2
Let t be 1739/65 - (-34)/(-221). Find c, given that -t*c**3 - 15*c**2 + 4/5 + 196/5*c**4 + 8/5*c = 0.
-2/7, 1/4, 1
Let o be 3/(-12) - (-9)/4. Suppose -q = o*q. Factor q + 2/11*y**2 - 2/11*y.
2*y*(y - 1)/11
Suppose o - 4*o + 12 = 0. Let c(g) be the first derivative of -3/4*g**o - 2 + 0*g - g**3 - 1/5*g**5 - 1/2*g**2. Suppose c(b) = 0. What is b?
-1, 0
Let z(b) = b**2 - 7*b + 3. Let t be z(4). Let x be 3/t*(-5 - 1). Factor 4*i - 4*i**2 - 1 - 1 - 10*i + 4*i**3 + x*i**5 + 6*i**4.
2*(i - 1)*(i + 1)**4
Suppose 6 = -7*d + 9*d - 2*v, 2*v + 6 = -5*d. Factor 1/2*u + d - 1/4*u**2.
-u*(u - 2)/4
Let i(k) = 6*k**3 - 2*k**2 - 6*k - 5. Let c(g) = 5*g**3 - 2*g**2 - 5*g - 4. Let q(x) = 7*c(x) - 6*i(x). Suppose q(v) = 0. Calculate v.
-2, -1, 1
Let q(d) = d**4 + 3*d**3 - d**2 - d. Let a(b) = -4*b**4 - 9*b**3 + 2*b**2 + 4*b. Let h(z) = 2*a(z) + 7*q(z). Factor h(g).
-g*(g - 1)**3
Let f be (-1)/(2/(-4) - (6 + -6)). Find d, given that -9/7*d - 3/7*d**f - 6/7 = 0.
-2, -1
Let b(x) be the third derivative of 0*x - 1/30*x**3 + 0 - 1/30*x**4 - 1/100*x**5 + 4*x**2. Let b(n) = 0. What is n?
-1, -1/3
Suppose 22 = 10*y - 8*y. Let o = -11 + y. Factor -1/4*i**2 + 0 + o*i + 1/4*i**3.
i**2*(i - 1)/4
Let c(n) = 2*n. Let b be c(1). Let j = 41 + -201/5. Factor j - 2/5*a**b - 2/5*a.
-2*(a - 1)*(a + 2)/5
Let a(r) be the first derivative of 3*r**5/20 - r**3/4 + 5. Factor a(b).
3*b**2*(b - 1)*(b + 1)/4
Let n(r) be the third derivative of r**8/560 - 3*r**7/280 + r**6/60 + r**3/6 + r**2. Let g(d) be the first derivative of n(d). Suppose g(i) = 0. Calculate i.
0, 1, 2
Let o(j) be the third derivative of -1/60*j**5 - j**2 + 0*j + 0 + 0*j**4 + 0*j**3. Suppose o(h) = 0. What is h?
0
Let i(r) be the first derivative of r**6/6 + 4*r**5/5 + r**4 - 3. Factor i(y).
y**3*(y + 2)**2
Let y(a) be the third derivative of -a**7/42 - a**6/12 + a**5/12 + 5*a**4/12 + 4*a**2. Determine b, given that y(b) = 0.
-2, -1, 0, 1
Let x be (0 + 6/(-3))*-2. Let f = 6 - x. Factor -z**2 - 2*z**4 - 2*z**5 + z**2 + 2*z**2 + f*z**3.
-2*z**2*(z - 1)*(z + 1)**2
Factor 0*v**3 + 4/9*v**2 + 2/9*v + 0 - 4/9*v**4 - 2/9*v**5.
-2*v*(v - 1)*(v + 1)**3/9
Suppose -7*i = -i - i. Let w(f) be the third derivative of 3*f**2 + 1/60*f**6 + 0*f**4 + 1/210*f**7 + i + 1/60*f**5 + 0*f + 0*f**3. Find u, given that w(u) = 0.
-1, 0
Factor 80*v - 4 + 16*v**2 - 16 - 81*v**2 + 15*v**3.
5*(v - 2)**2*(3*v - 1)
Suppose 4*g - 5 - 3 = 0. Let -14*d - 6*d**2 - 1 - 6*d**3 - 10*d**g - 2 - 1 = 0. What is d?
-1, -2/3
Let a be ((-2)/6*1)/(-1). Let k be (-2 - 2 - -4) + -1 + 4. Factor 0*v**2 + a - 1/3*v**4 - 2/3*v**k + 2/3*v.
-(v - 1)*(v + 1)**3/3
Let i(y) = 2*y**2 - y. Let g be i(-1). Factor -8*x**3 + 10*x**g - 2*x + 6*x - 6*x**2.
2*x*(x - 2)*(x - 1)
Let y = -3 - -3. Factor -2/5*i**5 + y + 0*i - 6/5*i**3 - 2/5*i**2 - 6/5*i**4.
-2*i**2*(i + 1)**3/5
Suppose 35 = k + 6*k. Suppose 0 = d - 0*d + 2*m, -3 = d + k*m. Factor 0 - 1/5*y**d - 1/5*y.
-y*(y + 1)/5
Let f(u) be the first derivative of u**4/36 + u**3/9 + u**2/9 - 40. Factor f(y).
y*(y + 1)*(y + 2)/9
Let g(q) be the first derivative of 1/5*q**2 + 4/5*q - 2/15*q**3 + 1. Let g(r) = 0. What is r?
-1, 2
Let v be (4 - 1 - 3)/(-1). Let k(y) be the first derivative of 1/8*y**4 - 3 + 0*y**2 + v*y - 1/6*y**3. Factor k(u).
u**2*(u - 1)/2
Factor -3 + 15/2*p - 9/2*p**2 + 3/2*p**4 - 3/2*p**3.
3*(p - 1)**3*(p + 2)/2
Let t = 4 - 0. Let s be (t + 0)*2/28. Factor 0 + 0*h - 2/7*h**2 - s*h**4 - 4/7*h**3.
-2*h**2*(h + 1)**2/7
Let p(k) be the first derivative of -1/3*k**3 + 1/6*k**4 + 1/2*k**2 - 1/30*k**5 + 1 + 0*k. Let h(a) be the second derivative of p(a). Let h(u) = 0. Calculate u.
1
Let n(k) be the third derivative of -k**5/160 + 5*k**4/32 - k**2 + 2. Determine j so that n(j) = 0.
0, 10
Let l = -29 - -43. Suppose -2*v**2 - 2*v**2 + l*v**4 - 18*v**5 + 18*v**3 - 10*v**4 = 0. What is v?
-1, 0, 2/9, 1
Let u(b) = 20*b**3 - 16*b**2 + 32*b - 12. Let c(r) = r**3 + r**2. Let q(k) = 12*c(k) - u(k). Factor q(t).
-4*(t - 1)**2*(2*t - 3)
Let g(y) be the third derivative of -2*y**2 + 0*y**3 + 0 + 0*y - 1/30*y**5 + 1/12*y**4. Solve g(t) = 0.
0, 1
Suppose 3*s + 11 - 29 = 0. Let v(f) = 4*f**2 + 8*f - 6. Let w(r) = -3*r**2 - 7*r + 5. Let u(j) = s*w(j) + 5*v(j). Factor u(o).
2*o*(o - 1)
Let l = 8 + -6. Let 2*i**3 + 6*i + 4*i**l - 2 + 2*i**2 + 4 = 0. Calculate i.
-1
Let o(j) be the third derivative of -j**5/270 - j**4/54 - j**3/27 + j**2. Factor o(l).
-2*(l + 1)**2/9
Factor -2*l**5 - 13*l**2 - 2*l**3 + 4*l**3 + 2*l**4 + 9*l**2 + 2*l**2.
-2*l**2*(l - 1)**2*(l + 1)
Suppose -2*d - 2*c = -0*d - 16, d - 28 = -5*c. Let v be (-2 + 3)*d/12. Factor 1/4*x**4 + 1/4*x**5 + 0 - 1/4*x**2 + 0*x - v*x**3.
x**2*(x - 1)*(x + 1)**2/4
Let r = -583/2 + 299. Let r*o**2 - 75/2*o**3 + 24*o + 6 = 0. Calculate o.
-2/5, 1
Let x = -1/225 - 629/225. Let f = x - -47/15. Factor -f + 0*u + 1/3*u**2.
(u - 1)*(u + 1)/3
Suppose 0 = -8*v + 15 + 9. Suppose 2/3 - 1/3*r**2 - r**v + r - 1/3*r**4 = 0. What is r?
-2, -1, 1
Let z be (4 - (-36)/(-4)) + 34/6. Factor 2/3*d**4 - 2/3*d**2 + 0 + z*d - 2/3*d**3.
2*d*(d - 1)**2*(d + 1)/3
Let b(p) be the second derivative of p**5/100 - p**4/30 - p**3/6 + 3*p**2/5 - 2*p. Suppose b(h) = 0. What is h?
-2, 1, 3
Let s(a) be the third derivative of -3*a**5/40 + 7*a**4/48 + a**3/6 - 4*a**2. Solve s(h) = 0.
-2/9, 1
Let 0 - 4/3*v**3 - 8/3*v**2 - 4/3*v = 0. Calculate v.
-1, 0
Let y = 3 + -1. Let a be 74/28*y - 3. Factor a*n**2 - 6/7*n**3 - 8/7*n + 0.
-2*n*(n - 2)*(3*n - 2)/7
Factor 8/5*j + 4/5*j**2 - 8/5*j**3 - 6/5 + 2/5*j**4.
2*(j - 3)*(j - 1)**2*(j + 1)/5
Let u(i) be the second derivative of i**7/70 - 13*i**6/300 + 3*i**5/200 + 3*i**4/40 - i**3/12 - 7*i. Factor u(o).
o*(o - 1)**3*(6*o + 5)/10
Let u(d) be the first derivative of -2*d**5/95 - 2*d**4/19 + 4*d**3/57 + 12*d**2/19 - 18*d/19 - 12. Factor u(f).
-2*(f - 1)**2*(f + 3)**2/19
Suppose 3*y + 18 = 3*o, 2*o = -0*y - y. Factor 5*m**2 + 3*m**4 + m**2 + 3*m**5 - 3*m - o*m**4 - 7*m**4.
3*m*(m - 1)**3*(m + 1)
Let z be 1*(4 + 0 + 1). Let x(u) be the first derivative of 4 + 1/9*u**4 - 2/9*u**3 - 4/9*u**2 + 2/45*u**z + 8/9*u. What is l in x(l) = 0?
-2, 1
Let p = -1 - 2. Let a be (p - 3)*1/(-2). Suppose -3*j**4 + 0*j**4 + 4*j**4 - j**a = 0. Calculate j.
0, 1
Let a(j) be the first derivative of -1/2*j**2 + 1/12*j**4 - 1 - 2/3*j + 0*j**3. Factor a(h).
(h - 2)*(h + 1)**2/3
Let b(h) be the third derivative of -h**6/600 - h**5/100 - h**4/40 - h**3/30 + 13*h**2. Determine o, given that b(o) = 0.
-1
Let q(w) = 6*w**2 + 2*w**3 - 3*w + 3*w**3 + 2*w**3 - 4*w**3. Let h(g) = g**4 + 4*g**3 + 5*g**2 - 2*g. Let j(z) = 3*h(z) - 2*q(z). Determine d so that j(d) = 0.
-1, 0
Let i(y) be the first derivative of 0*y - 3/2*y**2 + 5 + 5*y**3 - 3*y**4. Suppose i(a) = 0. Calculate a.
0, 1/4, 1
Let r = 22 + -19. Factor -6*s - 9*s**4 - 9*s**3 - 10*s**2 - 5*s**2 + 12*s**4 + r*s**5.
3*s*(s - 2)*(s + 1)**3
Factor -2*r - r - 2*r - 2*r**3 + 10*r**2 - 3*r**3.
-5*r*(r - 1)**2
Let j(g) be the first derivative of 4/3*g - 2 + 2/9*g**3 + g**2. Factor j(n).
2*(n + 1)*(n + 2)/3
Let h(s) = 3*s**2 + 13*s + 10. Let q(j) be the first derivative of -2*j**3/3 - 9*j**2/2 - 7*j - 1. Let l = 11 - 4. Let r(o) = l*q(o) + 5*h(o). Factor r(c).
(c + 1)**2
Let x(d) be the third derivative of 1/18*d**3 + 0 + 0*d**5 + 0*d - 1/630*d**7 - 1/180*d**6 - 5*d**2 + 1/36*d**4. Factor x(f).
-(f - 1)*(f + 1)**3/3