-2
Let i(j) be the first derivative of -4*j - 7 - 8/3*j**3 + 1/2*j**4 + 5*j**2. Find o such that i(o) = 0.
1, 2
Let o(m) be the second derivative of 3*m**5/80 - 3*m**4/16 + 3*m**3/8 - 3*m**2/8 - 8*m. Solve o(b) = 0.
1
Suppose -7 - 1 = -2*u. Suppose -7 = -u*y - c + 2, 11 = 5*y + c. Factor 0*w**4 + 0*w**y + 2/5*w**5 - 4/5*w**3 + 0 + 2/5*w.
2*w*(w - 1)**2*(w + 1)**2/5
Let n(o) be the first derivative of -1/5*o**4 - 9 + 0*o**3 + 2/25*o**5 - 2/5*o + 2/5*o**2. Factor n(y).
2*(y - 1)**3*(y + 1)/5
Let o(b) = -b**3 + 4*b**2 + 4*b + 4. Let q be o(4). Suppose 12 = 3*p, k + 3*p = -3*k + q. What is m in 1/5*m**3 - 3/5*m + 2/5 + 0*m**k = 0?
-2, 1
Suppose -25*w - 5*w = -120. Find c such that -2/5*c**5 + 4/5*c**w + 0 - 2/5*c**3 + 0*c**2 + 0*c = 0.
0, 1
Suppose 5 + 1 = 2*t. Suppose -7*h**t - 3*h**2 + 4*h**3 - 2*h + h - h**4 + 0*h = 0. What is h?
-1, 0
Suppose 5*w = -3*t + 20, 0*w + 25 = 4*t + 5*w. Suppose -5 = -t*x + 10. Solve x - 1 + 3*n + 0*n**2 + n**2 = 0.
-2, -1
Let -5/4*g + 5/4*g**4 + 1/4 + 5/2*g**2 - 1/4*g**5 - 5/2*g**3 = 0. What is g?
1
Let g = 2 + 0. Suppose 6*r - g*b + 2 = 4*r, 2*r = 3*b - 7. Factor 12*h**2 + r*h**2 + 2*h**4 + 2*h**3 + 8*h**3 + 8*h.
2*h*(h + 1)*(h + 2)**2
Let f be 4 + 30/(-9) + 0. Let v(t) be the third derivative of 3*t**2 + 0*t + 0 - 1/30*t**5 + 1/12*t**4 + f*t**3. Factor v(x).
-2*(x - 2)*(x + 1)
Let y(c) = -48*c**4 - 111*c**3 - 15*c**2 + 111*c + 129. Let x(t) = -3*t**4 - 7*t**3 - t**2 + 7*t + 8. Let z(h) = -33*x(h) + 2*y(h). Suppose z(i) = 0. What is i?
-2, -1, 1
Find o, given that 0 - 10/11*o**2 - 4/11*o - 8/11*o**3 - 2/11*o**4 = 0.
-2, -1, 0
Let x(i) be the third derivative of i**10/75600 + i**9/18900 - i**7/3150 - i**6/1800 - i**4/6 - 7*i**2. Let o(u) be the second derivative of x(u). Factor o(k).
2*k*(k - 1)*(k + 1)**3/5
Let f(n) = n**3 + 8*n**2 + 8*n + 9. Let q be f(-7). Suppose 8*z - q = 3*z + 4*c, 0 = -5*c + 10. Solve -6*d**2 - 4*d**3 + 0*d**z + 6*d**3 + 6*d - 2 = 0.
1
Let y(b) be the first derivative of b**4/10 + b**3/3 - 2*b**2/5 + b - 2. Let l(q) be the first derivative of y(q). Factor l(m).
2*(m + 2)*(3*m - 1)/5
Let p(r) be the second derivative of -1/40*r**5 + 0*r**3 + 1/84*r**7 + 0*r**4 + 0 + 0*r**6 - 4*r + 0*r**2. Factor p(n).
n**3*(n - 1)*(n + 1)/2
Let r(g) be the first derivative of -4*g**3/27 + 28*g**2/3 - 196*g + 64. Factor r(f).
-4*(f - 21)**2/9
Let t(c) be the third derivative of c**5/12 - 5*c**3/6 - 13*c**2. Solve t(g) = 0 for g.
-1, 1
Let k(y) be the third derivative of -2*y**6/45 + y**5/15 + 2*y**4/9 - 2*y**3/3 - 10*y**2. Determine w so that k(w) = 0.
-1, 3/4, 1
Let o(v) be the first derivative of 9*v**8/560 + 9*v**7/280 + v**6/40 + v**5/120 + 2*v**3/3 - 3. Let k(x) be the third derivative of o(x). Solve k(u) = 0 for u.
-1/3, 0
Let y(j) = -j**3 + 5*j**2 - 5*j + 6. Let b be y(4). Suppose -m**3 + 5*m**2 - 2*m**3 - 4*m + m + m**b = 0. Calculate m.
0, 1
Let f(j) be the first derivative of -4*j**5/5 - 5*j**4 - 32*j**3/3 - 8*j**2 + 10. Factor f(a).
-4*a*(a + 1)*(a + 2)**2
Let a(l) = -l**2 - 6*l - 6. Let d be a(-4). Suppose 2*q + 10 = 3*z, -4*q = z - 2*z + 10. Solve -2*u**2 + 2 + d*u**4 - z - u**5 + u + 0*u**2 = 0 for u.
-1, 0, 1
Let y(k) be the first derivative of -k**8/8400 - k**7/1400 - k**6/600 - k**5/600 + k**3 - 2. Let w(i) be the third derivative of y(i). Factor w(x).
-x*(x + 1)**3/5
Let b = 37 + -35. Factor 0 - 2/7*i**5 + 0*i**4 + 2/7*i**3 + 0*i**b + 0*i.
-2*i**3*(i - 1)*(i + 1)/7
Let d = -250/3 + 84. Let t(y) be the first derivative of 2/15*y**5 - 1/3*y**4 + 0*y**3 + d*y**2 + 2 - 2/3*y. Factor t(q).
2*(q - 1)**3*(q + 1)/3
Let j(z) be the second derivative of z**5/4 - 5*z**4/6 + 5*z**3/6 - 11*z. Factor j(q).
5*q*(q - 1)**2
Let c(x) be the second derivative of -x**6/270 + x**4/36 + x**3/27 - 32*x. Factor c(z).
-z*(z - 2)*(z + 1)**2/9
Let c(k) be the second derivative of k**5/20 - k**4/2 + 5*k**3/6 + 41*k. What is u in c(u) = 0?
0, 1, 5
Let i(j) = 15 - 26*j + 1 + 28*j + 4. Let a be i(-10). Factor 2/3*s**2 + a - 2/3*s.
2*s*(s - 1)/3
Let d(b) = -b**2 + 2*b - 3. Suppose 3*w - 4*j = 1, w - 5*j + 22 = 5*w. Suppose q - w = -2. Let o(a) = -1. Let x(l) = q*d(l) - 2*o(l). Factor x(g).
-(g - 1)**2
Let o = -63 - -41. Let m = o + 25. Let 0*z - 2/3*z**2 + 2*z**m + 0 = 0. What is z?
0, 1/3
Let q = 191 - 189. Let 1/5*s**q + 0 + 0*s = 0. Calculate s.
0
Let z(t) = -t**4 - t**3 + t**2. Let o(n) = -9*n**4 - 9*n**3 + 5*n**2. Let r(g) = -o(g) + 5*z(g). Find s such that r(s) = 0.
-1, 0
Suppose -4*z + 394 = 2*m, 1307 = 5*m - 4*z + 280. Let r = m - 1417/7. Factor -2/7*i**4 - 2/7 + r*i**2 + 0*i + 0*i**3.
-2*(i - 1)**2*(i + 1)**2/7
Let b(n) be the second derivative of -n**7/4200 + n**6/1800 + n**5/600 - n**4/120 - 5*n**3/6 + 4*n. Let i(y) be the second derivative of b(y). Factor i(f).
-(f - 1)**2*(f + 1)/5
Let l(s) be the second derivative of 0 + 0*s**2 - 1/30*s**4 - 3*s + 1/30*s**3. Factor l(d).
-d*(2*d - 1)/5
Let c(s) be the second derivative of 1/2*s**3 - 1/10*s**6 + 1/6*s**4 - 7*s - 1/42*s**7 + 1/2*s**2 - 1/10*s**5 + 0. Factor c(m).
-(m - 1)*(m + 1)**4
Let q(b) be the third derivative of 5*b**8/336 - b**6/24 - 19*b**2. Determine i so that q(i) = 0.
-1, 0, 1
Let u = 70 + -69. Factor -1/2*h**3 - u + 1/2*h + h**2.
-(h - 2)*(h - 1)*(h + 1)/2
Suppose -n = -4*l - 29, 4*l + 3*n - 39 = 8*l. Let v = l - -10. Determine u, given that 2*u + 4 - v*u**2 + 2*u + 2*u = 0.
-1/2, 2
Let d = 3 - 1. Let o(q) be the third derivative of -1/112*q**8 - 1/10*q**5 + 0*q + 1/3*q**3 + 0 - 4*q**d + 1/30*q**6 + 2/105*q**7 - 1/24*q**4. Factor o(p).
-(p - 1)**3*(p + 1)*(3*p + 2)
Let c be 1/(-3 - -2) + 21. Suppose k + k + c = 2*i, 5*i = 4*k + 45. Let -12*r**2 + 8*r**4 + 0*r - 5*r + 2*r - 20*r**4 - 3*r**i - 18*r**3 = 0. Calculate r.
-1, 0
Let u = 1 - -1. Factor -4*b**2 + 2 + 5*b**u + 2*b**4 - 5*b**2.
2*(b - 1)**2*(b + 1)**2
Let u = 25 - 17. Factor -2 - 5*q + u*q + 0 - q**3.
-(q - 1)**2*(q + 2)
Factor -4/3*u**2 + 2*u**3 + 1/3*u + 0 - 4/3*u**4 + 1/3*u**5.
u*(u - 1)**4/3
Suppose -8*h + 12 = -5*h. Suppose -72*x**3 - 39*x**4 - 80*x**2 - 4*x**5 + 11*x**h + 11*x - 43*x = 0. Calculate x.
-2, -1, 0
Let v(g) = 4*g - 4. Let m be v(2). Factor 8/9*a + 2/9 + 8/9*a**3 + 4/3*a**2 + 2/9*a**m.
2*(a + 1)**4/9
Let p be 8/(-20)*1/(-4). Let v(m) be the second derivative of 1/3*m**4 + 1/3*m**3 + 0 + p*m**5 + m + 0*m**2. Factor v(o).
2*o*(o + 1)**2
Let h(l) be the third derivative of l**9/7560 - l**8/1120 + l**6/90 + l**4/4 + 3*l**2. Let s(c) be the second derivative of h(c). Find g, given that s(g) = 0.
-1, 0, 2
Suppose 5*v - 12 = -v. Factor -6*f**2 - 3*f**4 + 5*f**v + 0*f**5 - 3*f**3 - f**5.
-f**2*(f + 1)**3
Let n(y) be the second derivative of -2*y**7/735 + y**6/84 - 2*y**5/105 + y**4/84 + y**2/2 - 5*y. Let z(f) be the first derivative of n(f). Factor z(c).
-2*c*(c - 1)**2*(2*c - 1)/7
Let d(t) be the second derivative of -t**7/840 + t**5/120 - t**3/24 + t**2/2 + 2*t. Let z(u) be the first derivative of d(u). Let z(s) = 0. Calculate s.
-1, 1
Suppose -2*x - 2*x = 36. Let s = x + 9. Solve 2/9*o**4 + 0 + 0*o**3 + s*o - 2/9*o**2 = 0.
-1, 0, 1
Let a(u) = 7*u**2 + 3*u - 6. Let w(m) = 13*m**2 + 5*m - 11. Let t(d) = -11*a(d) + 6*w(d). Factor t(o).
o*(o - 3)
Let a(z) be the second derivative of -z**10/12096 - z**9/10080 + z**8/6720 + z**4/6 + 3*z. Let k(f) be the third derivative of a(f). Let k(t) = 0. Calculate t.
-1, 0, 2/5
Let r = -524 + 198. Let h = 992/3 + r. Find b such that -10/3*b + h*b**2 - 4/3 = 0.
-2/7, 1
Suppose 21 = 3*m + 4*r, -5*m - 3 = -8*m + 2*r. Let j(h) be the second derivative of 2*h + 1/22*h**4 + 0 - 2/33*h**m + 0*h**2 - 1/110*h**5. Factor j(x).
-2*x*(x - 2)*(x - 1)/11
Factor -2/7*w**2 + 2/7*w**4 - 2/7*w + 0 + 2/7*w**3.
2*w*(w - 1)*(w + 1)**2/7
Let t(n) be the third derivative of n**6/25 + 33*n**5/50 + 14*n**4/5 + 12*n**3/5 - 16*n**2 - 2. Factor t(h).
6*(h + 2)*(h + 6)*(4*h + 1)/5
Factor 4/9*m - 2/9*m**5 + 0 + 2/3*m**3 + 2/9*m**4 - 10/9*m**2.
-2*m*(m - 1)**3*(m + 2)/9
Let l(z) be the third derivative of z**7/140 - 3*z**6/80 - z**5/8 + 3*z**4/16 + z**3 + 12*z**2 - z. Solve l(u) = 0.
-1, 1, 4
Suppose 5*z + z = -0*z. Let i(m) be the first derivative of 1 + z*m + 0*m**2 + 1/9*m**3 - 1/18*m**6 + 1/12*m**4 - 1/15*m**5. Factor i(p).
-p**2*(p - 1)*(p + 1)**2/3
Suppose -29 = -4*q - 5. Let v(t) be the third derivative of -4/45*t**5 - 1/27*t**3 + 0 - 1/12*t**4 + 3*t**2 + 0*t - 4/135*