-2 - 27/(-12)). Let a(n) = s*t(n) - y(n). Factor a(d).
2*(d - 1)*(d + 1)**3*(d + 2)
Let l(t) be the second derivative of 3*t + 0 + 0*t**3 + 0*t**2 + 0*t**4 - 1/40*t**6 + 3/80*t**5. Suppose l(y) = 0. What is y?
0, 1
Let o(f) = f + 44. Let k be o(0). Let m be k/6 - (11 + -7). Suppose 8/3*g**3 + 2/3*g**5 + 4/3*g**2 + 4/3 - m*g - 8/3*g**4 = 0. Calculate g.
-1, 1, 2
Determine j, given that 10/3*j**3 + 32/3*j - 8/3 - 34/3*j**2 = 0.
2/5, 1, 2
Let w(p) be the second derivative of -p**4/66 + p**3/11 - 2*p**2/11 - 24*p. What is j in w(j) = 0?
1, 2
Suppose -12*n = -15*n + 6. Determine a so that 0 - 1/3*a**3 - 4/3*a**n - 4/3*a = 0.
-2, 0
Let u(q) = q**3 + q**2 + q + 1. Let s(j) be the first derivative of 5*j**4/4 + 5*j**3 - 21*j**2/2 + 33*j + 2. Let f(z) = s(z) - 6*u(z). What is y in f(y) = 0?
3
Factor 5/2*y**2 - 5/4*y - 5/2*y**3 + 5/4*y**4 - 1/4*y**5 + 1/4.
-(y - 1)**5/4
Let w(g) = -g**2 + 16*g + 3. Let x be w(16). Factor 4*z - 2*z**4 - 8*z**x + 6*z**2 + 8*z**3.
-2*z*(z - 2)*(z + 1)**2
Let z(i) be the third derivative of i**8/896 - i**7/280 - i**6/320 + i**5/80 - 2*i**2. Solve z(d) = 0 for d.
-1, 0, 1, 2
Let m(t) = 2*t - 7. Let u be m(6). Suppose 3*h - 4*i + u = 0, 4*h + i = -0*h + 25. Factor 0*y + 2/3*y**4 - 8/9*y**h + 2/9*y**3 + 0 + 0*y**2.
-2*y**3*(y - 1)*(4*y + 1)/9
Let j(a) be the first derivative of a**6/3 - 3*a**4/2 + 4*a**3/3 + 8. Factor j(d).
2*d**2*(d - 1)**2*(d + 2)
Suppose 3*d + 4*l = -5 + 2, -2*d = 2*l. Suppose 8 = -h + 3*b - 4, d*b = 15. Solve 4*z**4 + z**4 - 3*z**4 + z**h = 0.
-1/2, 0
Let j be -1 - (-4 + (-52)/(-20)). Find q, given that -4/5 - j*q + 2/5*q**2 = 0.
-1, 2
Let c(i) = -1 + 0 + 3*i**3 - 2*i**3 - i**2. Let r(o) = -2*o**3 + 2*o**2 + 3. Let j(u) = -6*c(u) - 2*r(u). Determine s so that j(s) = 0.
0, 1
Suppose 52*k**3 + 10*k**2 - 15*k**4 - 23*k**3 - 24*k**3 = 0. Calculate k.
-2/3, 0, 1
Let r(u) = -16*u + 16. Let k(d) = -d**2 - 16*d + 16. Let x(g) = -4*k(g) + 5*r(g). Factor x(z).
4*(z - 2)**2
Let l(m) = 7*m**4 - 16*m**3 + 49*m**2 - 48*m + 23. Let i(z) = -3*z**4 + 8*z**3 - 24*z**2 + 24*z - 11. Let c(w) = -10*i(w) - 4*l(w). Let c(x) = 0. Calculate x.
1, 3
Factor 0*y + 3/7*y**4 - 6/7*y**2 + 0*y**3 + 3/7.
3*(y - 1)**2*(y + 1)**2/7
Factor -1/5*q**4 + q**3 + 0*q + 0 - 3/5*q**2 - 1/5*q**5.
-q**2*(q - 1)**2*(q + 3)/5
Let a(j) be the first derivative of j**7/280 + j**6/80 + j**5/80 - j**2 - 5. Let l(h) be the second derivative of a(h). Let l(b) = 0. What is b?
-1, 0
Suppose 3*m = -2*m + 25. Factor -1/2*w**4 - 1/2*w**m + 1/2*w**3 + 1/2*w**2 + 0 + 0*w.
-w**2*(w - 1)*(w + 1)**2/2
Let d(c) be the second derivative of -7*c**7/120 + 7*c**6/48 + c**5/80 - 5*c**4/24 - c**3/6 - 2*c**2 - c. Let o(v) be the first derivative of d(v). Factor o(n).
-(n - 1)**2*(7*n + 2)**2/4
Let i = -31 - -31. Let a(l) be the third derivative of -1/24*l**4 + i + 3*l**2 - 1/20*l**5 - 1/40*l**6 - 1/210*l**7 + 0*l + 0*l**3. Factor a(z).
-z*(z + 1)**3
Let w(p) be the first derivative of -p**8/840 + 2*p**7/525 - p**5/75 + p**4/60 - p**2 - 1. Let t(c) be the second derivative of w(c). What is y in t(y) = 0?
-1, 0, 1
Solve -6/5*a**3 + 9/5*a - 3/5*a**5 - 9/5*a**4 + 6/5*a**2 + 3/5 = 0.
-1, 1
Let 0*s + 0 - 4/9*s**2 - 8/9*s**4 + 2*s**3 = 0. What is s?
0, 1/4, 2
Suppose -8 - 16*y + 3*y**2 + 3*y**3 - 5*y**3 - 13*y**2 + 0 = 0. Calculate y.
-2, -1
Factor -40/11*k**3 - 2/11 - 8/11*k**5 + 0*k + 30/11*k**4 + 20/11*k**2.
-2*(k - 1)**4*(4*k + 1)/11
Let o(x) = 25*x**2 + 70*x - 80. Let y(b) = -b**2 - b. Let m(c) = -o(c) - 30*y(c). Solve m(g) = 0 for g.
4
Let l(j) be the third derivative of 0*j**3 + 0*j + 0*j**6 - 1/84*j**8 + 2*j**2 + 0 + 0*j**5 - 4/525*j**7 + 0*j**4. What is a in l(a) = 0?
-2/5, 0
Let x(d) be the second derivative of -d**6/135 - d**5/15 - 2*d**4/9 - 10*d**3/27 - d**2/3 + 2*d. Determine y so that x(y) = 0.
-3, -1
Let q = 2 + -4. Let x = q + 3. Let 3*h**3 - h**2 - 2*h**3 + x + 2*h - 3*h = 0. What is h?
-1, 1
Let p(s) be the third derivative of 1/56*s**8 + 6*s**2 - 1/12*s**4 + 0 + 4/105*s**7 - 2/15*s**5 + 0*s**3 + 0*s - 1/30*s**6. Determine q, given that p(q) = 0.
-1, -1/3, 0, 1
Suppose 5*m - 11 = -1. Determine j, given that j + 0*j**2 + 0*j - 3*j + 2*j**m = 0.
0, 1
Suppose -t - 3*t + 16 = 0. Suppose 0*a + t = 2*a. Factor -3*x + x**5 + 0 - 3*x**4 - a*x**3 + 1 + 2*x**2 + 4*x**3.
(x - 1)**4*(x + 1)
Suppose -2*o - 3*l + 4 = 0, 3*l = 4*o - 0*l - 8. Suppose 0*q - 4*q = -o*i - 12, 20 = 5*q. Factor 0*z**3 - 3*z**3 + z**4 + 5*z**3 + z**i.
z**2*(z + 1)**2
Let x(j) be the third derivative of -2*j**7/105 + j**6/10 - j**5/5 + j**4/6 - 4*j**2. Let x(f) = 0. What is f?
0, 1
Factor 1 + 21*d**2 + 4 - 2*d + 1 - 25*d.
3*(d - 1)*(7*d - 2)
Let j(b) be the first derivative of b**8/840 + b**7/140 - 8*b**3/3 - 3. Let f(q) be the third derivative of j(q). Factor f(g).
2*g**3*(g + 3)
Let k(d) = -d**2 + d + 1. Let v(n) = 5*n**2 - 7*n - 2. Let y(w) = -4*k(w) - v(w). Find g, given that y(g) = 0.
1, 2
Let b(t) be the second derivative of -t**5/80 + 3*t**4/16 - 9*t**3/8 + 27*t**2/8 + 4*t. Find m, given that b(m) = 0.
3
Let s = 4 - 3. Let f be (-2)/(-4) + s/(-2). Let 3*q + 3*q**2 - 5*q**3 + f*q - q = 0. What is q?
-2/5, 0, 1
Let y(x) be the first derivative of 3*x**6/2 + 6*x**5/5 - 2*x**4 - 2*x**3 - x**2/2 - 19. Factor y(g).
g*(g - 1)*(g + 1)*(3*g + 1)**2
Factor -9 - q**2 + 2*q**3 - 5*q**2 + 4*q + 9.
2*q*(q - 2)*(q - 1)
Let y = 19 - 17. Suppose 0 = 2*o - 4 - y. Factor 0*d + 0 + 2/3*d**o + 1/3*d**2.
d**2*(2*d + 1)/3
Let t(w) be the third derivative of -w**8/7560 + w**7/945 - w**6/405 - 3*w**3/2 + 5*w**2. Let i(v) be the first derivative of t(v). Solve i(s) = 0 for s.
0, 2
Let s be -6 + 3 - 3/(-15)*16. Let y(f) be the first derivative of 0*f**2 + 1/2*f**4 + 0*f - s*f**5 - 1 - 1/3*f**3. Factor y(w).
-w**2*(w - 1)**2
Let s(j) = 4 + 3 - 4 - j. Let l be s(3). Let 1/3*r**3 - r**2 + l*r + 4/3 = 0. Calculate r.
-1, 2
Factor 2/3*y**3 + 0*y + 2/3*y**4 + 0 + 0*y**2.
2*y**3*(y + 1)/3
Let n(a) be the third derivative of -2*a**2 + 0*a + 0 + 2/35*a**7 - 3/20*a**5 - 1/8*a**6 - 1/2*a**3 + 5/8*a**4. What is l in n(l) = 0?
-1, 1/4, 1
Factor 3/2*q**2 + 1/2*q + q**4 - 5/2*q**3 - 1/2.
(q - 1)**3*(2*q + 1)/2
Suppose -4*m = -s - 5*m + 3, 5*s - 65 = 5*m. Let i be 3/(-24) - (-161)/s. Factor 0 + 8/3*g + 125/3*g**4 + i*g**2 + 50*g**3.
g*(5*g + 2)**3/3
Factor -1/3*z**2 + 0*z + 0*z**4 + 1/6*z**5 - 1/2*z**3 + 0.
z**2*(z - 2)*(z + 1)**2/6
Let j(x) = -3*x - 30. Let p be j(-11). Let g(s) be the first derivative of 5/12*s**4 + 2/3*s - 5/6*s**2 - 2/9*s**p + 1. Let g(t) = 0. Calculate t.
-1, 2/5, 1
Let z(h) be the second derivative of 0*h**4 + 1/120*h**5 - 1/252*h**7 + 0*h**2 + 0*h**6 + 2*h + 0*h**3 + 0. What is g in z(g) = 0?
-1, 0, 1
Suppose -l = -4*l. Let a(m) be the third derivative of 1/24*m**4 + 1/120*m**6 + 0*m**3 + 2*m**2 + 1/30*m**5 + 0 + l*m. Factor a(j).
j*(j + 1)**2
Let d = 7 - 5. Factor -2*h**2 + 5*h**d - 2 + 2*h + 0*h**2 - 2*h**3 - h**2.
-2*(h - 1)**2*(h + 1)
Let d(t) be the second derivative of t**7/42 - t**6/15 + t**4/6 - t**3/6 + 10*t. Factor d(n).
n*(n - 1)**3*(n + 1)
Suppose 355 = -5*d - 2025. Let t = 2392/5 + d. Factor 1/5*m**3 + 6/5*m**2 + t*m + 8/5.
(m + 2)**3/5
Suppose -2*k - k = -6. Let 0*m**4 - 3*m**2 - 2*m**k - m - 4*m**4 + 0*m - 8*m**3 = 0. Calculate m.
-1, -1/2, 0
Let d(m) = -m**2 - 9*m - 18. Let o be d(-3). Factor o*t + 0*t**2 + 0 + 2/5*t**3.
2*t**3/5
Solve -9/4*y**2 - 3/4*y + 0 = 0.
-1/3, 0
Let b(n) be the second derivative of 3*n**5/80 + 3*n**4/16 + 3*n**3/8 + 3*n**2/8 - n. Let b(j) = 0. Calculate j.
-1
Let j(g) be the third derivative of -g**7/840 + g**5/240 - 6*g**2. Factor j(o).
-o**2*(o - 1)*(o + 1)/4
Let j(v) be the second derivative of -2*v**6/15 + 2*v**4/3 - 2*v**2 - 3*v. Factor j(l).
-4*(l - 1)**2*(l + 1)**2
Let x(p) be the third derivative of 0 - 1/6*p**3 - 1/1980*p**6 + 1/330*p**5 + 0*p - 1/132*p**4 + 3*p**2. Let g(i) be the first derivative of x(i). Factor g(r).
-2*(r - 1)**2/11
Let i be (117/(-24) - -6)*6/9. Factor 0*x**3 + 3/2*x**2 - 3/4*x**4 + 0*x - i.
-3*(x - 1)**2*(x + 1)**2/4
Let b(x) be the first derivative of x + 1/3*x**3 + x**2 - 1. Suppose b(h) = 0. What is h?
-1
Determine g, given that 28*g**3 - 12*g + 13*g**5 + 10*g**5 + 28*g**2 + 9*g**5 - 4 - 8*g**4 - 64*g**4 = 0.
-1/2, -1/4, 1
Let c(s) be the third derivative of 0 + 4/7*s**4 + 64/21*s**3 + 1/420*s**6 + 0*s - 9*s**2 + 2/35*s**5. Factor c(y).