ond derivative of 1/3*z**2 + 5/9*z**3 + 0 + r*z + 2/9*z**4. Factor b(t).
2*(t + 1)*(4*t + 1)/3
Let q(b) be the third derivative of -b**6/60 - b**5/30 + b**4/12 + b**3/3 + b**2. Factor q(l).
-2*(l - 1)*(l + 1)**2
Suppose 359 - 344 = 3*n. Factor 1/4*h**n + 1/4*h**2 - 3/4*h**3 - 1/4*h**4 + 0 + 1/2*h.
h*(h - 2)*(h - 1)*(h + 1)**2/4
Let d = 824/63 + -90/7. What is z in 2/3*z - 2/9*z**2 - d - 2/3*z**3 + 4/9*z**4 = 0?
-1, 1/2, 1
Suppose 0*i - 3*i + 6 = 0. Let t(n) = n + 1. Let o be t(-1). Factor 4/9*r**i + 2/3*r**3 + 0*r + o.
2*r**2*(3*r + 2)/9
Let l(v) be the second derivative of 2*v + 0 + 0*v**2 + 0*v**4 + 0*v**3 - 1/20*v**5. Suppose l(a) = 0. What is a?
0
Let x(t) be the second derivative of -t**5/10 - t**4/6 + t**3/3 + t**2 + 22*t. Solve x(h) = 0.
-1, 1
Let a be ((-2)/6)/(5/(-30)). Let f(b) be the second derivative of 0*b**3 + 1/40*b**5 + 1/60*b**6 + 0*b**2 - a*b - 1/24*b**4 + 0 - 1/84*b**7. Factor f(h).
-h**2*(h - 1)**2*(h + 1)/2
Let b(t) = -t**2 - 5*t + 2. Let g be b(-4). Suppose 8 = g*x - 2*x. Factor 0*p**x + 0*p + 0 - 2/5*p**4 + 0*p**3.
-2*p**4/5
Let g(u) be the third derivative of -u**7/2100 - 11*u**6/1800 + u**5/75 + 7*u**4/24 - 6*u**2. Let v(y) be the second derivative of g(y). Factor v(z).
-2*(z + 4)*(3*z - 1)/5
Let n = 141 - 2114/15. Let z(g) be the second derivative of 0*g**5 + 0 - 1/42*g**7 + 0*g**2 + n*g**6 + g + 1/6*g**3 - 1/6*g**4. Factor z(v).
-v*(v - 1)**3*(v + 1)
Let t(c) be the third derivative of -c**6/120 - c**5/30 - c**4/24 - 20*c**2. Let t(y) = 0. What is y?
-1, 0
Let t(j) be the second derivative of -j**4/12 + 7*j**3/6 - 3*j**2 - 17*j. Factor t(l).
-(l - 6)*(l - 1)
Let l = -938 + 75041/80. Let j(q) be the third derivative of 0*q**3 + 0*q - 1/20*q**5 - 3*q**2 - 1/16*q**4 - l*q**6 + 0. What is y in j(y) = 0?
-1, 0
Suppose r + 3 - 12 = 0. Find v such that r*v + 2*v**2 + 0*v**2 - 3*v**3 - 8*v**2 = 0.
-3, 0, 1
Suppose 0 = 3*z - 6*z - 15. Let g(b) = b + 7. Let u be g(z). Find j such that 2*j**5 + j**2 + 6*j**4 - j**2 + 6*j**3 + 2*j**u = 0.
-1, 0
Let z(l) be the third derivative of l**5/15 - l**4/24 + l**3/2 - 3*l**2. Let t(m) = 5*m**2 - 2*m + 4. Let j(u) = 3*t(u) - 4*z(u). Factor j(y).
-y*(y + 2)
Let b(g) be the third derivative of -g**6/72 + g**5/36 + 5*g**4/72 - 5*g**3/18 + 9*g**2. Find i, given that b(i) = 0.
-1, 1
Let p(g) be the second derivative of -g**4/12 + 5*g**3/12 + 3*g**2/4 - 17*g. Factor p(i).
-(i - 3)*(2*i + 1)/2
Let n(q) = -q**2 + 8*q - 9. Let a be n(6). Let w be 1*a + (-5)/15. Factor -8/3 - w*m - 2/3*m**2.
-2*(m + 2)**2/3
Suppose 4*y - m = 2*y, -2*y + 4*m = 12. Solve 2*o**2 - 3*o**y - o**2 = 0.
0
Let t = 5 + 0. Suppose -3*x - 2*x = t*g - 15, -4*x = 3*g - 11. Find q such that -2*q**5 - q - 2*q**4 - 18*q**2 + 28*q**x + 5*q + 6*q**3 = 0.
-1, 0, 2
Let m(g) = g - 4. Let s be m(6). Solve -3*o**2 + 2*o + 14 - 10 + o**s = 0 for o.
-1, 2
Let h = 132 + -132. Factor -1/2*t + h + 1/2*t**2.
t*(t - 1)/2
Let v(l) be the third derivative of -l**8/448 - 3*l**7/280 - 3*l**6/160 - l**5/80 + l**2. Factor v(f).
-3*f**2*(f + 1)**3/4
Let q(s) be the third derivative of s**5/140 - 2*s**3/7 + 4*s**2 - 9. Determine x, given that q(x) = 0.
-2, 2
Suppose 3*j - 5*j + 22 = 3*p, 0 = p - 4*j + 16. Suppose 0 = -3*q + p*q - 2. Factor 2/9*c**3 + 10/9*c**q + 8/9 + 16/9*c.
2*(c + 1)*(c + 2)**2/9
Let i be 5 - 21/9 - 2. What is y in -2/3*y**5 + 0*y**4 + i*y**3 + 0*y + 0 + 0*y**2 = 0?
-1, 0, 1
Suppose 3*d = -4*t + 15, -2*d + 10 = 5*t - 0*d. Let 0*b + t - 6/5*b**3 - 3/5*b**2 - 3/5*b**4 = 0. Calculate b.
-1, 0
Let f(q) = -2*q + 3. Let p be f(6). Let x = p - -29/3. Determine r so that -x + 4/3*r - 2/3*r**2 = 0.
1
Let x(j) = -j - 1. Let q be x(-3). Suppose i - q = -0. Factor 3*l**4 - 3*l**3 - l**5 + 5*l - 5*l + l**i.
-l**2*(l - 1)**3
Let u(g) be the second derivative of -g**10/11340 - g**9/7560 + g**8/10080 + g**4/6 + g. Let h(s) be the third derivative of u(s). Factor h(a).
-2*a**3*(a + 1)*(4*a - 1)/3
Suppose 4*f + 4*x - 65 = -f, -2*x = -3*f + 17. Suppose f*h - 4*h = 25. Determine o, given that 0*o + 8/5*o**2 + 18/5*o**h - 8/5*o**3 - 18/5*o**4 + 0 = 0.
-2/3, 0, 2/3, 1
Let q(y) be the first derivative of -6*y**5/25 + 19*y**4/10 - 28*y**3/5 + 36*y**2/5 - 16*y/5 + 2. Factor q(z).
-2*(z - 2)**3*(3*z - 1)/5
Let f(u) be the second derivative of u**8/8400 - u**7/4200 - u**6/1800 + u**5/600 - u**3/3 + u. Let m(d) be the second derivative of f(d). Factor m(y).
y*(y - 1)**2*(y + 1)/5
Let l(q) be the second derivative of 17*q**4/12 - 7*q**3/6 + 3*q. Suppose -2*b = -0*b - 6. Let c(y) = 50*y**2 - 20*y. Let s(j) = b*c(j) - 8*l(j). Factor s(v).
2*v*(7*v - 2)
Let y = -66 - -68. Let f(i) be the first derivative of 0*i - 1/3*i**3 - 1/2*i**y + 1. Solve f(k) = 0 for k.
-1, 0
Factor -1 - l + 7 + 0*l**2 - 5*l**2 + 4*l**2.
-(l - 2)*(l + 3)
Let y(k) be the third derivative of k**9/7056 + k**8/980 + k**7/490 - k**3/2 + 6*k**2. Let l(h) be the first derivative of y(h). Factor l(c).
3*c**3*(c + 2)**2/7
Let a = 20 + -18. Let 16 + x**a + 0*x**2 + 8*x + 0*x**2 = 0. What is x?
-4
Let c(h) be the second derivative of 6*h + 0*h**3 - 1/10*h**6 - 1/2*h**4 + 0*h**2 - 9/20*h**5 + 0. Factor c(d).
-3*d**2*(d + 1)*(d + 2)
Let q(f) = -4*f + 15. Let p be q(3). Suppose 3/4*z**p - 23/4*z**2 + 9/4*z**4 - 1/2 + 13/4*z = 0. Calculate z.
-2, 1/3, 1
Let n be (-4)/(-30)*3*80/160. Solve -n*t**3 + 3/5*t**2 - 3/5 + 1/5*t = 0 for t.
-1, 1, 3
Let l be 5*((-126)/(-15) + -1). Suppose k - 4*k**3 - l*k + 18*k**2 - 2*k**3 + 3*k**3 + 24 = 0. Calculate k.
2
Find j such that 8/7*j**3 + 6/7 - 20/7*j - 18/7*j**2 = 0.
-1, 1/4, 3
Let d = 80/247 - 66953/207480. Let w(f) be the third derivative of -1/60*f**4 + 0*f**6 + 2/525*f**7 + d*f**8 - 1/75*f**5 + 0*f + f**2 + 0*f**3 + 0. Factor w(j).
2*j*(j - 1)*(j + 1)**3/5
Solve 1/3*y**3 + 2/3 + 1/3*y**4 - 1/3*y - y**2 = 0 for y.
-2, -1, 1
Suppose 2*g + 0*n - 2 = -2*n, 4*g + 3*n = 3. Let b(c) be the second derivative of 1/12*c**4 + 1/2*c**3 + g + c**2 + 2*c. Factor b(t).
(t + 1)*(t + 2)
Let g(n) be the first derivative of 2 + 0*n - 14*n**4 - 2/3*n**3 + 2*n**2. Factor g(a).
-2*a*(4*a - 1)*(7*a + 2)
Suppose -21 - 7 = -2*c. Let i = -10 + c. Factor 1/4*x**i - 1/4*x**2 + 0 - 1/4*x + 1/4*x**3.
x*(x - 1)*(x + 1)**2/4
Let o(f) be the second derivative of f**5/20 - 2*f**4/3 + 13*f**3/6 - 3*f**2 + f. Factor o(p).
(p - 6)*(p - 1)**2
Suppose -2*n + 11*o - 9*o = 4, n - 2*o = -7. Factor -3/2*t**4 + 0*t + 0 - n*t**3 - 3/2*t**2.
-3*t**2*(t + 1)**2/2
Factor -10*g**4 + 7*g**4 + 9*g**2 - 14*g + 3*g**3 + 6 - g.
-3*(g - 1)**3*(g + 2)
Let a(k) be the third derivative of -3/4*k**4 - 1/6*k**5 - 2/3*k**3 + 3/20*k**6 + 1/15*k**7 + 0*k + 0 + 2*k**2. Factor a(w).
2*(w - 1)*(w + 1)**2*(7*w + 2)
Let w be 64/208*1/2. Determine j so that 0 + 0*j - w*j**2 = 0.
0
Let c = 0 + -1. Let h = c + 2. Factor -5*y**2 + 4*y + y**2 + 0 - h.
-(2*y - 1)**2
Let k(x) be the third derivative of x**8/84 + 4*x**7/35 + 7*x**6/15 + 16*x**5/15 + 3*x**4/2 + 4*x**3/3 - 5*x**2. Factor k(p).
4*(p + 1)**4*(p + 2)
Suppose 13*q + 152 - 178 = 0. Determine m, given that -3/5*m**4 + 3/5*m**3 + 0 - 3/5*m + 3/5*m**q = 0.
-1, 0, 1
Let y(v) be the first derivative of v**5 - 5*v**4/4 - 5*v**3/3 + 5*v**2/2 - 8. Factor y(p).
5*p*(p - 1)**2*(p + 1)
Let u(b) be the second derivative of -b**6/75 + b**5/10 - 3*b**4/10 + 7*b**3/15 - 2*b**2/5 + 14*b. What is n in u(n) = 0?
1, 2
Let f(d) = -2*d**3 - 2*d**2 + 6*d. Let k(s) = -4*s**3 - 4*s**2 + 13*s. Let o be (28/35)/((-4)/10). Let a(g) = o*k(g) + 5*f(g). Let a(l) = 0. Calculate l.
-2, 0, 1
Suppose 32 = 4*n - 2*n. Let y be 4/12 + n/6. Factor -3*k**y + 0*k**2 + 2*k**2 + 2*k**4 + 7*k**3.
2*k**2*(k + 1)**2
Suppose -3*t + 2 = -10. Let 8/7*m**t + 0 + 12/7*m**2 - 18/7*m**3 - 2/7*m = 0. What is m?
0, 1/4, 1
Let p = 21 + -15. Suppose -4*b = m - 4, -p*b + b - 3*m = 2. Factor -4*r**b + 2*r - 1/4.
-(4*r - 1)**2/4
Let l(i) = -i**3 + 4*i**2 + i + 5. Suppose -15 = -3*s + 2*d, 0 = 2*s + 5*d - 4 - 6. Let c(h) = h**3 - 4*h**2 - 2*h - 6. Let f(n) = s*c(n) + 6*l(n). Factor f(a).
-a*(a - 2)**2
Let z(l) be the first derivative of -1/12*l**3 + 1/2*l - 1/8*l**2 - 6. Factor z(s).
-(s - 1)*(s + 2)/4
Let o(k) be the first derivative of 2/11*k + 2 + 2/11*k**3 + 4/11*k**2. Factor o(f).
2*(f + 1)*(3*f + 1)/11
Suppose 6*c - 3*c = 9. Suppose c*n + 2*k = 2, -2*n = -3*k - 27 + 4. Suppose 2 - 4 + 5 - n - 9*x**2 - 6*x = 0. Calculate x.
-1/3
