5, 1
Let s(k) = 4*k - 2. Let u(z) = 5*z - 3. Let l(b) = 4*s(b) - 3*u(b). Let x(n) = -3*n**3 + 2*n**2 - 8*n - 9. Let o(c) = 18*l(c) + 2*x(c). What is y in o(y) = 0?
-1/3, 0, 1
Factor 4*m - 4*m**3 + 401*m**2 - 2*m**4 - 401*m**2 + 2.
-2*(m - 1)*(m + 1)**3
Let s(r) be the second derivative of -5*r**4/24 + 5*r**3/12 - 29*r. Suppose s(y) = 0. Calculate y.
0, 1
Let k(x) be the third derivative of 0*x + 0*x**4 - 1/450*x**6 + 0*x**3 + 0 + 1/450*x**5 - 1/525*x**7 + x**2. Suppose k(q) = 0. Calculate q.
-1, 0, 1/3
Suppose -2*v = 4*f - 14, -4*f = 5*v + 3 - 8. Let w(a) be the first derivative of 8/25*a**f + 9/10*a**4 + 1/5*a**2 + 4/5*a**3 - 2 + 0*a. Factor w(k).
2*k*(k + 1)**2*(4*k + 1)/5
Suppose -l - 2*t - 8 = 2, -5*l + t = -5. Let 0 + 1/4*p**2 - 1/4*p**4 + 0*p + l*p**3 = 0. What is p?
-1, 0, 1
Let i(u) be the third derivative of u**6/108 + u**5/60 - u**4/18 + u**3/6 + 2*u**2. Let z(w) be the first derivative of i(w). Suppose z(b) = 0. Calculate b.
-1, 2/5
Let v(g) be the first derivative of -2*g**6 + 4*g**5 - g**4 - 4*g**3/3 + 12. Factor v(x).
-4*x**2*(x - 1)**2*(3*x + 1)
Let f(z) = z**3 + z**2 - 9*z - 6. Let r be f(-3). Factor 0 - 1/4*o - o**2 - 3/4*o**r.
-o*(o + 1)*(3*o + 1)/4
Determine a, given that 18*a**2 - 4*a**4 - 4*a**2 - 10*a**4 - 4*a**3 + 4*a = 0.
-1, -2/7, 0, 1
Let m(g) = -g**3 + 4*g**2 + g - 4. Let p be m(4). Let s be 7/(1 - p/2). Factor -s - 2*u**2 + 3 + 0*u + 6*u.
-2*(u - 2)*(u - 1)
Let u(l) = -l**2 + 14*l + 32. Let y be u(16). Let s(h) be the first derivative of 0*h**3 + y*h**2 + 1/10*h**4 + 1/15*h**6 + 0*h + 4/25*h**5 - 2. Factor s(m).
2*m**3*(m + 1)**2/5
Let q(b) be the third derivative of -1/220*b**6 - 5/132*b**4 - 3*b**2 + 0*b + 1/33*b**3 + 0 + 7/330*b**5. Factor q(u).
-2*(u - 1)**2*(3*u - 1)/11
Let a(i) = -i - 3. Let j be 5 + -3 - (9 - 2). Let b be a(j). Factor b*s - 4*s**3 - 3*s + 5*s**3.
s*(s - 1)*(s + 1)
Let t(p) = -4*p**4 + 5*p**3 - p**2 - 5*p - 5. Let g(u) = 2*u**4 - 3*u**3 + u**2 + 3*u + 3. Let d(r) = -5*g(r) - 3*t(r). What is x in d(x) = 0?
-1, 0, 1
Suppose -5*u + 6 = -2*u + 5*x, 6 = 3*u + 2*x. Let l(k) be the first derivative of 1/2*k**4 + 0*k - u + 4/21*k**3 + 8/35*k**5 - 1/7*k**2. Factor l(o).
2*o*(o + 1)**2*(4*o - 1)/7
Let z(d) = -d**3 - d**2. Let r(v) = 3*v**3 + 3*v**2. Let s be (3/(-6) + 0)*-6. Let c(p) = s*r(p) + 12*z(p). Factor c(w).
-3*w**2*(w + 1)
Let b be 38/14 - -10*(-66)/(-1540). Find l such that -6/7 + 8/7*l**2 + b*l = 0.
-3, 1/4
Let q(y) be the second derivative of 3*y**7/14 - 7*y**6/5 + 7*y**5/2 - 13*y**4/3 + 17*y**3/6 - y**2 - 26*y. What is j in q(j) = 0?
1/3, 1, 2
Let g(w) be the first derivative of -4*w**5/35 + 4*w**3/7 + 4*w**2/7 - 2. Factor g(z).
-4*z*(z - 2)*(z + 1)**2/7
Let f be (-2)/(-4*3/(-6)). Let a be f + -9*(-2)/10. Factor a*w - 2/5 - 2/5*w**2.
-2*(w - 1)**2/5
Let i(o) be the third derivative of -o**4/24 + o**3/2 - 3*o**2. Let b be i(3). Factor b*v**2 + 2/7*v**3 + 4/7 - 6/7*v.
2*(v - 1)**2*(v + 2)/7
Let x be 1/(-3)*(3 - 4). Let w(k) be the second derivative of x*k**3 - k + 0*k**2 + 1/3*k**4 + 0 + 1/10*k**5. Factor w(s).
2*s*(s + 1)**2
Let f(r) be the first derivative of -8*r**5 + 15*r**4 + 70*r**3/3 - 75*r**2/2 - 45*r - 1. Solve f(u) = 0.
-1, -1/2, 3/2
Let x be (4/1)/((-1)/6). Let k be x/(-11) - 2/11. Find j such that 4*j + 10*j**k - 16 + 16 = 0.
-2/5, 0
Let h(v) be the third derivative of 0*v + 1/30*v**5 + 1/120*v**6 - 1/3*v**3 - 11*v**2 + 0 - 1/24*v**4. Solve h(u) = 0.
-2, -1, 1
Suppose -6*p**4 + 10*p**2 - 16*p**3 - p - p + 14*p**4 = 0. What is p?
0, 1/2, 1
Let b(h) be the first derivative of -1/7*h**2 + 1/14*h**4 + 1 - 2/7*h + 2/21*h**3. Factor b(d).
2*(d - 1)*(d + 1)**2/7
Let n = 424319/241470 - 9/5366. Let q = n + -14/9. Solve -2/5*y**3 - q*y**4 + 0*y**2 + 1/5 + 2/5*y = 0.
-1, 1
Let t(q) be the second derivative of q**7/1260 - q**5/60 - q**4/6 + 4*q. Let h(r) be the third derivative of t(r). Factor h(x).
2*(x - 1)*(x + 1)
Let f(k) be the first derivative of 2/11*k**2 + 3 + 2/33*k**3 + 2/11*k. Factor f(m).
2*(m + 1)**2/11
Let s = 8/11 + -5/22. Find m, given that m - s*m**2 - 1/2 = 0.
1
Let w(d) be the second derivative of -d**7/42 + d**6/15 + d**5/10 - d**4/3 - d**3/6 + d**2 - d. Factor w(z).
-(z - 2)*(z - 1)**2*(z + 1)**2
Let b(x) be the third derivative of -19*x**5/60 + x**4/12 - 4*x**2. Factor b(a).
-a*(19*a - 2)
Suppose 0*m = -4*m - 60. Let d be 1 + (9/m)/3. Solve 0 - 2/5*u**3 + d*u**2 - 2/5*u = 0 for u.
0, 1
Let k = -21/10 - -167/70. Let m = -508/91 - -80/13. Factor -2/7*c**2 - k*c + m.
-2*(c - 1)*(c + 2)/7
Let q = 0 - -4. Factor -3*x**q - 3*x**2 + 9*x - 9*x**3 + 0*x**4 - 2 + 8.
-3*(x - 1)*(x + 1)**2*(x + 2)
Let n = -5664/11 + 516. Let q = 59/44 - n. Factor -1/2 - 1/4*s + q*s**2.
(s - 2)*(s + 1)/4
Let y = 40 - 37. Suppose y*a - 21 = 3*s - 0*s, -a + 16 = -4*s. Factor 2/3 + 0*f**a - 1/3*f**5 - f - 2/3*f**2 + 4/3*f**3.
-(f - 1)**3*(f + 1)*(f + 2)/3
Let w = 13 - -9. Let y be w/70 + 20/70. What is a in -1/5*a**4 + 0 - y*a**3 - 1/5*a - 3/5*a**2 = 0?
-1, 0
Factor 392/13 + 2/13*i**2 - 56/13*i.
2*(i - 14)**2/13
Let h(r) be the third derivative of -r**8/420 + r**7/210 + r**3 - 7*r**2. Let x(p) be the first derivative of h(p). Factor x(i).
-4*i**3*(i - 1)
Suppose -4*n + n + 3*y = -6, -3*n - 2*y = 14. Let x(h) = h**5 + 4*h**4 - h**2 + 5*h. Let i(o) = 4*o**4 - 2*o**2 + 4*o. Let d(l) = n*x(l) + 3*i(l). Factor d(q).
-2*q*(q - 1)**3*(q + 1)
Let n(v) = 2*v**2 + 12*v + 10. Let w(i) = 0*i + 1 + 2*i - 4*i + 3*i. Let r(d) = n(d) - 10*w(d). Factor r(g).
2*g*(g + 1)
Let y(m) be the third derivative of 3*m**2 + 0*m + 0*m**4 + 0 - 1/150*m**5 + 1/15*m**3. Solve y(j) = 0.
-1, 1
Factor 4*p**3 - p**3 + 3*p**4 - 2*p - p - 3*p**2.
3*p*(p - 1)*(p + 1)**2
Let t = 3/43 + 209/86. Determine f so that -2*f**4 - t*f**3 + 0*f + 0 + f**2 + 3/2*f**5 = 0.
-1, 0, 1/3, 2
Suppose -10*x + 11 = -9. Factor 10/9*i**x - 4/9 + 2/3*i.
2*(i + 1)*(5*i - 2)/9
Let c(w) be the third derivative of w**10/50400 + w**9/20160 - w**8/3360 - 7*w**5/60 - 7*w**2. Let h(p) be the third derivative of c(p). Solve h(s) = 0 for s.
-2, 0, 1
Suppose -5*b - 5 = 0, 5*d + 4*b - 19 = 7. Suppose 5*s = 8*s - d. Solve -2/3*h**s - 2/3 - 4/3*h = 0 for h.
-1
Let q be (0 + 0)*11/22. Let 0*x - 1/4*x**5 + 1/4*x**3 - 1/4*x**2 + 1/4*x**4 + q = 0. What is x?
-1, 0, 1
Let 8*r**4 - 6*r**5 + 8/3*r + 0 + 10/3*r**3 - 8*r**2 = 0. What is r?
-1, 0, 2/3, 1
Let y(j) be the first derivative of -j**5/5 + 8. Factor y(f).
-f**4
Let t(s) be the first derivative of 23/5*s**3 - 3*s**5 - 6 + 3/20*s**4 + 39/10*s**2 - 7/5*s**6 + 6/5*s. Determine a so that t(a) = 0.
-1, -1/2, -2/7, 1
Let c = 181/12 + -83/6. Suppose 1/2*a**2 - c*a + 1/2 = 0. Calculate a.
1/2, 2
Let a = 28 + -26. Factor -p - 14*p**2 + 15*p**2 + a*p.
p*(p + 1)
Solve 72/7*t - 324/7 - 4/7*t**2 = 0.
9
Let v be -1 - (-121)/105 - 136/(-1020). What is m in 0 + 2/7*m**4 + v*m**2 + 0*m - 4/7*m**3 = 0?
0, 1
Let b(t) be the third derivative of -t**2 - 4/3*t**3 - 1/3*t**4 + 0*t + 0 - 1/30*t**5. Factor b(l).
-2*(l + 2)**2
Let j = 146 - 583/4. Factor -1/2 - 1/4*q + j*q**2.
(q - 2)*(q + 1)/4
Let k(j) = 2*j. Let w be k(2). Solve -336*s**3 + 35 - 45*s - 141*s**w - 3*s - 312*s**2 + 44 - 31 - 21*s**5 = 0 for s.
-2, -1, 2/7
Let c be 6*2/((-6)/(-1)). Factor 1 + 1 - f - f**c - 1 + f**3.
(f - 1)**2*(f + 1)
Factor 0 - 10/7*u**3 - 8/7*u + 2/7*u**4 + 16/7*u**2.
2*u*(u - 2)**2*(u - 1)/7
Let b(m) be the third derivative of -m**7/945 + m**6/1080 - m**4/24 - 2*m**2. Let o(j) be the second derivative of b(j). Factor o(s).
-2*s*(4*s - 1)/3
Let b(a) be the first derivative of 1/5*a**5 + 1/2*a**2 + a**3 + 3 + 3/4*a**4 + 0*a. Factor b(x).
x*(x + 1)**3
Factor 2*a**5 + 4*a**3 - 6*a**4 - a**2 - 12*a + 2 + 5*a**2 + 6*a.
2*(a - 1)**4*(a + 1)
Let f = -12/5 - -113/45. Let a(h) be the second derivative of -h + 2/3*h**2 - 1/9*h**3 - 1/2*h**4 - f*h**6 + 13/30*h**5 + 0. Factor a(n).
-2*(n - 1)**3*(5*n + 2)/3
Let y(j) be the third derivative of j**8/28 + 16*j**7/105 + 2*j**6/15 - 2*j**5/5 - 7*j**4/6 - 4*j**3/3 - 2*j**2. Solve y(c) = 0 for c.
-1, -2/3, 1
Let x(f) = f**3 + f**2 + f. Let g(o) = -5*o**3 - 5*o**2 - 3*o + 1. Let h(v) = -g(v) - 4*x(v). Let h(u) = 0. What is u?
-1, 1
Let b = -238 + 6427/27. Let h = b + 47/189. Determine j, given that 0 + 2/7*j - h*j**2 = 0.
0, 1
Let q(v) = v**2 + 15*v + 28. Let r be q(-13). Factor -2*u**3 + 4/3*u**2 - 4/3 + r*u.
-2*(u - 1)*(u + 1)*(3