 Suppose -2*c + 8 = 2*j, -b*j + j + 16 = 0. Factor c*i - 1/3*i**2 + 1/3.
-(i - 1)*(i + 1)/3
Let k(v) be the third derivative of v**6/240 + v**5/30 + 5*v**4/48 + v**3/6 + 4*v**2. Suppose k(h) = 0. What is h?
-2, -1
Suppose -5*a = -21 + 1. Factor 2*t**3 + 4*t - 6*t - 1 + 0*t**a + t**4.
(t - 1)*(t + 1)**3
Factor -12/5*c - 3/5*c**2 - 9/5.
-3*(c + 1)*(c + 3)/5
Let r(j) = 1237*j**3 + 1763*j**2 + 749*j + 64. Let t(u) = 618*u**3 + 882*u**2 + 374*u + 32. Let i(y) = 6*r(y) - 13*t(y). Factor i(m).
-4*(3*m + 2)**2*(17*m + 2)
Find a such that -1 + 37*a**2 - 3 - 41*a**2 + 8*a = 0.
1
Let n(k) be the first derivative of 3/4*k**4 + 0*k**2 + 0*k + 0*k**3 - 9. Factor n(o).
3*o**3
Suppose -4*v = 5*b - 25, 2*b + v = 4*b - 10. Suppose -18 = -b*y + 22. Suppose -q + 2 - 4*q - q + y*q**3 = 0. Calculate q.
-1, 1/2
Let y(j) be the first derivative of j**5/15 + j**4/3 + j**3/3 - 31. Factor y(i).
i**2*(i + 1)*(i + 3)/3
Suppose -h + 13 = 4*s - 0*h, 5*s - 3*h = 29. Determine q so that -2030/9*q**3 - 686/9*q**5 + 1960/9*q**s + 16/9 + 940/9*q**2 - 200/9*q = 0.
2/7, 1
Suppose 0*x - 4*s + 3 = x, -9 = -3*x - 2*s. Factor 2*n**2 + 3*n**x - n**4 - n**3 - 2*n - n**4.
-2*n*(n - 1)**2*(n + 1)
Let f(y) be the first derivative of y**9/6048 + y**8/1120 + y**7/560 + y**6/720 - 2*y**3/3 - 5. Let w(b) be the third derivative of f(b). Factor w(r).
r**2*(r + 1)**3/2
Let h(z) be the third derivative of z**8/10080 + z**7/3780 + z**4/8 - z**2. Let p(b) be the second derivative of h(b). Factor p(y).
2*y**2*(y + 1)/3
Let r(q) be the first derivative of -q**5/5 - q**4/3 + 2*q**3/9 + 2*q**2/3 + q/3 - 13. Let r(c) = 0. What is c?
-1, -1/3, 1
Suppose -2*d + 8 = 2, 0 = -5*t + 5*d. Let o(h) = -h - 12. Let j be o(-12). Determine f, given that j*f + 0 - 2/7*f**t - 18/7*f**4 + 2/7*f**2 + 18/7*f**5 = 0.
-1/3, 0, 1/3, 1
Let c(z) = 8*z**3 - 21*z**2 + 6*z - 5. Let x(a) = a**2 - 1. Let p(y) = 2*c(y) - 10*x(y). Determine n, given that p(n) = 0.
0, 1/4, 3
Let f(t) be the third derivative of -1/60*t**5 + t**2 + 1/6*t**3 + 1/180*t**6 + 0 + 0*t - 1/6*t**4. Let j(m) be the first derivative of f(m). Factor j(h).
2*(h - 2)*(h + 1)
Let 3 + t**2 - 3 - 2*t**4 - 3*t**3 + t**5 + 3*t**2 + 4*t = 0. What is t?
-1, 0, 2
Let o(i) be the first derivative of 3/8*i**4 + 0*i + 0*i**2 - 3/4*i**3 + 3/20*i**5 + 6. Solve o(a) = 0 for a.
-3, 0, 1
Suppose 2*f - 21 = -2*v - 1, -5*v + 26 = f. Suppose f*g - 3*g - 13 = 2*d, 3*d - 3 = -3*g. Suppose 0*b**2 + 2/3*b + 0 - 2/3*b**g = 0. Calculate b.
-1, 0, 1
Let t(v) = v**2 - 106*v - 506. Let h(j) = 2*j**2 - 107*j - 507. Let m(q) = 6*h(q) - 7*t(q). Factor m(s).
5*(s + 10)**2
Let j(b) be the first derivative of 5*b**6/6 - 2*b**5 - 17. Factor j(o).
5*o**4*(o - 2)
Let o be (-5)/(-5)*(-4)/(-8)*0. Determine q, given that o + 26/7*q**4 - 38/7*q**3 - 4/7*q + 22/7*q**2 - 6/7*q**5 = 0.
0, 1/3, 1, 2
Find k, given that 3 - 3/7*k**3 + 15/7*k**2 + 39/7*k = 0.
-1, 7
Let x = 70 - 70. Suppose -2/3*d + x - 2/3*d**3 - 4/3*d**2 = 0. What is d?
-1, 0
Let n(w) be the third derivative of -1/330*w**5 + 1/132*w**6 + 0*w**3 + 1/616*w**8 + 0*w**4 + 0*w + 5*w**2 - 1/165*w**7 + 0. Factor n(c).
2*c**2*(c - 1)**2*(3*c - 1)/11
Let j = -6 + 5. Let c(l) = 2*l**3 - 2*l**2 + 3*l - 3. Let s(q) = -q**3 + q**2 - q + 1. Let t = 4 + -7. Let w(u) = j*c(u) + t*s(u). What is f in w(f) = 0?
0, 1
Suppose 5*k = -2 + 7, -2*y = 2*k - 8. Let x(w) be the third derivative of 0*w + 0 + w**2 - 1/6*w**4 + 1/30*w**5 + 1/3*w**y. Let x(p) = 0. What is p?
1
Let s(a) be the first derivative of 5*a**3/3 - 5*a**2/2 - 10*a - 27. Factor s(d).
5*(d - 2)*(d + 1)
Let v(z) be the first derivative of 1/6*z**3 + 2 + 0*z + 1/4*z**2. Suppose v(g) = 0. What is g?
-1, 0
Let y(d) = -1. Let u(s) = s + 6. Let c(o) = u(o) + 3*y(o). Let a be c(-3). Suppose a*l**3 + 0 - 2/7*l + 4/7*l**4 - 4/7*l**2 + 2/7*l**5 = 0. Calculate l.
-1, 0, 1
Let 0*i - 2/11*i**2 + 0 = 0. Calculate i.
0
Let z(j) be the second derivative of 1/12*j**4 + 0*j**2 + 0 + 0*j**3 + 3*j. Factor z(h).
h**2
Factor -6*p**3 - 16*p + 8/3 + 58/3*p**2.
-2*(p - 2)*(p - 1)*(9*p - 2)/3
Determine b, given that 25/2*b + 5/4*b**2 + 125/4 = 0.
-5
Let m(q) be the third derivative of q**7/1680 + q**6/480 + q**5/480 - 39*q**2. Determine u, given that m(u) = 0.
-1, 0
Let t(p) be the third derivative of 0*p**3 + 1/36*p**4 + 0 - p**2 + 1/90*p**5 + 0*p. Suppose t(m) = 0. Calculate m.
-1, 0
Let f be ((-21)/18 - -2)*11/55. Let 0 + 1/6*y**3 + f*y**2 - 1/3*y = 0. Calculate y.
-2, 0, 1
Let h be 2 + 0 + 0/(-2). Factor -q + 4 - 3*q**2 + 2*q**2 + 3*q**h - 5.
(q - 1)*(2*q + 1)
Suppose 3/2*i**3 - 3*i**2 + 0 + 0*i + 3/2*i**4 = 0. Calculate i.
-2, 0, 1
Let q(b) be the second derivative of b**6/15 - b**5/10 - b**4/2 + 5*b**3/3 - 2*b**2 - 3*b. Factor q(t).
2*(t - 1)**3*(t + 2)
Let h(m) be the first derivative of -22*m**3/39 + 9*m**2/13 + 4*m/13 - 6. Factor h(w).
-2*(w - 1)*(11*w + 2)/13
Let w(i) be the first derivative of -2*i**3/21 - 4*i**2/7 - 6*i/7 + 8. Factor w(x).
-2*(x + 1)*(x + 3)/7
Factor -3/4*o + 1/4*o**2 + 0.
o*(o - 3)/4
Let o = -7 + 10. Suppose 0 = 2*v + 4*k - 24, 0 = 3*v + k - 6*k + 19. Find d such that -2*d**o + 0 + 2*d - 2 + 6*d**v - 4*d**2 = 0.
-1, 1
Let y(u) be the first derivative of 2*u**3/15 + 2*u**2/5 + 2*u/5 - 3. Solve y(v) = 0.
-1
Suppose 4*q - q = 9. Let 10/3*w**q - 4*w**2 + 4*w**4 - 2*w + 4/3 = 0. What is w?
-1, 1/2, 2/3
Let v(a) be the second derivative of -3*a**5/20 + 3*a**4/4 + a**3/2 - 9*a**2/2 + 22*a. Factor v(f).
-3*(f - 3)*(f - 1)*(f + 1)
Suppose -3*g + 8 = 2, 4*p = -3*g + 46. Let i = p + -8. Factor -4*u**3 + 4 - 4 + i*u + 2*u**5.
2*u*(u - 1)**2*(u + 1)**2
Let g(r) be the third derivative of -r**5/15 + r**4/2 + 8*r**3/3 + 17*r**2. Find p such that g(p) = 0.
-1, 4
Let f = 181 - 178. Let k(o) be the first derivative of 32/15*o**f - 8/5*o**2 + 2/5*o + 3. What is r in k(r) = 0?
1/4
Let t be (6/(-5))/((-18)/(-300)). Let g be ((-6)/(-10))/((-4)/t). Factor -8*v**2 - 3*v**4 + 6*v - 4*v**g - 7*v**2 + 16*v**3.
-3*v*(v - 2)*(v - 1)**2
Let t(j) = j + 2. Let m be t(7). Suppose -3*k + m = 3*q, -5*q + 9 + 6 = 3*k. Factor -34*c**3 - 154*c**2 - 31*c**3 + 162*c**4 - 7*c**q - 8 + 72*c.
2*(c - 1)*(c + 1)*(9*c - 2)**2
Factor 0 + 0*y**3 + 0*y - 1/3*y**2 + 1/3*y**4.
y**2*(y - 1)*(y + 1)/3
Let z(k) = -k - 1. Let l(h) = h**2 - 9*h - 4. Let w(d) = -5*l(d) + 30*z(d). Factor w(v).
-5*(v - 2)*(v - 1)
Suppose 3*v - 3 = 3. Solve 0 + 0*k + 2/9*k**v + 0*k**3 - 2/9*k**4 = 0 for k.
-1, 0, 1
Solve -11 - 20*y**2 - 15*y - 11 + 27 = 0.
-1, 1/4
Let z(b) be the second derivative of -b**5/100 - b**4/60 + 3*b. Factor z(a).
-a**2*(a + 1)/5
Let j(r) be the second derivative of 1/2*r**2 - 1/40*r**5 + 0 - 1/12*r**4 + 6*r + 1/12*r**3. Factor j(l).
-(l - 1)*(l + 1)*(l + 2)/2
Let c(p) be the second derivative of 1/72*p**4 + 1/36*p**3 + 0 + 0*p**2 - 3*p. Factor c(y).
y*(y + 1)/6
Let j(n) be the first derivative of -4*n**7/1365 - n**6/195 - n**5/390 + 2*n**2 + 3. Let y(c) be the second derivative of j(c). Factor y(p).
-2*p**2*(2*p + 1)**2/13
Let k(a) be the second derivative of 5*a**7/189 - 4*a**6/45 + a**5/10 - a**4/27 + 44*a. Factor k(m).
2*m**2*(m - 1)**2*(5*m - 2)/9
Suppose 7*j - 6 = 15. Let m(h) be the first derivative of -3 + 1/18*h**j + 1/6*h - 1/6*h**2. Factor m(g).
(g - 1)**2/6
Suppose -4*g - 3*g - 49 = 0. Let z be g/(-39) - 30/(-195). Solve 0 + 2/3*p**3 + 0*p - 1/3*p**4 - z*p**2 = 0.
0, 1
Let d(t) be the first derivative of 1/5*t + 1/15*t**3 + 1/5*t**2 - 3. Factor d(r).
(r + 1)**2/5
Let f be 1/((-4)/6)*-2. Factor 2*d - 3*d - 1 + 0*d**2 + d**f + d**2.
(d - 1)*(d + 1)**2
Let h = 1 - -2. Suppose -12*d**3 + 13*d**3 - 9*d**h - 6*d**4 - 2*d**2 = 0. What is d?
-1, -1/3, 0
Let t(p) = -1. Let h(m) = -16*m**2 - 12*m + 10. Let n(j) = h(j) + 6*t(j). Factor n(k).
-4*(k + 1)*(4*k - 1)
Suppose -5*l - u + 22 = -15, 0 = l - 4*u - 20. Let r = l + -2. Let v**3 + 6 + v**3 - r + 10*v**4 + 8*v**5 = 0. What is v?
-1, -1/4, 0
Let z be 25/2*(1 + (-372)/(-28)). Solve -200/7*x - 900/7*x**2 - z*x**4 - 16/7 - 250*x**3 = 0.
-2/5, -1/5
Let m(o) be the first derivative of -o**5/40 + o**4/24 + o**3/12 - o**2/4 + 3*o + 1. Let d(r) be the first derivative of m(r). Let d(x) = 0. Calculate x.
-1, 1
Let r(s) be the first derivative of s**3/3 + 2*s**2 + 4*s + 26. Factor r(v).
(v + 2)**2
Let v(a) be the third derivative of a**9/362880 + a**8/60480 + a**7/30240 + a**5/12 + 7*a**2. Let q(f) 