 1
Let v = 6 - 4. Suppose 3*s - 4 = v. Let -110*k**3 - 7*k**s + 1 - 183*k**2 + 48*k**4 - 9 + 32*k**5 - 72*k = 0. Calculate k.
-2, -1, -1/4, 2
Let a(y) be the first derivative of 2*y**3/21 + 3*y**2/7 - 8*y/7 + 380. What is v in a(v) = 0?
-4, 1
Let u(o) = -o + 7. Let k be u(3). Solve 6 - r**2 - k*r - 2 + 4*r = 0 for r.
-2, 2
Let u be 15*(-2)/(-27)*(-90)/15. Let v = -6 - u. What is p in 2/3*p**2 - 2/3*p**4 - 2/3*p**3 + v*p + 0 = 0?
-1, 0, 1
Let b(u) = 7*u**3 + 9*u**2 - 15*u + 11. Let q(r) = -r**3 - r**2 + r - 1. Let t(z) = -b(z) - 6*q(z). Let t(n) = 0. What is n?
-5, 1
Suppose -9*r = -4792 - 2138. Let j be (-1)/11 - (-994)/r. Factor -2/5*o**3 + 0*o - j*o**2 + 8/5.
-2*(o - 1)*(o + 2)**2/5
Factor -8*h**3 - 46*h**2 + 3*h**3 + 44*h**2 - 166*h**2 + h**3.
-4*h**2*(h + 42)
Let c be 30/4*((-6)/(-9) + 0). Factor -9*t - 3*t - 8 - 12*t**2 + c*t**2 + 3*t**2.
-4*(t + 1)*(t + 2)
Factor -273*m**2 - 296*m**2 + 176*m - 192 + 827*m**2 - 290*m**2 - 4*m**3.
-4*(m - 2)**2*(m + 12)
Let w(f) be the first derivative of 5*f**6/6 + 2*f**5 - 5*f**4/4 - 10*f**3/3 + 27. Suppose w(x) = 0. What is x?
-2, -1, 0, 1
Let t(j) = -j**3 - j**2 + 1. Let g(v) = -683*v**3 - 291*v**2 - 42*v - 5. Let i(w) = -2*g(w) - 6*t(w). Factor i(h).
4*(7*h + 1)**3
Let i be 16/104 + (-152)/(-26). Suppose -2*m + i = -0*m. Solve -4*p + m*p + 0*p**2 + 2*p - p**2 + 2 = 0.
-1, 2
Let v(l) be the third derivative of l**6/15 + 3*l**5/25 - 7*l**4/10 + 4*l**3/15 - 2*l**2 - 27*l. Solve v(t) = 0 for t.
-2, 1/10, 1
Let a be (-1752)/(-803) - 2/11. Let l be 20/6 + 0 + -2. Suppose 6*u**a - l*u - 26/3*u**3 + 0 + 4*u**4 = 0. Calculate u.
0, 1/2, 2/3, 1
Factor 2/5*o**4 + 0 + 22/5*o**2 - 2*o - 14/5*o**3.
2*o*(o - 5)*(o - 1)**2/5
Solve -y**2 + 5565 - 14*y - y**2 - 5577 = 0 for y.
-6, -1
Let g(h) be the first derivative of h**7/168 + h**6/72 - 5*h**5/24 + 5*h**4/8 - 3*h**3 - 9. Let n(b) be the third derivative of g(b). Find d such that n(d) = 0.
-3, 1
Let x be (-1 - (-55)/(-65)) + -1 + -3. Let q = x + 862/143. Determine m, given that -2/11*m**2 + q*m + 0 = 0.
0, 1
Let a(v) be the second derivative of 2*v**7/315 + v**6/90 + 3*v**2/2 + 6*v. Let x(i) be the first derivative of a(i). Factor x(z).
4*z**3*(z + 1)/3
Let z = 23 - 21. Factor a - 61*a**z + 3*a**3 + 30*a**2 + 35*a**2.
a*(a + 1)*(3*a + 1)
Let j(n) be the third derivative of -n**10/151200 + n**9/30240 + n**5/6 + n**3/6 - 16*n**2 + 1. Let w(d) be the third derivative of j(d). Factor w(c).
-c**3*(c - 2)
Let h(r) = 10*r**2 + 16*r + 16. Let v(a) = 2*a**2 + 3*a + 3. Let o(n) = 3*h(n) - 16*v(n). Factor o(z).
-2*z**2
Suppose 13 - 7 = 3*b. Factor -2*m**3 + 2*m**5 - m**3 - 14*m**2 + 12*m**b - m**5.
m**2*(m - 2)*(m + 1)**2
Let w(z) be the first derivative of -2*z**2 - 1/12*z**4 - 1/180*z**5 - 1/2*z**3 - 4 + 0*z. Let f(k) be the second derivative of w(k). Factor f(d).
-(d + 3)**2/3
Let v(f) be the first derivative of -3/2*f**4 + 9 + 15/2*f**2 + f**3 + 6*f. Find i, given that v(i) = 0.
-1, -1/2, 2
Let v be ((-65)/(-4))/13 + (7 - 8). Let z(y) be the second derivative of -5*y**2 - v*y**5 - 5/3*y**4 + 0 + 7*y - 25/6*y**3. Find n, given that z(n) = 0.
-2, -1
Let o(l) = 9*l**3 - 245*l**2 + 3333*l - 7935. Let b(t) = 29*t**3 - 735*t**2 + 9998*t - 23805. Let w(y) = 2*b(y) - 7*o(y). Let w(p) = 0. What is p?
3, 23
Let j(f) be the first derivative of 4*f**5 + 16*f**4 + 24*f**3 + 16*f**2 + 4*f - 74. Let j(c) = 0. Calculate c.
-1, -1/5
Factor 2/9*s**2 + 4/9*s - 2/3.
2*(s - 1)*(s + 3)/9
Let f(j) be the third derivative of j**9/3780 - j**8/560 + j**7/315 - 7*j**4/8 - 6*j**2 + 2. Let c(u) be the second derivative of f(u). Factor c(v).
4*v**2*(v - 2)*(v - 1)
Factor -24/17*d - 30/17*d**3 + 0 + 184/17*d**2.
-2*d*(d - 6)*(15*d - 2)/17
Let w(f) be the second derivative of -1336/33*f**3 - 70*f**4 - 128/11*f**2 - 2597/55*f**5 + 343/165*f**6 + 39*f + 0. Factor w(h).
2*(h - 16)*(7*h + 2)**3/11
Let v = 15243 + -45727/3. Factor -v*r**3 - 2/3*r**2 + 2/3*r**4 + 2/3*r + 0.
2*r*(r - 1)**2*(r + 1)/3
Find q such that 1806/5*q**3 + 282*q + 354/5*q**4 + 3486/5*q**2 + 24/5*q**5 - 120 = 0.
-5, -4, -1, 1/4
Let j(c) be the second derivative of -6*c - 1/4*c**5 + 0 + 5/6*c**4 + 10/3*c**3 - 20*c**2. Factor j(z).
-5*(z - 2)**2*(z + 2)
Let v be -5 + -2 + 2 + (-14)/(1372/(-518)). Factor -8/7*g**2 + 8/7 + 2/7*g - v*g**3.
-2*(g - 1)*(g + 1)*(g + 4)/7
Let a be 3 + 2*1/2. Factor f**2 - a*f - f**2 - f**2 - 4.
-(f + 2)**2
Let z(p) be the second derivative of -p**7/189 + p**6/45 - p**5/45 - 2*p + 80. Factor z(h).
-2*h**3*(h - 2)*(h - 1)/9
Determine r, given that 2/3*r**2 - 12 - 34/3*r = 0.
-1, 18
Factor -21*o**2 - 241*o**2 - 202*o - 6*o - 15 - 76*o**2 - 17.
-2*(13*o + 4)**2
Let o(r) be the third derivative of -r**5/225 - 49*r**4/180 + 5*r**3/9 + 54*r**2. Factor o(h).
-2*(h + 25)*(2*h - 1)/15
Let w(y) = -6*y**4 + 12*y**3 + 31*y**2 - 5*y - 11. Let m(t) = 2*t**4 - 4*t**3 - 10*t**2 + 2*t + 4. Let p = -67 - -63. Let s(c) = p*w(c) - 14*m(c). Factor s(o).
-4*(o - 3)*(o - 1)*(o + 1)**2
Let h be ((-1175)/(-290) + -4)*46/3. Let s = h + 1/145. Factor -2/5 - 2/5*k**2 + s*k.
-2*(k - 1)**2/5
Let n(t) = -4*t**3 - 4*t**2 - 6*t - 6. Let k(o) = 9*o**3 + 7*o**2 + 12*o + 14. Let i(u) = 3*k(u) + 7*n(u). Factor i(a).
-a*(a + 1)*(a + 6)
Let m(d) = 13*d - 143. Let o be m(11). Let i(a) be the second derivative of 0*a**3 - 13*a + 0*a**2 + o - 5/12*a**4. Factor i(z).
-5*z**2
Let w be (-2)/(-20) + 4209/3660. Factor -5/4*u + w*u**3 + 1/2 - 1/2*u**2.
(u - 1)*(u + 1)*(5*u - 2)/4
Let q(j) be the first derivative of 5/2*j**2 - 3 + 10/3*j**3 - 5*j. Factor q(z).
5*(z + 1)*(2*z - 1)
Suppose -24*p**2 + 19*p**2 - 70 + 0*p**2 - 45*p = 0. Calculate p.
-7, -2
Let d(s) = -s**2 + 2*s + 2. Let q(m) = 2*m**2 + 11*m - 52. Let u(v) = d(v) - q(v). Determine t, given that u(t) = 0.
-6, 3
Let r be ((-2)/32*1)/((-51)/204). Let l(q) be the first derivative of 0*q + 1/2*q**2 + r*q**4 - 8 + 2/3*q**3. Solve l(c) = 0.
-1, 0
Let n(d) be the third derivative of -d**6/380 - d**5/285 + 17*d**4/228 - 4*d**3/19 + 9*d**2 - 9. Suppose n(y) = 0. Calculate y.
-3, 1, 4/3
Let u(s) be the first derivative of s**4/12 + 2*s**3/9 - 5*s**2/6 - 2*s - 99. Factor u(c).
(c - 2)*(c + 1)*(c + 3)/3
Let n = 1/12005 - -460991/12005. Solve 3/5 + 48/5*o + n*o**2 = 0.
-1/8
Suppose 2*k = 5*i - k - 109, -4*i + 89 = -3*k. Solve 37 - 25 + 12*n**2 - i*n - 4*n**2 = 0.
1, 3/2
Let g(t) be the second derivative of -t**5/20 + t**4 + 10*t**3 + 32*t**2 + 281*t. Suppose g(a) = 0. Calculate a.
-2, 16
Let s be 10 + 17/(51/(-28)). Determine n so that -s - 2/3*n + 2/3*n**2 + 2/3*n**3 = 0.
-1, 1
Let x(s) be the first derivative of -2*s**3/27 + 50*s**2/9 + 49. Find o such that x(o) = 0.
0, 50
Suppose -1/2*u**3 + 0 + 15/2*u**2 + 0*u = 0. Calculate u.
0, 15
Let u(w) be the first derivative of -4*w**3/9 - 14*w**2/3 - 16*w - 73. Factor u(y).
-4*(y + 3)*(y + 4)/3
Suppose -4*q = q - 15. Let i = 10 + -7. Factor -l**q - 2 - 2*l**3 + 3*l + 2*l**i.
-(l - 1)**2*(l + 2)
Let h(m) be the third derivative of -m**7/840 + m**6/240 + 7*m**5/240 - 5*m**4/24 + m**3/2 - 128*m**2. Let h(d) = 0. What is d?
-3, 1, 2
Let m(w) be the second derivative of -5*w**5/12 + 5*w**4/12 + 11*w**2/2 + 4*w. Let v(c) be the first derivative of m(c). Factor v(x).
-5*x*(5*x - 2)
Let a(g) be the third derivative of -g**8/896 - g**7/56 - 3*g**6/160 + 7*g**5/40 + 7*g**4/64 - 9*g**3/8 + 184*g**2. Let a(r) = 0. Calculate r.
-9, -2, -1, 1
Let i = 140 - 146. Let d(c) = c**2 - 14*c - 118. Let x be d(i). Find m, given that -2/13*m**5 + 0*m**x + 0*m**3 + 0 + 0*m - 4/13*m**4 = 0.
-2, 0
Let r(x) be the first derivative of x**5/40 - x**4/16 - x**3/2 + 2*x**2 - 1. Let v(k) be the second derivative of r(k). Let v(c) = 0. Calculate c.
-1, 2
Let m(n) = n**2 + 7*n - 28. Let j be m(-11). Let o be (-32)/(-36) - j/72. Find u such that o*u + 2/9*u**2 + 0 = 0.
-3, 0
Let o(j) be the second derivative of 0 + 1/3*j**3 - 2*j**2 - 7/60*j**5 - 5/24*j**4 + 4*j. Let x(p) be the first derivative of o(p). Solve x(d) = 0 for d.
-1, 2/7
Find q such that q**5 - q**3 + 66*q**4 + 2*q**2 - 65*q**4 - 3*q**2 = 0.
-1, 0, 1
Let g(v) = 2*v**3 - 46*v**2 - 53*v + 123. Let t be g(24). Suppose -12 = 4*h + 3*x, 5*h = h - 4*x - 16. Factor h + 2/13*b**t + 2/13*b**2 - 4/13*b.
2*b*(b - 1)*(b + 2)/13
Let l(k) = k + 14. Let u(p) = -p - 7. Let f be u(3). Let t be l(f). Let -1/2*q**t - 3/2*q**3 + 0 - 3/2*q**2 - 1/2*q = 0. Wh