- 2*u**6/165 + 4*u**5/55 - u**4/33 - 7*u**3/33 + 4*u**2/11 + 15*u - 4. Suppose i(x) = 0. What is x?
-4, -1, 1
Let w(h) = 2*h**3 + 30*h**2 - 254*h + 15. Let j be w(6). Factor 0 - 2/3*t**2 + 0*t - 1/9*t**j.
-t**2*(t + 6)/9
Let k be 10/8 + 3/4. Let s be (-4)/k - 42/(-7). Find p such that -4*p - 5*p**2 - 10*p**3 - s*p**2 + 2*p = 0.
-1/2, -2/5, 0
Let o = -267 + 271. Let y(g) be the third derivative of -3/2*g**3 + 12*g**2 - 3/8*g**6 + 0*g - 2/35*g**7 - 13/8*g**o + 0 - 21/20*g**5. Factor y(z).
-3*(z + 1)**3*(4*z + 3)
Let q(p) = -8*p**3 + 88*p**2 - 87*p + 7. Let k(o) = 4*o**3 - 44*o**2 + 43*o - 3. Let g(i) = 7*k(i) + 3*q(i). What is l in g(l) = 0?
0, 1, 10
Let r(g) be the second derivative of g**4/15 + 46*g**3/15 + 44*g**2/5 - 57*g - 1. Factor r(j).
4*(j + 1)*(j + 22)/5
Let k be 28/(-35) + (-72)/(-15). Find p such that 1206*p**2 - 7*p - 1214*p**2 + k*p**3 + 8*p**4 + p + 2*p**5 = 0.
-3, -1, 0, 1
Let v be ((-11)/(-33))/(3/1737*-1). Let m = v - -773/4. Find y, given that -1/2*y + 3/4 - m*y**2 = 0.
-3, 1
Suppose 2*t + z + 10 = 0, 3*z = 2*t + 4 - 2. Let q be (3 - (t - -5))*2. Determine u so that -u**3 - 4*u**3 - u - q*u + 10*u = 0.
-1, 0, 1
Let k(w) be the first derivative of 22*w**4/7 + 26*w**3/3 + 37*w**2/7 - 20*w/7 - 162. Solve k(z) = 0 for z.
-5/4, -1, 2/11
Let r = -1761 + 1765. Let -15/4*k**2 + 3/2*k + 0 + 15/4*k**r - 3/2*k**3 = 0. What is k?
-1, 0, 2/5, 1
Let y(a) = 50*a**3 - 45*a**2 - 1505*a - 1470. Let j(o) = -7*o**3 + 6*o**2 + 215*o + 210. Let l(k) = 15*j(k) + 2*y(k). Factor l(t).
-5*(t - 7)*(t + 1)*(t + 6)
Let a(m) = -1 + m**3 + m**4 - m**4 - m**4. Let p(h) = -1 - 3 + 1 + 7*h**2 + h + 19*h**3 + 16*h**4 - 7*h**4. Let y(f) = -3*a(f) + p(f). Factor y(l).
l*(2*l + 1)**2*(3*l + 1)
Let j(b) = 2*b**3 - 10*b**2 - 9*b - 14. Let v be j(6). Factor 13 + 3*d**3 + 13*d - v*d**3 + 2*d**2 - 3 + 0*d**2.
-(d - 5)*(d + 1)*(d + 2)
Let g(s) be the second derivative of s**8/2016 - s**7/315 + s**6/144 - s**5/180 - 19*s**2/2 + 25*s. Let l(t) be the first derivative of g(t). Factor l(y).
y**2*(y - 2)*(y - 1)**2/6
Factor 0 - 3/2*a + 1/2*a**4 - 5/2*a**3 + 7/2*a**2.
a*(a - 3)*(a - 1)**2/2
Let w = -1753 + 1757. Let p(i) be the second derivative of 1/4*i**2 - 3*i + 1/72*i**w - 1/9*i**3 + 0. Suppose p(n) = 0. Calculate n.
1, 3
Let i(y) = y**2 - 24*y + 97. Let c be i(5). Let 0*b - 3/4*b**3 + 0 + 0*b**c - 3/4*b**4 = 0. What is b?
-1, 0
Let h(n) = -2*n**3 - 14*n**2 + 2*n + 18. Let v(j) = j**3 + 12*j**2 - j - 15. Let b(u) = -3*h(u) - 4*v(u). Solve b(w) = 0.
-1, 1, 3
Let b(j) be the third derivative of -j**5/60 - 11*j**4/6 - 242*j**3/3 - 15*j**2 + 3. Factor b(k).
-(k + 22)**2
Let m(h) be the second derivative of h**8/3360 + h**7/84 + 5*h**6/24 + 25*h**5/12 + 5*h**4/12 + 38*h. Let f(l) be the third derivative of m(l). Factor f(g).
2*(g + 5)**3
Suppose -22 = -4*h - 2*p, 2*h - 2*p + 4 + 0 = 0. Let t = 172 + -170. Solve -2/5*y + 4/5 - 2*y**h - 16/5*y**t = 0 for y.
-1, 2/5
Let k be (-14)/4 - (-15111)/2898. Factor -4/7*w**2 + 16/7 + k*w.
-4*(w - 4)*(w + 1)/7
Let h be (-4004)/(-5280) + (-1)/(-24). Let h*o**4 + 4/5*o**3 + 44/5*o - 16/5 - 36/5*o**2 = 0. What is o?
-4, 1
Let i(p) be the second derivative of -13*p + 4/9*p**3 + 0 - 7/6*p**4 + 1/3*p**2. Factor i(a).
-2*(3*a - 1)*(7*a + 1)/3
Let t(v) = v**2 + v. Let i = 66 - 68. Let f(d) = -1. Let w(o) = i*f(o) - t(o). Let w(g) = 0. What is g?
-2, 1
Suppose 26*g = -21*g. Factor 4/3*y + 4/3*y**2 + g.
4*y*(y + 1)/3
Solve 22*p - 39*p + 0*p**5 + 12*p - 12 + 3*p**5 + 17*p + 15*p**2 - 3*p**4 - 15*p**3 = 0.
-2, -1, 1, 2
Let p(s) be the second derivative of -1/210*s**7 + 0*s**2 + 1/30*s**3 + 0 + 0*s**5 + 1/30*s**4 - 1/75*s**6 + 15*s. Suppose p(g) = 0. Calculate g.
-1, 0, 1
Let k(c) = 19*c + 249. Let q be k(-13). Factor 20/7*i**3 + 180/7*i - 1/7*i**4 - 81/7 - 118/7*i**q.
-(i - 9)**2*(i - 1)**2/7
Let y(n) be the second derivative of n**4/42 - 152*n**3/21 + 151*n**2/7 + 384*n + 2. Determine u, given that y(u) = 0.
1, 151
Let j(h) = -h**4 - h**3 + h**2 + h + 1. Let x(i) = 3*i**4 + 3*i**3 + i**2 - 7*i - 4. Let z(o) = 4*j(o) + x(o). Factor z(f).
-f*(f - 1)**2*(f + 3)
Let a(j) be the third derivative of j**6/120 - 3*j**4/8 + j**2 + 59. Determine g so that a(g) = 0.
-3, 0, 3
Let h(z) be the first derivative of -5*z**6/51 - 16*z**5/85 + 9*z**4/34 + 16*z**3/51 - 4*z**2/17 - 296. Find y such that h(y) = 0.
-2, -1, 0, 2/5, 1
Let m(b) = -3*b**3 + 98 - 98. Let z be m(-1). Find s such that 22 + 11*s**2 - 4*s**z - 26 + 4*s + 6*s**3 - 4*s**2 = 0.
-2, 1/2
Let h(u) = -2*u**2 + 29*u - 102. Let j be h(8). Factor 8/3*l**j + 0 + 0*l + 4/3*l**3.
4*l**2*(l + 2)/3
Let v = -15 - -6. Let p be (v - -11)/((-2)/(-4)). Factor -6*n**2 + 0*n**2 - 2*n**2 + n**5 + 6*n**p + n**5.
2*n**2*(n - 1)*(n + 2)**2
Let h(d) be the second derivative of d**4/114 + 8*d**3/57 + 22*d - 1. Solve h(t) = 0.
-8, 0
Let k be (12/(-34))/(20 + -25 + 4). Solve 16/17*g**4 + 0 + 0*g + 22/17*g**3 - 8/17*g**5 + k*g**2 = 0.
-1/2, 0, 3
Let x(k) be the third derivative of k**6/90 + 17*k**5/45 + 31*k**4/18 + 10*k**3/3 + 58*k**2. Let x(r) = 0. Calculate r.
-15, -1
Let z(c) be the third derivative of -c**6/300 - c**5/75 + 7*c**4/60 - 4*c**3/15 - 5*c**2 + 3*c. Suppose z(y) = 0. What is y?
-4, 1
Let y(g) be the third derivative of -g**7/504 + g**6/48 - g**5/12 - 7*g**4/24 + 10*g**2. Let p(n) be the second derivative of y(n). Solve p(t) = 0.
1, 2
Let b = -1973 - -1985. Factor 21/2*i**3 + 57/2*i**2 - 6 + b*i.
3*(i + 1)*(i + 2)*(7*i - 2)/2
Suppose 0 = 2*c - 3*n - 6, 104*n = -2*c + 106*n + 4. Let g(m) be the second derivative of 1/12*m**4 + c*m**3 + 1/20*m**5 - 7*m + 0*m**2 + 0. Factor g(w).
w**2*(w + 1)
Let w(l) be the first derivative of 3*l**5/20 - 3*l**3/2 + 3*l**2 - 8*l + 6. Let g(s) be the first derivative of w(s). Factor g(t).
3*(t - 1)**2*(t + 2)
Let b(g) be the first derivative of 2/13*g**2 - 2/3*g**3 + 12/13*g**4 - 18/65*g**5 + 8 + 0*g. Factor b(z).
-2*z*(z - 2)*(3*z - 1)**2/13
Let u be 2/24 - (10 + (-1837)/132). Let f(r) be the first derivative of -3/2*r**2 + 3/4*r**u + r**3 + 1 - 3*r. Suppose f(b) = 0. Calculate b.
-1, 1
Find c such that 81 + 39*c**3 + 81*c - 3*c**5 + 37*c**2 - 74*c**3 + 21*c**4 + 5*c**3 - 91*c**2 = 0.
-1, 3
Let b(h) be the first derivative of 6 - 1/12*h**4 + 0*h**3 + 1/30*h**5 + 0*h + 2*h**2. Let f(o) be the second derivative of b(o). Factor f(n).
2*n*(n - 1)
Let o(d) be the second derivative of -d**6/120 - d**5/40 + d**3 - 14*d. Let l(s) be the second derivative of o(s). Factor l(r).
-3*r*(r + 1)
Let i = -73/2 + 953/26. Suppose 0*j - 2/13 + i*j**2 = 0. Calculate j.
-1, 1
Let k(w) = -2*w + 1. Let u(l) = -l**2 - 8*l + 11. Let x(v) = 6*k(v) + 3*u(v). Factor x(f).
-3*(f - 1)*(f + 13)
Let f(d) be the first derivative of d**8/840 - d**6/150 + d**4/60 + 3*d**2/2 - 2. Let t(p) be the second derivative of f(p). Factor t(q).
2*q*(q - 1)**2*(q + 1)**2/5
Let b = 112 - 126. Let j = b + 16. Factor 0 - 1/7*r**4 + 1/7*r**j - 1/7*r + 1/7*r**3.
-r*(r - 1)**2*(r + 1)/7
Let z(d) be the third derivative of -d**5/140 + 8*d**3/7 + 23*d**2 - 1. Find r such that z(r) = 0.
-4, 4
Let -72/5*u**2 + 0 - 3/5*u**5 - 48/5*u - 3/5*u**3 + 18/5*u**4 = 0. Calculate u.
-1, 0, 4
Let m(w) = -4*w**3 - 2*w**2 + 2*w + 2. Let x(z) be the third derivative of -z**6/120 + z**4/24 + z**3/6 - 6*z**2. Let a(h) = -m(h) + 2*x(h). Factor a(q).
2*q**2*(q + 1)
Suppose -91*m = -88*m + 5*c - 11, -c + 1 = 0. Factor 0*u + 1/4*u**4 - u**3 + 0 + u**m.
u**2*(u - 2)**2/4
Suppose 2*s = 4*n + 2, 5*n = -4*s - 1 - 8. Let o(a) = 42*a**3 + 36*a**2 - 15*a. Let g(u) = -u**3 - u**2 + u. Let z(q) = n*o(q) - 18*g(q). Factor z(j).
-3*j*(2*j + 1)*(4*j + 1)
Let g(t) be the second derivative of -8/105*t**7 - 27/5*t**2 - 19*t + 3/2*t**4 - 4/15*t**6 + 0*t**3 + 1/5*t**5 + 0. Factor g(m).
-2*(m - 1)**2*(2*m + 3)**3/5
Let j(y) = y**5 + y**2 - y + 1. Let l(s) = -7*s**5 + 30*s**4 - 9*s**3 - 34*s**2 + 10*s + 2. Let r(c) = -2*j(c) + l(c). Let r(k) = 0. What is k?
-1, 0, 1/3, 2
Let f(a) be the second derivative of -a**8/11200 - a**7/1050 - a**6/400 + 11*a**4/6 + 8*a. Let c(m) be the third derivative of f(m). Factor c(b).
-3*b*(b + 1)*(b + 3)/5
Let h(c) be the first derivative of c**4/16 - 41*c**3/12 - c**2/8 + 41*c/4 - 46. Factor h(g).
(g - 41)*(g - 1)*(g + 1)/4
Suppose -4*b - 5 + 21 = 0. Let o(a) be the first derivative of -1/5*a**4 - 2/5*a**3 + 0*a - b + 2/5*a**2. Factor o(u).
