
-1, 0, 2
Let f(h) be the second derivative of h**7/147 + 2*h**6/105 - h**5/35 - 2*h**4/21 + h**3/21 + 2*h**2/7 + 7*h. Solve f(u) = 0.
-2, -1, 1
Let k be 2 + 3 + -1 + 77. Factor 0*b - 6 + 9*b - 84*b**3 + 0*b + 0 + k*b**2.
-3*(b - 1)*(4*b - 1)*(7*b + 2)
Let q = 135 + -1619/12. Let a(v) be the third derivative of -1/15*v**5 + 0*v**3 + 0 + q*v**4 - v**2 + 1/60*v**6 + 0*v. Find z, given that a(z) = 0.
0, 1
Let w(x) = -x + 1. Let s be w(1). Suppose n - 5*d - 20 = 26, 2*n + 3*d - 27 = s. Factor -3*h**3 + 9*h**2 - 27*h - n*h**2 - 6*h**2.
-3*h*(h + 3)**2
Let q(h) = h**2 - 7*h + 5. Let u be q(7). Solve -8 - 6*m**2 + 2*m**u - 5*m**5 - 4*m**3 + 6 + 8*m**4 + 7*m = 0 for m.
-1, 2/3, 1
Let a = 23 - 14. Factor -q**3 - 7 - 4*q**2 + a + 2*q**2 + q.
-(q - 1)*(q + 1)*(q + 2)
Factor 8/9*n + 0 + 2/9*n**2.
2*n*(n + 4)/9
Suppose -3/7 - 6/7*l - 3/7*l**2 = 0. What is l?
-1
Let z(u) = 42*u - 11. Let b be z(5). Let y = 999/5 - b. Find n, given that -4/5 + y*n**2 + 2/5*n - 2/5*n**3 = 0.
-1, 1, 2
Let i = 31301/50 - 626. Let q(z) be the second derivative of 0 - 1/6*z**4 - 4/5*z**2 + 8/15*z**3 + z + i*z**5. Solve q(s) = 0.
1, 2
Factor -7/4*l**4 - 5/4*l**5 + 0 + 0*l + 0*l**2 - 1/2*l**3.
-l**3*(l + 1)*(5*l + 2)/4
Let n = -32/7 - -174/35. Let b(s) = -s**2 - 12*s - 23. Let d be b(-9). Suppose 0*r**2 + 0 + 8/5*r + n*r**d - 6/5*r**3 = 0. What is r?
-1, 0, 2
Let v(a) be the third derivative of -a**6/300 + a**5/10 - 5*a**4/4 + 25*a**3/3 - 26*a**2. What is s in v(s) = 0?
5
Let x(h) = -h**3 - h**2 - h - 1. Let r(q) = -3*q**3 - 2 - 4 + 2*q - 6*q**2 - 12*q**2 + q**3. Let a(g) = -r(g) + 6*x(g). Factor a(t).
-4*t*(t - 2)*(t - 1)
Let n = 1/8 - -3/8. Let z be 2 - 0/1 - 0. Determine k, given that -1/2 - n*k**z + k = 0.
1
Solve -8/9*r**5 - 4/3*r**3 - 2/9*r**2 + 0*r - 2*r**4 + 0 = 0.
-1, -1/4, 0
Let d(v) = -v**2 - 4*v. Let n be d(-4). What is m in m**2 - 1 + m + 0 + m**3 + n*m**3 - 2*m**3 = 0?
-1, 1
Suppose 69*l = 71*l - 8. Let t(j) be the third derivative of 2/15*j**3 + 0*j + 0 - 3*j**2 + 1/60*j**l - 1/150*j**5. Let t(r) = 0. What is r?
-1, 2
Let c(a) = a**3 + 6*a**2 - 7*a - 2. Let y be c(-7). Let m be ((-6)/3)/y + 8. Find q such that -5 + q**2 + 0*q**3 + 2 - 10*q**2 + 3*q**3 + m*q = 0.
1
Let u(t) = -2 + 7*t**2 + 0 + 5*t**3 + 6*t - 8*t**4 + 1 - 5. Let w(k) = -7*k**4 + 4*k**3 + 6*k**2 + 5*k - 5. Let s(f) = 5*u(f) - 6*w(f). Factor s(q).
q**2*(q + 1)*(2*q - 1)
Let j = 287/582 + 2/291. Factor -j*f - 1/4*f**2 - 1/4.
-(f + 1)**2/4
Let w(b) be the second derivative of b**5/180 + b**2/2 + 3*b. Let y(d) be the first derivative of w(d). Suppose y(r) = 0. What is r?
0
Let u(n) be the third derivative of -1/60*n**6 - 1/30*n**5 + 1/105*n**7 + 1/12*n**4 + 0*n + 0*n**3 + 0 - 2*n**2. Let u(x) = 0. What is x?
-1, 0, 1
Let m(w) = 2*w**5 - 8*w**3 - 2*w**2 + 6*w + 4. Let j(r) = -r**5 - r**4 + r**2 + r + 1. Let b(c) = 2*j(c) - m(c). What is n in b(n) = 0?
-1, -1/2, 1
Determine u so that -6/7 - 2/7*u + 2/7*u**3 + 6/7*u**2 = 0.
-3, -1, 1
Let h = 494 + -494. Factor -4/5*n + h - 2/5*n**2.
-2*n*(n + 2)/5
Let k(t) be the third derivative of -t**10/56700 + t**9/30240 + t**8/30240 - t**5/30 - t**2. Let y(u) be the third derivative of k(u). Factor y(w).
-2*w**2*(w - 1)*(4*w + 1)/3
Let w(b) be the third derivative of -b**6/480 + b**5/240 + b**4/48 - 12*b**2. Find d such that w(d) = 0.
-1, 0, 2
Suppose 8*m - 24 = 5*m. Let d be (-3)/(-5)*(m + -3). Suppose -2 + 3*a - 1 - 6*a**3 + 6*a**4 + 3*a - d*a**4 = 0. Calculate a.
-1, 1
Let c be 2/(3 - (-1308)/(-428)). Let f = c + 36. Factor f*q**2 - 1/3 - 1/3*q + 1/3*q**3.
(q - 1)*(q + 1)**2/3
Let z(h) = -2*h**2 + 10*h - 2. Let g be z(7). Let r be ((-20)/(-50))/((-8)/g). Let -r*b**2 + 1/2*b**3 + 3/2*b - 1/2 = 0. Calculate b.
1
Suppose -5*b = -22 - 8. Let s(i) = -i**2 + 7*i - 7. Let v(l) = -l + 1. Let a(k) = b*v(k) + 2*s(k). Suppose a(n) = 0. Calculate n.
2
Factor -2/13*w**2 + 2/13*w - 2/13*w**3 + 2/13*w**4 + 0.
2*w*(w - 1)**2*(w + 1)/13
Let j(m) be the second derivative of 2/33*m**3 + 1/11*m**2 - m + 0*m**4 - 1/55*m**5 + 0 - 1/165*m**6. Determine y so that j(y) = 0.
-1, 1
Let x be (-3)/12*-4 + -1. Determine n, given that 0*n**3 + 2/3*n**4 + x*n + 0 + 1/3*n**5 + 0*n**2 = 0.
-2, 0
Let k(a) = 2*a**3 + a**2 + a - 1. Let s be k(1). Suppose 0 = -6*n + s*n + 24. Factor f**2 + 1 + 7 + n*f + f**2.
2*(f + 2)**2
Let s be -6*1*3/(-6). Factor 3*t + 3*t**2 - 4*t**4 + t**3 - 4*t**s + t**4.
-3*t*(t - 1)*(t + 1)**2
Let s(u) be the second derivative of u**4/24 - u**3/12 + 27*u. Find m such that s(m) = 0.
0, 1
Let v(l) be the third derivative of l**5/20 + l**4/24 - 2*l**3/3 + 13*l**2. Determine w, given that v(w) = 0.
-4/3, 1
Find s such that 2*s**3 - 29*s**2 - 20*s**2 + 53*s**2 - 3*s**3 + 11*s + 6 = 0.
-1, 6
Let z(g) = -5*g**3 + 14*g**2 + 2*g + 2. Let o(u) = 81*u**3 - 225*u**2 - 33*u - 33. Let p(h) = -2*o(h) - 33*z(h). Suppose p(b) = 0. Calculate b.
0, 4
Let b = -9 - -13. Suppose 3*v = b*v - 2. Suppose -2*f - f**2 + 0*f**2 - f**v = 0. What is f?
-1, 0
Let a(f) be the third derivative of -f**9/5040 + f**7/280 + f**6/120 - f**4/6 - 2*f**2. Let t(g) be the second derivative of a(g). Solve t(k) = 0 for k.
-1, 0, 2
Let m(r) be the second derivative of -r**6/10 + 3*r**5/20 + r**4/4 - r**3/2 - r. Suppose m(w) = 0. What is w?
-1, 0, 1
Let i(d) be the third derivative of -d**2 + 0 + 4/9*d**3 + 1/90*d**6 + 1/315*d**7 + 0*d - 1/9*d**4 - 1/30*d**5. Find y such that i(y) = 0.
-2, 1
Let u(a) be the first derivative of -2/5*a**5 + 1/2*a**4 + 7/2*a**2 + 8/3*a**3 + 2*a - 6 - 1/6*a**6. Find y, given that u(y) = 0.
-1, 2
Let 7/4*l**4 + 0 + 2*l**2 + 19/4*l**3 - l = 0. What is l?
-2, -1, 0, 2/7
Let y be (-2)/6*-3*5/15. Factor 2/3 - y*g**2 - 1/3*g.
-(g - 1)*(g + 2)/3
Let k(u) be the first derivative of -3*u**4/4 + 2*u**3/3 + 28. Solve k(p) = 0.
0, 2/3
Let d(b) be the third derivative of -b**5/60 + b**3/6 - 3*b**2. Let d(x) = 0. What is x?
-1, 1
Let p(x) = x**2 + 1. Let n(u) = 2. Suppose 4*a + 3 = 3*k, -4*a = -3*a. Let t(g) = k*n(g) - p(g). Suppose t(o) = 0. What is o?
-1, 1
Suppose 4 = 14*u - 10*u. Let r be u*-4 + (-117)/(-26). Solve r*x**2 + 2 - 2*x = 0.
2
Let i(b) be the third derivative of b**6/120 + b**5/40 - b**4/4 + b**3/3 - 6*b**2. Let o(g) be the first derivative of i(g). Find x such that o(x) = 0.
-2, 1
Let b(r) be the first derivative of 3 - 1/3*r**2 + 0*r - 2/9*r**3. Factor b(o).
-2*o*(o + 1)/3
Factor 1/3*y + 2/3*y**2 + 0 + 1/3*y**3.
y*(y + 1)**2/3
Let u = 0 - -3. Determine r, given that -9*r + 4*r**2 + 2 + 7 - u*r + 0 = 0.
3/2
Suppose 5*i - 1 = 3*c, -5*i + 3 = 2*c - 13. Solve 2 - 4*o**2 + 4*o**c - o**3 + o**2 - o + o**4 - 2*o**3 = 0 for o.
-2, -1, 1
Find t, given that 3/2*t**3 + 0 + 0*t + 0*t**2 + 3/2*t**4 = 0.
-1, 0
Let j(l) be the third derivative of l**6/720 + l**5/120 + l**4/72 - 8*l**2. What is r in j(r) = 0?
-2, -1, 0
Let w(h) = 3*h**2 + 6*h. Let q(b) = 3*b**2 + 7*b. Let y(p) = -3*q(p) + 4*w(p). Factor y(m).
3*m*(m + 1)
Factor 16/15*o - 6/5 + 2/15*o**2.
2*(o - 1)*(o + 9)/15
Factor 2*q**2 + 2*q**3 + 0*q**2 - 2*q**2 + 2*q**2.
2*q**2*(q + 1)
Let q(s) be the first derivative of 0*s - 2/3*s**3 + 4 - 5/14*s**4 - 2/35*s**5 - 3/7*s**2. Factor q(j).
-2*j*(j + 1)**2*(j + 3)/7
Let q(z) be the first derivative of -z**4/8 + z**3/3 - 1. Factor q(n).
-n**2*(n - 2)/2
Suppose -2*r = 2*a + 40, 0*r - a = -4*r - 85. Let g be -3 + 5/((-30)/r). Factor 0*o**2 + 0*o**4 + g*o**5 + 0 - 1/2*o**3 + 0*o.
o**3*(o - 1)*(o + 1)/2
Let n be (-1)/3*((-99)/(-12) - 9). Factor -3*f - n*f**3 + 2 + 3/2*f**2.
-(f - 2)**3/4
Let i(g) be the first derivative of -5 - 1/3*g**3 - g + g**2. Factor i(h).
-(h - 1)**2
Let j(q) be the first derivative of -q**5/20 - q**4/8 + 3*q**2/2 - 2. Let d(n) be the second derivative of j(n). Factor d(c).
-3*c*(c + 1)
Let v = -154/13 - -1720/143. Let v + 4/11*d + 2/11*d**2 = 0. Calculate d.
-1
Suppose 0 = 3*i - 2 - 4. Let q(w) be the second derivative of -w**i + 0 + 1/6*w**4 - 2*w - 1/10*w**5 + 1/3*w**3. Solve q(t) = 0.
-1, 1
Let l(h) be the third derivative of h**9/6048 - h**7/840 + h**5/240 - 5*h**3/6 - 3*h**2. Let j(n) be the first derivative of l(n). Solve j(d) = 0 for d.
-1, 0, 1
Suppose g**4 + 2/3*g + 0 - 2/3*g**3 - g**2 = 0. What is g?
-1, 0, 2/3, 1
Let u be (-1)/5 - 427/(-35). Let l be 9/u - (-3)/12. Solve -1/2*h + l - 1/2*h**2 = 0 for h.
-2, 1
Let r(a) be the second derivative of -a**8/2240 + a**7/1120 + 5*