7
Let d = 116 - 810/7. Factor -2/7*t - d + 2/7*t**3 + 2/7*t**2.
2*(t - 1)*(t + 1)**2/7
What is m in -3/5 - 1/5*m**2 - 4/5*m = 0?
-3, -1
Let o(v) = 2*v**2 - v + 1. Let g(x) = 14*x**2 - 24*x - 22. Let t(j) = -g(j) + 8*o(j). Let t(h) = 0. What is h?
-5, -3
Let j = -383 - -11491/30. Let r(y) be the second derivative of 0*y**5 + 0*y**3 + 0*y**2 - 1/42*y**7 - j*y**6 + 0*y**4 + 2*y + 0. What is b in r(b) = 0?
-1, 0
Let o(t) = -5*t**2 + 7*t - 5. Let u(i) = -4*i**2 + 8*i - 6. Let g(n) = 2*o(n) - 3*u(n). Factor g(l).
2*(l - 4)*(l - 1)
Factor 7*p**2 - 2*p**3 + 2*p**2 - 5*p**4 - p - 4*p**2 + p**2 + 3*p**5 - 1.
(p - 1)**3*(p + 1)*(3*p + 1)
Let u be (-27)/(-21) + 10/(-35). Suppose -7 = -4*y + u. Find l such that 2/3*l**y + 0*l + 4/3*l**4 + 1/3*l**5 + 5/3*l**3 + 0 = 0.
-2, -1, 0
Let f(v) be the first derivative of -v**6/10 - 3*v**5/10 + v + 4. Let c(a) be the first derivative of f(a). What is b in c(b) = 0?
-2, 0
Let q = -142 + 145. Let v(n) be the first derivative of -q*n**3 + 1 - 27*n - 1/4*n**4 - 27/2*n**2. Factor v(t).
-(t + 3)**3
Let l(z) = 9*z**4 - 16*z**3 + 15*z**2 - 13*z + 5. Let v(c) = 5*c**4 - 8*c**3 + 7*c**2 - 7*c + 3. Let x(t) = 3*l(t) - 5*v(t). Solve x(q) = 0.
0, 1, 2
Suppose 0 = -2*g + 6 + 34. Let w = 35 - g. Let -w*d + 15*d + 3*d**4 + 3*d**5 = 0. Calculate d.
-1, 0
Let m be ((-6)/(-33) + 120/(-297))*-3. What is a in -2 + m*a**2 - 4/3*a = 0?
-1, 3
Let w(l) = -9*l**2 + 45*l - 10. Let g(v) = 2*v**2 - 9*v + 2. Let h(o) = 11*g(o) + 2*w(o). Let h(a) = 0. What is a?
1/4, 2
Let c(n) = -5*n**3 + 24*n**2 + 19*n + 23. Let g(d) = 3*d**3 - 12*d**2 - 9*d - 12. Let z(x) = -6*c(x) - 11*g(x). Factor z(m).
-3*(m + 1)**2*(m + 2)
Let s be (-2)/1*(-4)/60. Let p(i) be the first derivative of 4/3*i**2 - 2/3*i - s*i**5 + 2/3*i**4 - 4/3*i**3 + 1. Solve p(y) = 0 for y.
1
Let f be (12/(-18))/(2/(-76)). Let x = f - 25. Factor x*r**2 - 1/3*r + 0.
r*(r - 1)/3
Let r(c) = -c**2 - 11*c - 10. Let y(j) = j**2 + 6*j + 5. Let g(q) = 4*r(q) + 9*y(q). Solve g(k) = 0.
-1
Let c(z) be the second derivative of -2/3*z**3 - 3*z**2 - 3*z + 0 - 1/18*z**4. Factor c(b).
-2*(b + 3)**2/3
Factor -31*f**3 - 14*f**2 + 35*f**3 - 10*f**2 - 32 + 48*f.
4*(f - 2)**3
Let f = -39 + 57. Let j be f/63*1/1. Find g, given that j*g + 0*g**2 + 0*g**4 + 2/7*g**5 + 0 - 4/7*g**3 = 0.
-1, 0, 1
Let i = -14 + 44/3. Find x such that -4/9*x**4 + 2/3*x**5 + 0*x + 4/9*x**2 - i*x**3 + 0 = 0.
-1, 0, 2/3, 1
Let a(q) = q**3 + q - 1. Let s(f) = 5*f**3 + f**2 + 3*f - 5. Let d(j) = -12*a(j) + 3*s(j). Factor d(t).
3*(t - 1)*(t + 1)**2
Let p(w) be the second derivative of 1/15*w**6 + 0 - 1/6*w**4 - 1/10*w**5 - 4*w + 0*w**2 + 1/3*w**3. Factor p(m).
2*m*(m - 1)**2*(m + 1)
Let c be (-85)/(-20) - (-1 + 5). Let t(r) be the second derivative of c*r**5 - 1/30*r**6 + 2/3*r**3 + 2*r + 0*r**2 - 2/3*r**4 + 0. Find l, given that t(l) = 0.
0, 1, 2
Let j(y) be the third derivative of 245*y**8/48 + 42*y**7 + 35*y**6/24 - 487*y**5/6 + 155*y**4/2 - 100*y**3/3 - 20*y**2. Let j(r) = 0. Calculate r.
-5, -1, 2/7
Suppose -2*m + 12 = -6*x + 2*x, -4*x = 5*m + 12. Suppose -2/3*p**2 + 0*p + 2/3*p**3 + m = 0. Calculate p.
0, 1
Let z(v) be the first derivative of v**6/12 + 3*v**5/10 - 2*v**3/3 + 39. Let z(c) = 0. What is c?
-2, 0, 1
Solve -2/5*r**3 + 2/5 + 2/5*r - 2/5*r**2 = 0 for r.
-1, 1
Let u(n) = -n**3 + 12*n**2 + 11*n + 29. Let g be u(13). Suppose 3*x = 13 + 2. Factor 0*v**2 + 5*v**3 + v**4 + v**2 + 2*v**g - x*v**3.
v**2*(v + 1)**2
Let a(j) be the third derivative of -j**9/45360 + j**8/10080 + 5*j**4/24 - 5*j**2. Let k(g) be the second derivative of a(g). Factor k(y).
-y**3*(y - 2)/3
Let p(w) be the third derivative of -w**8/504 - 2*w**7/315 + 2*w**2. Factor p(v).
-2*v**4*(v + 2)/3
Suppose 1075 = -15*u + 1105. Factor 2/3*t**3 - u + 14/3*t - 10/3*t**2.
2*(t - 3)*(t - 1)**2/3
Let j(l) be the first derivative of l**6/3 - l**4/2 + 6. Determine p, given that j(p) = 0.
-1, 0, 1
Let v(j) be the first derivative of -3*j**3 - 21*j**2 - 24*j + 11. Factor v(s).
-3*(s + 4)*(3*s + 2)
Let k(z) = -2*z - 2. Let s(g) = -g**2 - g. Let w(a) = -2*k(a) - 4*s(a). Factor w(t).
4*(t + 1)**2
Let s(y) = y + 7. Let d be s(-5). Let r be (-2)/4*(-12)/d. Factor 0 + 0*q - 2/3*q**4 - 1/3*q**5 + 0*q**2 - 1/3*q**r.
-q**3*(q + 1)**2/3
Let q = -63/13 - -5. Factor 4/13 + q*g**3 - 4/13*g**2 - 2/13*g.
2*(g - 2)*(g - 1)*(g + 1)/13
Factor -2/5*y**2 + 14/5*y**4 - 8/5*y**5 + 0*y - 4/5*y**3 + 0.
-2*y**2*(y - 1)**2*(4*y + 1)/5
Let x(n) be the second derivative of 0*n**4 - 1/1260*n**6 - 2*n + 0 + 0*n**2 - 1/210*n**5 + 1/3*n**3. Let h(g) be the second derivative of x(g). Factor h(j).
-2*j*(j + 2)/7
Let p = 7 + -5. Let a be 1 + -2 - -5 - -2. Find o, given that 6*o**4 - 12*o**p + 9*o + 47*o**3 - 17*o**3 - 15*o**5 - 12*o - 12*o + a = 0.
-1, 2/5, 1
Let y(a) = 9*a**2 + 10*a - 3 - 19*a**3 + 3. Suppose 0 = f - 1 - 1. Let m(n) = 4*n**3 - 2*n**2 - 2*n. Let b(j) = f*y(j) + 11*m(j). Factor b(i).
2*i*(i - 1)*(3*i + 1)
Let d(z) = -z**3 - z**2 - z. Let g(i) = 4*i**4 - 2*i**3 - 6*i**2 - 6*i. Let b(s) = -6*d(s) + g(s). Suppose b(m) = 0. Calculate m.
-1, 0
Let z be (1 + 27)*(33/9 - 3). Factor 98/3*x**2 - z*x + 8/3.
2*(7*x - 2)**2/3
Let v = 67/68 + -4/17. Solve 1/4 - v*c**2 + 1/2*c = 0.
-1/3, 1
Let b(o) be the first derivative of -o**2 - 2*o**5 + 5 - 11/3*o**3 + 0*o - 19/4*o**4. Suppose b(t) = 0. What is t?
-1, -1/2, -2/5, 0
Solve -m**2 + 6*m + 0*m**2 - 4*m - m = 0 for m.
0, 1
Let t(x) be the first derivative of -3*x**4/32 + 3*x**3/8 - 3*x/2 - 20. Suppose t(f) = 0. What is f?
-1, 2
Let b be (4 - 4) + (-6)/(-1). Let z be 3/b*3 + -1. Factor 0 + q - 1/2*q**3 - z*q**2.
-q*(q - 1)*(q + 2)/2
Suppose 7*h - 8 = 3*h. Suppose l = -h*f - l - 6, -l = 5*f - 5. Factor 3 + 3/2*b**f - 9/2*b.
3*(b - 2)*(b - 1)/2
Let w = 773/231 + -55/21. Suppose -14/11*l**5 - 28/11*l**2 + 2*l - w*l**3 - 4/11 + 32/11*l**4 = 0. Calculate l.
-1, 2/7, 1
Let s(b) be the third derivative of b**4/24 + 2*b**3 - 8*b**2. Let v be s(-9). Suppose -2/3*u**v - 2/3*u**2 + 0 - 2/9*u**4 - 2/9*u = 0. What is u?
-1, 0
Let u = 6 - 1. Let w = 8 - u. Determine f, given that f**3 + f**3 - 3*f**w - f**2 = 0.
-1, 0
Let w = -2/1407 + 544519/7035. Let n = w + -77. Factor -n*b**2 + 0*b + 0.
-2*b**2/5
Suppose 0 = 2*y - 2, -2*m + 1 = -4*y - 1. Let j(b) be the first derivative of 5/6*b**2 + 4/9*b**3 + 2/3*b + m + 1/12*b**4. Factor j(l).
(l + 1)**2*(l + 2)/3
Let l(z) be the first derivative of 3*z**4 - 64*z**3/3 + 30*z**2 + 72*z + 4. Suppose l(u) = 0. Calculate u.
-2/3, 3
Let n(c) = 125*c**4 + 910*c**3 + 1415*c**2 + 855*c + 140. Let i(j) = -9*j**4 - 65*j**3 - 101*j**2 - 61*j - 10. Let h(w) = -85*i(w) - 6*n(w). Factor h(k).
5*(k + 1)**2*(k + 2)*(3*k + 1)
Let v(m) be the third derivative of -5/72*m**4 - 4*m**2 - 1/1008*m**8 + 1/126*m**7 + 1/18*m**3 + 1/18*m**5 - 1/36*m**6 + 0*m + 0. Factor v(l).
-(l - 1)**5/3
Let c(z) = -z**3 - z**2 + z + 1. Let s(l) = 3*l**3 + 3*l**2 - 6*l - 6. Let v(k) = -6*c(k) - s(k). Factor v(y).
3*y**2*(y + 1)
Let y(k) be the third derivative of -k**6/30 - 2*k**5/5 - 2*k**4 - 16*k**3/3 - 7*k**2 - k. Determine j, given that y(j) = 0.
-2
Let f = 3 + -1. Suppose f*z = 3 + 3. Suppose g**4 + 2*g**2 + 0*g**3 - 4*g**2 + g**z = 0. What is g?
-2, 0, 1
Let y(l) = l**3 + l**2. Let i(a) = a**3 + 26*a**2 - 15*a. Let q(g) = i(g) - 6*y(g). Factor q(c).
-5*c*(c - 3)*(c - 1)
Let d(p) be the third derivative of p**5/360 - p**4/144 + 2*p**2. Factor d(x).
x*(x - 1)/6
Let p(u) = -45*u + 497. Let z be p(11). Suppose -2*w**3 - 21*w - 25/2*w**z - 9/2 = 0. Calculate w.
-3, -1/4
Let t(u) = u**3 - u**2 - u + 1. Let b(k) = 9*k**3 - 12*k**2 - 5*k + 8. Let v(x) = -3*b(x) + 24*t(x). What is h in v(h) = 0?
0, 1, 3
Let f(o) be the first derivative of -o**5 + 5*o**4/4 + 5*o**3 - 5*o**2/2 - 10*o - 21. Factor f(c).
-5*(c - 2)*(c - 1)*(c + 1)**2
Let f(c) be the second derivative of -5*c**4/3 + 5*c**3/6 - 32*c. Factor f(i).
-5*i*(4*i - 1)
Let h(u) be the first derivative of -u**8/1176 + u**6/210 - u**4/84 - u**2/2 - 3. Let g(k) be the second derivative of h(k). Factor g(d).
-2*d*(d - 1)**2*(d + 1)**2/7
Let w be (6 - 4)*(-3)/(-1). Factor w*f - 2*f**2 + f**2 - 2*f**2.
-3*f*(f - 2)
Let x(u) = -6*u + 9. Let q(d) = -17*d + 26. Let l(c) = -4*q(c) + 11*x(c). Let n be l(4). Let -i**5 - i + i**4 - 2 + 0*i**2 + 2*i**n - 2*i**2 + 3 = 0. What is i?
-1, 1
Factor 5*h**3 + 2*h**5 - 3*h**4 - h**2 - 2*h**3 