3*x + 0.
2*x*(x - 2)*(x + 3)/13
Let t be 1 - 8/10 - (-102)/90. Suppose -5/3*c**3 + t*c - 2*c**2 - 1/3*c**4 + 8/3 = 0. What is c?
-2, 1
Let c(o) = 1. Let f(u) = -3*u**2 + 24*u - 53. Let x(j) = 5*c(j) + f(j). Let x(y) = 0. What is y?
4
Suppose 0 = m + 11 - 6. Let d(n) = n**2 - 5*n. Let y(g) = g**2 - 6*g. Let q(s) = m*d(s) + 4*y(s). Factor q(f).
-f*(f - 1)
Let k be (1 - 27/15)/((-84)/70). Let r(x) be the third derivative of 0*x - 4*x**2 - 1/60*x**6 + 1/4*x**4 + k*x**3 + 0 + 0*x**5. Solve r(v) = 0.
-1, 2
Let v(m) = -3*m - 1. Let j be v(-3). Suppose -r - 11 = -3*g, 4*g + j*r - 3*r + 17 = 0. Factor 3*o**4 - 2*o**2 + 2 - 2*o**g + 0 - o**4.
2*(o - 1)**2*(o + 1)**2
What is g in -2/15*g**3 + 4/15 + 0*g**2 + 2/5*g = 0?
-1, 2
Let z(m) be the second derivative of m**4/60 + 2*m**3/15 - m**2/2 - 8*m. Factor z(y).
(y - 1)*(y + 5)/5
Let q be 3*3*(-24)/(-108). Suppose 14 = 5*w + q*d, 0 = 4*w - 3*d - 1 - 1. Determine i, given that -10/11*i + 14/11*i**w - 4/11 = 0.
-2/7, 1
Let s(m) = m**3 + 6*m**2 + 4*m - 3. Let o be s(-5). Determine y so that -2/3*y**4 + 4/3*y + 2*y**o + 0*y**3 + 0 = 0.
-1, 0, 2
Let c = 451/4 + -5847/52. What is q in -22/13*q - 18/13*q**2 - c = 0?
-1, -2/9
Suppose -m + 15 = -0*m. Suppose m = b - 1. Determine o, given that 16 - b + 6*o**2 + 21*o**3 = 0.
-2/7, 0
Suppose -2*v - 2*v - 2*j + 14 = 0, -4*j - 2 = -2*v. Suppose 0 = 3*s - 0 - 12. Factor 3*d**3 + 5*d**2 - 2*d**v - s*d**2.
d**2*(d + 1)
Let t = -8/3 + 10/3. Let y(b) be the second derivative of -1/5*b**5 - b**2 + 1/6*b**4 + t*b**3 + 0 - 3*b. What is s in y(s) = 0?
-1, 1/2, 1
Factor -3/7*f + 9/7*f**3 + 6/7 - 12/7*f**2.
3*(f - 1)**2*(3*f + 2)/7
Let g(p) be the third derivative of -4*p**2 - 1/480*p**5 + 0*p + 0*p**3 + 1/96*p**4 + 0. Factor g(b).
-b*(b - 2)/8
Suppose -5*d + 4*d = 0. Suppose 2*y = -d*y. Let -2/3*r + 2/3*r**3 + y + 2/3*r**4 - 2/3*r**2 = 0. Calculate r.
-1, 0, 1
Let m(r) = 6*r**2 - 2*r - 4. Suppose 1 - 5 = -n. Suppose -5*q = -3*q + 2. Let i(u) = u**2 - 1. Let o(y) = n*i(y) + q*m(y). Factor o(w).
-2*w*(w - 1)
Suppose 4 = c - 0. Let b be 2/(-20) + 2/c. Factor -2/5*y - 2/5 + b*y**3 + 2/5*y**2.
2*(y - 1)*(y + 1)**2/5
Suppose 27 = 2*i + 25. Let 1/2*h - 1/2*h**2 + i = 0. Calculate h.
-1, 2
Let m(o) = -340*o**3 - 1955*o**2 - 2210*o + 680. Let q(a) = 20*a**3 + 115*a**2 + 130*a - 40. Let d(x) = -2*m(x) - 35*q(x). Find l such that d(l) = 0.
-4, -2, 1/4
Let f(h) be the third derivative of h**7/3780 - h**6/540 - h**5/60 - h**4/24 - h**2. Let w(q) be the second derivative of f(q). Factor w(g).
2*(g - 3)*(g + 1)/3
Factor 1/2 + 3/4*p + 1/4*p**2.
(p + 1)*(p + 2)/4
Let u = -4/21 + 11/21. Let k = 35/78 - 3/26. Factor s**2 - s**3 - k*s + u*s**4 + 0.
s*(s - 1)**3/3
Let b(c) = c**3 + 7*c**2 + 7*c + 8. Suppose 2*q = 4*q + 12. Let t be b(q). Factor 3*o**t - 4*o + 0 - 9*o**2 + 1 + 1.
-2*(o + 1)*(3*o - 1)
Factor -16/3*s - 128/3 - 1/6*s**2.
-(s + 16)**2/6
Let q = -59 - -75. Factor 0 + 8/3*i**3 + 0*i + 70/3*i**5 + 0*i**2 + q*i**4.
2*i**3*(5*i + 2)*(7*i + 2)/3
Factor 4/15*s**3 + 0*s**4 - 2/15*s**5 + 0 + 0*s**2 - 2/15*s.
-2*s*(s - 1)**2*(s + 1)**2/15
Let a = -4/3 + 29/21. Let s(i) be the second derivative of -1/42*i**4 - a*i**3 + 0*i**2 - 2*i + 0. Suppose s(o) = 0. What is o?
-1, 0
Let w(d) be the first derivative of d**3/3 + d**2/2 - 2. Let a be w(1). Factor -7*x - 1 + a*x - 3*x**2 + x.
-(x + 1)*(3*x + 1)
Let s(u) = u + 8. Let c be s(-5). Let f(b) be the second derivative of -1/40*b**5 - 3*b - 1/12*b**4 - 1/12*b**c + 0 + 0*b**2. Factor f(j).
-j*(j + 1)**2/2
Let q = -40 - -42. Solve -1/3*t**5 - 4*t**2 - q*t**4 + 0 - 13/3*t**3 - 4/3*t = 0 for t.
-2, -1, 0
Let u be (-3 - -1)/((-6)/9). Factor 0*c**2 + 5*c - 2*c - 2*c + 2*c**2 + c**u.
c*(c + 1)**2
Find n such that n**2 - 37 - 35 + 72 - 3*n = 0.
0, 3
Let r be (2 + (-3)/2)*0. Let p = -4 + 6. Let 15*q**3 - 12*q**p + 6*q**2 + r*q + 0*q = 0. Calculate q.
0, 2/5
Let c(o) = 2*o - 6. Suppose 0 = w - 7 + 3. Let a be c(w). Determine u, given that -u**a - 3*u**2 + 6*u**2 + 4*u = 0.
-2, 0
Factor -2/9*m**3 - 2/3*m + 2/3*m**2 + 2/9.
-2*(m - 1)**3/9
Let h(v) = v**3 - 13*v**2 + 7*v + 29. Let k(q) = -9*q**3 + 129*q**2 - 69*q - 291. Let z(f) = 21*h(f) + 2*k(f). Suppose z(w) = 0. Calculate w.
-1, 3
Let c(x) be the third derivative of x**6/360 + x**5/360 - 5*x**4/144 + x**3/18 - 14*x**2. Find h such that c(h) = 0.
-2, 1/2, 1
Determine y, given that 10*y**2 + 14/5*y**4 + 8/5 - 32/5*y - 2/5*y**5 - 38/5*y**3 = 0.
1, 2
Suppose j + y = -3, 4*j - y - 15 = -j. Let p(h) be the first derivative of -5/2*h**2 + 10/3*h**3 - j + h**5 + h - 5/2*h**4 - 1/6*h**6. Solve p(d) = 0 for d.
1
Suppose 4*u - 8*u - 16 = 0. Let b be 2/u - 27/(-6). Let -1/3*d**3 + 1/3*d**b + 0 + 1/3*d - 1/3*d**2 = 0. Calculate d.
-1, 0, 1
Let o(b) be the first derivative of b**8/280 + b**7/420 - b**6/90 - b**3 - 2. Let q(l) be the third derivative of o(l). Factor q(r).
2*r**2*(r + 1)*(3*r - 2)
Factor 0*v**2 - 2/9 - 1/3*v + 1/9*v**3.
(v - 2)*(v + 1)**2/9
Let r be (3/2)/(15/(-20)). Let g be (4/6)/(r/(-6)). Factor 0 + 1/2*b - 3/4*b**g.
-b*(3*b - 2)/4
Suppose 4*o + 3*m + 4 = 0, -3*m = -4*o - 0*o + 20. Factor 0 - 1/4*q**o + 1/4*q.
-q*(q - 1)/4
Determine b so that 5*b**5 + 25*b**3 - b**4 - 6*b + 6*b - 19*b**4 - 10*b**2 = 0.
0, 1, 2
Let j = -6 - -10. Factor -29*r**3 + r**4 - 3*r**j + 33*r**3 - 2*r**2.
-2*r**2*(r - 1)**2
Suppose 2*w = 6*w + 48. Let o be -3*(2 - (-38)/w). Suppose -7/2*a**3 - a**2 + 1 + o*a = 0. What is a?
-1, -2/7, 1
Let g(z) be the second derivative of z**4/60 - z**3/30 - 3*z**2/5 + 33*z. Determine y so that g(y) = 0.
-2, 3
Suppose -3*d + 10 = 2*d. Determine j so that 0*j + 4*j + 9*j**4 + 0*j + 20*j**2 + 23*j**3 - d*j**4 = 0.
-2, -1, -2/7, 0
Suppose 62 = 3*b + 20. Factor -38*u - 15*u**2 - 3 + b*u - 3 - 3.
-3*(u + 1)*(5*u + 3)
Let t = 19 + -17. Let g(m) be the first derivative of 3/14*m**4 + 1 + 0*m + 2/7*m**3 + 1/7*m**t + 2/35*m**5. Find o such that g(o) = 0.
-1, 0
Factor -61*v**3 - 4*v**5 - 16*v + 11*v**2 - 59*v**3 + 8*v**4 - 27*v**2 + 132*v**3.
-4*v*(v - 2)**2*(v + 1)**2
Let a(p) be the first derivative of 9/8*p**2 - 9 + 5/16*p**4 - 1/2*p - p**3. Determine g so that a(g) = 0.
2/5, 1
Let c(a) be the first derivative of a**8/840 - a**7/210 + a**5/30 - a**4/12 + 2*a**3 - 4. Let l(j) be the third derivative of c(j). Factor l(n).
2*(n - 1)**3*(n + 1)
Let v(i) be the second derivative of 0*i**2 + 1/42*i**3 + 1/84*i**4 + 8*i + 0. Factor v(f).
f*(f + 1)/7
Suppose 1 = -5*n + 16. Factor 10*s**2 - 2*s - 4*s**5 + 14*s**4 + 104 - 18*s**n - 104.
-2*s*(s - 1)**3*(2*s - 1)
Let x(l) = 10*l**2 + 80*l + 146. Let p(y) = -2*y**2 - 16*y - 29. Let m(o) = -14*p(o) - 3*x(o). Determine s so that m(s) = 0.
-4
Suppose 2*l + j - 1 = 0, -4*l - 1 = -3*j + 2*j. Factor l*h**2 + 4*h**2 + 8 - 5*h**2 + 3*h**2 + 8*h.
2*(h + 2)**2
Let b = 301/5 - 8749/145. Let c = 70/87 + b. Suppose -2/3*k**2 + 2/3*k**3 - c*k + 2/3 = 0. What is k?
-1, 1
What is h in 3*h**3 - 6 + 1 + 9*h - 6*h**3 - 1 = 0?
-2, 1
Let s = -30449/75 + 406. Let o(h) be the second derivative of 0*h**5 + 0*h**3 + 1/30*h**4 + 0 - h + 0*h**2 - s*h**6. Suppose o(d) = 0. What is d?
-1, 0, 1
Let y be 4/14 + 60/35. Let -8*f**y + f**3 + 3*f**3 - 10*f - 6*f**3 - 4 = 0. What is f?
-2, -1
Let k(m) = -m**2 + 34*m + 71. Let g(n) = -3*n**2 + 69*n + 141. Let q(x) = -4*g(x) + 9*k(x). Solve q(j) = 0 for j.
-5
Let a = -106228/7 + 15212. What is v in -192/7*v**4 - 156/7*v**2 - 4/7 - 54/7*v**5 - a*v**3 - 6*v = 0?
-1, -1/3, -2/9
Let u(o) = o**4 + 9*o**3 - 5*o**2 + 3*o. Let j(p) = p**4 + p**2. Let x(s) = -4*j(s) + u(s). Factor x(h).
-3*h*(h - 1)**3
Let m = 47/136 + 26/17. Let r(h) be the first derivative of m*h**4 + 1/4*h**2 + 1/3*h**6 - 13/10*h**5 + 0*h - 7/6*h**3 + 3. Factor r(j).
j*(j - 1)**3*(4*j - 1)/2
Let u = -443467378/365 + 1214978. Let a = 6/73 - u. Determine l, given that -a*l**2 - 2/5*l**4 + 0 - 2/5*l - 6/5*l**3 = 0.
-1, 0
Suppose -2*l = -2 - 8. Determine q so that 12*q - l*q**2 - 13*q + 6*q**2 = 0.
0, 1
Let c(j) = 2*j**2 + 2*j - 9. Let l = -12 - -17. Let a(m) = m**2 + m - 4. Let s(u) = l*a(u) - 2*c(u). Factor s(f).
(f - 1)*(f + 2)
Let 0 - 4*k**2 + 11/3*k**3 + 4*k**4 - 7/3*k**5 - 4/3*k = 0. Calculate k.
-1, -2/7, 0, 1, 2
Suppose -2 = i - 7. Suppose -5*s + 21 = -l + i, 0 = 3*l - 3*s. Solve 3*g**2 - 3*g**2 - 3*g**2 + l*g**2 - g**4 = 0 for g.
-1, 0, 1
Let y(f) be the first derivative of -1/2*f**4 - 8*f 