*(q - 2)*(q - 1)
Suppose 3*v - 2*j = 10, 2*v - 9 - 3 = 4*j. Let a be v/4 - 0/9. Factor 3/2*b**2 + 3/2*b**3 + 1/2*b + 0 + a*b**4.
b*(b + 1)**3/2
Let x(h) be the second derivative of 5*h**4/16 + 13*h**3/8 - 9*h**2/4 - 2*h. Determine u, given that x(u) = 0.
-3, 2/5
Suppose -3*n - 2*n = -3*f - 3, -3*n + 29 = 5*f. Factor -2*d**2 + d - d + d + n*d**2.
d*(d + 1)
Suppose 11*t = 36 + 19. Factor 0*r**2 + 0 - 2/3*r**4 + 0*r + 0*r**3 + 2/3*r**t.
2*r**4*(r - 1)/3
Let l(d) = 4*d**2 - 4*d - 3. Let s be -2 - (-2 - (-2 + -2)). Let o(y) = 5*y**2 + 3*y + 0*y - 8*y - 4. Let n(f) = s*l(f) + 3*o(f). Factor n(z).
-z*(z - 1)
Let r be 63/18 + (-3 - -2) + -2. Find s, given that 0 + 3/2*s**2 + r*s + 3/2*s**3 + 1/2*s**4 = 0.
-1, 0
Let s = -1 + 5. Let k(m) = -m + 6. Let f be k(3). Factor -1/2*n + 0 - 1/4*n**s + 1/4*n**2 + 1/2*n**f.
-n*(n - 2)*(n - 1)*(n + 1)/4
Let o(j) = 24*j**2 - 14*j - 24. Let u(b) = 5*b**2 - 3*b - 5. Let r(k) = 6*o(k) - 28*u(k). Factor r(y).
4*(y - 1)*(y + 1)
Let u(n) be the first derivative of 3*n**4/4 - 4*n**3 + 9*n**2/2 + 31. Factor u(v).
3*v*(v - 3)*(v - 1)
Suppose -15 = -4*p - i, p - i = -3*p + 25. Let z = -3 + p. Factor -z*o**2 + 5 + 2*o**4 - 5.
2*o**2*(o - 1)*(o + 1)
Let w(u) = -5*u**3 + 3*u**2 + 21*u + 13. Let c(z) = 16*z**3 - 8*z**2 - 64*z - 40. Let o(n) = -6*c(n) - 20*w(n). Suppose o(j) = 0. Calculate j.
-1, 5
Let t(d) be the third derivative of 0*d + 1/120*d**6 + 5/96*d**4 + 0 - 1/24*d**3 + 3*d**2 - 1/30*d**5. Factor t(m).
(m - 1)*(2*m - 1)**2/4
Suppose -22 - 38 = -5*q. Factor 2*o**4 - q*o**2 - 2*o**4 + 3*o - 6*o**4 - 6*o**4 + 18*o**3 + 3*o**5.
3*o*(o - 1)**4
Suppose 9*s - 30 = 3*s. Let p(h) be the third derivative of 1/135*h**7 + 0 + 23/540*h**6 + 1/10*h**s + 13/108*h**4 + 0*h - h**2 + 2/27*h**3. Factor p(l).
2*(l + 1)**3*(7*l + 2)/9
Let g(m) be the third derivative of m**8/672 + m**7/420 - m**6/240 - m**5/120 + m**2. Factor g(t).
t**2*(t - 1)*(t + 1)**2/2
Let m = -13 - -17. Factor 2*p**3 - 11*p**3 - p**3 - 4 + m*p**2 + 10*p.
-2*(p - 1)*(p + 1)*(5*p - 2)
Let q(r) be the third derivative of -r**7/42 - r**6/24 + r**5/2 + 5*r**4/6 - 20*r**3/3 - 20*r**2. Factor q(o).
-5*(o - 2)*(o - 1)*(o + 2)**2
Let t(b) be the second derivative of b**4/84 - b**3/7 + 5*b**2/14 - 17*b. Suppose t(z) = 0. What is z?
1, 5
Let i(w) be the first derivative of 81*w**4/20 + 42*w**3/5 - 34*w**2/5 + 8*w/5 - 41. Find s such that i(s) = 0.
-2, 2/9
Solve 11*j**2 + 0*j + 4*j**2 + 0*j**2 - 21*j**3 + 6*j = 0.
-2/7, 0, 1
Let u(c) be the second derivative of c**7/735 - c**6/105 + 2*c**5/105 + 2*c**2 - c. Let w(j) be the first derivative of u(j). Factor w(z).
2*z**2*(z - 2)**2/7
Factor -1/6*j**2 - 1/6 - 1/3*j.
-(j + 1)**2/6
Let j = 14 + -12. Factor -5 - i**j - i + 5.
-i*(i + 1)
Let m(y) be the second derivative of 0*y**4 + 0 + 1/15*y**5 + 0*y**2 + 2*y + 1/45*y**6 + 0*y**3. Factor m(u).
2*u**3*(u + 2)/3
Let m be 1 - (3 + 2)/(-5). What is g in -4/5 + 8/5*g**m - 6/5*g**3 + 2/5*g = 0?
-2/3, 1
Let f = -7 - -10. Suppose 0*t**f + t**2 - 2*t**3 - t + 2*t = 0. What is t?
-1/2, 0, 1
Let 15/2*t**5 - 9/2*t**3 + 21/2*t**2 - 3*t - 21/2*t**4 + 0 = 0. Calculate t.
-1, 0, 2/5, 1
Let w be (186/(-27) + 7)*3. Solve -3*y**2 + 9*y + w*y**3 - 9 = 0 for y.
3
Let n(m) be the first derivative of m**4/2 - 4*m**3/3 + m**2 - 40. Suppose n(u) = 0. Calculate u.
0, 1
Let s = 188 + -186. Factor 0*v**s + 0 + 2/7*v**3 - 2/7*v.
2*v*(v - 1)*(v + 1)/7
Let g(w) be the third derivative of -w**8/1680 - w**7/840 + w**6/360 + w**5/120 + 5*w**3/6 - 5*w**2. Let q(c) be the first derivative of g(c). Factor q(n).
-n*(n - 1)*(n + 1)**2
Let t be 1*(-2)/(-1) + 4. Let m(g) = -g + 8. Let k be m(t). Solve 3*f**k + 0*f**2 + f**4 - 2*f**2 + 2*f**3 = 0 for f.
-1, 0
Let a be -3*(-32)/189 - (-2)/(-9). Factor 4/7*j - a*j**2 + 0.
-2*j*(j - 2)/7
Let r = -2 + 7/3. Let z(t) be the second derivative of 1/3*t**6 + 0*t**3 + 0*t**2 + 0 + 3/10*t**5 + 2*t - r*t**4. Find x, given that z(x) = 0.
-1, 0, 2/5
Let x = 95 - 664/7. Let n(z) be the second derivative of 2/105*z**6 - 1/42*z**4 + 1/7*z**3 - 3/70*z**5 + 0 + z - x*z**2. Determine q, given that n(q) = 0.
-1, 1/2, 1
Let c(w) = w**2 - 8*w + 8. Let h = 11 - 4. Let l be c(h). Find g, given that 0 + 10*g - 3 + 14*g**2 - l = 0.
-1, 2/7
Let k be 4*(1 - 0) - (-97)/(-97). Factor -2/3 - k*p - 3*p**2.
-(3*p + 1)*(3*p + 2)/3
Suppose 5*c = 2*c - 93. Let o = c - -125/4. Let o - 1/2*w - 1/4*w**4 + 1/2*w**3 + 0*w**2 = 0. What is w?
-1, 1
Let l = -83 + 250/3. Suppose 1/3*f**2 + 0*f - l = 0. What is f?
-1, 1
Determine g, given that 0 - 40*g**3 + 8*g**2 + 0 + 23*g**4 + 27*g**4 = 0.
0, 2/5
Suppose 4*h - 2*h = -5*h. Determine b, given that 1/2*b**4 + 0*b + 1/2*b**3 + h - 1/2*b**5 - 1/2*b**2 = 0.
-1, 0, 1
Suppose 14*o = 11*o + 300. Let y be (-8)/14 - o/(-126). Factor 2/9*d**2 + y*d + 0.
2*d*(d + 1)/9
Let h(j) be the second derivative of 0*j**2 - 1/5*j**5 + 0 + 1/6*j**4 + 0*j**3 + 1/20*j**6 - 3*j. Factor h(x).
x**2*(x - 2)*(3*x - 2)/2
Let u(z) be the first derivative of -5*z**6/6 + 10*z**4 + 10*z**3 - 35*z**2/2 - 30*z + 40. Suppose u(i) = 0. What is i?
-2, -1, 1, 3
Let f(p) be the third derivative of 1/108*p**4 + 0 + 0*p**3 + 3*p**2 + 0*p - 1/270*p**5. Determine b so that f(b) = 0.
0, 1
Let r(f) be the second derivative of f**4/8 - 3*f**3/4 + 3*f**2/2 - 7*f. Factor r(k).
3*(k - 2)*(k - 1)/2
Let h(i) be the second derivative of i**4/6 - 16*i**3/3 + 64*i**2 + 7*i. Factor h(q).
2*(q - 8)**2
Let c(j) = -2*j**2 + 6*j + 2. Let v(l) = -17*l**2 + 4*l + 17. Let o(b) = 6*b**2 - b - 6. Let a(h) = 11*o(h) + 4*v(h). Let m(z) = 6*a(z) - 5*c(z). Factor m(x).
-2*(x - 1)*(x + 1)
Let w(t) be the first derivative of 6*t**2 - t - 4. Let n be w(1). Factor 2*h**4 + n*h**3 - 8*h - 5*h**4 - 16*h - 36*h**2 - 29*h**3.
-3*h*(h + 2)**3
Let b(n) = -n**2 + 10*n + 2. Let r be b(8). Factor 8*k + 9*k - 2*k**2 + 11*k**2 + 16*k + r.
3*(k + 3)*(3*k + 2)
Factor 0*h**4 + 1/7*h**5 + 0 - 2/7*h**3 + 1/7*h + 0*h**2.
h*(h - 1)**2*(h + 1)**2/7
Let y = -3 - -2. Let d(z) = 6 + 0*z**4 + z**2 - z**3 + z + 5*z**4 + 0*z**4. Let c(p) = -p**4 - 1. Let u(s) = y*d(s) - 6*c(s). Factor u(x).
x*(x - 1)*(x + 1)**2
Suppose -2*n + 0*i + 6 = i, -2*n = 3*i - 6. Let r = -32 + 37. Factor -r*d**4 - 1 + 5*d + d**5 + 0 + 5*d**3 - 10*d**2 + 5*d**n.
(d - 1)**5
Let p = 13 - 11. Let t(j) = -3*j**4 - 6*j**3 - 7*j**2 - 7*j + 7. Let c(v) = -v**4 - 2*v**3 - 2*v**2 - 2*v + 2. Let m(r) = p*t(r) - 7*c(r). Factor m(l).
l**3*(l + 2)
Let v = -13 + 15. Determine z, given that 14 - 3*z**2 - 14 + 2*z**v - z = 0.
-1, 0
Let n = 10 + -8. Suppose n*r - 24 = -4*r. What is c in 0 - 4/5*c**2 - 2/5*c**3 + 2/5*c + 4/5*c**r = 0?
-1, 0, 1/2, 1
Let d be 1 - 1*(-2)/10. Determine x, given that -d*x**2 + 4/5 - 2*x = 0.
-2, 1/3
Let m(n) be the first derivative of n**5/5 - 9*n**4/8 + 7*n**3/3 - 9*n**2/4 + n - 41. Factor m(w).
(w - 2)*(w - 1)**2*(2*w - 1)/2
Let w(h) be the first derivative of -9/2*h**6 - 4*h**2 + 0*h - 45/2*h**4 - 81/5*h**5 - 44/3*h**3 - 2. Solve w(z) = 0.
-1, -2/3, 0
Let x(r) be the second derivative of -r**5/30 + r**3/3 - 2*r**2/3 - 2*r. Factor x(y).
-2*(y - 1)**2*(y + 2)/3
Let l = 254 + -2284/9. Solve 2/9*x**3 + 2/9*x**2 - 2/9*x - l = 0.
-1, 1
Let b be (-4)/8 + 1711/(-14). Let k = b - -123. Factor 0 + k*l**2 + 4/7*l.
2*l*(l + 2)/7
Let q(s) be the second derivative of s**4/3 + 8*s**3/3 + 6*s**2 + 3*s. Let q(c) = 0. What is c?
-3, -1
Suppose -4*i + 6 = -2. Determine z, given that 11*z - 10*z**2 - 2*z + 2*z**i - 13*z - z**4 - 5*z**3 = 0.
-2, -1, 0
Suppose -8*i + 6*i = -4. Factor 19*f - 40*f**3 - 39*f + 144*f**i + 4*f**4 - 196*f + 108.
4*(f - 3)**3*(f - 1)
Let m(u) be the first derivative of -8/11*u**3 + 0*u + 3 - 8/11*u**2 - 3/11*u**4 - 2/55*u**5. Factor m(z).
-2*z*(z + 2)**3/11
Let s(l) = 12*l + 24. Let m(b) = b**2 - 25*b - 47. Let v(x) = 4*m(x) + 7*s(x). Factor v(z).
4*(z - 5)*(z + 1)
Factor 2/7*g**2 + 8/7*g + 6/7.
2*(g + 1)*(g + 3)/7
Suppose 2*h + 5*r = 10, 0 = 3*h - 2*r + 4 - 0. Let u be ((-6)/(-16))/(21/14). Factor h + u*f + 1/4*f**2.
f*(f + 1)/4
Suppose -f + 5*w - 8 = 0, 5*f - 14 = f - 3*w. Let -4/5 + 2/5*h**f - 2/5*h = 0. What is h?
-1, 2
Let j(r) = -4*r - 2 + 3*r + 3. Let f(i) = 1 - i - 11*i**2 + 9*i**2 - 6. Let y(g) = -f(g) - 3*j(g). Factor y(v).
2*(v + 1)**2
Let y(k) = -k**2 + k + 60. Let o be y(8). Find q such that -16/7 - 24/7*q - 4/7*q**2 + 2/7*q**o + 6/7*q**3 = 0.
-2, -1, 2
Let q(c