m(n) = n**2 + 10*n + 10. Let j be m(-10). Factor 2 + 13*p**2 - 6*p**3 + 9*p**2 - 8*p**2 - j*p.
-2*(p - 1)**2*(3*p - 1)
Suppose 4 = -4*o - 0. Let l = 4 + o. Suppose 4/7*q**2 + 0 + 2/7*q**l + 2/7*q = 0. What is q?
-1, 0
Let t = -32 + 38. Let f(p) be the second derivative of 0 - 1/10*p**5 + 0*p**3 + 3*p + 0*p**2 - 1/30*p**t - 1/12*p**4. Factor f(g).
-g**2*(g + 1)**2
Factor -3/7*t**2 - 9/7*t + 0.
-3*t*(t + 3)/7
Let u(j) = -10*j**5 + 10*j**4 + 11*j**3 - 11*j**2 - j + 10. Let m(r) = -r**5 + r**4 + r**3 - r**2 + 1. Let d(t) = -18*m(t) + 2*u(t). Factor d(i).
-2*(i - 1)**3*(i + 1)**2
Let h(s) = 3*s**2 + 5*s - 4. Let z(g) = -g**2 - g + 1. Let l(j) = h(j) + 4*z(j). Suppose l(f) = 0. Calculate f.
0, 1
Suppose -1 - 180*r + 180*r + r**2 = 0. Calculate r.
-1, 1
Suppose -10*v**5 + 2*v**5 + 4*v**2 + 12*v**4 + 3*v**5 + 12*v**3 + 9*v**5 = 0. What is v?
-1, 0
Let c(u) = u**3 - u**2 + u - 3. Let s be c(0). Let y be 0 - 2*s/9. Find p such that 0*p + 2/3*p**2 - y*p**3 + 0 = 0.
0, 1
Let f(o) = 10*o**4 + 6*o**3 - 15*o**2 - 25*o + 7. Let z(p) = -9*p**4 - 6*p**3 + 15*p**2 + 24*p - 6. Let g(w) = 6*f(w) + 7*z(w). Factor g(r).
-3*r*(r - 2)*(r + 1)*(r + 3)
Determine o, given that 2/9*o**2 + 2/9 - 4/9*o = 0.
1
Suppose -4*p - 5*n + 55 + 37 = 0, -2*n + 115 = 5*p. Factor p + 4*y**2 - 23 + y - 5*y.
4*y*(y - 1)
Let h(z) be the second derivative of -z**6/10 + 3*z**5/5 - 3*z**4/4 - 2*z**3 + 6*z**2 + 4*z. Factor h(f).
-3*(f - 2)**2*(f - 1)*(f + 1)
Let w(n) be the first derivative of 75*n**5 + 200*n**4 + 210*n**3 + 108*n**2 + 27*n + 18. Factor w(j).
(3*j + 1)*(5*j + 3)**3
Let c = -10 + 14. Let t(s) be the third derivative of 0*s**3 + 1/120*s**5 + 0 - 1/140*s**7 + 0*s + 2*s**2 - 1/120*s**6 + 0*s**c. What is q in t(q) = 0?
-1, 0, 1/3
Let a(r) be the second derivative of -r**6/15 - 14*r**5/5 - 37*r**4 - 364*r**3/3 - 169*r**2 + 3*r + 3. Factor a(s).
-2*(s + 1)**2*(s + 13)**2
Factor -1/8*v**5 + 0*v + 0*v**2 + 0 + 0*v**3 - 3/8*v**4.
-v**4*(v + 3)/8
Let z(b) = -b**3 + 6*b**2 - 2*b - 5. Let y be 2/2*(5 + 0). Let k be z(y). Factor -k*v**4 + 3*v**5 - v**3 + 13*v**3 + 0*v + v - 6*v**2.
v*(v - 1)**3*(3*v - 1)
Let a be 172/(-6)*(-10)/(-55). Let p = -50/11 - a. Factor -2/3 + p*s**2 + 0*s.
2*(s - 1)*(s + 1)/3
Let u = 2/313 - -620/939. Let 0 - 2/3*y**3 + 0*y + u*y**2 = 0. What is y?
0, 1
Suppose 0 = 4*w - 5*q - 19 - 8, 4*w + 4*q = 0. Factor -3*l**2 - 2*l**4 - l**2 + 4*l**2 + 6*l**w - 8*l.
-2*l*(l - 2)**2*(l + 1)
Let h(c) be the second derivative of -c**8/2240 - 3*c**7/560 - c**6/40 - c**5/20 + c**4/12 + 3*c. Let o(f) be the third derivative of h(f). Factor o(x).
-3*(x + 2)**2*(2*x + 1)/2
Let d(k) be the third derivative of -k**8/168 + k**7/105 + k**6/30 - k**5/15 - k**4/12 + k**3/3 - 3*k**2. Suppose d(p) = 0. Calculate p.
-1, 1
Let v = -7 + 11. Factor -11*h**5 - 3*h**3 - 2*h**v + 13*h**5 - h**3.
2*h**3*(h - 2)*(h + 1)
Let i(t) be the first derivative of 8/15*t**6 + 38/5*t**2 + 4 - 8/5*t + 241/20*t**4 - 46/3*t**3 - 104/25*t**5. Determine b so that i(b) = 0.
1/4, 2
Let z = 13/24 + 1/8. Suppose -1/3*a**2 - 1/3 - z*a = 0. Calculate a.
-1
Let k(j) be the first derivative of 3*j**5/40 - j**4/16 - j**3/8 + j**2/8 - 2. Factor k(q).
q*(q - 1)*(q + 1)*(3*q - 2)/8
Suppose -4*c - 4*g = -28, 5*g + 1 = 11. Factor 0 + 1/2*v**4 + 0*v**3 + 1/4*v**c - 1/4*v - 1/2*v**2.
v*(v - 1)*(v + 1)**3/4
Suppose 2*m = -3*j, -2*m = -0*j + 2*j + 2. Let 4*c - 4 + 0*c + j + c**2 - 3*c = 0. Calculate c.
-2, 1
Solve -2*u + 3*u**2 + 1/2*u**4 - 2*u**3 + 1/2 = 0 for u.
1
Let f(c) be the second derivative of -35*c**4/36 - 115*c**3/18 - 5*c**2 + c + 14. Factor f(s).
-5*(s + 3)*(7*s + 2)/3
Let g be 26/13 + (-4)/3. Let l(d) be the first derivative of 1/2*d**4 + g*d**3 + 2 + 0*d + 0*d**2. Factor l(s).
2*s**2*(s + 1)
Let d(h) be the second derivative of h**4/42 + 6*h**3/7 + 81*h**2/7 + 21*h. Factor d(f).
2*(f + 9)**2/7
Let h(z) be the second derivative of -z**2 + 2/3*z**3 + 0*z**4 + 2*z + 1/15*z**6 + 0 - 1/5*z**5. What is m in h(m) = 0?
-1, 1
Let v(b) be the first derivative of -3*b**5/5 + 3*b**4/4 + 3*b**3 - 15*b**2/2 + 6*b + 18. Factor v(y).
-3*(y - 1)**3*(y + 2)
Let c(d) be the second derivative of -d**5/4 - 5*d**4/3 + 29*d. Factor c(n).
-5*n**2*(n + 4)
Let v be (-2 - -4) + (-345)/130. Let i = -2/13 - v. Find d such that -i*d + 17/4*d**3 + 3/4*d**2 + 0 + 3*d**4 = 0.
-1, -2/3, 0, 1/4
Let d(b) = b**3 - 7*b**2 + 9*b - 6. Let n be d(7). Let h = -39 + n. Determine a, given that 3*a + a - h*a**2 + 8*a - 2 = 0.
1/3
Let j(r) = 5*r**4 - 3*r**3 - r**2 - r. Let u(s) = -s**4 + s**3. Let v(m) = -j(m) - 4*u(m). Factor v(x).
-x*(x - 1)*(x + 1)**2
Let h(k) be the second derivative of -k**8/36960 + k**7/13860 - 5*k**4/12 - k. Let z(m) be the third derivative of h(m). Solve z(d) = 0 for d.
0, 1
Factor 24*n - 8*n + 1708 + 0*n**3 + 2*n**3 + 10*n**2 - 1700.
2*(n + 1)*(n + 2)**2
Let w(k) be the first derivative of -3*k**4/16 - k**3 - 15*k**2/8 - 3*k/2 + 15. Suppose w(h) = 0. What is h?
-2, -1
Let y(r) be the first derivative of -r**5/30 + r**4/3 - 4*r**3/3 - 9*r**2/2 - 8. Let a(g) be the second derivative of y(g). Factor a(c).
-2*(c - 2)**2
Let k(r) be the second derivative of -r**4/4 - 2*r**3 + 15*r**2/2 - 16*r. Find d such that k(d) = 0.
-5, 1
Let y(a) = -8*a**4 - 4*a**3 + 12*a**2 + 4*a + 4. Let x(g) = g**4 - g**2 - g - 1. Let n(c) = -4*x(c) - y(c). Factor n(b).
4*b**2*(b - 1)*(b + 2)
Let m(u) be the second derivative of -u**5/80 + u**4/24 + u**3/24 - u**2/4 + 5*u. Factor m(n).
-(n - 2)*(n - 1)*(n + 1)/4
Let k(u) = -5*u**2 + u + 7. Suppose -2*l - 14 = -3*l. Let n(c) = 24*c**2 - 4*c - 34. Let g(v) = l*k(v) + 3*n(v). Let g(x) = 0. What is x?
-2, 1
Let s = -277/4 - -70. Let x be 2 + (0 - -1 - (8 - 7)). Solve 0 - s*o**4 - 1/4*o - 5/4*o**x - 7/4*o**3 = 0 for o.
-1, -1/3, 0
Let b = -10 + 14. Let r be (4/5)/(b/20). Find h such that 1/3*h + 0 - 1/3*h**r + h**3 - h**2 = 0.
0, 1
Let h(w) = 7*w**3 - 11*w**2 + 20*w - 16. Let l(n) = -57*n**3 + 87*n**2 - 159*n + 129. Let m(x) = -33*h(x) - 4*l(x). Factor m(p).
-3*(p - 2)**2*(p - 1)
Let t be 10/(-4)*(-32)/20. Let u(l) = -l**2 + 5*l + 2. Let b be u(t). Factor -b*w**3 + 3*w + w**5 + 0*w + 2*w**4 + w - 2*w**2 + w**5.
2*w*(w - 1)**2*(w + 1)*(w + 2)
Let g be 2/(-1 + -3)*-14. Let w = -5 + g. Factor 5 - 2*n**3 + 3*n + n**3 - 2*n**3 - w - 3*n**2.
-3*(n - 1)*(n + 1)**2
Let u(q) = -3*q**2 + 5*q - 10. Let b(a) = 12*a**2 - 21*a + 39. Let t be (6/15)/(1/(-10)). Let y(l) = t*b(l) - 15*u(l). Factor y(k).
-3*(k - 2)*(k - 1)
Let o be ((-2)/6)/(1/(-18)). Factor 2 + 5 + 3*m + 3*m**3 + o*m**2 - 7.
3*m*(m + 1)**2
Let p(w) = 2*w**5 - 2*w**4 - 10*w**3 - 2*w**2. Let d(n) = -n**3 - 9*n**4 + 8*n**4 + 2*n**3 - n**5. Let k(c) = -4*d(c) - p(c). Factor k(u).
2*u**2*(u + 1)**3
Suppose 0 = 5*z - 5*y - 20, -z + 10 - 3 = 2*y. Factor 2/5 - 4/5*i**2 - 2/5*i**z + 2/5*i**4 + 4/5*i**3 - 2/5*i.
-2*(i - 1)**3*(i + 1)**2/5
Factor 567*m**4 + 165*m**2 - 108*m - 513*m**3 + 197*m - 81*m**5 - 107*m.
-3*m*(m - 6)*(3*m - 1)**3
Let f = 53 - 53. Let y(k) be the third derivative of 3*k**2 - 1/120*k**6 + 0 + 0*k + 1/24*k**4 + 0*k**3 + f*k**5. Determine x, given that y(x) = 0.
-1, 0, 1
Suppose v + 1 = -1. Let d(r) = 4*r**2 + 4*r. Let l(q) = 3*q**2 + 3*q. Let h be (-2)/8 + 39/12. Let m(p) = h*l(p) + v*d(p). Solve m(u) = 0 for u.
-1, 0
Let a be (-5 - (-155)/40)*(-2)/3. Suppose 1/4*g + a*g**2 - 1/2 - 1/4*g**3 - 1/4*g**4 = 0. What is g?
-2, -1, 1
Let i(g) = 2*g**2 - 4*g + 11. Let j(w) = w**2 - 2*w + 6. Suppose 2*l + 9 = h, -2*l - 2*l + 15 = h. Let m(t) = h*j(t) - 6*i(t). Factor m(a).
-a*(a - 2)
Let k = 5/14 - -27/14. Suppose -k*r**4 + 24/7*r**3 + 4/7*r - 16/7*r**2 + 4/7*r**5 + 0 = 0. Calculate r.
0, 1
Let z(j) be the second derivative of -j**7/273 + 4*j**6/195 - 3*j**5/65 + 2*j**4/39 - j**3/39 + j. Factor z(k).
-2*k*(k - 1)**4/13
Suppose g = 3*g - 6. Factor 9*d**5 - d**4 - 2*d**2 - 2*d**g - 1 - 8*d**5 + 4*d**2 + d.
(d - 1)**3*(d + 1)**2
Let t(b) be the third derivative of -b**7/2520 + b**6/180 - b**5/30 + b**4/12 + b**2. Let y(h) be the second derivative of t(h). Factor y(f).
-(f - 2)**2
Let p(j) = -j**5 - 15*j**4 + 16*j**3 - 2*j**2 - 2*j + 2. Let h(w) = -w**5 - 30*w**4 + 31*w**3 - 5*w**2 - 5*w + 5. Let f(o) = -2*h(o) + 5*p(o). Factor f(l).
-3*l**3*(l - 1)*(l + 6)
Let o(f) = 4*f**3 - 9*f**2 + 8*f - 1. Let b(k) = k**3 - k**2 + k + 1. Let n(q) = -b(q) + o(q). Factor n(y).
(y - 1)*