
Let m = 63 - 57. Factor -22*x**3 + 16 + 18*x**2 + 51*x - 135*x + 66*x**2 + m*x**3.
-4*(x - 4)*(x - 1)*(4*x - 1)
Suppose -g + 4 = -j + 1, -4*j - 3*g + 23 = 0. Suppose -j*i + 7 = 3. Factor 0*v - 2/3*v**i + 0.
-2*v**2/3
Let m be (-3)/(-15) + (6/(-3))/(-10). Suppose 1/5*i**2 - 3/5 + m*i = 0. What is i?
-3, 1
Let y(z) be the first derivative of -13/7*z**3 - 18 - 108/7*z + 3/28*z**4 + 72/7*z**2. Factor y(t).
3*(t - 6)**2*(t - 1)/7
Let x be -8 + 0 - 14678/(-895). Factor -18/5*s**3 - x*s**2 - 8/5 - 32/5*s.
-2*(s + 1)*(3*s + 2)**2/5
Let q = 11329/9912 + -45/472. Let 2/21*n**3 - 10/21 - 2/3*n**2 + q*n = 0. What is n?
1, 5
Suppose -1899 = -7*i - 275. Let s be 6/(-39) - (i/(-156) - 0). Find u, given that 4*u**2 - s*u**3 + 4/3 - 4*u = 0.
1
Suppose 8*y**2 + 0 + 1/3*y**3 + 0*y = 0. What is y?
-24, 0
Let j(h) be the third derivative of -4*h**7/105 + 4*h**6/45 + h**5/60 - h**4/12 - 7*h**3/3 + 9*h**2. Let z(n) be the first derivative of j(n). Factor z(x).
-2*(x - 1)*(4*x - 1)*(4*x + 1)
Let s(b) be the first derivative of 1/2*b**2 + 1/5*b**5 + 0*b - 1/4*b**4 - 1/3*b**3 + 26. What is r in s(r) = 0?
-1, 0, 1
Let u(h) be the first derivative of 2*h**3/33 + 50*h**2/11 + 1250*h/11 - 2. Factor u(l).
2*(l + 25)**2/11
Let s(x) be the third derivative of -x**8/504 - 19*x**7/105 - 241*x**6/60 + 2521*x**5/90 - 220*x**4/3 + 100*x**3 + 28*x**2. Find w such that s(w) = 0.
-30, 1
Let s be (-350 + 346)*(189/(-96))/3. Solve 0 - 3/2*w + 9/2*w**2 + s*w**3 = 0.
-2, 0, 2/7
Let o(m) = m**2 + m - 1. Let k(y) = -7*y**2 - 7*y + 5. Let f(g) = -k(g) - 6*o(g). Let p(x) = -4*x**2 - 17*x + 31. Let d(q) = -15*f(q) - 3*p(q). Factor d(i).
-3*(i - 6)**2
Let z = -47 - -57. Factor m**2 - z*m**5 - m**4 - m**3 + 3*m**5 + 8*m**5.
m**2*(m - 1)**2*(m + 1)
Let g(w) be the first derivative of -w**6/72 + 5*w**5/12 - 125*w**4/24 - 20*w**3/3 - 18. Let s(m) be the third derivative of g(m). Factor s(h).
-5*(h - 5)**2
Let z(c) be the first derivative of -c**5/5 + 3*c**4/4 - 2*c**2 + 450. Factor z(i).
-i*(i - 2)**2*(i + 1)
Let x(z) be the first derivative of 0*z**3 - 2/5*z**2 + 1/20*z**4 - 1/100*z**5 + 6*z - 5. Let o(s) be the first derivative of x(s). Factor o(c).
-(c - 2)**2*(c + 1)/5
Let l(i) be the second derivative of 0*i**2 - 2 + 1/30*i**4 + 1/25*i**6 + 0*i**3 - 3/50*i**5 - 1/105*i**7 + 9*i. Factor l(v).
-2*v**2*(v - 1)**3/5
Let g(q) be the third derivative of -q**6/30 + 2*q**5/15 + 7*q**4/6 + 8*q**3/3 + 300*q**2. Factor g(n).
-4*(n - 4)*(n + 1)**2
Let x(d) = d**3 + 7*d**2 + 7*d + 3. Let n be x(-6). Let v be 16/n*-3 - 2. Find j, given that 15 - 2*j - 30 - j**2 + v = 0.
-1
Let i be 2 + -2 + 12/2. Suppose 4*u - 8 = 2*u. Solve -l**2 + u*l + i - 8 - 2 = 0.
2
Let d be 6/(-8)*5/(-6). Let x(h) be the first derivative of d*h**2 + 1/6*h**3 - 1/4*h**4 + 4 - 1/24*h**6 + 1/2*h - 1/5*h**5. Factor x(t).
-(t - 1)*(t + 1)**3*(t + 2)/4
Let m(b) = -b**3 + 57*b**2 - 112*b + 112. Let k be m(55). Factor -2/5*t**3 + 6/5*t + 0 - 4/5*t**k.
-2*t*(t - 1)*(t + 3)/5
Let g(c) be the first derivative of c**3/9 + 130*c**2/3 + 16900*c/3 - 144. Factor g(p).
(p + 130)**2/3
Let c(h) be the third derivative of -h**7/840 - h**6/20 - 9*h**5/10 - 17*h**4/24 + 20*h**2. Let n(b) be the second derivative of c(b). Factor n(w).
-3*(w + 6)**2
Suppose 3*g - 8*g + 15 = 3*l, 2*l - 4*g = -12. Let v(z) be the second derivative of 5*z + 0*z**3 + l*z**4 - 1/40*z**5 + 0 + 0*z**2. Let v(h) = 0. What is h?
0
Let i be (4/(-14))/(15/(-42)). Let c = -3/10 + i. Determine g, given that -2*g**3 - c*g**4 + 0 - 5/2*g**2 - g = 0.
-2, -1, 0
Suppose 14 = d + 3. Let j(w) = 6 + d + 18*w + 6*w**2 - 5. Let a(k) = 2*k**2 + 6*k + 4. Let o(t) = 10*a(t) - 3*j(t). Factor o(h).
2*(h + 1)*(h + 2)
Factor -1/5*s**3 + 1/5*s + 13/5 - 13/5*s**2.
-(s - 1)*(s + 1)*(s + 13)/5
Let n = -2663 - -66587/25. Let l(v) be the first derivative of 3/10*v**2 + 4 - 6/5*v + 6/5*v**3 - n*v**5 + 3/10*v**6 - 3/5*v**4. Find h, given that l(h) = 0.
-1, -2/3, 1
Suppose 39 = -3*x - 5*u, -90 = -4*x + 2*u - 64. Determine h so that 0 - 3/2*h**4 + h**3 - 4*h + 6*h**x = 0.
-2, 0, 2/3, 2
Let u = 300 + -294. Let y(l) be the third derivative of 0*l**3 - 10*l**2 + 0*l**4 + 1/30*l**5 - 1/80*l**u + 0 - 1/420*l**7 + 0*l. Factor y(z).
-z**2*(z - 1)*(z + 4)/2
Let n(a) be the third derivative of 0 + 0*a + 3*a**2 - 1/120*a**4 + 1/300*a**5 - 1/5*a**3. Determine t, given that n(t) = 0.
-2, 3
Let u(y) = -y**2 - 6*y - 5. Let i be u(-4). Solve 5 + 36*o**i + 169*o**3 + 390*o**2 - 80*o**4 - 75*o**5 + 35 + 220*o = 0 for o.
-1, -2/3, -2/5, 2
Let p(v) be the second derivative of -2*v**7/105 - v**6/75 + 3*v**5/50 + v**4/30 - v**3/15 + v - 11. Find o, given that p(o) = 0.
-1, 0, 1/2, 1
Let q be (-30)/(-120) - 3/12. Let w(b) be the third derivative of 0*b + 1/780*b**6 - 1/156*b**4 - 4*b**2 + q*b**3 + 0 + 0*b**5. Factor w(o).
2*o*(o - 1)*(o + 1)/13
Let c(x) = -x**3 - 2*x**2 + 28*x + 23. Let a be c(-6). Let f be 2/(-30) - a*8/40. Factor -6/5 - f*q**2 - 4/5*q.
-2*(q + 3)**2/15
Let y = 287 + -284. Suppose -5*k + 5 = -r - 9, -5*r = 2*k + 16. Factor 98*s + 18*s**3 - y*s**k - 27*s**4 - 98*s.
-3*s**2*(3*s - 1)**2
Factor 14*p**3 - 5*p**2 - 3*p**3 - 6*p**3 - 2*p**3 - 6*p - 2*p**3.
p*(p - 6)*(p + 1)
Let 710*c + 2/13*c**3 + 30246/13 - 278/13*c**2 = 0. Calculate c.
-3, 71
Let p(c) be the third derivative of -c**7/2520 - c**6/240 + 7*c**4/12 - 14*c**2. Let k(m) be the second derivative of p(m). Find h such that k(h) = 0.
-3, 0
Let k(w) = -w**3 + 2*w**2 + 98*w + 16. Let a be k(11). Let s(i) be the first derivative of 10*i + 6 + 55/2*i**2 + 85/4*i**4 + a*i**5 + 35*i**3. Factor s(x).
5*(x + 1)**3*(5*x + 2)
Let d = 35 + -14. Let v = d + -15. Factor 4 - 6*h**3 - 4 - 3*h**5 - 3*h**4 + v*h**5.
3*h**3*(h - 2)*(h + 1)
Factor -64/7 - 12/7*t**2 - 48/7*t - 1/7*t**3.
-(t + 4)**3/7
Let i(m) be the first derivative of -4*m**5/15 + 6*m**4 + 52*m**3/3 + 40*m**2/3 - 255. Factor i(y).
-4*y*(y - 20)*(y + 1)**2/3
Suppose 0 = -228*z + 218*z + 50. Let v(u) be the third derivative of 2/21*u**4 + 0*u - 1/210*u**5 - z*u**2 - 16/21*u**3 + 0. Determine f, given that v(f) = 0.
4
Let d(z) be the second derivative of -z**8/336 + z**7/70 - z**6/40 + z**5/60 - 2*z**2 + 9*z. Let b(f) be the first derivative of d(f). Solve b(u) = 0.
0, 1
Factor -135/7 - 54/7*c - 3/7*c**2.
-3*(c + 3)*(c + 15)/7
Let m(l) be the first derivative of l**7/2100 + l**6/900 - l**5/150 - 7*l**3 + 17. Let n(a) be the third derivative of m(a). Factor n(h).
2*h*(h - 1)*(h + 2)/5
Let k = -11 + 21. Suppose -k = -6*n + 2. Let -2*f - 11*f**2 + 5*f**2 + 3*f**n + f**2 = 0. Calculate f.
-1, 0
Suppose 0 = -17*x + 3*x + 28. Let o(j) be the second derivative of 2*j - 1/100*j**5 + 0 + 0*j**3 - 1/20*j**4 + 0*j**x. Suppose o(w) = 0. Calculate w.
-3, 0
Let j = 817/189 + -55/27. Let v(h) be the first derivative of -j*h**2 - 24/7*h - 10 - 2/3*h**3 - 1/14*h**4. Factor v(b).
-2*(b + 2)**2*(b + 3)/7
Let -9*q**3 - 114*q**3 - 51*q**4 + 159*q**2 + 3*q**5 - 676879 + 240*q + 676651 = 0. Calculate q.
-2, 1, 19
Suppose 2*z - 3 = 4*p - 11, 4*z = -5*p + 23. Factor 9*f**2 - 5*f**2 - 3*f**2 - p*f**3 - 7*f**2.
-3*f**2*(f + 2)
Let n(m) be the first derivative of -m**4/18 + 10*m**3/27 + 2*m**2/3 - 183. Let n(p) = 0. What is p?
-1, 0, 6
Let o(w) = -w. Let u be o(-12). Factor 1 - 3 - u*q**2 - 3 + 2 + 15*q.
-3*(q - 1)*(4*q - 1)
Factor -4/3*d**4 - 16/3*d**3 + 8/3 - 4/3*d**2 + 14/3*d + 2/3*d**5.
2*(d - 4)*(d - 1)*(d + 1)**3/3
Factor 110/7*r + 2/7*r**3 + 12 + 4*r**2.
2*(r + 1)*(r + 6)*(r + 7)/7
Let j(q) be the third derivative of -q**6/30 + 4*q**5/5 - 55*q**4/8 + 175*q**3/6 + 344*q**2. Factor j(w).
-(w - 7)*(2*w - 5)**2
Let b(j) be the second derivative of 1/4*j**4 + 1/10*j**5 + 3*j - 2*j**2 - 1/30*j**6 - 2/3*j**3 + 0. Suppose b(d) = 0. What is d?
-1, 2
Let s(z) = 11*z**2 + 40*z - 6. Let i(b) = -15*b**2 - 41*b + 8. Let x(a) = -3*i(a) - 4*s(a). Factor x(o).
o*(o - 37)
Let w(b) be the first derivative of -2*b**6/3 + 144*b**5/5 - 323*b**4 - 48*b**3 + 648*b**2 - 513. Let w(i) = 0. Calculate i.
-1, 0, 1, 18
Let d be ((-6)/25*-5)/(32/40). Let s(v) be the first derivative of -v**3 - 6 + d*v**2 + 6*v. What is a in s(a) = 0?
-1, 2
Let y be (5/(-10))/(1/(-12)). Let h be (2 - 1)*y/2. Let -9 + 5*b**2 + 7*b + 12 - 2*b**h + 3*b**3 = 0. What is b?
-3, -1
Let i = 418 + -415. Let w(u) be the second derivative of 0*u**2 + 1/30*u**4 - 2*u + 0 + 0*u**i + 1/100*u**5