 2
Let m(x) be the third derivative of -x**8/23520 + x**7/2940 - x**5/6 + 21*x**2. Let o(p) be the third derivative of m(p). Factor o(z).
-6*z*(z - 2)/7
Suppose 3*s + 2*s - l - 24 = 0, 5*s = -3*l + 8. Factor 2*r**2 - r**2 + s*r**3 - r**2 + 4*r**2.
4*r**2*(r + 1)
Let q(y) = 3*y**2 + 49*y + 16. Let h be q(-16). Factor 0*k + h + 7/3*k**4 + 3*k**3 + 2/3*k**2.
k**2*(k + 1)*(7*k + 2)/3
Suppose 0 = -o - 3*o + 36. Suppose -u + o = -1. Factor 3 + 6*i**2 + u*i + i**3 + 2*i**2 + i**3 + 1.
2*(i + 1)**2*(i + 2)
Let j(d) be the third derivative of d**5/90 + 56*d**4/9 + 12544*d**3/9 + 321*d**2. Factor j(m).
2*(m + 112)**2/3
Let s(k) be the third derivative of -k**7/315 + k**6/90 + 4*k**5/45 + 147*k**2. Factor s(t).
-2*t**2*(t - 4)*(t + 2)/3
Suppose 2*a + 14*l = 13*l + 4, -2*a = 2*l - 8. Let i(y) be the third derivative of 0*y**3 - 1/100*y**5 + 0*y + 3*y**2 - 1/40*y**4 + a. Factor i(v).
-3*v*(v + 1)/5
Let v(h) be the third derivative of 15*h**2 + 0*h + 1/280*h**7 - 1/80*h**5 - 1/160*h**6 + 0 + 0*h**3 + 0*h**4 + 1/448*h**8. Factor v(a).
3*a**2*(a - 1)*(a + 1)**2/4
Let s(f) be the third derivative of -f**5/300 - 17*f**4/10 - 1734*f**3/5 - 120*f**2. Factor s(x).
-(x + 102)**2/5
Let x = 241 + -3359/14. Let l(j) be the first derivative of -3 + 1/14*j**6 + x*j**4 + 15/14*j**2 - 3/7*j - 3/7*j**5 - 10/7*j**3. Factor l(y).
3*(y - 1)**5/7
Let f be 24/(-10)*(-2310)/2772. Factor 30/17*y**3 + 18/17*y**4 + 2/17*y + 14/17*y**f + 0.
2*y*(y + 1)*(3*y + 1)**2/17
Let f(m) = -2*m**4 - 21*m**3 - 13*m**2 + 16*m. Let d(b) = 2*b**4 + 11*b**3 + 7*b**2 - 8*b. Let k(j) = 5*d(j) + 3*f(j). What is p in k(p) = 0?
-1, 0, 1, 2
Let m(d) be the first derivative of d**6/360 + d**5/360 - d**4/36 + 10*d**3/3 - 9. Let v(c) be the third derivative of m(c). Solve v(h) = 0 for h.
-1, 2/3
Let l be (-6)/(-21) + 22*36/(-28). Let a be 16/l*(-14)/20. Let 0*y - a*y**2 + 0 = 0. What is y?
0
Let y be 261/(-174)*(-8)/6. Let t(j) be the first derivative of j - 2/3*j**3 + 1/5*j**5 + 0*j**y + 0*j**4 - 7. Factor t(c).
(c - 1)**2*(c + 1)**2
Let h(w) be the third derivative of w**8/840 + 2*w**7/105 + w**6/50 - 14*w**5/75 - 7*w**4/60 + 6*w**3/5 + w**2 - 160. Solve h(m) = 0 for m.
-9, -2, -1, 1
Let l(q) = 57*q + 1200. Let g be l(-21). Let 0 + 0*y + 2/11*y**g + 2/11*y**4 - 4/11*y**2 = 0. What is y?
-2, 0, 1
Let k(u) be the second derivative of -u**7/84 + u**6/30 + 3*u**5/10 - 5*u**4/3 + 8*u**3/3 + 34*u - 6. Factor k(a).
-a*(a - 2)**3*(a + 4)/2
Find d such that 0 - 253/5*d**3 - 33*d**2 + 90*d - 31/5*d**4 - 1/5*d**5 = 0.
-15, -2, 0, 1
Let w(u) = 2*u**2 + 4*u + 4. Let i be w(-3). Let g be 2/(-10) - (-22)/i. Factor -4*k**4 + 0*k**g - 47*k**3 + 4*k**2 + 4*k**5 + 43*k**3.
4*k**2*(k - 1)**2*(k + 1)
Let t(y) be the first derivative of 17 - 1/2*y - 3/8*y**4 + 5/6*y**3 - 1/4*y**2. What is h in t(h) = 0?
-1/3, 1
Let m(j) be the second derivative of -j**4/18 - 4*j**3 - 108*j**2 - 14*j. Factor m(t).
-2*(t + 18)**2/3
Let h(g) = -g. Let o be h(1). Let v be 12/78*o + 80/182. Solve v*i - 4/7 + 2/7*i**2 = 0 for i.
-2, 1
Let d(p) be the first derivative of p**4 - 20*p**3/3 - 12*p**2 - 35. Factor d(q).
4*q*(q - 6)*(q + 1)
Let y(m) be the second derivative of 3*m**7/112 - m**6/10 - 33*m**5/160 + 7*m**4/8 - 3*m**3/4 - m - 50. Let y(o) = 0. What is o?
-2, 0, 2/3, 1, 3
Let i(m) be the first derivative of -m**6/6 + 2*m**5 - 13*m**4/4 - 20*m**3 - 18*m**2 + 370. Factor i(w).
-w*(w - 6)**2*(w + 1)**2
Suppose -20*a - 2*a**2 + 17*a + 3*a**2 - 4 = 0. Calculate a.
-1, 4
Let o(l) be the first derivative of -36*l**5 - 573*l**4 + 652*l**3/3 + 178*l**2 - 104*l + 413. Suppose o(m) = 0. What is m?
-13, -2/5, 1/3
Let n(r) be the first derivative of -2/15*r**3 + 2/5*r**2 - 22 + 0*r - 1/10*r**4. Factor n(p).
-2*p*(p - 1)*(p + 2)/5
Let u = 493/5 - 1439/15. Factor 8/9 + 4/9*w**3 + u*w + 2*w**2.
2*(w + 2)**2*(2*w + 1)/9
Let l(j) = -22*j - 130. Let x be l(-6). Let u(p) be the second derivative of 0*p**3 + 0 + 0*p**4 + 1/100*p**5 + 1/150*p**6 + 0*p**x + 6*p. Factor u(z).
z**3*(z + 1)/5
Let q be 40/(-88)*(-2 - (-24)/15). Find o, given that -4/11*o**2 + q*o**3 + 0 - 6/11*o = 0.
-1, 0, 3
Solve 3 + 4*t**4 - 8*t - 13*t**2 + 9 + 8*t**3 + 7*t**2 - 10*t**2 + 0*t**3 = 0 for t.
-3, -1, 1
Let q(p) be the second derivative of 1/9*p**3 + 0 - 1/150*p**5 - 1/90*p**4 - 1/5*p**2 + 16*p. Factor q(z).
-2*(z - 1)**2*(z + 3)/15
Suppose 0 = 2*b - 7*b + 35. Suppose -5*c + 10*c = 20. Factor -b*o + 3 - o**3 + 3*o**3 + 3*o**c + 18*o**2 + 19*o + 10*o**3.
3*(o + 1)**4
Let j(x) be the third derivative of -x**6/80 - 11*x**5/40 - 5*x**4/8 + 3*x**2 + 18*x. Factor j(y).
-3*y*(y + 1)*(y + 10)/2
Suppose 0 = 11*l + 3*l + 196. Let x be (-22)/(-77) + (-31)/l. Factor -5/2*v**4 + 5*v**3 + x*v - 1/2 + 1/2*v**5 - 5*v**2.
(v - 1)**5/2
Let t(w) be the first derivative of 331*w**3/3 + w**2 - 70. Factor t(y).
y*(331*y + 2)
Let v(c) be the third derivative of 0 + 1/80*c**6 + 14*c**2 + 1/12*c**3 - 1/120*c**5 - 1/16*c**4 + 0*c. Factor v(k).
(k - 1)*(k + 1)*(3*k - 1)/2
What is r in -r**4 + 16*r**2 + 25 + 13/2*r**3 - 185/4*r - 1/4*r**5 = 0?
-5, 1, 4
Let d = -983 - -3937/4. What is v in 0 + d*v**3 - 1/2*v**2 - v**4 + 1/4*v**5 + 0*v = 0?
0, 1, 2
Let k(n) be the second derivative of n**6/540 - n**4/36 - n**3 + 5*n. Let y(s) be the second derivative of k(s). Factor y(c).
2*(c - 1)*(c + 1)/3
Suppose -10*l = x - 6*l - 28, -2*x = 2*l - 26. Suppose 7*m**3 + 21*m**4 + 10*m**2 - 16*m**4 + x*m**3 = 0. Calculate m.
-2, -1, 0
Suppose 155*g - 160*g + 3 = -4*v, 0 = -4*v + 4*g. Let s(r) be the first derivative of -1/4*r**2 + 8 + 7/12*r**v + 0*r. Find c, given that s(c) = 0.
0, 2/7
Let x(f) be the third derivative of f**6/24 + 149*f**5/30 - 425*f**4/24 + 61*f**3/3 + 2*f**2 - 79*f. Let x(r) = 0. Calculate r.
-61, 2/5, 1
Let v(o) = -o**2. Let s(y) = -3*y**2 - 11*y. Let t(x) = 5*s(x) - 10*v(x). Suppose t(k) = 0. Calculate k.
-11, 0
Let j(k) be the third derivative of -47*k**2 + 1/20*k**6 - 4/15*k**5 + 0*k**3 + 1/3*k**4 + 0 + 0*k - 1/168*k**8 + 2/105*k**7. Solve j(t) = 0 for t.
-2, 0, 1, 2
Let b = 162 + -160. Let r be (-19 - -14)*b/2 + 7. Factor 4/5*g + 6/5 - 2/5*g**r.
-2*(g - 3)*(g + 1)/5
Suppose -b - 7 = -5*k, 3*b = -k + 19 - 8. Let d(y) be the first derivative of 0*y**3 - b + 0*y**2 + 0*y**4 + 3/5*y**5 + 0*y. Factor d(n).
3*n**4
Let x = -58 - -63. Suppose 0 = -4*v + x*q + 8, -3*q = -5*v + q + 10. Factor 2/7*r**3 + 0 - 2/7*r**v + 0*r - 2/7*r**5 + 2/7*r**4.
-2*r**2*(r - 1)**2*(r + 1)/7
Suppose -6 = -16*g + 13*g. Factor -33*o**2 + 4*o - 126*o**2 - 29*o**g + 8 + 176*o**3.
4*(o - 1)*(4*o - 1)*(11*o + 2)
Let y(v) = -v**2 - v - 1. Let n(q) = 1805*q**3 + 341*q**2 - 133*q + 7. Let f(d) = -n(d) + y(d). Factor f(w).
-(5*w + 2)*(19*w - 2)**2
Let o(f) be the third derivative of f**8/141120 + f**7/35280 - f**6/2520 - 19*f**5/60 + 22*f**2. Let l(t) be the third derivative of o(t). Factor l(s).
(s - 1)*(s + 2)/7
Let n be (12/(-7))/(-2)*(10 - 221/34). Factor 1/8*j + 1/8*j**n - 1/4*j**2 + 0.
j*(j - 1)**2/8
Let l be (4/30)/((-31545)/810 + 39). Factor 0*h**2 - 3/5*h**4 + 0 - l*h**3 + 0*h.
-3*h**3*(h + 4)/5
Let l = 1/1586 + 1583/4758. Factor 2/3*t**2 + 1/2*t**3 - l - 5/6*t.
(t - 1)*(t + 2)*(3*t + 1)/6
Let h(t) be the third derivative of -t**6/345 + 3*t**5/230 - t**4/138 - 169*t**2. Solve h(l) = 0 for l.
0, 1/4, 2
Factor 2/7*d**2 + 6/7*d - 2/7 - 6/7*d**3.
-2*(d - 1)*(d + 1)*(3*d - 1)/7
Let q be 2006/590*(2 + (-32)/17). Factor -10 + 4*s - q*s**2.
-2*(s - 5)**2/5
Let l = 11935 + -83543/7. Determine w so that -l*w**2 - 6/7*w + 0 = 0.
-3, 0
Let t(c) be the second derivative of -3*c**5/20 + c**4/2 + c**3/2 - 3*c**2 - 58*c. Determine o, given that t(o) = 0.
-1, 1, 2
Let x(h) be the third derivative of -h**6/24 + 25*h**5/12 - 55*h**4/12 - 40*h**3 + 235*h**2. Determine u, given that x(u) = 0.
-1, 2, 24
Let c(v) be the first derivative of -v**5/60 - 3*v**2 + 1. Let d(t) be the second derivative of c(t). Factor d(m).
-m**2
Let l be 24/(-11)*(-4)/18 - (-102)/561. Factor l*s**3 + 1/3 - 1/3*s**2 - 2/3*s.
(s - 1)*(s + 1)*(2*s - 1)/3
Let a(i) be the second derivative of i**7/70 + i**6/5 + 3*i**5/4 - i**4 - 8*i**3 - 9*i**2/2 - 28*i. Let q(m) be the first derivative of a(m). Factor q(j).
3*(j - 1)*(j + 1)*(j + 4)**2
What is r in 0 + 4/7*r**3 + 52/7*r**2 - 20/7*r**4 - 36/7*r = 0?
-9/5, 0, 1
Let m(o) be the third derivative of o**7/525 - o**6/30 - 23*o**5/150 - o**