-3*z**2*(z - 1)**3/4
Suppose -4*h + 20 = k, 0 = h + 3*k - 7 - 9. Let m = -143 - -146. Determine u so that 3*u**2 + u**2 - 3*u**h - u**4 - 8*u**2 - 8*u**m = 0.
-1, 0
Let r(q) be the second derivative of 1/42*q**4 + 21*q + 4/7*q**2 - 4/21*q**3 + 0. Let r(p) = 0. Calculate p.
2
Let c = 15229/9 - 1691. Find d, given that 4/9*d + 0 - 10/9*d**3 + 2/3*d**5 - 10/9*d**2 + c*d**4 = 0.
-2, -1, 0, 1/3, 1
Let h(d) be the second derivative of d**7/630 + 2*d**6/45 + 8*d**5/15 + 13*d**4/12 - 11*d. Let u(z) be the third derivative of h(z). Factor u(g).
4*(g + 4)**2
Let b(y) be the third derivative of -y**8/1344 - y**7/126 + y**4/3 + 8*y**2. Let d(s) be the second derivative of b(s). Factor d(l).
-5*l**2*(l + 4)
Suppose -4*w + 2*w + 27 = p, -4*w + 3*p = -79. Suppose -v - w = -5*v. Factor -2/3*u**2 - 6 + v*u.
-2*(u - 3)**2/3
Let a(s) be the second derivative of -s**8/23520 - s**7/4410 - s**6/2520 - 13*s**4/12 - 6*s. Let g(v) be the third derivative of a(v). Factor g(r).
-2*r*(r + 1)**2/7
Let g be (-447)/(-18)*-1 - 2/12. Let i = g - -27. Factor 0 + 1/2*y**i - 3/2*y.
y*(y - 3)/2
Let x = 13 + -4. Suppose -5 = -4*m - 3*n, -2*m = 2*m - n - x. Determine u so that -u**2 + u**2 + 2 + 3*u + u + m*u**2 = 0.
-1
Let m(p) = -p**2 - p. Let b(s) = 7*s**2 - 139*s + 2592. Let a(f) = -2*b(f) - 10*m(f). Factor a(r).
-4*(r - 36)**2
Let x = 3 - 3. Suppose -y = -0*m + m - 6, 2*y - m = x. Suppose -69*a + 16 - 5*a**y - 2*a**2 - a**3 + 61*a = 0. Calculate a.
-4, 1
Let l(u) be the third derivative of u**5/210 - 3*u**4/28 - 22*u**3/21 + 2*u**2 - 251*u. Factor l(s).
2*(s - 11)*(s + 2)/7
Let r(q) = -q**3 + 14*q**2 + 16*q - 3. Let a be r(15). Suppose a = 5*j + 2. Factor -8*x**2 - 10*x**3 - 5*x**4 - 3*x - x**5 + 2*x - 4*x - j*x**2 - 1.
-(x + 1)**5
Let f(d) be the first derivative of -20*d**3/3 - 125*d**2/2 - 105*d - 509. Factor f(u).
-5*(u + 1)*(4*u + 21)
Factor 579*z**3 + 114*z**2 + 3*z**5 + 90*z**4 - 1554*z**2 + 530*z + 238*z.
3*z*(z - 1)**2*(z + 16)**2
Factor -1/2*f**2 - 30*f - 450.
-(f + 30)**2/2
Let u(n) = -n**2 - 1. Let y(s) = 0 - 10*s - 4 - 17*s**2 + 18*s**2. Let h(j) = 4*u(j) - y(j). Solve h(w) = 0.
0, 2
Factor 1/4*c**3 - 5/4*c**2 + 0 + c.
c*(c - 4)*(c - 1)/4
Suppose 8*m = 33 - 9. Suppose -12 = -3*g - m. Determine p, given that -30*p**2 - 40 + 7*p**g - 3*p**3 + 60*p + 0*p**3 + p**3 = 0.
2
Suppose 0 = k - h + 5, 0 = -3*k - 2*h - 2*h + 6. Let i be (k - -1)/(13/(-559)). Factor -i*f**2 + 8 + 72*f**2 + 4*f - 33*f**2.
-4*(f - 2)*(f + 1)
Let t(k) = 3*k**4 + 17*k**3 + 29*k**2 + 23*k - 4. Let b(i) = -4*i**4 - 18*i**3 - 29*i**2 - 25*i + 5. Let v(q) = 4*b(q) + 5*t(q). Suppose v(m) = 0. Calculate m.
-1, 0, 15
Suppose -30 = 2*y - 5*z, -10*z + 6 = 2*y - 9*z. Factor -2/5*p**2 + 0*p + y.
-2*p**2/5
Let a(g) = 8*g**5 - 3*g**4 + 5*g**3 - 30*g**2 + 17*g - 30. Let p(l) = l**5 - l**4 - l - 2. Let w(z) = -4*a(z) + 44*p(z). Solve w(b) = 0.
-2, 2/3, 1, 2
Let u(b) be the second derivative of -2*b**7/147 + b**6/35 + 33*b**5/70 + 13*b**4/42 - 5*b**3/7 - 461*b. Let u(o) = 0. What is o?
-3, -1, 0, 1/2, 5
Let r(a) be the first derivative of -2*a**4 - 16/3*a**3 + 4/5*a**5 + 12*a + 4 + 4*a**2. Factor r(i).
4*(i - 3)*(i - 1)*(i + 1)**2
Factor 66/5*p + 1/5*p**2 + 0.
p*(p + 66)/5
Let -3*q**4 + 4*q**2 + 7*q**3 - 9/2*q - 1 - 5/2*q**5 = 0. Calculate q.
-2, -1, -1/5, 1
Let y(s) be the second derivative of s**7/336 - s**6/240 - s**5/80 + s**4/48 + s**3/48 - s**2/16 + 185*s. Solve y(b) = 0.
-1, 1
Let m = -687 - -3436/5. Let j(l) be the third derivative of 7*l**2 + 1/18*l**5 + 0 + m*l**3 + 1/6*l**4 + 0*l. Factor j(d).
2*(5*d + 3)**2/15
Let y(s) be the third derivative of -s**7/630 + s**6/180 + s**5/12 + s**4/18 - 10*s**3/9 + 2*s**2 + 177*s. Factor y(u).
-(u - 5)*(u - 1)*(u + 2)**2/3
Let r = -5767/4 - -1443. Let a(v) be the first derivative of 2*v - 2/5*v**5 + 8 + 0*v**3 + 5/2*v**2 - r*v**4. What is m in a(m) = 0?
-2, -1, -1/2, 1
Let o(f) be the first derivative of 2*f**3/9 + 11*f**2/3 + 16*f - 80. Factor o(h).
2*(h + 3)*(h + 8)/3
Let x(d) be the first derivative of d**3/3 - 2*d**2 + 3*d - 5. Find t such that x(t) = 0.
1, 3
Let b(g) = -6*g**4 - 13*g**3 + 6*g**2 - 4*g + 17. Let c(k) = 2*k**4 + 4*k**3 - 2*k**2 + 2*k - 6. Let n(j) = 6*b(j) + 17*c(j). Factor n(s).
-2*s*(s - 1)*(s + 1)*(s + 5)
Let d be ((-13)/13)/(2/(-116)). Factor d + 29*f**2 - 60*f + f**2 - 9*f**3 + 4*f**3 - 18.
-5*(f - 2)**3
Factor 134398/7*q - 88804/7 + 6/7*q**3 - 256*q**2.
2*(q - 149)**2*(3*q - 2)/7
Suppose 4 = 4*k + 2*f, -2*f - 2*f - 16 = 0. Suppose -k*c + 3 = b, 4*b = 3*b + 3. Factor 1/2*h + c + 1/2*h**2.
h*(h + 1)/2
Let r(h) be the third derivative of -1 - 1/1470*h**7 + 0*h**3 + 0*h - 21*h**2 - 1/280*h**6 - 1/168*h**4 - 1/140*h**5. Find n, given that r(n) = 0.
-1, 0
Let g be 550/(-7)*1 + 4/7. Let j = -233/3 - g. Factor 0 + j*p - 1/3*p**2.
-p*(p - 1)/3
Suppose 3*f + 9 = 3*a, 0 = 6*f - 3*f + 2*a - 11. Let d(h) = h**3. Let z(g) = -4*g**4 + 12*g**3 + 8*g**2 - 4. Let u(p) = f*z(p) - 12*d(p). Factor u(t).
-4*(t - 1)**2*(t + 1)**2
Let k be 4/(-1 - -9 - 2). Suppose 3 = -26*s + 27*s. Determine v, given that -8/3*v - 4*v**2 - k - 8/3*v**s - 2/3*v**4 = 0.
-1
What is l in 5/3*l - 1/3*l**5 - 4/3*l**4 - 4/3*l**3 + 2/3*l**2 + 2/3 = 0?
-2, -1, 1
Let v be 0*(-1 + 5/2 + -2). Suppose -5 = 5*d + 2*x - 15, v = 5*d + x - 10. Factor 0 - 2/9*q**3 + 0*q - 2/9*q**d.
-2*q**2*(q + 1)/9
Factor -200/3 - 1/6*p**2 - 20/3*p.
-(p + 20)**2/6
Let f(n) = n**2 - 9*n + 15. Let y be f(3). Let h(j) = -3*j - 5. Let q be h(y). Factor 4/9*a**q + 0*a**3 - 2/9*a**5 + 2/9*a + 0 - 4/9*a**2.
-2*a*(a - 1)**3*(a + 1)/9
Let z(y) = -y**2 + 4*y + 1. Let s be z(3). Suppose -25 = -5*m + 5*w, m + w - 3 = -0*m. Suppose m*t**s + 2*t**4 - 12*t**3 + 6*t**4 - 3*t**5 = 0. Calculate t.
0, 2
Let t(v) be the second derivative of -v**4/4 - 9*v**3/2 - 12*v**2 + 3*v + 53. Find a such that t(a) = 0.
-8, -1
Let f(s) be the first derivative of -s**5/40 + s**4/16 + s**3/24 - s**2/8 - 231. Factor f(i).
-i*(i - 2)*(i - 1)*(i + 1)/8
Let t(q) be the third derivative of 0*q - 11*q**2 + 0*q**3 - 1/35*q**7 + 0 + 0*q**5 + 1/40*q**6 + 1/112*q**8 + 0*q**4. Determine f, given that t(f) = 0.
0, 1
Let y(w) be the first derivative of w**8/560 - w**7/140 + w**6/120 - 8*w**3/3 + 5. Let b(x) be the third derivative of y(x). Factor b(r).
3*r**2*(r - 1)**2
Let x(n) be the second derivative of 0 + 17*n + 1/10*n**2 - 1/30*n**3 - 1/60*n**4 + 1/100*n**5. Factor x(g).
(g - 1)**2*(g + 1)/5
Let a be (4/22 - 370/1430) + 10855/507. Solve -a*i - 5/3*i**3 - 38/3*i**2 + 32/3 = 0 for i.
-4, 2/5
Let m(l) = -2*l**2 - 2*l. Let w(z) = -3*z**2 - 3*z. Let q(t) = -4*m(t) + 3*w(t). Factor q(o).
-o*(o + 1)
Let w(f) be the second derivative of -f**6/10 + 3*f**5/20 + 15*f**4/4 + 23*f**3/2 + 15*f**2 - 136*f. Suppose w(i) = 0. Calculate i.
-2, -1, 5
Factor -100*f + 145*f**3 - 48 - 25*f**2 - 31*f**2 - 149*f**3.
-4*(f + 1)**2*(f + 12)
Let g be 164/60 + (-35)/25. Suppose -g*o - 2/15*o**2 - 10/3 = 0. What is o?
-5
Factor 0*g + 1/2*g**2 + 3/2*g**3 - 2*g**4 + 0.
-g**2*(g - 1)*(4*g + 1)/2
Let h = 18 - 14. Factor 2*u**2 - 20*u**4 + 18*u**h + 2*u**3 + 0*u**5 - 2*u**5.
-2*u**2*(u - 1)*(u + 1)**2
Factor 466*t - 20*t**3 - 286*t - 6*t**2 - 216 + 4*t**4 - 6*t**2.
4*(t - 3)**2*(t - 2)*(t + 3)
Let l(d) be the second derivative of 0 + 0*d**3 + 0*d**2 - d - 7/120*d**6 + 1/8*d**4 - 19/80*d**5. Factor l(x).
-x**2*(x + 3)*(7*x - 2)/4
Let m(c) be the third derivative of 1/1260*c**7 + 0 + 1/60*c**5 - 1/144*c**6 + 10*c**2 + 0*c + 1/36*c**4 - 2/9*c**3. Let m(n) = 0. Calculate n.
-1, 2
Let i(h) be the first derivative of 2*h**5/45 + 8*h**4/9 + 40*h**3/9 + 723. Factor i(l).
2*l**2*(l + 6)*(l + 10)/9
Let s(t) be the third derivative of 1/8*t**6 + 0*t**3 + 0*t - 5/8*t**4 + 0 - 1/70*t**7 + 1/20*t**5 - 3*t**2. Factor s(g).
-3*g*(g - 5)*(g - 1)*(g + 1)
Let f be (156/(-65))/((-2)/(-45)). Let m = f + 59. Factor 0*c - 1/5*c**4 + 0 - 1/5*c**3 + 1/5*c**m + 1/5*c**2.
c**2*(c - 1)**2*(c + 1)/5
Suppose -3*c = 3, -4*m - c = -m - 17. Factor -6*d**4 + d**4 + 8*d**3 + 3*d**4 - m*d**2.
-2*d**2*(d - 3)*(d - 1)
Let q = -364 - -364. Let l be 3/15*15/2. What is d in 3*d + q - 3/2*d**5 + 9/2*d**3 + l*d**4 - 15/2*d**2 = 0?
-2, 0, 1
Let b(c) = -c**3 + 4*c**2 - 2*c + 2. Let q be b(3). Let a be 1 + (8/2 - q). Suppose a + 6/7*z - 2/7*z**2 = 0. What is z?
0, 3
Suppose -18 = -2*s + 3*p, -68*s + 70*s - 5*p - 26 = 0. Solve 0*b