 - 24*m. Factor w(p).
4*(p - 2)*(p + 1)**2
Let y(g) be the first derivative of 270000*g**4 + 18000*g**3 + 450*g**2 + 5*g + 53. Solve y(b) = 0 for b.
-1/60
Let w(t) be the second derivative of 11*t**7/15120 - t**6/480 - t**5/360 + 3*t**4/4 - 22*t. Let s(r) be the third derivative of w(r). Factor s(v).
(v - 1)*(11*v + 2)/6
Let t(x) be the second derivative of -x**6/15 + x**4/6 + 12*x. Factor t(u).
-2*u**2*(u - 1)*(u + 1)
Let g = -81 - -811/10. Let s(q) be the first derivative of 1/4*q**4 - 3 + g*q**5 - 1/2*q**2 - 1/6*q**3 + 0*q. Factor s(z).
z*(z - 1)*(z + 1)*(z + 2)/2
Let j be (-4)/3*(5 + 301/(-56)). Factor -17/2*q - j*q**4 - 17/2*q**2 - 3 - 7/2*q**3.
-(q + 1)**2*(q + 2)*(q + 3)/2
Let t(x) = x**3 + 5*x**2 + 6*x + 6. Let m be t(-4). Let v be 132/77 + m/(-7). Factor z**4 - z**3 - 2*z**3 + 2*z**2 + z**3 + v*z - 3*z**4.
-2*z*(z - 1)*(z + 1)**2
Factor 4/7 - 4/7*y**2 + 2/7*y - 2/7*y**3.
-2*(y - 1)*(y + 1)*(y + 2)/7
Let r(n) be the third derivative of -n**5/270 + 4*n**4/27 - 16*n**3/9 + 454*n**2. Factor r(a).
-2*(a - 12)*(a - 4)/9
Let r(b) be the third derivative of -b**8/20160 - 19*b**7/20160 + b**6/576 + 13*b**5/60 + 30*b**2. Let d(s) be the third derivative of r(s). Factor d(w).
-(w + 5)*(4*w - 1)/4
Factor 2/9*d**5 - 10/9*d**4 - 16/9*d - 14/3*d**3 + 0 - 46/9*d**2.
2*d*(d - 8)*(d + 1)**3/9
Factor -1/2*a**2 - 29*a - 841/2.
-(a + 29)**2/2
Let m(i) be the first derivative of -4*i**5/5 - 3*i**4 - 4*i**3/3 + 6*i**2 + 8*i - 73. Solve m(n) = 0.
-2, -1, 1
Let f(h) = h**3 + 201*h**2 + 394*h + 199. Let j(g) = 100*g**2 + 198*g + 100. Let s(t) = -2*f(t) + 5*j(t). Solve s(m) = 0 for m.
-1, 51
Let h(d) be the second derivative of 0 + 3*d**2 + 1/18*d**4 + 20*d + 10/9*d**3. Factor h(f).
2*(f + 1)*(f + 9)/3
Let b(a) be the first derivative of -a**6/30 + 9*a**5/20 - 9*a**4/4 + 9*a**3/2 - 27*a + 18. Let v(k) be the first derivative of b(k). Solve v(y) = 0.
0, 3
Let n(j) be the first derivative of j**7/1050 + j**6/150 + j**5/100 + 6*j**2 + 7. Let h(i) be the second derivative of n(i). Factor h(d).
d**2*(d + 1)*(d + 3)/5
Suppose -2*a**3 + 4/3 + 2*a - 2/3*a**2 - 2/3*a**4 = 0. What is a?
-2, -1, 1
Suppose -2/9*d**2 + 22/3*d + 0 = 0. Calculate d.
0, 33
Let x(n) be the second derivative of -3/8*n**5 + n**3 - 9/4*n**4 + 6*n**2 + 7*n + 2/5*n**6 + 3/28*n**7 + 0. Suppose x(t) = 0. Calculate t.
-2, -2/3, 1
Find a, given that 3816/7*a - 432/7 - 5043/7*a**4 + 13038/7*a**3 - 11379/7*a**2 = 0.
12/41, 1
Let m be (-54)/(-6) - (0 + 4). Let r be 8/(-28) - 23/(-7). Factor -3*x + m*x + 3*x**2 - r*x + 4*x.
3*x*(x + 1)
Suppose -2*p = -8 + 2. Factor p + 7 + 3*v**2 - 7 - 6*v.
3*(v - 1)**2
Let j be 312/169 + (-2)/(-13). Let h(d) = -2*d**2 - 24*d + 1. Let c(o) = 1. Let f(k) = j*h(k) - 2*c(k). Factor f(z).
-4*z*(z + 12)
Let v(o) be the first derivative of 19*o**4/22 + 40*o**3/33 + o**2/11 + 477. Factor v(r).
2*r*(r + 1)*(19*r + 1)/11
Let l(d) = d**3 - 5*d**2 - 8*d + 14. Let n be l(6). Suppose -3*j**5 - 10*j**2 - 3*j**4 - 11*j**2 + 24*j**n + 3*j**3 = 0. Calculate j.
-1, 0, 1
Solve 218/9*w + 4/9*w**4 - 8/9*w**2 - 76/9*w**3 - 140/9 + 2/9*w**5 = 0 for w.
-7, -2, 1, 5
Let q(d) = -d + 9. Let m be q(3). Suppose 2*f + 0 = m. Factor -c - c - 2*c + 18*c**f + c + 9*c**5 - 24*c**4.
3*c*(c - 1)**3*(3*c + 1)
Factor 28/3*j**2 + 2/9*j**4 + 86/9*j**3 + 0*j + 0.
2*j**2*(j + 1)*(j + 42)/9
Let n = -11 - -7. Let q(z) be the first derivative of -z**2/2 - z - 12. Let y(l) = 2*l**5 - 2*l**3 - 4*l - 4. Let g(b) = n*q(b) + y(b). Let g(t) = 0. What is t?
-1, 0, 1
Let b(t) be the second derivative of -3/20*t**5 - 4*t + 0 - 1/4*t**3 + 0*t**2 - 5/16*t**4 - 1/40*t**6. Factor b(r).
-3*r*(r + 1)**2*(r + 2)/4
Let x(n) = 7*n - 54. Let z be x(8). Let a(c) be the first derivative of 9/2*c**z + 6 + 3/4*c**4 + 5*c**3 - 27*c. Factor a(p).
3*(p - 1)*(p + 3)**2
Let f(z) be the second derivative of z**6/15 + 22*z**5/5 + 121*z**4 + 5324*z**3/3 + 14641*z**2 + 39*z. Solve f(r) = 0.
-11
Let q = -60461/13 + 4651. Factor 12/13*c**2 - q + 6/13*c**4 + 16/13*c**3 + 0*c.
2*(c + 1)**3*(3*c - 1)/13
Let y = 3004 + -3002. Factor 1/8*w + 1/8*w**4 - 1/4*w**y + 1/8*w**5 + 1/8 - 1/4*w**3.
(w - 1)**2*(w + 1)**3/8
Determine o, given that 5/2*o**5 + 15*o**3 - 20*o**2 - 35/2*o + 0 + 20*o**4 = 0.
-7, -1, 0, 1
Let k(p) be the third derivative of -23*p**6/10 - 14*p**5/3 - p**4/6 + 247*p**2. Factor k(w).
-4*w*(w + 1)*(69*w + 1)
Suppose -7*r = -13*r + 18. Suppose 9 = 4*p - f, 3*f - 4 = -r*p + f. Factor 2/7*m + 4/7*m**p - 2/7.
2*(m + 1)*(2*m - 1)/7
Let r(d) be the third derivative of d**6/220 - 309*d**5/110 + 31827*d**4/44 - 1092727*d**3/11 - 41*d**2. Factor r(i).
6*(i - 103)**3/11
Let -15/2*p - 3/2*p**2 + 21 = 0. Calculate p.
-7, 2
Let v(x) = -x**2 + 5*x + 50. Let r be v(10). Suppose r - 2/7*y**4 - 6/7*y**3 + 8/7*y + 0*y**2 = 0. Calculate y.
-2, 0, 1
Let g = -20869 + 20869. Factor -4/9*m + g - 2/3*m**2 - 2/9*m**3.
-2*m*(m + 1)*(m + 2)/9
Let g be 30/165 + (-480)/(-22). Let c = -4 + g. Find y such that -8*y - 3*y**2 + c + 19*y - 8*y = 0.
-2, 3
Let c(b) be the second derivative of b**6/135 - 11*b**5/90 + 5*b**4/6 - 3*b**3 + 6*b**2 + 4*b - 1. Determine a so that c(a) = 0.
2, 3
Let o = 73763/331974 + 1/36886. Solve 0*s - o*s**2 + 2/9 = 0 for s.
-1, 1
Let w(b) be the first derivative of -2*b**3/3 + 5*b**2 + 3*b - 8. Let j be w(5). Let -4*f**4 - 4*f**3 + 0*f**5 - 2*f**5 + 10*f**j = 0. Calculate f.
-3, 0, 1
Suppose -892*c + 1125*c - 699 = 0. Factor 1/2*j**5 - 7/2*j**4 + c*j + 0 + 17/2*j**3 - 17/2*j**2.
j*(j - 3)*(j - 2)*(j - 1)**2/2
Let z(k) be the second derivative of 1/45*k**5 + 1/12*k**4 + k + 1/540*k**6 + 0*k**3 + 0 + k**2. Let u(h) be the first derivative of z(h). Factor u(t).
2*t*(t + 3)**2/9
Let q(a) be the third derivative of -a**5/50 + 89*a**4/60 + 2*a**3 + 2*a**2 - 36*a. Factor q(k).
-2*(k - 30)*(3*k + 1)/5
Let y = 16 - 4. Find d such that -4*d + 42*d**3 + y*d**2 + 5*d + 8 - 40*d**3 + 17*d = 0.
-4, -1
Let f(v) = 6*v**2 + 30*v - 4. Let m be f(-4). Let o be (-140)/(-147) - (-8)/m. Determine c so that -2/3*c**2 - 2/3*c**3 + o + 2/3*c = 0.
-1, 1
Let a(q) be the third derivative of q**8/504 + 2*q**7/105 + 13*q**6/180 + 2*q**5/15 + q**4/9 - 75*q**2. Solve a(f) = 0.
-2, -1, 0
Let r be (-338)/1638*-3 - 2/7. Suppose 0 + r*l**2 - 1/6*l = 0. Calculate l.
0, 1/2
Find g, given that 30*g**3 + 18 - 123/2*g**2 - 9/2*g**4 + 30*g = 0.
-1/3, 2, 3
Let n = 24886 - 1368877/55. Let k = n - -36/11. Solve 0 + k*t**3 + 0*t - 3/5*t**2 = 0.
0, 1
Let r be 2/(-36) - (-8 + 11538/2268). Factor -6/7*b**4 + 16/7*b - 8/7*b**2 - r*b**3 + 0.
-2*b*(b + 2)**2*(3*b - 2)/7
Let u(z) = z**2 + 2*z + 4. Let r(y) be the second derivative of -1/12*y**4 + 0 - 1/3*y**3 - 5/2*y**2 - 4*y. Let l(i) = -3*r(i) - 4*u(i). Factor l(m).
-(m + 1)**2
Suppose 29*s - 88 = 7*s. Let r(j) be the third derivative of 0*j**5 + 0*j**7 + 0*j + s*j**2 + 1/2856*j**8 - 1/510*j**6 + 1/204*j**4 + 0*j**3 + 0. Factor r(m).
2*m*(m - 1)**2*(m + 1)**2/17
Let n = 50/33 - 2/11. Let k = 4/189 + 2012/189. Factor -14/3*t**3 - 22/3*t + k*t**2 + n.
-2*(t - 1)**2*(7*t - 2)/3
Factor 6 - 3*d**3 + 3 - 5 + 11*d**2 - 12*d.
-(d - 2)*(d - 1)*(3*d - 2)
Let c(a) = a**2 + 3*a + 4. Let h be c(-3). Suppose 2*m - 4*m = -h. Determine y, given that y**5 + 8*y**3 + y**2 - 2*y + 7*y**5 - 22*y**4 + 10*y**3 - 3*y**m = 0.
-1/4, 0, 1
Let j(k) be the first derivative of -11*k**6/18 + 14*k**5/5 - 3*k**4 - 8*k**3/9 - 106. Factor j(g).
-g**2*(g - 2)**2*(11*g + 2)/3
Let s(l) be the second derivative of 7*l - 5/3*l**3 + 6*l**2 + 0 + 1/6*l**4. Factor s(v).
2*(v - 3)*(v - 2)
Let p(w) be the third derivative of -w**5/390 - w**4/26 - 3*w**3/13 - 2*w**2 - 7. Factor p(u).
-2*(u + 3)**2/13
Let d(k) be the third derivative of 0 - 6*k**2 + 5/12*k**4 + 0*k - 5/6*k**3 - 1/12*k**5. Suppose d(w) = 0. What is w?
1
Suppose 0 = 3*v + 9, 27 - 9 = 5*k + 4*v. Let n(x) be the third derivative of 1/54*x**4 + 0*x**3 + 0 + 1/180*x**k - 1/54*x**5 + 0*x + 3*x**2. Factor n(q).
2*q*(q - 1)*(3*q - 2)/9
Let d be 8 + -6 + -2*(-60)/(-70). Solve d*r**5 + 6/7*r**4 - 2/7*r**3 - 6/7*r**2 + 0*r + 0 = 0 for r.
-3, -1, 0, 1
Let t(l) = l**2 - l + 2. Let g be t(2). Suppose 0 = 3*n + g*r + 7, 4*r + 25 = 3*n - 0*n. Let -1/5*w**4 + 0*w + 0 + 1/5*w**2 + 0*w**n = 0. What is w?
-1, 0, 1
Let -625*m**5 - 200*m**3 - 10 + 95*m**4 - 530*m**2 - 135*m + 529*m**4 + 876*m**4 = 0. What is m?
-1/5, 1, 2
Let x(w) = -7*w**4 - 1