et n(t) be the third derivative of -t**6/270 + 31*t**5/30 - 805*t**4/9 - 4900*t**3/27 + 2192*t**2. Factor n(i).
-2*(i - 70)**2*(2*i + 1)/9
Let l be -75 - (-54576)/252 - 77. Let -l*v + 128/7 - 2*v**4 - 114/7*v**2 + 452/7*v**3 = 0. What is v?
-1, 2/7, 1, 32
Let h(r) = -45*r**3 + 402*r**2 + 32*r - 402. Let k(j) = -21*j**3 + 201*j**2 + 15*j - 201. Let q(l) = 6*h(l) - 13*k(l). Factor q(v).
3*(v - 67)*(v - 1)*(v + 1)
Let m(k) be the second derivative of -1/80*k**6 - 1/4*k**3 + 11*k + 3/80*k**5 + 3/32*k**4 + 10*k**2 + 0. Let y(u) be the first derivative of m(u). Factor y(z).
-3*(z - 2)*(z + 1)*(2*z - 1)/4
Factor 304*y + 1482 - 7*y**4 + 81*y**3 + 1632 - 300*y**2 - 2922.
-(y - 4)**3*(7*y + 3)
Let f be 39/(-26) + 22/4. Find o such that -20*o**3 + 4*o**5 + f*o + 10*o + 2*o = 0.
-2, -1, 0, 1, 2
Let n(y) be the first derivative of 7*y**4/10 - 74*y**3/15 + 38*y**2/5 - 16*y/5 - 1323. Let n(i) = 0. Calculate i.
2/7, 1, 4
What is y in 36*y + 123/7*y**3 - 1/7*y**4 + 0 + 376/7*y**2 = 0?
-2, -1, 0, 126
Let j(z) = -10*z**3 - 184*z**2 + 12*z. Let l(y) = -11*y**3 - 184*y**2 + 14*y. Let f(w) = 7*j(w) - 6*l(w). Factor f(m).
-4*m**2*(m + 46)
Let f(w) be the third derivative of w**8/784 + 3*w**7/98 - 12*w**6/35 + 4*w**5/7 + 10*w**2 + 16*w. What is y in f(y) = 0?
-20, 0, 1, 4
Let b(z) = -4*z**4 - z**3 - 3*z**2 + z - 1. Let o(d) = 43*d**4 + 13*d**3 + 33*d**2 - 13*d + 12. Let p(f) = 22*b(f) + 2*o(f). Solve p(w) = 0 for w.
-1, 1
Find v, given that 65*v**2 - 224*v + 67*v**2 + 12*v**2 + v**4 + v**4 - 30*v**3 = 0.
0, 4, 7
Factor 600 + 5898*t**2 - 2948*t**2 - 2955*t**2 + 595*t.
-5*(t - 120)*(t + 1)
Let o(s) be the third derivative of 0 + 127*s**2 + 13/16*s**3 - 5/96*s**4 - 1/480*s**5 + 0*s. Let o(i) = 0. Calculate i.
-13, 3
Let n(b) be the second derivative of b**4/9 - 6*b**3 - 56*b**2/3 - 850*b - 1. Determine y, given that n(y) = 0.
-1, 28
Let x be 0*((-143)/26 - -6). Let f(v) be the third derivative of 0*v**3 + 1/42*v**7 + 7/12*v**5 + x*v - 16*v**2 - 5/8*v**4 + 0 - 5/24*v**6. Factor f(y).
5*y*(y - 3)*(y - 1)**2
Let z(d) be the first derivative of -d**4/20 + 17*d**3/15 - 19*d**2/2 + 35*d + 743. Solve z(o) = 0.
5, 7
Let l(j) = -260*j**2 + 2859*j + 11. Let g be l(11). Let g + 12/5*q**4 + 9/5*q**3 + 0*q - 3/5*q**2 = 0. What is q?
-1, 0, 1/4
Factor -34659603/2 - 3/2*f**2 + 10197*f.
-3*(f - 3399)**2/2
Let s be 2 + 44/(-16) - 44/(-16). Factor 4*f - f**s - 31*f + 9*f - 400 - 22*f.
-(f + 20)**2
Let a be 9/((-108)/16) + 226/3. Factor 3*r**2 + a*r - 2*r + 28*r - 104 + r**2.
4*(r - 1)*(r + 26)
Let t(g) = 6*g**3 - 2*g**2 + 4*g - 4. Let f(p) be the third derivative of -p**7/210 - p**4/24 + p**3/6 + 41*p**2. Let v(k) = 4*f(k) + t(k). Factor v(c).
-2*c**2*(c - 1)*(2*c - 1)
Let r(g) be the third derivative of -g**6/30 - 52*g**5/15 - 239*g**4/6 - 376*g**3/3 - 3*g**2 + 55*g. Let r(m) = 0. Calculate m.
-47, -4, -1
Suppose -3*h - 2*u - 13 + 56 = 0, 0 = -3*h - 3*u + 45. Suppose 120 = 73*r - h*r. Factor 2/11*a**r - 2/11*a**3 + 0 + 0*a.
-2*a**2*(a - 1)/11
Solve 306*j + 174/7*j**2 + 2/7*j**3 - 78030/7 = 0.
-51, 15
Let w(o) = 4*o**5 + 142*o**4 - 278*o**3 + 135*o**2 - 3*o. Let i(h) = -10*h**5 - 284*h**4 + 556*h**3 - 269*h**2 + 7*h. Let b(j) = 6*i(j) + 14*w(j). Factor b(q).
-4*q**2*(q - 69)*(q - 1)**2
Let f(l) be the first derivative of -2*l**3/33 + 680*l**2/11 - 1358*l/11 + 7749. Factor f(t).
-2*(t - 679)*(t - 1)/11
Suppose 0 = 4*n + 5*b + 15, 4 = -59*n + 58*n - b. Let t be (n/((-100)/45) - 2)*12. Factor 3 - 3/5*a**t - 33/5*a + 21/5*a**2.
-3*(a - 5)*(a - 1)**2/5
Let w = 1084/4301 + -39/187. Let u(h) be the second derivative of 7*h + w*h**2 + 0*h**3 + 0 - 1/138*h**4. Factor u(l).
-2*(l - 1)*(l + 1)/23
Let w(z) = -z**4 - z**3 - 9*z**2 + 1. Let p(g) = 4*g**4 + 20*g**3 + 12*g**2 + 18*g + 6. Let t(j) = 2*p(j) - 4*w(j). Suppose t(q) = 0. Calculate q.
-1, -2/3
Let f(y) be the first derivative of -y**3/5 - 45*y**2 - 888*y/5 + 7965. Let f(z) = 0. What is z?
-148, -2
Suppose -3*c = 2*v - 85, -7 - 8 = -3*v. Suppose 9506*j**3 - 7*j**2 - c*j**2 - 9614*j**3 - 34*j**4 + 6*j**5 = 0. Calculate j.
-2, -1/3, 0, 8
Let c = -8035/3 + 2721. Let p(d) = d**3 + 14*d**2 + 24*d + 2. Let h be p(-12). Suppose -2/3*k**h - c - 32/3*k = 0. What is k?
-8
Let o = -6040 + 6042. Let u(n) be the first derivative of 0*n**2 - 1/8*n**4 + 10 - 1/2*n**3 + o*n. Find h, given that u(h) = 0.
-2, 1
Suppose 5*v + 25 - 6 = 2*g, -v + 1 = 2*g. Let d be (1 - 5)*(-5)/40. Solve 0*l + d - 3/2*l**g - l**3 = 0 for l.
-1, 1/2
Let h = 95 + -46. Factor -m**2 - 8 + 10*m - 17*m**3 + h*m**3 - 33*m**3.
-(m - 2)*(m - 1)*(m + 4)
Let x = 50 - 36. Solve -38*i**2 + 38*i**4 + 484*i - x*i**5 + 8*i**3 + 18*i**3 - 496*i = 0 for i.
-1, -2/7, 0, 1, 3
Let k(p) be the third derivative of 4*p**7/1785 + 13*p**6/1020 - p**5/6 - 59*p**4/102 - 8*p**3/17 - 113*p**2. Solve k(m) = 0.
-6, -1, -1/4, 4
Let f(i) be the third derivative of -11*i**8/336 + 34*i**7/105 - 23*i**6/120 - 131*i**5/30 - 16*i**4/3 + 16*i**3/3 - 307*i**2. Determine a so that f(a) = 0.
-1, 2/11, 4
Solve -3/7*j**3 + 0*j + 3/7*j**5 + 12/7*j**4 + 0 - 12/7*j**2 = 0 for j.
-4, -1, 0, 1
Let f(a) = -4*a + 11. Let l be f(9). Let z(t) = 11*t - 36 - 46*t - 28*t**2 + 29*t**2. Let j(c) = -5*c**2 + 140*c + 145. Let u(x) = l*z(x) - 6*j(x). Factor u(q).
5*(q + 1)*(q + 6)
Solve -1581/2*r**2 - 660*r + 3/2*r**5 + 129/2*r**4 + 726 + 1317/2*r**3 = 0.
-22, -1, 1
Let a(f) be the third derivative of f**6/540 + 11*f**5/54 + 199*f**4/108 - 85*f**3/9 + 541*f**2. Factor a(h).
2*(h - 1)*(h + 5)*(h + 51)/9
Suppose 17*d = 119 + 17. Suppose -l + d = 6. Suppose 4/3*p**4 + 2/3*p**5 + 0*p**l + 0*p + 2/3*p**3 + 0 = 0. Calculate p.
-1, 0
Determine u, given that 111/2*u + 105/4*u**4 + 0 - 105/4*u**2 + 3/4*u**5 - 225/4*u**3 = 0.
-37, -1, 0, 1, 2
Let m(x) be the first derivative of x**3/3 + 25*x**2 + 49*x + 2060. Solve m(b) = 0.
-49, -1
Let w(v) = -v**5 + 3*v**3 - 2*v**2 + v - 1. Let m(k) = 6*k**5 - 33*k**4 - 371*k**3 - 458*k**2 - 141*k - 3. Let f(b) = m(b) - 3*w(b). Factor f(p).
p*(p - 9)*(p + 4)*(3*p + 2)**2
Let a(c) be the second derivative of -1/36*c**4 - 147/2*c**2 - 7/3*c**3 + 4*c + 1. Solve a(p) = 0 for p.
-21
Let i = 791/111 - -131/37. Factor -86/3*l**2 + 10/3*l**3 + 44/3*l + i.
2*(l - 8)*(l - 1)*(5*l + 2)/3
Let l = -1552 - -1556. Let b(a) be the third derivative of 1/84*a**l + 0*a + 0*a**5 + 0 + 0*a**3 + 14*a**2 - 1/420*a**6. Find w, given that b(w) = 0.
-1, 0, 1
Let i(j) be the third derivative of 0*j**3 + 2/525*j**7 + 0 - 20*j**2 + 32/25*j**5 - 11/75*j**6 + 48/5*j**4 + 0*j. Solve i(z) = 0.
-2, 0, 12
Let v = -1325 - -1326. Let q be 9/v - 4623/552. What is j in 9/8*j + q*j**2 - 1/4 = 0?
-2, 1/5
Let h(f) be the second derivative of -f**4/18 - 26*f**3/9 - f - 402. Factor h(u).
-2*u*(u + 26)/3
Let d(u) = -2*u + 33. Let z be d(15). Suppose 3*a + 105 = -0*j + z*j, 0 = -5*j + 3*a + 177. Factor 31*w**4 + 5*w**2 + 0*w**2 + 5*w**3 - j*w**4 - 5*w.
-5*w*(w - 1)**2*(w + 1)
Let a be (2 - 7/2)/(-5 + 497/112). Let y(k) be the first derivative of 2/9*k**3 + a*k + 5/3*k**2 - 17. Factor y(i).
2*(i + 1)*(i + 4)/3
Suppose -9 = -3*d, 4*l + 0*d - 3 = -d. Suppose 2*p + 1 = -3, -3*j - 4*p - 5 = l. Factor -j + 0*f + f + 3 - f**2.
-(f - 2)*(f + 1)
Let l(g) = -g**2 + 7*g - 6. Let s be l(6). Let u = 10 + s. Solve 2*r**5 - 17 + u*r**3 - 4*r**4 - 12*r**3 + 4*r**2 + 17 = 0.
-1, 0, 1, 2
Suppose -2*c = 2 - 4, -2*f + 3*c + 49 = 0. Suppose -b = -4*i - f, 0 = -3*i - 0*i - 3. Factor -b*v + 16 - 14*v**2 + 18*v**2 + 128 - 26*v.
4*(v - 6)**2
Let i be 12*((-20)/(-15) + -1) + 0. Suppose 4 + 17 + 5*s**i + 30*s**2 - 20*s - 20*s**3 + 0*s - 16 = 0. What is s?
1
Factor -1/6*k**2 + 56/3*k - 56/3*k**3 + 0 + 1/6*k**4.
k*(k - 112)*(k - 1)*(k + 1)/6
Let 32 + 1/8*d**2 - 257/8*d = 0. Calculate d.
1, 256
Let s = -384 - -387. Let k be (s + -3)*(-7 - (-18)/3). Solve 12/5 + k*m - 3/5*m**2 = 0.
-2, 2
Suppose 3 = m - 3. Let a be 8/m*(-4 + 7). Factor 8*c**2 - 31 + 31 + a*c.
4*c*(2*c + 1)
Let x = 982611/5 - 196521. Solve -1/5*w**4 + x + 3/5*w**2 + 11/5*w - 3/5*w**3 = 0.
-3, -1, 2
Let l(k) be the second derivative of -1/12*k**3 + 11/20*k**5 - 19/48*k**4 - 23/120*k**6 + 0*k**2 - 6*k - 3. Factor l(r).
-r*(r - 1)**2*(23*r + 2)/4
Let f(y) be the third derivative of -154*y**2 - 5/21*y**3 - 3/35*y**5 + 0*y - 4/21*y**4 - 2/105*y**6 + 0 - 1/735*y**7. Factor f(q).
-2*(q + 1)**3*(q + 5)/7
Let g be (13 + -3 - 3) + 