 Let k = 1136 + a. Factor 8/3*z + k - 2/3*z**2.
-2*z*(z - 4)/3
Let -260/3*t**3 + 0*t**2 + 256/3*t**4 + 0*t + 0 + 4/3*t**5 = 0. Calculate t.
-65, 0, 1
Solve 7263/2*b**3 + 100 - 9373/6*b**4 - 98/3*b**5 + 3206/3*b + 11039/3*b**2 = 0.
-50, -2/7, -1/4, 3
Suppose 2*j = -h + 12, 2*j - 17*h + 12 = -12*h. Let t(c) be the second derivative of 1/6*c**3 + 0*c**2 + 13*c - 1/12*c**j + 0. Factor t(a).
-a*(a - 1)
Let 26/3*h**3 + 1/3*h**4 + 9 - 26/3*h - 28/3*h**2 = 0. Calculate h.
-27, -1, 1
Solve -62/7*w + 2/21*w**2 + 184/21 = 0 for w.
1, 92
Factor 2691/5*w - 2688/5*w**2 + 0 - 3/5*w**3.
-3*w*(w - 1)*(w + 897)/5
Find t such that -32*t + 6*t**2 + 4 + 28*t - 135*t**2 - 4 = 0.
-4/129, 0
Let u = -41 - -42. Let y(z) = -z**2 + z. Let n(w) = -4*w**2 - w**3 - 6 + 13*w - 21*w - 3*w**2 + 2. Let a(v) = u*n(v) - y(v). Factor a(c).
-(c + 1)**2*(c + 4)
Suppose 3*h + 0*y = -y + 21, -4*y - 12 = 0. Let c(x) = -x - 1. Let b(g) = 10*g**2 + 12*g + 8. Let l(k) = h*c(k) + b(k). Suppose l(v) = 0. What is v?
-2/5, 0
Factor -3/2*q**3 - 2997/2*q + 177/2*q**2 + 10935/2.
-3*(q - 27)**2*(q - 5)/2
Suppose 5*m + 25 = 0, 38*m + 1 = -3*w + 36*m. Suppose 492*s**3 + 592*s**2 - 20*s**4 + 2*s**w - 122*s**3 - 320 - 624*s = 0. Calculate s.
-2, -2/5, 1, 20
Let p = -3065/7 - -30657/70. Let v(a) be the second derivative of 1/100*a**5 + 36*a - 1/10*a**4 + 2 + p*a**3 + a**2. What is h in v(h) = 0?
-1, 2, 5
Let j be 42/(-28)*-4*1/3. Let w be (2 + 51/(-27))/((-27)/(2673/(-110))). Solve -1/5*a - w*a**3 + 3/10*a**j + 0 = 0.
0, 1, 2
Let v = 1031 - 1026. Factor -20/11*w**4 - 80/11*w**2 + 2/11*w**v + 0 + 32/11*w + 6*w**3.
2*w*(w - 4)**2*(w - 1)**2/11
Let u(q) be the first derivative of q**5/4 - 5*q**4/2 - 75*q**3 - 37. Solve u(c) = 0.
-10, 0, 18
Let t(q) be the second derivative of q**5/40 - q**4/16 - 3*q**3/2 + 20*q**2 - 48*q - 1. Let g(h) be the first derivative of t(h). Factor g(y).
3*(y - 3)*(y + 2)/2
Let p(y) be the third derivative of 0*y**5 + 13*y**2 - 3 + 1/70*y**7 + 0*y**3 + 0*y - 1/224*y**8 - 1/80*y**6 + 0*y**4. Factor p(t).
-3*t**3*(t - 1)**2/2
Let p(g) be the third derivative of g**7/168 + g**6/32 - 3*g**5/2 - 135*g**4/8 + 820*g**2. Let p(q) = 0. What is q?
-6, 0, 9
Let l(t) be the first derivative of -5*t**4/4 - 100*t**3/3 + 345*t**2/2 - 1278. Factor l(v).
-5*v*(v - 3)*(v + 23)
Let w(c) = -c**2 + 5190*c - 6734151. Let k(b) = b**2 - 5190*b + 6734133. Let r(o) = 7*k(o) + 6*w(o). Factor r(y).
(y - 2595)**2
Let u = -3/116 - -967/1508. Suppose 859*o - 855*o + 4*s - 48 = 0, 4*o - 5*s = -60. Factor u*m + o*m**2 + 0 - 2/13*m**4 - 6/13*m**3.
-2*m*(m - 1)*(m + 2)**2/13
Let d(o) = 4*o + 92. Let b be d(-20). Factor b*h + 5*h**2 - 21 - 6*h**2 + 10*h.
-(h - 21)*(h - 1)
Suppose -46 - 50 = -6*v. Suppose 2*r = -4*t - v, 0 = r + 4*t + 3 + 15. Factor -388*l + 2*l**4 - 17*l - 225*l**r - 55*l**3 + 5*l**4 - 12*l**4 - 270.
-5*(l + 2)*(l + 3)**3
Let r(c) = -7*c**2 + 108*c + 653. Let q(n) = -19*n**2 + 213*n + 1307. Let l(s) = 2*q(s) - 5*r(s). Factor l(v).
-3*(v + 7)*(v + 31)
Let i(d) be the second derivative of -21*d**5/20 - 233*d**4/4 - 348*d**3 - 270*d**2 + 347*d. Suppose i(c) = 0. Calculate c.
-30, -3, -2/7
Let i(d) be the third derivative of -d**5/210 - 61*d**4/42 - 440*d**3/7 - 2*d**2 - 10586*d. Find b, given that i(b) = 0.
-110, -12
Let b(i) be the second derivative of -i**6/600 + i**5/60 - 7*i**4/120 + i**3/10 + 165*i**2/2 - 59*i - 1. Let q(o) be the first derivative of b(o). Factor q(y).
-(y - 3)*(y - 1)**2/5
Let r(o) = -2*o**2 - 30*o + 3. Let q be r(-15). Let v be 65/(-130) + 2 + -1. Solve -2*c + 25/2*c**q + 25/8*c**2 - v = 0 for c.
-2/5, -1/4, 2/5
Let z(s) be the second derivative of s**5/15 + s**4/6 - 4*s**3/3 + 31*s**2 - 56*s. Let h(i) be the first derivative of z(i). Suppose h(o) = 0. What is o?
-2, 1
Let d = 26357/30 + -4392/5. Let a(p) be the third derivative of -5/12*p**5 + 5/12*p**4 + 1/14*p**7 + 0*p + 4*p**2 + 0*p**3 - d*p**6 + 0. Factor a(z).
5*z*(z - 2)*(z + 1)*(3*z - 1)
Let u be 117/468*(624/(-14))/(-13). Factor -4374/7 + 324/7*j - u*j**2.
-6*(j - 27)**2/7
Let w(x) be the third derivative of -55/12*x**5 - 95/8*x**4 + 0 + 121/24*x**6 - 15/2*x**3 - 40*x**2 + 0*x. Factor w(s).
5*(s - 1)*(11*s + 3)**2
Let f(w) be the first derivative of -2*w**4 - 3*w**4 + 31*w**2 + 6*w**4 + 84 - 33*w**2. What is r in f(r) = 0?
-1, 0, 1
Let v(m) be the third derivative of -m**6/120 + m**5/60 + m**2 - 17*m. Let l(j) = j**4 - 6*j**2 + 2*j + 3. Let a(f) = -l(f) - 2*v(f). Let a(s) = 0. What is s?
-1, 1, 3
Let x = 347 + -210. Factor 4*w**3 - 67*w**2 - 4*w - 94*w**2 + x*w**2 + 24.
4*(w - 6)*(w - 1)*(w + 1)
Let q(c) be the first derivative of c**4/10 + 77*c**3/15 + 37*c**2/10 - 38*c/5 + 1824. Factor q(f).
(f + 1)*(f + 38)*(2*f - 1)/5
Let t(a) be the third derivative of -1/900*a**6 + 0 + 1/6*a**4 - 14/3*a**3 - 35*a**2 + 1/100*a**5 + 0*a. Let b(v) be the first derivative of t(v). Factor b(w).
-2*(w - 5)*(w + 2)/5
Suppose -85/2*n + 11/2*n**2 - 1/6*n**3 + 575/6 = 0. Calculate n.
5, 23
Let b(m) be the third derivative of m**5/270 - 1753*m**4/54 + 3073009*m**3/27 - 2*m**2 + 989*m. Factor b(n).
2*(n - 1753)**2/9
Find u such that 243/2*u**2 - 1/2*u**4 - 187*u + 84 - 18*u**3 = 0.
-42, 1, 4
Let p be (450/300)/(6/8). Factor 33 - 9*h**2 + 18*h**2 - 5*h**p - 30*h - 3*h**2 - 4*h**2.
-3*(h - 1)*(h + 11)
Solve -40*k - 4 - 6313526*k**4 + 6313522*k**4 + 52*k**2 + 4 - 8*k**3 = 0 for k.
-5, 0, 1, 2
Let 74*v - 29*v**2 + 116*v + 9025 + 30*v**2 = 0. Calculate v.
-95
Let j = -55194 + 386366/7. Suppose -40/7*b + 22/7*b**2 - j = 0. Calculate b.
-2/11, 2
Let l(o) = -4*o**3 + 2181*o**2 - 23*o - 2154. Let m(s) = 5*s**3 - 2180*s**2 + 25*s + 2150. Let p(a) = 10*l(a) + 9*m(a). Solve p(d) = 0.
-438, -1, 1
Let p(v) = 234*v - 13568. Let w be p(58). Let m(t) be the second derivative of -1/7*t**2 + 1/42*t**3 + 0 + 1/84*t**w + 24*t. Suppose m(u) = 0. Calculate u.
-2, 1
Let s(m) be the third derivative of m**7/525 - 7*m**6/50 + 109*m**5/30 - 177*m**4/5 + 108*m**3 + 1861*m**2. Let s(b) = 0. Calculate b.
1, 5, 18
Let l(o) be the third derivative of o**8/2520 - 17*o**7/1575 + 13*o**6/150 - 7*o**5/225 - 67*o**4/36 - 5*o**3 - 2643*o**2 + 1. Determine h, given that l(h) = 0.
-1, 5, 9
Let q(j) be the first derivative of -j**4/46 + 1078*j**3/69 + 47*j**2 + 1082*j/23 + 3460. Factor q(c).
-2*(c - 541)*(c + 1)**2/23
Let b(w) be the first derivative of 14 - 2/7*w**2 + 0*w + 2/21*w**3. Factor b(d).
2*d*(d - 2)/7
Let b(z) be the first derivative of -z**5/60 - 5*z**4/24 - z**3 + z**2 - 59*z - 6. Let h(i) be the second derivative of b(i). Factor h(v).
-(v + 2)*(v + 3)
Let n(q) be the first derivative of 4/25*q**5 - 51 + 24/5*q**3 + 4*q - 32/5*q**2 - 8/5*q**4. Solve n(l) = 0.
1, 5
Factor -2/3*l**4 + 8*l - 50/3*l**2 + 28/3*l**3 + 0.
-2*l*(l - 12)*(l - 1)**2/3
Let r(g) be the second derivative of g**7/630 - g**6/180 + g**4/36 - g**3/18 - 11*g**2/2 + 2*g + 3. Let w(m) be the first derivative of r(m). Factor w(u).
(u - 1)**3*(u + 1)/3
Let g be (-5 + 7 - 0)/(2/10). Suppose 4*z - 140 = -g*z. Factor -8 - 6*p + 6*p - 16*p + z*p**2.
2*(p - 2)*(5*p + 2)
Let r(t) be the second derivative of -t**6/3 + 49*t**5/55 + 193*t**4/66 + 28*t**3/33 - 12*t**2/11 - 1602*t. Let r(l) = 0. Calculate l.
-1, -2/5, 2/11, 3
Let x = 93854 - 93851. Solve 16/9*i**4 + 0 + 32/9*i**2 + 2/9*i**5 + 0*i + 40/9*i**x = 0 for i.
-4, -2, 0
Let f(m) be the third derivative of -m**7/105 - m**6/10 - 11*m**5/30 - m**4/2 + 196*m**2 - 5*m. Let f(n) = 0. What is n?
-3, -2, -1, 0
Let i(w) be the first derivative of -w**4/14 + 16*w**3/21 - 5*w**2/7 - 115*w + 60. Let t(h) be the first derivative of i(h). Suppose t(x) = 0. What is x?
1/3, 5
Let v(c) = c**3 + 4*c**2 - 14*c - 7. Let u be v(-6). Factor -5*a - 16 + 22 - u*a**2 + 4.
-5*(a - 1)*(a + 2)
Let s(k) be the second derivative of k**5/70 + 53*k**4/42 - 18*k**3/7 + 1434*k. Factor s(m).
2*m*(m - 1)*(m + 54)/7
Suppose 36 + 21 = 19*l. Suppose -l*y + 2 = 3*i - 2*i, 4*i + 7 = 3*y. Solve 25/4*n**2 - 5*n + y = 0.
2/5
Let k(r) = r**2 - 5*r + 5. Let i(u) = 6*u**3 + u**2 - u. Let d be i(1). Let j be k(d). Factor 4*p**4 - j + 11 + 4*p**3.
4*p**3*(p + 1)
What is i in 5774405 - 17097*i - 7071*i - 43*i**2 - 54*i**2 + 30731359 + 101*i**2 = 0?
3021
Let m(d) = -2*d**3 + 12*d**2 - 7*d + 10. Let o be m(9). Let l = o + 539. Factor -2/3*w**2 + l*w**3 + 2/3*w**4 + 0 + 0*w.
2*w**2*(w - 1)*(w + 1)/3
Let r