 n = 324 + -325. Let l(c) = c**3 + c - 1. Let q(o) = n*s(o) + 2*l(o). Factor q(z).
-2*(z + 2)**3
Suppose 8 = -4*s + 5*s. Suppose -50*l + 48*l + 10 = 0. Factor 13*k**5 - 7*k**2 - s*k**l + 20*k**4 - 11*k**2 - 25*k - 10 + 8*k**2 + 20*k**3.
5*(k - 1)*(k + 1)**3*(k + 2)
Let m(t) = 283*t**2 - 23205*t - 80. Let i be m(82). Factor -750 + 100*n + 5/2*n**3 + 85/2*n**i.
5*(n - 3)*(n + 10)**2/2
Let k(v) be the third derivative of 47*v**2 - 1/90*v**5 + 0 + v**3 - 2/9*v**4 + 0*v. What is x in k(x) = 0?
-9, 1
Let m(u) be the second derivative of 1/45*u**6 + 1/30*u**5 - 1/9*u**3 + 70*u + 0 - 1/18*u**4 + 0*u**2. Solve m(v) = 0 for v.
-1, 0, 1
Let p(m) = -m**3 - 2*m**2 + 2*m + 11. Let d be p(0). Suppose 20 = d*l - l. Suppose -1471*v + 0*v**l + 48 + 3*v**2 + 1447*v = 0. Calculate v.
4
Let s(x) be the first derivative of 2*x**3/51 - 346*x**2/17 + 59858*x/17 + 6351. Factor s(v).
2*(v - 173)**2/17
Let a be 52/35 - (-4)/(-14). Let d = 231605 - 1158024/5. Factor a + d*h**2 + h.
(h + 2)*(h + 3)/5
Let x = -351454/441 + 7156/9. Let s = 1954/637 + x. Factor -40/13*o - 14/13*o**3 + s - 4*o**2.
-2*(o + 2)**2*(7*o - 2)/13
Let g(t) = -10*t + 150. Suppose 5*c - 5*j - 65 = 20, 4*c - 5*j = 71. Let a be g(c). Solve -5/4*w**2 + 0 + a*w = 0 for w.
0, 8
Let i(s) be the third derivative of -s**7/420 - s**6/36 + s**5/10 + 43*s**3/3 + 78*s**2. Let a(c) be the first derivative of i(c). Factor a(o).
-2*o*(o - 1)*(o + 6)
Solve -8/9*f**3 + 2/9*f**5 + 0 - 32/3*f**2 + 0*f + 8/3*f**4 = 0.
-12, -2, 0, 2
Let r be 6/(-21) + 4/7. Let l = 2042/14441 + 3/2063. Solve l*b**4 + 0 + r*b**3 + 0*b + 0*b**2 = 0.
-2, 0
Let h(j) be the third derivative of j**5/15 - 1469*j**4/2 + 8812*j**3/3 - 14258*j**2. Factor h(z).
4*(z - 4406)*(z - 1)
Let b(n) = -3*n**4 - 8*n**3 + 7*n**2 + 16*n + 2. Let u(i) = 2*i**4 + i**2 + i - 1. Let p(t) = b(t) + 2*u(t). Factor p(y).
y*(y - 6)*(y - 3)*(y + 1)
Let m(b) be the second derivative of b**6/150 + b**5/10 + 31*b**4/60 + b**3 + 2115*b. Let m(o) = 0. Calculate o.
-5, -3, -2, 0
Let d be 970/9 - (-76)/342. Let 16 + 2*k**4 + 50*k - 12*k**2 + 2*k**3 - d*k + 50*k = 0. What is k?
-2, 1, 2
Let l be 5/(-4) - ((-8040)/288 + 26). Solve -8/21*s**2 + l + 18/7*s = 0.
-1/4, 7
Let p(g) be the second derivative of -g**4/6 - 2852*g**3/3 - 2033476*g**2 - 5257*g. Determine o, given that p(o) = 0.
-1426
Suppose -14*x - 4 + 74 = 0. Let y be (2142/36)/17 + (0 - 1). Solve x*m - y*m**2 - 5/2 = 0 for m.
1
Find p such that 214/17*p**2 + 5850/17 + 2/17*p**3 - 2290/17*p = 0.
-117, 5
Suppose 820125/2 + 135/2*u**2 + 18225/2*u + 1/6*u**3 = 0. What is u?
-135
Let b be (294/(-12))/(-1 + 2). Let p = b - -149/6. Factor 1/9*j**5 + 0 + 0*j + 0*j**2 + 2/9*j**3 - p*j**4.
j**3*(j - 2)*(j - 1)/9
Suppose -216*z = -261*z + 487*z. Suppose z*d - 176/3*d**2 + 0 + 4/3*d**3 = 0. Calculate d.
0, 44
Let v(g) be the second derivative of -g**6/660 + g**4/132 + 7*g**2/2 - 15*g - 5. Let d(o) be the first derivative of v(o). Suppose d(m) = 0. What is m?
-1, 0, 1
Let h(t) be the second derivative of t**5/45 + 67*t**4/27 - 92*t**3/9 + 13427*t. Factor h(g).
4*g*(g - 2)*(g + 69)/9
Factor 97*w**2 - 12 - 314*w + 19 - 119*w**2 + 340*w**2 - 11.
2*(w - 1)*(159*w + 2)
Let n(a) be the first derivative of -6*a**5/35 + 43*a**4/7 - 274*a**3/21 + 54*a**2/7 + 1986. What is g in n(g) = 0?
0, 2/3, 1, 27
Factor 0*x + 0 - 4/7*x**4 + 1804/7*x**3 + 1808/7*x**2.
-4*x**2*(x - 452)*(x + 1)/7
Let f = 374297/3 + -124764. Find k such that -f*k + 1 + 7/9*k**2 - 1/9*k**3 = 0.
1, 3
Let w = -106 - -109. Determine y so that y**4 + 4 + y**5 + 4*y + w*y**5 - 5*y**2 - 5*y**3 + 3*y**5 - 6*y**5 = 0.
-2, -1, 1, 2
Suppose 522*n = 256*n + 42*n - 469*n. What is k in 1/7*k**3 + 2/7*k**2 + 0 + n*k = 0?
-2, 0
Let x(w) be the second derivative of -w**6/160 + w**5/60 + 7*w**4/24 + 2*w**3/3 - 23*w**2/2 - w + 8. Let g(j) be the first derivative of x(j). Factor g(a).
-(a - 4)*(a + 2)*(3*a + 2)/4
Let c be ((-182)/(-572))/((-13)/(-143)). Factor 18 - 15*v + c*v**2 - 1/4*v**3.
-(v - 6)**2*(v - 2)/4
Solve -4/7*x**2 + 184/7*x - 96 = 0.
4, 42
Let s = 697 + -616. Suppose -s + 77 = -c. Factor -3/4*d**3 + 0*d + 1/4*d**5 + 0 + 0*d**c - 1/2*d**2.
d**2*(d - 2)*(d + 1)**2/4
Let m(p) = 2*p**2 + 38*p + 1. Let a(z) = z**2 + 194*z - 1477. Let k(n) = -a(n) - 2*m(n). Factor k(d).
-5*(d - 5)*(d + 59)
Factor -2656/9 + 2/9*s**2 - 1324/9*s.
2*(s - 664)*(s + 2)/9
Let m(x) = -x**2 + x + 2. Let w(y) = 9 - 5 - 39*y**2 + 2*y**3 + 8*y**2 - 7*y**2 + 164*y. Let k(q) = -4*m(q) + 2*w(q). Factor k(g).
4*g*(g - 9)**2
Let d be (-60)/(-10)*(-2)/(-4). Factor -f**3 - 3961*f**4 + 3937*f**4 + d*f**5 + 49*f**3.
3*f**3*(f - 4)**2
Let k be ((-8)/10)/(10/(-525)). Suppose -2*f + 4*r + 100 = 0, -58 = -4*f - 2*r + 102. Let -k*q - 2*q**3 + 0*q**2 + f*q - 2*q**2 = 0. Calculate q.
-1, 0
Suppose -87*x - 1 = 49*x - 1. Let q(y) be the second derivative of 1/33*y**3 + x - 20*y + 1/66*y**4 + 0*y**2. Factor q(l).
2*l*(l + 1)/11
Let g(h) be the second derivative of -h**5/30 + 11*h**4/3 + 5*h**2/2 + 11*h. Let i(v) be the first derivative of g(v). Factor i(m).
-2*m*(m - 44)
Suppose 46*s**4 - 52*s**2 - 14*s**5 + 21*s**3 + 22*s**2 - 232*s**2 + 149*s**3 + 60*s = 0. What is s?
-3, 0, 2/7, 1, 5
Let d(r) = -60*r - 958. Let v be d(-16). Find f such that -231/4*f + 15*f**v - 363/2 - 3/4*f**3 = 0.
-2, 11
Let w(o) be the third derivative of 3/44*o**4 - 2/55*o**5 + 9*o**2 + 0*o - 5 + 1/11*o**3. Factor w(h).
-6*(h - 1)*(4*h + 1)/11
Let r(k) be the first derivative of -k**5/60 + k**4/10 - 2*k**3/15 + 18*k**2 - 89. Let g(t) be the second derivative of r(t). Determine d so that g(d) = 0.
2/5, 2
Suppose 4*q = -99*d + 106*d + 35, 3*q - 63 = -7*d. Factor 0 + 6/7*f**4 - 2/7*f**5 - 4/7*f**d + 0*f**2 + 0*f.
-2*f**3*(f - 2)*(f - 1)/7
Let w(y) be the first derivative of 18 - 1/11*y - 41/22*y**2 + 14/11*y**3. Factor w(u).
(u - 1)*(42*u + 1)/11
Let m be (4/18)/(((-244)/(-36) - -10) + -11). Let h(j) be the first derivative of -2/13*j + m*j**4 - 2/13*j**3 - 29 + 3/13*j**2. Let h(d) = 0. What is d?
1
Let q(s) = 2*s**3 + 4*s**2 + 5*s - 9. Let h be q(-4). Let p = 45 - h. Find b, given that 285*b**2 + 5*b - p*b**2 - 142*b**2 = 0.
-1, 0
Let u(s) = s**2 + s + 1. Let j(w) = -w - 5. Let k be j(-6). Let t(i) = 14*i - 16. Suppose 57 = -35*g - 45 + 32. Let f(n) = g*u(n) + k*t(n). Factor f(q).
-2*(q - 3)**2
Factor 125/2 + 32*y**2 - 377/4*y - 1/4*y**3.
-(y - 125)*(y - 2)*(y - 1)/4
Let v(z) be the second derivative of -11/10*z**5 - 1/6*z**4 + 121*z + 1/42*z**7 + 11/2*z**2 - 3/10*z**6 + 7/2*z**3 + 0. Factor v(f).
(f - 11)*(f - 1)*(f + 1)**3
Let w(a) be the second derivative of 81*a + 5/18*a**3 + 0*a**2 - 5/36*a**4 + 0. Factor w(t).
-5*t*(t - 1)/3
Suppose -93 + 717*l**2 + 1203/2*l + 45/2*l**3 = 0. What is l?
-31, -1, 2/15
Let t(r) be the first derivative of -r**7/945 + r**6/180 + r**5/270 - r**4/36 - 195*r**2/2 - 101. Let o(s) be the second derivative of t(s). Factor o(v).
-2*v*(v - 3)*(v - 1)*(v + 1)/9
Suppose -3*d - 12 = 0, 5*d + 13 = 3*o - 13. Determine m so that 407*m + 169*m + 256 - 363*m**5 - 495*m**4 + 1308*m**3 + 1968*m**o - 208 = 0.
-2, -1, -2/11, 2
Let o(s) = 0*s + 2*s**3 + 2*s + 10*s - 2*s - 9. Let n(x) = 3*x**3 + x**2 + 18*x - 19. Let a(r) = -3*n(r) + 5*o(r). Solve a(b) = 0 for b.
-2, 2, 3
Let a(h) = -h**3 - h + 1. Let n(f) = -f**2 + 5*f + 3. Let w be ((-19)/(-5) - 3)/((-2)/(-10)). Let u(p) = w*a(p) + 4*n(p). Solve u(k) = 0 for k.
-2, -1, 2
Let t(v) be the second derivative of v**4/6 - v**3/6 - v**2/2 - 2*v + 10. Let m(p) = 11*p**2 + 15*p + 95. Let w(y) = m(y) - 5*t(y). Factor w(x).
(x + 10)**2
Let v be -4 - (558/(-96)*-62 - 6). Let p = -358 - v. Factor -1/8*d**2 + p*d - 1/4.
-(d - 2)*(d - 1)/8
Suppose -12*q = 12*q - 57 - 39. Let s(t) be the first derivative of 61/2*t**2 + 32 + 14*t - 7/4*t**q + 40/3*t**3. Factor s(k).
-(k - 7)*(k + 1)*(7*k + 2)
Let c be 20/(-6)*(-27)/45. Factor 4 + 17 - 10 - 80*z - 12*z**c + 17.
-4*(z + 7)*(3*z - 1)
Factor -225*p**3 + 737*p**3 + 64*p**2 + 9*p**4 - 247*p**3 - 218*p**3 + 12*p.
p*(p + 2)*(p + 3)*(9*p + 2)
Factor 455*h**2 - 1367*h**2 + 454*h**2 - 1292*h + 208658 + 460*h**2.
2*(h - 323)**2
Let h(p) = -p**3 + 396*p**2 + 29*p - 408. Let t(j) = 2*j**3 - 1187*j**2 - 93*j + 1226. Let d(w) = 13*h(w) + 4*t(w). Factor d(z).
-5*(z - 80)*(z - 1)*(z + 1)
Let n(y) be the first derivative of 10*y - 120 - 4*y**3 + 2/5*y**5 - 4*y**2 + 2*y**4. Factor