Let i(d) be the third derivative of -1/180*d**4 + 2/15*d**3 - 1/450*d**5 + k - 2*d - 5*d**2. Factor i(y).
-2*(y - 2)*(y + 3)/15
Let b(c) = 14*c + 6*c + 2562 + 5*c**2 - 4*c**2 - 2473. Let n be b(-14). Find r, given that 2/7*r + 0*r**3 + 5/7*r**4 - 2/7*r**n + 0 - 5/7*r**2 = 0.
-1, 0, 1/2, 1, 2
Determine h so that -177*h**3 + 23*h**2 + 4*h**4 + 149*h**3 + 41*h**2 - 33*h - 15*h = 0.
0, 2, 3
Let i = -5633 - -5636. Let b(l) be the second derivative of 0*l**2 + 1/3*l**i + 0 - 11*l + 1/12*l**4 - 1/20*l**5. Determine q so that b(q) = 0.
-1, 0, 2
Let b(h) be the first derivative of -73 + 7/9*h**2 - 8/3*h - 2/27*h**3. Factor b(w).
-2*(w - 4)*(w - 3)/9
Let g = -6116 + 6116. Let s(f) be the second derivative of 15*f - 3/4*f**5 + 1/3*f**6 + 15/2*f**2 - 5/6*f**3 - 15/4*f**4 + g. Factor s(l).
5*(l - 3)*(l + 1)**2*(2*l - 1)
Factor -6*i + 1/3*i**3 + i**2 + 0.
i*(i - 3)*(i + 6)/3
Suppose -287*v = -296*v + 2286. Let a be (-107)/(-1391) - v/(-78). Suppose -22/3*b**2 + a*b**3 + 2*b + 2*b**4 + 0 = 0. Calculate b.
-3, 0, 1/3, 1
Let z(j) = -11*j**3 + 38*j**2 + 41*j. Let x(d) = -5*d**3 - 2*d**2 - d. Let q(y) = 4*x(y) - 2*z(y). Factor q(w).
2*w*(w - 43)*(w + 1)
Let k be (209/(-627))/(27/6 + -5). Factor -1/2*j + k*j**2 + 0 - 1/6*j**3.
-j*(j - 3)*(j - 1)/6
Let r = 41 + -39. Suppose 3*p + r*o = 79, 0*p - o = 2*p - 52. Factor 41*g - 180 + p*g - 6*g - 5*g**2.
-5*(g - 6)**2
Let b(n) be the first derivative of -n**4/24 - n**3/2 + 43*n**2/4 - 119*n/6 - 6970. Factor b(u).
-(u - 7)*(u - 1)*(u + 17)/6
Let j(h) be the third derivative of -h**6/180 - h**5/3 - 21*h**4/4 - 1876*h**2. Find a, given that j(a) = 0.
-21, -9, 0
Suppose -58 = -31*u - 4*o, 7*o - 10*o - 1 = u. Factor -3/2*c**3 + 0 + 3/2*c + 0*c**u.
-3*c*(c - 1)*(c + 1)/2
Let k = 1843 - 1843. Let x(g) be the first derivative of 3/22*g**4 - 2/55*g**5 - 2/11*g**3 + k*g + 1/11*g**2 - 2. Suppose x(m) = 0. Calculate m.
0, 1
Let c be 366 + (13/(-3) - (-100)/(-60)). Suppose c*g - 359*g = 2. Factor -g*q + 5/2 - 1/2*q**2.
-(q - 1)*(q + 5)/2
Suppose -2*p - 15 = -23. What is x in -p*x**3 + 6*x**5 + 12*x**2 + 708*x + 16 - 8*x**4 - 22*x**3 - 668*x = 0?
-1, -2/3, 2
Let i(n) be the third derivative of -n**7/210 - n**6/120 + n**5/15 + n**4/6 + 4086*n**2. Factor i(w).
-w*(w - 2)*(w + 1)*(w + 2)
Let z(a) be the third derivative of 0*a - 1/75*a**5 - 1/60*a**4 + 0*a**3 + 2/525*a**7 + 0*a**6 - 106*a**2 + 0 + 1/840*a**8. Factor z(j).
2*j*(j - 1)*(j + 1)**3/5
Factor -22/3*j + 40/3 - 19/3*j**2 + 1/3*j**3.
(j - 20)*(j - 1)*(j + 2)/3
Find f, given that -1257*f - 1636*f - 270*f - 180 + 5614*f - 116732*f**2 + 6753*f - 23716*f**3 = 0.
-5, 3/77
Let w(i) be the second derivative of i**7/42 - 29*i**6/30 + 63*i**5/10 - 12*i**4 + 2*i + 381. Factor w(y).
y**2*(y - 24)*(y - 3)*(y - 2)
Let b be (((-28)/(-1))/(-14))/(-3). Let i(t) be the second derivative of 20*t + 5/36*t**4 + 4/9*t**3 + 0 + b*t**2 + 1/60*t**5. Let i(l) = 0. Calculate l.
-2, -1
Let g(m) = -22*m + 47. Let f be g(2). Solve 3*u**2 + 23*u**4 - 3*u**5 - 11*u**4 - 9*u**f + 12*u - 15*u**2 = 0.
-1, 0, 1, 2
Let j(s) be the second derivative of 0 - 17/50*s**5 + 0*s**2 + s**4 + 0*s**3 + 1/75*s**6 - 25*s. Factor j(b).
2*b**2*(b - 15)*(b - 2)/5
Suppose 0 = 2*x - 3*w - 16, w - 4*w - 8 = 2*x. Let n = 156490 + -156490. Suppose 0*f + 1/3*f**4 - 1/3*f**x + n + 0*f**3 = 0. What is f?
-1, 0, 1
Let n = -700165 + 700168. What is k in 390*k**2 - 5/2*k**n - 20280*k + 351520 = 0?
52
Factor f - 31/6*f**2 + 0 + 8/3*f**3 + 3/2*f**4.
f*(f - 1)*(f + 3)*(9*f - 2)/6
Let c(f) = -f**2 - 385*f + 390. Let s(u) = -6*u**2 - 2697*u + 2730. Let o(k) = 27*c(k) - 4*s(k). Factor o(d).
-3*(d - 130)*(d - 1)
Suppose 1009*k + 694*k = 83*k - 134*k + 3508. Factor 48/7 + 52/7*w**k - 2/7*w**3 - 14*w.
-2*(w - 24)*(w - 1)**2/7
Let d(j) be the third derivative of 93*j**2 + 1/168*j**8 + 0*j + 0 - 1/15*j**7 - 7/6*j**4 - 1/20*j**6 + 0*j**3 + 23/30*j**5. Let d(c) = 0. Calculate c.
-2, 0, 1, 7
Let q(n) be the first derivative of 2*n**3/15 + 2216*n**2/5 + 2455328*n/5 + 9288. Factor q(o).
2*(o + 1108)**2/5
Let y(v) be the third derivative of -v**5/60 + 35*v**4/12 - 68*v**3/3 - 1620*v**2. Factor y(f).
-(f - 68)*(f - 2)
Let d(s) be the second derivative of -s**4/12 - 16*s**3/3 - 87*s**2/2 - 264*s - 1. Find p such that d(p) = 0.
-29, -3
Let -1/3*j**3 + 0*j + 0 - 632/3*j**2 = 0. Calculate j.
-632, 0
Suppose 8*q - 6231 = -23. Let o = q - 312. Suppose 33*u + 3*u**3 + 482 + 0*u + 18*u**2 - o = 0. What is u?
-3, -2, -1
Let k(a) = -a**2 - 23*a + 78. Let m be k(-26). Factor 1 + 277*s**2 - 1 - 3*s**4 - 250*s**2 + m.
-3*s**2*(s - 3)*(s + 3)
Let a = 5 - -1. Suppose -a*r - 16 = -10*r. Solve 22 + 184*b**2 - 18 + 44*b + 108*b**5 + 360*b**3 + 362*b**4 - 38*b**r = 0 for b.
-1, -1/3
Let c be 300/48 - 5/(-3)*(-60)/25. Let i(b) be the second derivative of c*b**3 + 3/40*b**5 + 0 - 3*b**2 - 14*b - 3/4*b**4. Determine s, given that i(s) = 0.
1, 4
Let y(q) be the second derivative of -q**7/168 - q**6/12 - 37*q**5/80 - 4*q**4/3 - 13*q**3/6 - 2*q**2 - 28*q + 12. What is p in y(p) = 0?
-4, -2, -1
Suppose -36*r + 24*r - 48 = 0. Let t(z) = -z. Let a(m) = -3*m**2 - 4*m - 6*m**2 - 4 + 2*m**2 + 5*m**2. Let b(d) = r*t(d) - 2*a(d). Factor b(u).
4*(u + 1)*(u + 2)
Let t be (-40)/(-140) + (92 - 92)/(5 - (0 - -2)). Factor 0 + 2*p**3 + 0*p - t*p**4 + 0*p**2.
-2*p**3*(p - 7)/7
Suppose 0 = -4*y + 2*v + 110, 12*y = 10*y + 3*v + 57. Factor 24*m**4 - 24 - 54*m**2 + y*m**5 + 207*m**3 + 24 + 132*m**4.
3*m**2*(m + 3)**2*(9*m - 2)
Let p(y) = -5*y**2 + 157*y + 696. Let x(m) = -4*m**2 + 158*m + 688. Let o(w) = 2*p(w) - 3*x(w). Determine d so that o(d) = 0.
-4, 84
Suppose -2*j = 4 - 8. Suppose -j*l + 25 = 21. Find y such that -40*y - y**2 + 4*y - l*y**2 - 205 + 97 = 0.
-6
Factor 0 - 549081*v - 741*v**2 - 1/4*v**3.
-v*(v + 1482)**2/4
Let q(i) be the second derivative of -i**4/3 - 10*i**3/3 + 600*i**2 - 2398*i - 2. Factor q(m).
-4*(m - 15)*(m + 20)
Let i(p) be the first derivative of 8*p**3/3 - 33*p**2 - 164*p - 919. Solve i(q) = 0 for q.
-2, 41/4
Factor 61*o - 9*o**2 + 0*o**2 - 186*o + 420 + o**2 + 3*o**2.
-5*(o - 3)*(o + 28)
Let n(t) be the third derivative of -7/9*t**3 + 74 + 0*t + 1/45*t**5 + t**2 + 13/36*t**4. Factor n(w).
2*(w + 7)*(2*w - 1)/3
Let v(c) = 26*c**4 + 95*c**3 + 36*c**2 - 39*c - 18. Let b(u) = -u**2 - u - 3. Let l(t) = -4*b(t) + v(t). Suppose l(z) = 0. What is z?
-3, -1, -2/13, 1/2
Suppose 8*o + 2*z + 12 = 11*o, 0 = 5*z + 30. Let m(g) be the first derivative of 0*g**4 + 0*g + o*g**5 + 0*g**2 + 19 + 0*g**3 - 1/24*g**6. Solve m(b) = 0.
0
Find r such that 18637844 + 213323*r + 47*r**2 + 5070316 + 2024*r**2 + 210037*r + 5*r**3 + 449*r**2 = 0.
-168
Let s = -3/5000 + 1663/105000. Let d(h) be the third derivative of 1/60*h**4 - 21*h**2 + 0*h + 0*h**3 - s*h**7 + 1/25*h**6 + 1/20*h**5 + 0. Factor d(z).
-z*(z - 2)*(4*z + 1)**2/5
Determine v so that 93*v**2 + 17*v**2 + 4*v**4 - 188472 + 188472 + 82*v**3 - 76*v = 0.
-19, -2, 0, 1/2
Let w(r) be the first derivative of r**3/9 - 65*r**2/6 - 22*r + 3804. Solve w(t) = 0.
-1, 66
Let p(n) = 7*n - 72. Let t be p(11). Suppose 0*x = 4*x - 8, -t*j - 5*x + 10 = 0. What is c in j*c**3 + 10 + 22*c - 5*c**3 - 7*c + 0*c**3 = 0?
-1, 2
Find c, given that -101/3*c**3 + 99*c**2 + 1/3*c**4 - 295/3*c + 98/3 = 0.
1, 98
Let o(k) be the first derivative of k**4/8 + 241*k**3/3 - 4895*k**2/4 + 6150*k - 12753. Determine s, given that o(s) = 0.
-492, 5
Let j = 252 - 249. Let 71*w**j + 253*w**2 - 408*w**2 - w**4 + 197*w**2 - 30*w**3 = 0. Calculate w.
-1, 0, 42
Let r(c) be the first derivative of c**4/26 - 22*c**3/39 + 16*c**2/13 + 168*c/13 - 18. Determine d so that r(d) = 0.
-2, 6, 7
Factor 0 + 340/13*k**2 + 2/13*k**4 + 0*k + 342/13*k**3.
2*k**2*(k + 1)*(k + 170)/13
Let k(y) be the third derivative of -4/15*y**5 + 4*y**2 + 3/70*y**7 + 0 - 11/120*y**6 + 0*y**3 + 0*y + 1/6*y**4. Suppose k(c) = 0. What is c?
-1, 0, 2/9, 2
Let z(w) = -w**5 - w**4 + w**3 + 1. Let q(c) = 8*c**5 + 16*c**4 - 18*c**2 - 6. Let n = -116 - -89. Let v = n + 28. Let o(a) = v*q(a) + 6*z(a). Factor o(j).
2*j**2*(j - 1)*(j + 3)**2
Let t(l) = 2*l**2 + 38*l + 5. Let h be t(-19). Factor -4*s**3 + 4*s + 11*s**2 + 0*s**2 - 17 + 1 + h*s**2.
-4*(s - 4)*(s - 1)*(s + 1)
Let n(a) be the first derivative of -4/3*a**3 - 250 + 424/7*a**2 - 240/7*a. Factor n(g).
-4*(g - 30)*(7*g - 2)/7
Let a(z) be the second derivative of -z*