1. Factor -16 - 8*c**3 + 8*c**2 - c**k + 2*c**4 + 8*c + c**5 - 2*c**4 + 8*c.
(c - 2)**2*(c - 1)*(c + 2)**2
Let z(d) be the third derivative of -d**8/50400 + 7*d**7/1800 - 2*d**6/75 - 47*d**5/15 - 138*d**2 - 1. Let a(f) be the third derivative of z(f). Factor a(q).
-2*(q - 48)*(q - 1)/5
Let r(s) = 5*s**2 - 764*s - 721. Let b(g) = 51*g**2 - 7665*g - 7212. Let t(u) = 2*b(u) - 21*r(u). Factor t(d).
-3*(d - 239)*(d + 1)
Suppose 88*b + 18700*b**2 + 50 - 37355*b**2 + 18693*b**2 = 0. Calculate b.
-25/19, -1
Let r(k) be the third derivative of k**5/120 + 19*k**4/24 + 88*k**3/3 - 379*k**2 - 2*k. Find m such that r(m) = 0.
-22, -16
Let s = 340505/97286 - 2/48643. Factor 1/2*i**2 + 0 + s*i.
i*(i + 7)/2
Let t be ((-6)/(-90))/((-2)/3)*-80*13/416. Factor 0 + 11/4*k**2 - t*k**5 + 1/4*k**4 + k + 9/4*k**3.
-k*(k - 4)*(k + 1)**3/4
Let p(u) be the second derivative of u**7/13860 - u**6/1980 - u**4/2 + u**2 + 22*u. Let o(s) be the third derivative of p(s). Let o(q) = 0. What is q?
0, 2
Let b(l) be the first derivative of l**5/4 - 1185*l**4/16 - 795*l**3/4 - 1195*l**2/8 + 778. Factor b(y).
5*y*(y - 239)*(y + 1)**2/4
Suppose 0 = 147*c + 141*c + 233 - 809. Let 0 - 14/11*u**5 + 260/11*u**c + 136/11*u**4 + 362/11*u**3 + 48/11*u = 0. Calculate u.
-1, -2/7, 0, 12
Suppose 24*w**3 - 5280*w + 522*w**3 + 274*w**3 + 1725*w**4 + 125*w**5 - 4965*w**2 - 1675*w**2 - 1040 = 0. Calculate w.
-13, -2, -2/5, 2
Factor -548/3*v + 2840/3 - 4/3*v**2.
-4*(v - 5)*(v + 142)/3
Suppose -3*q + 12 = 0, 2*l - 2*q - 24 = q. Let y be (-18)/(1 + -7) - (-61 + 1). Suppose -l*b - y + 3*b**2 + 27 + 6*b - 4*b**2 = 0. Calculate b.
-6
Let 2/3*t**3 - 24*t + 0 - 70/3*t**2 = 0. What is t?
-1, 0, 36
Let w(t) be the second derivative of -4/9*t**2 + 16*t - 121/54*t**4 + 44/27*t**3 + 2. Suppose w(l) = 0. What is l?
2/11
Let w(y) be the third derivative of -y**8/16800 - y**7/8400 + y**6/200 - y**5/12 - 63*y**2. Let f(l) be the third derivative of w(l). Factor f(o).
-3*(o + 2)*(2*o - 3)/5
Let w(m) be the second derivative of m**7/63 - m**6/45 - m**5/30 + m**4/18 - 266*m. Factor w(y).
2*y**2*(y - 1)**2*(y + 1)/3
Let w be 6*((-12)/30 - (-32)/30). Suppose -w*s = 5 - 13. Determine t, given that -7 + s - 3*t**3 + 24 - 9*t**2 - 7 = 0.
-2, 1
Suppose 0 = -7*i - 52 + 115. Suppose 8 = -j + 2*p, j - 4*p + 25 - i = 0. Find o, given that -3/5*o**2 + j*o + 3/5 = 0.
-1, 1
Suppose -2 = -3*d + 3*n + 10, -2*d + 9 = -3*n. Suppose 0 = 4*c - f - 12, -9 = 3*c - d*f - 27. Suppose 28 - 9*g - 80 + 37*g - 2*g**c - 46 = 0. What is g?
7
Find x such that -23/2*x**2 - 1/10*x**3 - 25281/10 - 3763/10*x = 0.
-53, -9
Let v(a) = -a**3 - 12*a**2 + 556*a + 5760. Let f be v(-10). Factor f + 2/9*r**2 - 34/9*r.
2*r*(r - 17)/9
Let q(o) = -22*o - 12*o + 46*o + 16 - 13*o. Let v be q(11). Find g, given that -4*g**4 - 4*g**5 - 21*g**2 + 0*g**v + 4*g**3 + 25*g**2 = 0.
-1, 0, 1
Factor -1440/13 + 124/13*k + 2/13*k**2.
2*(k - 10)*(k + 72)/13
Let p be (92/(-276))/(1/(-1176)). Let w be (16/56)/(8/p). Factor 1/2*z**5 + 4*z**4 + 25/2*z**3 + 19*z**2 + 4 + w*z.
(z + 1)**2*(z + 2)**3/2
Let l(z) be the first derivative of 5*z**4/12 - 17*z**3/12 - 3*z**2/2 - 82*z - 84. Let s(m) be the first derivative of l(m). Factor s(o).
(o - 2)*(10*o + 3)/2
Let u be ((-12)/(-16))/(2/8). Suppose u*f + 9 = -y, -7 = 2*y + 3*f - 1. Factor -8*i**4 - 4*i**3 + 4 - 15*i**3 + 39*i**2 - 3*i**5 + 25*i**4 - 20*i - 18*i**y.
-(i - 2)*(i - 1)**3*(3*i - 2)
Let y(j) be the third derivative of 29*j**2 - 4/3*j**3 + 0*j + 1/72*j**6 + 5/24*j**4 + 0 + 1/12*j**5. Let d(h) be the first derivative of y(h). Factor d(l).
5*(l + 1)**2
Let y(w) be the first derivative of -2*w**3/15 + 9*w**2/5 - 28*w/5 + 656. Factor y(u).
-2*(u - 7)*(u - 2)/5
Let q = -70438 + 352214/5. Factor 9*y**2 + 0 - 6/5*y + q*y**3.
3*y*(y + 2)*(8*y - 1)/5
Let k(a) = -a**3 - 2*a**2 + a - 1. Let s(x) = 141 - 16*x + x**2 - 143 - 2*x**3 - 7*x**3 + 6*x. Let i(y) = 6*k(y) - s(y). Factor i(d).
(d - 2)**2*(3*d - 1)
Let v(a) = -281*a - 84019. Let l be v(-299). Factor 0*o**2 + 0*o + l + 32/3*o**3 - 4/3*o**5 + 28/3*o**4.
-4*o**3*(o - 8)*(o + 1)/3
Suppose -27*v - 17 = -24 + 7. Let j(b) be the third derivative of 0*b**4 + 1/660*b**6 + 29*b**2 + 0 + v*b - 2/165*b**5 + 0*b**3. Suppose j(d) = 0. What is d?
0, 4
Let d(x) = -8*x - 153. Let p be d(-20). Let s be -4 + (1218/30)/p. Factor 0 - 3/5*j**4 + s*j**2 - 6/5*j + 0*j**3.
-3*j*(j - 1)**2*(j + 2)/5
Let p = -651463 + 651466. Let -2*f**p + 26/3*f**2 + 0 - 8/3*f = 0. What is f?
0, 1/3, 4
Let s(p) be the second derivative of 0*p**3 + 135*p + 1/9*p**2 + 0 - 1/54*p**4. Solve s(q) = 0.
-1, 1
Suppose 28 = -8*s + 7*s + 3*v, 0 = 5*s + 4*v + 64. Let q be -9*(-5)/(-3)*s/400. Suppose 0 + q*r**2 + 3/5*r = 0. Calculate r.
-1, 0
Let l(m) be the second derivative of m**6/1800 - m**5/5 + 30*m**4 - 73*m**3/6 + 2*m - 42. Let d(r) be the second derivative of l(r). Factor d(c).
(c - 60)**2/5
Let b(w) be the first derivative of w**5/10 - 29*w**4/4 + 577*w**3/6 + 1914*w**2 + 8712*w - 1106. Suppose b(c) = 0. What is c?
-4, 33
Let p(r) be the third derivative of -r**6/120 + r**5/20 + r**4/8 - r**3 + 11*r**2. Let t be p(3). Find j such that j**2 - j - 2*j**3 - 8 + 6*j + j**2 + t*j = 0.
-2, 1, 2
Let w(p) be the second derivative of p**4/12 + 481*p**3/3 - 963*p**2/2 + 9317*p. Factor w(q).
(q - 1)*(q + 963)
Solve -98 + 13*v**2 - 1378 - 432 - 14*v**2 - 624*v + 5*v**2 = 0.
-3, 159
Let -2/9*n**4 + 8/3 - 40/9*n + 4/3*n**3 + 2/3*n**2 = 0. Calculate n.
-2, 1, 6
Suppose 23*z - 30 = 8*z. Factor 16*d - 124*d**4 + 20*d**3 + 58*d**4 - 32*d**z + 62*d**4.
-4*d*(d - 2)**2*(d - 1)
Let d(i) be the first derivative of 196/3*i - 87 + 4/9*i**3 + 28/3*i**2. Factor d(v).
4*(v + 7)**2/3
Factor 594/5 + 84/5*k + 2/5*k**2.
2*(k + 9)*(k + 33)/5
Let v(i) be the second derivative of 0 + 1/12*i**4 - 33/2*i**2 - 230*i + 16/3*i**3. Let v(z) = 0. What is z?
-33, 1
Let g = -23116 - -23118. Let x = 19/6 + -2/3. Factor -7/2*j**g + x*j**3 + 3/2*j - 1/2*j**4 + 0.
-j*(j - 3)*(j - 1)**2/2
Find m, given that -4824*m - 2*m**2 + m**2 + 4512*m + 3*m**2 + 3072*m + 952200 = 0.
-690
Factor 8/5*b**3 + 4232/5 + 17112/5*b + 738/5*b**2.
2*(b + 46)**2*(4*b + 1)/5
Let s be -5*(-3)/15*0. Let r be s/(((-2)/6)/((-30)/90)). Factor -2/17*i**5 + 0 + 4/17*i**3 - 2/17*i + r*i**2 + 0*i**4.
-2*i*(i - 1)**2*(i + 1)**2/17
Let s = 360 + -307. Factor -s*d**2 - 4*d**5 + 12*d - 3*d + 3*d + 21*d**2 + 24*d**3.
-4*d*(d - 1)**3*(d + 3)
Let y = 834958/3 + -278318. Factor -y*z - 2/3*z**3 - 2*z**2 + 0.
-2*z*(z + 1)*(z + 2)/3
Let g(o) = 1220*o**3 + 3275*o**2 + 3355*o - 6695. Let m(h) = -133*h**3 - 364*h**2 - 373*h + 744. Let d(r) = -6*g(r) - 55*m(r). Factor d(z).
-5*(z - 75)*(z - 1)*(z + 2)
Let g(n) be the second derivative of 0 + 5/8*n**4 + 1/20*n**5 + 0*n**3 + 18*n**2 - 17*n. Let r(i) be the first derivative of g(i). Let r(x) = 0. What is x?
-5, 0
Let y(t) be the second derivative of -t**5/140 + 7*t**4/12 - 110*t**3/21 - 5*t - 14. Factor y(g).
-g*(g - 44)*(g - 5)/7
Let b(h) = 3*h**2 + 29*h + 39. Let z be b(-9). Let a be (z/56 + 3/(-72))*6. Factor 1 - 4/3*f + 1/3*f**a.
(f - 3)*(f - 1)/3
Factor -141/2*v**2 + 35/4*v**3 - 1/4*v**4 + 486 - 135*v.
-(v - 18)**2*(v - 2)*(v + 3)/4
Let x(i) be the first derivative of 605*i**4/4 + 275*i**3 + 120*i**2 + 20*i + 409. Find d such that x(d) = 0.
-1, -2/11
Let c(j) be the second derivative of -2*j**7/3 + 16*j**6 - 319*j**5/5 - 542*j**4 - 3560*j**3/3 - 1200*j**2 - 2687*j. Let c(a) = 0. What is a?
-1, -6/7, 10
Let q be (4 - 2)*(2080 + -3 + 4). Let u = q - 2018. Let -2135*c**3 + 5*c + 5*c**4 - 27*c**2 - 2*c**4 + u*c**3 + 10*c = 0. What is c?
-5, 0, 1
What is z in 1/4*z**4 + 19/2*z - 9/2*z**3 + 0 - 21/4*z**2 = 0?
-2, 0, 1, 19
Let k(n) be the second derivative of -n**5/8 - 65*n**4/3 - 2*n - 420. Solve k(y) = 0.
-104, 0
Let t(w) be the second derivative of -6/19*w**2 - 5/57*w**3 - 25*w - 7/190*w**5 + 23/114*w**4 + 0 - 1/57*w**6. Suppose t(a) = 0. What is a?
-3, -2/5, 1
What is m in 116*m**3 - 4/3*m**4 + 88/3*m + 0 + 117*m**2 = 0?
-1/2, 0, 88
Let r = 64 + -70. Let h be ((-1)/(-2) - 0)*(r - -14). Factor -h*u**2 - 14*u - 80 + 3*u**2 + 31.
-(u + 7)**2
Let a(r) be the third derivative of 5*r**5/12 + 795*r**4/8 + 475*r**3/3 + 5529*r**2. Find i, given that a(i) = 0.
-95, -2/5
Let k be ((-200)/35)/(20/(-70)). Let h be (-9)/(-6)*k*(-12)/(-315). Factor 2/7*w**4 - 2/7*w**2 + 0 - h*w + 8/7