04. Solve 0 - 72/17*k**w + 0*k + 2/17*k**3 = 0 for k.
0, 36
Let j(w) be the third derivative of -w**5/120 - 29*w**4/48 - 23*w**3/2 - 96*w**2 - 2*w. What is v in j(v) = 0?
-23, -6
Factor 162*c + 13122 + 1/2*c**2.
(c + 162)**2/2
Let p = -8471895/28 + 302632. Let a = -445/7 + p. Solve -3/4*w**2 + a*w**4 + 0 - 3/4*w**3 + 3/4*w = 0.
-1, 0, 1
Let k(j) be the second derivative of j**6/6 + 21*j**5/2 + 535*j**4/4 + 2020*j**3/3 + 1320*j**2 - 1663*j + 1. Find t such that k(t) = 0.
-33, -4, -1
Let h = 304 - 282. Let t be ((-8)/(-16))/(h/(-48))*-1. Factor t*a**2 + 30/11*a + 16/11 - 2/11*a**3.
-2*(a - 8)*(a + 1)**2/11
Suppose -5*r - 1585 = -2*r + 2*t, 537 = -r - 5*t. Let m = -523 - r. Suppose 0 + 6/5*v**2 + 0*v - 3/5*v**m + 3/5*v**3 = 0. What is v?
-1, 0, 2
Let k(p) be the third derivative of p**7/504 + 7*p**6/144 - 37*p**4/12 - 56*p**2. Let i(o) be the second derivative of k(o). Factor i(c).
5*c*(c + 7)
Let q(o) be the third derivative of -o**8/1176 + 2*o**7/147 + 31*o**6/420 - 44*o**5/105 + 4*o**4/7 + 7*o**2 - 11*o - 1. Let q(h) = 0. Calculate h.
-4, 0, 1, 12
Let p = 233 + -184. Find r, given that -102*r**3 + 7*r + p*r**3 + 8*r**2 + r + 55*r**3 = 0.
-2, 0
Let -1/2*o**4 - 9/2*o + 0 - 87/8*o**2 - 55/8*o**3 = 0. Calculate o.
-12, -1, -3/4, 0
Let l(z) be the third derivative of 9*z**2 - 1/48*z**3 - 5/192*z**4 - 1/2688*z**8 - 2 - 1/48*z**5 - 1/96*z**6 + 0*z - 1/336*z**7. Factor l(c).
-(c + 1)**5/8
Let n(j) be the second derivative of j**5/80 + 25*j**4/48 + 9*j**3/2 - 81*j**2/2 - 1944*j + 1. Factor n(i).
(i - 2)*(i + 9)*(i + 18)/4
Let h(n) be the first derivative of -4*n**3/9 + 1020*n**2 - 780300*n - 721. Factor h(u).
-4*(u - 765)**2/3
Factor -93750 - 2/3*x**2 - 500*x.
-2*(x + 375)**2/3
Let t(c) be the second derivative of -c**7/3780 - c**6/405 - c**5/180 + 91*c**3/6 - c**2 + 2*c - 34. Let w(u) be the second derivative of t(u). Factor w(k).
-2*k*(k + 1)*(k + 3)/9
Suppose 7*o - 4*o + 9 = 0, 276 = 3*u - 2*o. Let k = -87 + u. Solve -5*q - 7 + 5*q**k + 10*q**2 + 0 - 3 = 0.
-2, -1, 1
Let g(x) = 139*x**3 - 31*x**2 - 537*x - 855. Let p(t) = 31*t**3 - 8*t**2 - 134*t - 214. Let w(v) = 2*g(v) - 9*p(v). Factor w(j).
-(j - 18)*(j + 2)*(j + 6)
Let p(m) = -4302*m**2 + 2150*m**2 - 25*m + 2 + 2151*m**2. Let x be p(-25). Factor -2/11*y**5 - 14/11*y**4 - 40/11*y**x - 36/11*y**3 - 16/11*y + 0.
-2*y*(y + 1)*(y + 2)**3/11
Let z be (-1 + (-1)/8)/(13287/(-35432)). Factor 33/8*i**2 + 3/2 - 9/2*i + 3/8*i**5 - 3/8*i**z - 9/8*i**4.
3*(i - 2)*(i - 1)**3*(i + 2)/8
Let j = -4 - -20. Let k = j - 11. Factor 10 - 9*l**2 - 5*l**3 + 6*l**3 + 4*l**3 - k*l - l**2.
5*(l - 2)*(l - 1)*(l + 1)
Let d(z) = -z**2 - 53*z - 150. Let j = 541 + -591. Let a be d(j). Determine l so that -2/5*l**2 - 6/5*l**3 + a + 4/5*l = 0.
-1, 0, 2/3
Let a(d) be the first derivative of -5*d**6/6 + 138*d**5 + 1765*d**4/2 + 6400*d**3/3 + 4995*d**2/2 + 1430*d - 5453. Let a(r) = 0. What is r?
-2, -1, 143
Let z(b) be the second derivative of 13/4*b**3 + 3/8*b**4 - 3/40*b**5 - 35*b - 2 - 45/4*b**2. Solve z(j) = 0.
-3, 1, 5
Let c = -19660 + 19663. Solve 105/2*q + 3/2*q**c - 39/2*q**2 + 147/2 = 0 for q.
-1, 7
Let c(o) be the third derivative of o**7/6 + o**6/3 - 9*o**5/4 - 20*o**4/3 - 10*o**3/3 + 1274*o**2. Suppose c(l) = 0. Calculate l.
-2, -1, -1/7, 2
Let m(s) be the first derivative of 867*s**4/20 - 17*s**3/5 - 312*s**2/5 - 192*s/5 - 2035. Determine q, given that m(q) = 0.
-8/17, 1
Let -1/8*l**2 - 1/4*l + 899/8 = 0. What is l?
-31, 29
Let w(j) be the second derivative of -j**6/10 + 183*j**5/20 - 1089*j**4/4 + 4131*j**3/2 + 19683*j**2 + 470*j - 4. Factor w(h).
-3*(h - 27)**2*(h - 9)*(h + 2)
Let a be 1085/2174 - (42/(-7) + 6). Let u = 1/1087 + a. Factor 1/4*g**3 + u*g**2 + 0 + 1/4*g.
g*(g + 1)**2/4
Suppose 0 = -22*g + 70*g - 144. Let u(k) be the first derivative of 11 + 9/2*k**2 + 4*k**g - 3*k. Factor u(q).
3*(q + 1)*(4*q - 1)
Factor -11/2 + 6*w - 1/2*w**2.
-(w - 11)*(w - 1)/2
Let x be (-4 + 1)/(106 - 109). Let t be x/(-3)*((3 - 2) + -1). What is w in 6/5*w + t + 3/5*w**2 = 0?
-2, 0
Let v = -299 - -303. Let a(d) be the second derivative of -1/22*d**5 + 1/165*d**6 + 0 + 0*d**3 + 0*d**2 + 29*d + 1/11*d**v. Factor a(x).
2*x**2*(x - 3)*(x - 2)/11
Suppose -208 = 4275*j - 208. Factor j - 30/17*s**3 - 4/17*s + 2*s**2.
-2*s*(s - 1)*(15*s - 2)/17
Let n(g) be the second derivative of -4*g**2 + 4*g + 4/3*g**4 - 4/15*g**6 - 3/5*g**5 + 0 + 2*g**3. Solve n(m) = 0.
-2, -1, 1/2, 1
Let n(o) = -11*o**2 - 9*o - 2. Let t be n(-1). Let z be t + 3 - (-4 + (-55)/(-19)). Find x such that 16/19*x + z*x**2 + 32/19 = 0.
-4
Let p(x) be the second derivative of -x**6/135 - 3*x**5/10 - 17*x**4/18 - 25*x**3/27 - 6*x - 7. Determine f so that p(f) = 0.
-25, -1, 0
Let g(w) be the first derivative of 29 + 23/2*w**3 + 21/8*w**4 - 12*w - 33/2*w**2. Suppose g(x) = 0. Calculate x.
-4, -2/7, 1
Let t(h) be the third derivative of 0*h**3 + 0 - 1/15*h**5 + 0*h**4 + 0*h + 1/30*h**6 + 65*h**2. Factor t(z).
4*z**2*(z - 1)
Let m(j) be the first derivative of -j**3/7 + 828*j**2/7 - 228528*j/7 + 967. Determine k, given that m(k) = 0.
276
Let m(p) = 49*p**2 - 273*p + 503. Let x(n) = -11*n**2 + 68*n - 126. Let w(j) = -10*m(j) - 45*x(j). Factor w(h).
5*(h - 64)*(h - 2)
Let t(o) = -2*o**2 + 328*o - 13392. Let l be t(77). Factor -l*s + 0 + 1/3*s**2.
s*(s - 18)/3
Let c(b) be the third derivative of -b**6/1440 - b**5/120 - 50*b**3/3 + 103*b**2. Let y(x) be the first derivative of c(x). Factor y(n).
-n*(n + 4)/4
Let b = 18636/5 - 3727. Let y(c) be the first derivative of -9/10*c**2 + 0*c + b*c**3 - 1. Factor y(v).
3*v*(v - 3)/5
Let p be (-244)/4514 + (6 - 292/74). Let m be ((-3)/27)/((-1)/3). Factor 8/3*u**p - 50/3 + 5/3*u + m*u**3.
(u - 2)*(u + 5)**2/3
Let r(u) be the second derivative of u**7/630 + u**6/180 - u**5/180 - u**4/36 + 27*u**2/2 - 81*u. Let y(n) be the first derivative of r(n). Factor y(f).
f*(f - 1)*(f + 1)*(f + 2)/3
Suppose -2*v = 4*r - 3*v - 6, -2*v + 14 = 5*r. Let u = 1/23 - -89/69. Let 2/3 - r*h**2 - u*h = 0. What is h?
-1, 1/3
Suppose -5*k + m - 11 = 0, 0 = 6*k + 176*m - 171*m - 117. Suppose -56/15*x - 4/3*x**k - 2 + 8/15*x**3 + 2/15*x**4 = 0. What is x?
-5, -1, 3
Let c(z) = -z**3 - 2246*z**2 - 310803*z + 77835. Let v(t) = t**3 + 4497*t**2 + 621605*t - 155668. Let j(i) = 14*c(i) + 6*v(i). Determine p so that j(p) = 0.
-279, 1/4
Let t(w) be the third derivative of 1/15*w**5 + 0*w**4 + 0*w + 0*w**3 - 1/30*w**6 + 9 + 4*w**2. Factor t(x).
-4*x**2*(x - 1)
Let u = -9 + 100. Suppose 2*g - 13 = u. Solve 8*s**3 - 32*s - g*s**2 - 8 + 17 + 12*s**4 + 7 = 0.
-2, -1, 1/3, 2
Let t = -458 - -808. Factor 142*j + 33*j**3 - 122*j + t*j**4 + 245*j**5 - 100*j**2 - 48*j**3.
5*j*(j + 1)**2*(7*j - 2)**2
Let x(c) = -c**3 + c. Let m(f) = 2*f**4 - 1638*f**3 - 4908*f**2 - 4906*f - 1638. Let i(o) = -m(o) + 6*x(o). Find j such that i(j) = 0.
-1, 819
Let l(n) be the second derivative of -2/57*n**4 - 8/57*n**3 + 1/285*n**6 + 4 + 1/95*n**5 + 7*n + 0*n**2. Factor l(g).
2*g*(g - 2)*(g + 2)**2/19
Suppose -4*p = -5*l - 61, -8*l - 46 = -4*p - 6*l. Find j, given that 2*j**3 + 12 - 23*j**3 + 0*j**3 + 3*j**4 - 39*j + p*j**2 + 36*j**2 = 0.
1, 4
Let b(x) be the third derivative of 0*x**3 + 15*x**2 + 0*x + 1/240*x**5 - 1/16*x**4 + 0 + 1/480*x**6. Let b(m) = 0. What is m?
-3, 0, 2
Factor -23/2*y**3 - 1/4*y**4 + 3/4*y**2 + 34*y - 23.
-(y - 1)**2*(y + 2)*(y + 46)/4
Solve -240/13 - 2/13*o**2 + 86/13*o = 0 for o.
3, 40
Suppose 26*w + 7 = 59. Factor -10*d**3 + d**4 + d**3 + 9*d + 10 + 0*d**4 - 7*d**w - 4*d**2.
(d - 10)*(d - 1)*(d + 1)**2
Let k(a) be the second derivative of 0 + 315*a + 2/21*a**3 - 1/35*a**5 + 2/105*a**6 + 24/7*a**2 - 13/21*a**4. Let k(j) = 0. What is j?
-3, -1, 1, 4
Let u(p) = -45*p**2 + 33*p + 148. Let x be u(-5). Let o = -1140 - x. Factor 0*c - 2/9*c**o + 8/9.
-2*(c - 2)*(c + 2)/9
Let j(u) = -u**4 + 134*u**3 + 259*u**2 + 321*u + 109. Let b(d) = 26*d**3 + 52*d**2 + 64*d + 22. Let o(p) = -11*b(p) + 2*j(p). Determine k, given that o(k) = 0.
-4, -3, -1
Let v = -93 - -139. Solve -9*p**4 + 6*p**4 - 768 + v*p**3 - 136*p**3 + 1440*p - 579*p**2 = 0 for p.
-16, 1
Let d = -32768/5 + 6555. Let s(b) be the first derivative of 22/15*b**3 - 7 - d*b**2 + 2/5*b - 1/2*b**4. Factor s(g).
-2*(g - 1)**2*(5*g - 1)/5
Let n(q) be the second derivative of -q**8/4760 - 19*q**7/7140 + 7*q**6/1530 - 77*q**3/2 + 3*q + 48. L