 5. Suppose 0 = o + 5*i + 14, 4*o - 2*o + i + 19 = 0. Let l be k(o). Factor -l + 13*h**2 + 22*h**2 - 30*h**2.
5*(h - 1)*(h + 1)
Let x(b) = -4*b + b**3 + 17*b**2 - 15*b - 1 - 5. Let y be x(-18). Factor 6*s**2 - 6 - 3*s**3 + 6 + y*s - 15*s**2.
-3*s*(s - 1)*(s + 4)
Let r(q) be the first derivative of q**4/18 - 2*q**3/27 - 10*q + 36. Let p(n) be the first derivative of r(n). Suppose p(u) = 0. What is u?
0, 2/3
Let o(m) be the second derivative of -32*m**6/105 + 408*m**5/35 - 953*m**4/21 + 512*m**3/7 - 414*m**2/7 + 10191*m. Suppose o(k) = 0. Calculate k.
3/4, 1, 23
Let o(b) be the first derivative of b**5/420 - b**4/84 - 4*b**3/21 + 2*b**2 + 2*b + 146. Let f(u) be the second derivative of o(u). What is g in f(g) = 0?
-2, 4
Suppose 3 = -3*u, -245 = -4*q - 0*q + u. Suppose -q*s = -48*s. Factor s*v + 6/5*v**4 + 0*v**3 - 3/5*v**5 + 0 + 0*v**2.
-3*v**4*(v - 2)/5
Factor -8/3*t**2 - 7/3 + 29/6*t + 1/6*t**3.
(t - 14)*(t - 1)**2/6
Let y(s) = -15*s**2 - 452700*s + 733018805. Let j(b) = b**2 + 32336*b - 52358486. Let w(z) = 85*j(z) + 6*y(z). Factor w(h).
-5*(h - 3236)**2
Factor -2/15*a**4 + 0 + 8/3*a**3 + 0*a - 38/15*a**2.
-2*a**2*(a - 19)*(a - 1)/15
Let r be ((-385)/42)/(-11) - (-62)/(-124). Find b such that -10/3*b**2 + r*b**3 + 0 + 3*b = 0.
0, 1, 9
Suppose -g + 4*i = 1, 8 = g - i + 6*i. Let 40*y**2 + 0*y**4 - 3*y**3 - 35*y - 49*y**g + 14*y**4 + 51*y = 0. Calculate y.
-2/7, 0, 2
Let b = 1004 + -1030. Let l be (-117)/b*3/((-63)/(-8)). Factor -3/7*d**5 - 48/7*d - 57/7*d**3 - l - 75/7*d**2 - 3*d**4.
-3*(d + 1)**3*(d + 2)**2/7
Find s, given that -374/5*s - 756/5 + 2/5*s**2 = 0.
-2, 189
Let q(o) be the third derivative of o**8/10080 - o**7/210 + o**6/10 + o**5/15 + 3*o**2 + 18. Let w(g) be the third derivative of q(g). Factor w(y).
2*(y - 6)**2
Let h = 877 - 439. Find i such that 0*i**2 - 163*i + 48*i - 188 + h - 5*i**2 = 0.
-25, 2
Factor -98/3*d - 196/3 + 4/3*d**2 + 2/3*d**3.
2*(d - 7)*(d + 2)*(d + 7)/3
Let l = 6925/231 + -346/11. Let p = l - -197/105. Factor 72/5 - 24/5*x + p*x**2.
2*(x - 6)**2/5
Let y(o) = -o**2 + 577*o - 16409. Let s be y(547). Factor -s - 10/3*q**2 - 13/3*q.
-(q + 1)*(10*q + 3)/3
Factor -3/4*g**2 + 189/2 + 15/4*g.
-3*(g - 14)*(g + 9)/4
Factor 207955/3*h - 1092025/3 + 2065/3*h**2 + 5/3*h**3.
5*(h - 5)*(h + 209)**2/3
Let z = -404704 - -404707. Factor 0 + 36/5*q**z - 32/5*q**2 - 4/5*q.
4*q*(q - 1)*(9*q + 1)/5
Let q be 25029/9270*(-1 - -7). Factor -19/5*t**2 - q + 99/5*t + 1/5*t**3.
(t - 9)**2*(t - 1)/5
Let c be ((-174)/(-3770)*-3)/(6/(-26)). Suppose -h + 4/5 - c*h**2 - 1/5*h**4 + h**3 = 0. Calculate h.
-1, 1, 4
Determine c, given that 0 - 44/17*c**4 + 24/17*c - 14/17*c**5 + 32/17*c**2 - 22/17*c**3 = 0.
-2, -1, 0, 6/7
Factor -4265/2*b - 285/2*b**2 + 75.
-5*(b + 15)*(57*b - 2)/2
Let b(u) = 4*u**2 + 4864*u + 1392424. Let c(y) = 6*y + 1. Let m(h) = b(h) - 24*c(h). Factor m(n).
4*(n + 590)**2
Suppose -116 = -2*g - 4*o, -96 = -2*g + 3*o - 8. What is i in -g*i + 2*i - 32*i**3 + 4*i**4 + 85*i**2 + 17*i**2 - 26*i**2 = 0?
0, 1, 3, 4
Let s = 31 + -27. Let z(f) be the first derivative of -75*f - s*f**3 + 15*f**2 - 6 + 2 + 2*f**3 + f**3. Factor z(m).
-3*(m - 5)**2
Find b, given that 1210*b**4 + 0 + 32*b + 300*b**5 + 944/3*b**2 + 3094/3*b**3 = 0.
-3, -1/2, -4/15, 0
Let c(s) = -10*s**4 + 190*s**3 + 224*s**2 - 183*s - 214. Let h(w) = 3*w**4 - 64*w**3 - 74*w**2 + 62*w + 71. Let t(v) = -2*c(v) - 7*h(v). Solve t(d) = 0.
-1, 1, 69
Let a(k) be the third derivative of -k**7/1365 + 9*k**5/130 + 9*k**4/26 - 46*k**2 - 23. Factor a(d).
-2*d*(d - 6)*(d + 3)**2/13
What is p in 5*p**3 - 17555 - 451*p**2 + 17555 + 8*p**2 - 272*p**2 + 710*p = 0?
0, 1, 142
Let n(b) be the third derivative of -b**7/175 - b**6/50 + 11*b**5/50 + 3*b**4/5 - 1029*b**2. Factor n(g).
-6*g*(g - 3)*(g + 1)*(g + 4)/5
Let p(m) be the first derivative of m**5/15 + 2*m**4/3 + 22*m**3/9 + 4*m**2 - 142*m - 72. Let o(l) be the first derivative of p(l). Find x such that o(x) = 0.
-3, -2, -1
Let n(b) be the first derivative of 1/9*b**6 - 1/6*b**4 + 23 + 0*b**5 + 0*b**3 + 0*b**2 + 0*b. Determine l, given that n(l) = 0.
-1, 0, 1
Let i(f) be the first derivative of 4*f**5/5 + 13*f**4/4 - 49*f**3/3 - 73*f**2/2 - 15*f + 529. Determine h so that i(h) = 0.
-5, -1, -1/4, 3
Suppose 32*s + 2 = -27*s + 60*s. Let v(k) be the third derivative of 1/16*k**4 + 0*k + 8*k**s + 0*k**3 + 0 + 1/40*k**5. Factor v(b).
3*b*(b + 1)/2
Factor 3*i**2 - 483 + 923 + 63 + 1396 - 171*i + 141.
3*(i - 40)*(i - 17)
Let f(u) be the first derivative of -u**5/40 - u**4/2 - 11*u**3/24 + 4*u**2 + 15*u/2 + 8182. Determine r so that f(r) = 0.
-15, -2, -1, 2
Let s(p) be the first derivative of p**7/315 + p**6/40 + p**5/15 + p**4/18 + p**2 + 52*p - 20. Let t(a) be the second derivative of s(a). Factor t(g).
g*(g + 2)**2*(2*g + 1)/3
Let j(i) be the third derivative of i**6/240 + 63*i**5/40 - 241*i**4/12 + 97*i**3 - 2355*i**2. Factor j(t).
(t - 3)*(t - 2)*(t + 194)/2
Let f = 894/14927 - -2/253. Let b = 405/118 + f. Suppose -2 - 1/2*j**5 - 3/2*j**4 + 1/2*j**3 + b*j**2 + 0*j = 0. Calculate j.
-2, -1, 1
Let x be 10*(-13)/(104/(-12)). Suppose x + 9 = 6*c. Suppose 0 + 0*i**2 - 3/4*i**5 + 15/4*i**3 - 3*i + 0*i**c = 0. What is i?
-2, -1, 0, 1, 2
Determine q so that -3/7*q**4 + 27/7 + 18/7*q - 24/7*q**2 - 18/7*q**3 = 0.
-3, -1, 1
Let l be (-40 - 1528/(-40))*55/(-6). Factor l*u**2 - 24*u + 27/2*u**3 - 6.
3*(u - 1)*(u + 2)*(9*u + 2)/2
Let w = -12 + 44. Let k be (w/(-24))/((-4)/6). Factor -11*x**4 + k*x**2 + 9*x**4 - 9*x**3 - 2*x + 11*x**3.
-2*x*(x - 1)**2*(x + 1)
Let r(z) be the third derivative of -z**6/60 - z**5/5 - z**4/4 + 10*z**3/3 - 697*z**2. Factor r(w).
-2*(w - 1)*(w + 2)*(w + 5)
Let z be (2 + -2 + 30)/2. Suppose z*w - 60 = -5*w. Suppose 1/3*i**4 + 1/3*i**2 - 2/3 - i**w + i = 0. What is i?
-1, 1, 2
Let f(z) be the first derivative of 35/3*z**3 - 25/2*z**2 + 36 + 0*z + 1/5*z**5 - 11/4*z**4. Factor f(h).
h*(h - 5)**2*(h - 1)
What is z in 5*z**5 + 457*z**3 + 393*z**3 + 345 - 731 + 105*z**4 + 3511 + 3250*z**2 + 5625*z = 0?
-5, -1
Let f(z) = -z - 11. Let h be f(-15). Suppose 4*l + 16 = 2*d, 7*l = h*d + 2*l - 23. Determine o so that -2*o**d + 2*o**2 - 14*o + 15 + 4*o - 5*o**2 = 0.
-3, 1
Factor -2066*z - 508*z + 36*z + 1415*z**2 - 491*z + 1425 + 184*z + 5*z**3.
5*(z - 1)**2*(z + 285)
Let f = 12065/8 + -1508. Let h(b) be the second derivative of -1/12*b**3 - 1/48*b**4 + 9*b + 0 - f*b**2. Suppose h(o) = 0. What is o?
-1
Let c = -5224 - -47018/9. Let i(u) = u**2 + 10*u + 23. Let r be i(-3). Let -32/9*a + 0 - c*a**3 - 16/9*a**r = 0. What is a?
-4, 0
Let y(k) be the second derivative of -k**5/15 + 13*k**4 - 1014*k**3 + 49*k**2/2 + 5*k - 26. Let q(b) be the first derivative of y(b). Let q(m) = 0. What is m?
39
Suppose -4*p + g = 4, -3*g = -5*g + 8. Suppose p = -26*w + 22*w + 240. Factor -29*f - w*f**2 - 27*f + 110*f**3 - 16 + 256*f**2.
2*(f + 2)*(5*f - 2)*(11*f + 2)
Let f(z) be the first derivative of 8*z**2 - 28/3*z**3 + 48*z - 181 + z**4. Determine m, given that f(m) = 0.
-1, 2, 6
Let z(d) be the second derivative of -d**5/190 + 91*d**4/114 + d**3/57 - 91*d**2/19 - 3473*d. What is s in z(s) = 0?
-1, 1, 91
Let x(z) = 2*z**3 + 94*z**2 + 98*z + 4606. Let v be x(-47). Determine t so that -2/3*t**5 + 2/3*t**3 + 0*t + v - 2*t**2 + 2*t**4 = 0.
-1, 0, 1, 3
Let b = -51 + 56. Suppose 22 = b*l + 2*p, 0 = -2*l - 2*p + 3 + 7. Factor l*v**2 + 0*v - 4*v - 3*v + 3*v.
4*v*(v - 1)
Let w be 352/(-2288) - ((-1126)/(-624) + -2). Let t(i) be the third derivative of 0*i - 12*i**2 + 0*i**5 + 0 + 0*i**3 + w*i**6 - 5/24*i**4. Factor t(a).
5*a*(a - 1)*(a + 1)
Let o(l) be the first derivative of -l**6/60 - l**5/15 + 7*l**4/12 - 4*l**3/3 + l**2/2 - 9*l - 42. Let b(c) be the second derivative of o(c). Factor b(i).
-2*(i - 1)**2*(i + 4)
Suppose -4867200/7 - 6240/7*h - 2/7*h**2 = 0. Calculate h.
-1560
Let h be (15 + (-2205)/135)*378/(-44). Factor 2/11*g**3 + 18522/11 + 2646/11*g + h*g**2.
2*(g + 21)**3/11
Let k = 249067 - 249065. Factor 28/3 - 46/3*p + k*p**2.
2*(p - 7)*(3*p - 2)/3
Let k(c) be the second derivative of -3*c**4/2 - 25*c**3/2 - 6*c**2 - 1518*c + 1. Let k(y) = 0. What is y?
-4, -1/6
Let y be (21*7/28 + 2 + -6)*4. Let i(c) be the second derivative of -1/40*c**y + 0*c**2 + 0 - 1/12*c**4 - 1/12*c**3 - 20*c. Factor i(x).
-x*(x + 1)**2/2
Let f(y) = 493*y - 87261. Let n be f(177). Facto