tive of 5*m**3/3 - 33*m**2/8 - 81*m/4 - 2965. Factor d(u).
(u - 3)*(20*u + 27)/4
Let d(r) be the second derivative of 3*r - 46 - 7/5*r**5 + 10/3*r**3 + 1/6*r**4 + 3*r**2. Solve d(u) = 0 for u.
-1/2, -3/7, 1
Let t(h) be the third derivative of h**7/840 - 31*h**6/240 + h**5/4 + 31*h**4/48 - 61*h**3/24 - 2*h**2 - 222*h. Determine v so that t(v) = 0.
-1, 1, 61
Let p = -14585 + 14589. Let f(a) be the second derivative of -1/24*a**p + 1/20*a**5 + 9*a - 1/2*a**3 + 0 + 1/120*a**6 + 9/8*a**2. Determine i so that f(i) = 0.
-3, 1
Let c(h) = 12*h**3 - 9*h**2 - 9*h + 15. Suppose 10*r - 12 = -22. Let v(o) = o**4 + o + 1. Let k(u) = r*c(u) + 3*v(u). Suppose k(m) = 0. What is m?
-1, 1, 2
Let q be (-50)/40 + (-27)/(-12). Let x(u) = -2*u**2 - u - 1. Let z(c) = -5*c**2 + 15*c - 18. Let d(w) = q*z(w) - 2*x(w). Solve d(v) = 0 for v.
1, 16
Let n(x) be the first derivative of -x**4/2 - 28*x**3/3 + 61*x**2 + 340*x + 8205. Factor n(b).
-2*(b - 5)*(b + 2)*(b + 17)
Let k = 545 - 308. Let j = 237 - k. Factor -3/10*g + j + 1/10*g**2.
g*(g - 3)/10
Suppose 0 = 4*t - 2*w - 46, 25 = -0*t + t - 5*w. Suppose -56 = -3*g + 5*s, g - 38 + t = 4*s. Determine i so that -2/3*i**4 + 2*i**2 + 8/3*i**3 + 0 - g*i = 0.
-2, 0, 3
Suppose 0 = -2*q + 90 - 66. Let b**2 - 6*b**2 + 7*b**2 - q*b - 8*b = 0. Calculate b.
0, 10
Let s(n) = 2*n**3 - 4*n**2 - 13*n. Let x(k) be the third derivative of -k**6/60 + k**5/15 + k**4/2 - 8*k**2. Let p(w) = -6*s(w) - 7*x(w). Factor p(y).
2*y*(y - 3)*(y + 1)
Factor -1/5*r**2 + 6/5 - r.
-(r - 1)*(r + 6)/5
Let x = -714374/13 + 54952. Find n, given that x*n**3 - 6/13*n + 4/13*n**2 + 0 = 0.
-3, 0, 1
Solve -1/4*u**3 - 45/2*u**2 - 6750 - 675*u = 0 for u.
-30
Let 73441/4 + 271/2*d + 1/4*d**2 = 0. What is d?
-271
Let h be ((-28)/2 - 4)*(-6)/(-4). Let t = h + 32. Factor -10*f**4 - 20*f**3 + 16*f**2 + t*f**4 + 9*f**2.
-5*f**2*(f - 1)*(f + 5)
Let i = -343 + 357. Factor -8*b - 18 - 3*b**2 - 4*b**3 + i + b**4 + 6*b**3.
(b - 2)*(b + 1)**2*(b + 2)
Solve 2/3*o**5 + 676*o + 0 + 38/3*o**4 - 2054/3*o**2 - 14/3*o**3 = 0.
-13, 0, 1, 6
What is h in -7*h**3 - 143 + 6*h**3 - 44*h**2 + 164*h + 413 - 21*h - 92*h = 0?
-45, -2, 3
Let n(q) = 47*q**2 + 45*q**2 + 2*q - q**3 - 90*q**2. Let d(w) = 2*w**3 - w**2 - w. Let s(z) = -2*d(z) - 3*n(z). Factor s(x).
-x*(x + 2)**2
Let h = 2768/5 - 553. Suppose -30*o + 17 = -103. Solve -18/5*y**2 - 3*y**3 + 24/5 + 12/5*y - h*y**o = 0 for y.
-2, 1
Let i(k) be the first derivative of -k**5/450 - k**4/36 - 4*k**3/45 + 3*k**2 + 7*k - 68. Let t(m) be the second derivative of i(m). Suppose t(s) = 0. What is s?
-4, -1
Let p(t) = -t**2 - 21*t - 17. Let k be p(-20). Suppose k = -15*r + 33. Factor -3/4*g**r + 3*g - 3.
-3*(g - 2)**2/4
Let t = -617 - -618. Suppose 3*a = -2*c - t, -2*a = -4*c + 8*c + 6. Factor 2*w**2 - 7/2*w - a.
(w - 2)*(4*w + 1)/2
Let k(n) = -3*n**4 + n**2 + n + 1. Let c(d) = 4*d**4 - 18*d**3 - 32*d**2 - 16*d - 2. Let u(j) = c(j) + 2*k(j). What is o in u(o) = 0?
-7, -1, 0
Suppose -10 = 18*p - 0 - 10. What is q in -4/3*q**5 - 16/3*q**2 + p + 16/3*q**4 - 4*q**3 + 16/3*q = 0?
-1, 0, 1, 2
Let f(p) be the first derivative of -5/14*p**4 - 6/7*p**3 + 48/7*p + 26/7*p**2 + 85. Factor f(r).
-2*(r - 2)*(r + 3)*(5*r + 4)/7
Find i such that 816/5 - 411/5*i**2 + 402/5*i + 3/5*i**3 = 0.
-1, 2, 136
Let o = 32362409/789 - 41017. Let b = o - -3961/3156. Solve -5/2*n**2 - 1/4*n**5 + 1/2*n**3 + b + 5/4*n**4 - 1/4*n = 0.
-1, 1, 5
Let g(o) be the third derivative of o**7/840 - 11*o**6/240 - 5*o**5/16 - 21*o**2 + 96. Determine x so that g(x) = 0.
-3, 0, 25
Let k(d) be the first derivative of 52/3*d**2 - 147 - 100/9*d**3 + 4/3*d**4 - 20/3*d. Factor k(s).
4*(s - 5)*(s - 1)*(4*s - 1)/3
Let g be (-51)/(1071/30)*(1 + (-19)/5). Let k(d) be the first derivative of 24 + 1/22*d**g + 0*d + 0*d**2 + 0*d**3. Determine p, given that k(p) = 0.
0
Suppose -12*h - 72 = -30*h. Suppose -10*l = -13*l + h*t - 10, l - 18 = -4*t. Factor 2/9*p**l + 14/9 - 16/9*p.
2*(p - 7)*(p - 1)/9
Let y(o) be the third derivative of 0 - 13/12*o**5 + 0*o**3 + 3/40*o**6 + 0*o + 116*o**2 + 7/12*o**4. Solve y(s) = 0.
0, 2/9, 7
Let x(j) be the second derivative of 24*j - 5/12*j**4 + 1 + 0*j**2 + 70/3*j**3. Find l such that x(l) = 0.
0, 28
Let l(v) = 2*v**4 - 2*v**3 + 2*v**2 + v. Let k(b) = -6*b**4 + 190*b**3 + 306*b**2 - 1193*b + 688. Let i(g) = k(g) + 5*l(g). Factor i(t).
4*(t - 1)**2*(t + 4)*(t + 43)
Let z(l) be the first derivative of 0*l - 8/15*l**3 + 6/5*l**2 + 12 - 1/5*l**4. Let z(s) = 0. Calculate s.
-3, 0, 1
Let o(h) = -3*h**2 - 789*h + 18. Let q(f) = -f**2 - 225*f + 5. Let k(m) = -5*o(m) + 18*q(m). Factor k(j).
-3*j*(j + 35)
Let r(b) be the first derivative of -b**4/4 - 201*b**3 - 45900*b**2 - 270000*b - 1337. Factor r(z).
-(z + 3)*(z + 300)**2
Let u(l) be the second derivative of l**5/40 - 55*l**4/8 - 83*l**3/6 + 6426*l. Find s such that u(s) = 0.
-1, 0, 166
Let m(v) = v**2 + 4751*v - 2832167. Let j(n) = n**2 - 3*n + 11. Let y(r) = 6*j(r) - 2*m(r). Determine z so that y(z) = 0.
1190
Let x = 4/640809 - -854408/640809. Factor x*i + 1/3*i**3 + 0 - 5/3*i**2.
i*(i - 4)*(i - 1)/3
Let i(v) = -5*v**3 + 325*v**2 + 601*v + 319. Let s(b) = -4*b**3 + 323*b**2 + 610*b + 319. Let y(g) = -3*i(g) + 4*s(g). Factor y(p).
-(p - 319)*(p + 1)**2
Let h(b) be the first derivative of 0*b**3 + b**4 + 130 + 2/5*b**5 - 2*b**2 - 2*b. Factor h(s).
2*(s - 1)*(s + 1)**3
Let c = 1772071/393794 + 1/196897. Suppose -3*x = -2*x + 4*b + 6, 3*x - 16 = 5*b. Factor 21/4*k**x + c + 69/4*k.
3*(k + 3)*(7*k + 2)/4
Let u(j) = 2110*j + 27433. Let f be u(-13). Factor 0 + 2/11*t**2 + 3/11*t - 1/11*t**f.
-t*(t - 3)*(t + 1)/11
Let v(k) be the third derivative of -k**8/4480 - 3*k**7/2240 - k**6/480 - 56*k**3/3 + 2*k**2 - 14*k. Let b(t) be the first derivative of v(t). Factor b(z).
-3*z**2*(z + 1)*(z + 2)/8
Factor 0 - 2/7*o**2 + 34*o.
-2*o*(o - 119)/7
Let h(v) be the third derivative of 0*v**3 + 1/84*v**8 + 2/3*v**5 + 1 + 0*v + 1/10*v**6 + 0*v**4 - 4/35*v**7 - 14*v**2. Factor h(y).
4*y**2*(y - 5)*(y - 2)*(y + 1)
Let i(b) be the third derivative of -b**6/180 + 248*b**5/45 - 493*b**4/9 + 656*b**3/3 + 8955*b**2. Factor i(y).
-2*(y - 492)*(y - 2)**2/3
Suppose -3*r + 3 = -4*i, -4*r = -93*i + 88*i - 5. Let o(a) be the first derivative of 0*a + 2/33*a**i + 3/55*a**5 + 0*a**2 + 5/44*a**4 - 32. Factor o(b).
b**2*(b + 1)*(3*b + 2)/11
Factor -g**2 - 162*g - 2*g**2 + 127*g + 137*g - 99.
-3*(g - 33)*(g - 1)
Let v be ((-2)/(-2))/((-45)/(-270)*36/16). Find r such that -76/3*r**3 + 0 - v*r**2 + 0*r - 66*r**4 - 27*r**5 = 0.
-2, -2/9, 0
Let v(k) be the first derivative of k**6/21 + 26*k**5/35 + 11*k**4/7 + 5547. Factor v(b).
2*b**3*(b + 2)*(b + 11)/7
Let c(q) be the third derivative of -1/120*q**5 + 0 + 0*q - 1/8*q**3 - 116*q**2 - 1/960*q**6 + 11/192*q**4. Factor c(b).
-(b - 1)**2*(b + 6)/8
Suppose 756*y = -747*y + 1520*y - 34. Solve -30/13*u + 28/13 + 2/13*u**y = 0 for u.
1, 14
Let w(p) be the first derivative of 259 - 10/39*p**3 + 8/13*p**2 - 6/13*p. Factor w(r).
-2*(r - 1)*(5*r - 3)/13
Factor 918/5 + 312/5*c + 2/5*c**2.
2*(c + 3)*(c + 153)/5
Factor 4 - 157*z + 43*z + 35*z**4 + 21 + 420*z**2 - 135*z - 250*z**3 + 19*z.
5*(z - 5)*(z - 1)**2*(7*z - 1)
Let w(g) be the second derivative of -g**4/3 + 506*g**3/3 + 722*g. Solve w(c) = 0.
0, 253
Let t(z) = -6*z**2 + 302*z - 2955. Let m be t(37). Find w, given that 80/3*w**3 + 5/3*w**m + 85/3*w**4 + 0 + 0*w**2 + 0*w = 0.
-16, -1, 0
Let x(n) be the first derivative of -2*n**5/35 + 123*n**4/14 - 242*n**3/7 + 361*n**2/7 - 240*n/7 + 1159. Factor x(u).
-2*(u - 120)*(u - 1)**3/7
Let i = 1933/231 - 262/33. Let f(c) be the first derivative of 0*c - 2/21*c**6 + 8/21*c**3 + 0*c**2 + i*c**4 + 0*c**5 + 9. Factor f(l).
-4*l**2*(l - 2)*(l + 1)**2/7
Suppose 3/5*f**4 - 54/5*f**3 + 288/5*f**2 + 0 - 96*f = 0. Calculate f.
0, 4, 10
Let k = 141274 + -141274. Factor -2/9*m**5 - 38/3*m**4 - 13718/9*m**2 + k*m + 0 - 722/3*m**3.
-2*m**2*(m + 19)**3/9
Let x be (-50)/(-63)*456/(-418). Let v = x + 22/21. Let 12/11*z**3 + v*z**5 + 8/11*z**2 + 0 + 8/11*z**4 + 2/11*z = 0. What is z?
-1, 0
Factor 56/13 - 2/13*j**2 + 54/13*j.
-2*(j - 28)*(j + 1)/13
Let h(a) be the second derivative of a**6/105 - a**5/70 - 11*a**4/21 + 40*a**3/21 - 3*a - 46. Factor h(s).
2*s*(s - 4)*(s - 2)*(s + 5)/7
Let f(p) be the third derivative of 0*p + 3*p**2 - 35/12*p**4 - 3/4*p**5 + 2