 1532*p**3 + 115520*p**2 + 18*p + 12. Let k(a) = 55*f(a) - 6*g(a). Factor k(c).
5*c**2*(c - 152)**2
Let m(r) be the first derivative of -r**5/7 - 403*r**4/28 + 1412*r**3/21 - 670*r**2/7 + 48*r - 2933. Determine n, given that m(n) = 0.
-84, 2/5, 1, 2
Let g = -362006 - -1810034/5. Factor g*t**3 - 224/5*t + 44/5*t**2 + 48.
4*(t - 2)**2*(t + 15)/5
Let b(u) = u**2 + u - 2. Let f be b(2). Suppose -f*j = j - 70. Solve 25 + j*w**2 + w - 33*w - 2*w**3 - 1 = 0.
2, 3
Let w(c) be the third derivative of c**8/1680 + c**7/150 + 11*c**6/600 - 7*c**5/300 - c**4/10 + 5*c**2 + 6*c. Let w(q) = 0. Calculate q.
-4, -3, -1, 0, 1
Let q(w) be the first derivative of -5*w**4/8 - 961*w**3/6 + 964*w**2/5 - 386*w/5 + 1614. What is m in q(m) = 0?
-193, 2/5
Let v(o) be the first derivative of -7*o**4/18 + 34*o**3/9 - 28*o**2/3 + 40*o/9 - 795. Determine u so that v(u) = 0.
2/7, 2, 5
Let q(p) = 262*p**3 - 263*p**3 - 2 + p**2 + 3. Let y(l) = l**4 + 5*l**3 - 8*l**2 - 2*l - 5. Let z(x) = -10*q(x) - 2*y(x). Suppose z(w) = 0. What is w?
-1, 0, 2
Suppose -6*r + 11 = -n, 3*r - 32*n - 1 = -27*n. Solve 18/5 - 6/5*o - 7/2*o**r - 1/10*o**4 + 6/5*o**3 = 0 for o.
-1, 1, 6
Let z(a) be the third derivative of a**5/450 + 41*a**4/90 - 623*a**3/45 + 27*a**2 + a + 6. Factor z(y).
2*(y - 7)*(y + 89)/15
Determine g so that 70/3*g**2 - 650/9*g - 2/3*g**3 - 2/9*g**4 + 0 = 0.
-13, 0, 5
Suppose 4*q - 9 = -5*f + 27, 0 = -5*f + 4*q + 4. Let x(u) be the first derivative of u**f + 8*u - 7 - 4/5*u**5 + 4*u**3 - 10*u**2. Let x(w) = 0. What is w?
-2, 1
Let t(g) = -87*g**3 + 3*g**2 - 3*g - 21. Let i(c) = 5*c**3 + 1. Let v(h) = -18*i(h) - t(h). Factor v(s).
-3*(s - 1)*(s + 1)**2
Let t(p) be the first derivative of 0*p - 1/9*p**3 + p**2 + 157. Factor t(a).
-a*(a - 6)/3
Let l(q) be the first derivative of 27 - 3/2*q**2 + q**5 - 10*q + 41/3*q**3 - 33/4*q**4. Factor l(i).
(i - 5)*(i - 1)**2*(5*i + 2)
Let -105*d - 65*d**3 + 2*d**2 + 66*d**3 - 9*d**2 + 35*d - 104 = 0. Calculate d.
-4, -2, 13
Factor -38095*o - 4*o**3 + 10*o**2 + 3*o**3 + 38071*o.
-o*(o - 6)*(o - 4)
Let i(b) be the third derivative of -11*b**8/100800 - b**7/1260 + b**6/900 + b**5/60 + b**4/4 + 71*b**2. Let w(u) be the third derivative of i(u). Factor w(l).
-(l + 2)*(11*l - 2)/5
Let m(g) be the third derivative of -g**6/420 - g**5/70 - g**4/42 - 16*g**2 + 4. Let m(q) = 0. Calculate q.
-2, -1, 0
Let j(z) be the second derivative of z**10/3360 - z**9/720 + z**8/1120 + z**4/12 - 37*z**3/6 - z + 1. Let w(c) be the third derivative of j(c). Factor w(n).
3*n**3*(n - 2)*(3*n - 1)
Let k = 334498 - 334498. Factor -1/3*l**4 - 7/3*l**3 - 10/3*l**2 + k + 0*l.
-l**2*(l + 2)*(l + 5)/3
Let n = -1231/5 + 247. Suppose 0 = -224*k + 134*k. Solve k*x + n*x**5 + 0 + 8/5*x**3 + 2/5*x**2 + 2*x**4 = 0.
-1, -1/2, 0
Let y(g) be the third derivative of g**5/12 - 25*g**4/24 + 10*g**3/3 - 475*g**2. Factor y(v).
5*(v - 4)*(v - 1)
Let z(a) = a**2 - 13*a + 49. Let u be z(5). Let d(y) = -30*y**2 - 33*y. Let v(q) = -7*q**2 - 8*q. Let s(x) = u*v(x) - 2*d(x). Factor s(m).
-3*m*(m + 2)
Let f(q) be the first derivative of -q**8/1008 - q**7/1260 + q**6/54 + q**5/45 + 15*q**3 + q**2 - 34. Let i(o) be the third derivative of f(o). Factor i(m).
-m*(m - 2)*(m + 2)*(5*m + 2)/3
Let g(k) = -k**4 - 257*k**3 + 1175*k**2 - 420*k - 1872. Let c(z) = 86*z**3 - 392*z**2 + 140*z + 624. Let v(n) = 7*c(n) + 2*g(n). Suppose v(h) = 0. What is h?
-1, 2, 4, 39
Suppose l + 6 = 4*l. Let k = 3/58829 - -235277/764777. Factor -k*u - 2/13*u**l + 16/13.
-2*(u - 2)*(u + 4)/13
Suppose -419 = -4*r + 525. Factor -18*m + r*m**4 - 200*m**3 - 2*m - 145*m**2 + 4*m**4.
5*m*(3*m - 4)*(4*m + 1)**2
Let q(x) be the third derivative of 0*x + 1/32*x**4 + 1/8*x**3 + 1/448*x**8 + 69*x**2 - 1/40*x**5 + 1/280*x**7 - 1/80*x**6 - 2. Suppose q(r) = 0. Calculate r.
-1, 1
Let i(t) = -t**3 - 31*t**2 + 28*t - 83. Let x be i(-32). Solve 19*v - 20*v**3 + 49*v**4 + v**5 - x*v**4 + 0*v**5 + 10*v**2 - 14 = 0.
-7, -1, 1, 2
Suppose -4*o + 1 = x, -o = -2*x - 2*o + 9. Suppose -l + 0*l - 16 = -x*d, 0 = 5*l + d - 24. Factor -51*u**2 - 4*u**l + 43*u**2 + u**3 - 13*u**3.
-4*u**2*(u + 1)*(u + 2)
Let y(l) be the second derivative of -l**5 - 76*l**4/3 - 470*l**3/3 - 88*l**2 - 203*l + 9. Let y(g) = 0. What is g?
-11, -4, -1/5
Let w(a) = -a - 7. Let h be w(5). Let u be ((-2)/h)/((-8)/(-8)). Factor 2/3*p**5 - 1/6*p**2 + 3/2*p**3 + 0 - u*p - 11/6*p**4.
p*(p - 1)**3*(4*p + 1)/6
Let f(s) = -2*s**2 + 30*s + 36. Let v(n) = -2*n**2 + 29*n + 34. Let z(i) = -3*f(i) + 4*v(i). Solve z(c) = 0.
-1, 14
Let w(z) be the first derivative of z**5/6 - 5*z**4/3 + 5*z**3 - 20*z**2/3 + 25*z/6 + 1022. Find s such that w(s) = 0.
1, 5
Let i(z) be the third derivative of z**7/1050 - z**6/200 - 13*z**5/30 + 5986*z**2. Factor i(s).
s**2*(s - 13)*(s + 10)/5
Find f, given that -3 - 33/5*f**3 - 18/5*f**4 - 43/5*f + 277/5*f**2 = 0.
-5, -1/6, 1/3, 3
Let v(d) = -d**2 + 5*d + 6. Let h be v(5). Suppose -5*s = -h*s + 76. Factor s - 9*t**2 - 76 + 3*t**4 - 6*t.
3*t*(t - 2)*(t + 1)**2
Let v(j) = j**3 - 5*j**2 - 2*j - 5. Let b be v(6). Let n = -17 + b. Factor 17*i - 21*i - 4*i**n + 0*i**2 + 8.
-4*(i - 1)*(i + 2)
Let q(l) be the first derivative of l**8/8400 - l**7/4200 - l**6/360 - l**5/200 - 64*l**3/3 + 106. Let z(h) be the third derivative of q(h). Factor z(y).
y*(y - 3)*(y + 1)**2/5
Let a(r) = 24*r**2 + 11*r - 6. Let o be a(1). Let p be o/4 + -4 - (-26)/(-13). Find b, given that p*b**2 - 1/4*b**3 - 9/4 - 3/4*b = 0.
-1, 3
Let i be (3 - 3)/(20/(-4)). Let o(b) be the first derivative of 1/2*b**2 + i*b + 1/8*b**4 + 1/2*b**3 - 5. Factor o(r).
r*(r + 1)*(r + 2)/2
Let 3/2*t**4 - 93/2*t**3 + 0*t + 297*t**2 + 0 = 0. What is t?
0, 9, 22
Let w(h) = -12*h - 343. Let t be w(-32). Solve 11609*c - t - c**2 - 11647*c + 3*c**2 + 1 = 0.
-1, 20
Let q = -242 - -270. Factor -710 + 27*c**2 + 6*c - q*c**2 + 705.
-(c - 5)*(c - 1)
Let n = 247 - 245. Let o(p) = -p**3 + 3*p**2 - 6*p + 10. Let f be o(n). Factor 12/5*k + 6/5*k**f + 0 - 6/5*k**3.
-6*k*(k - 2)*(k + 1)/5
Let w(r) be the first derivative of -2*r**5/25 - 1432*r**4/5 - 2050624*r**3/5 - 1468246784*r**2/5 - 525632348672*r/5 - 5473. Factor w(a).
-2*(a + 716)**4/5
Let v(y) be the second derivative of y**7/112 + y**6/80 - 33*y**5/160 + 7*y**4/32 + 5*y**3/8 - 3*y**2/2 + 3052*y - 2. Find q, given that v(q) = 0.
-4, -1, 1, 2
Let w = 976/35 - -19577/105. Let j = 217 - w. What is v in -40/3*v**5 + j*v + 166/3*v**4 + 94/3*v**2 - 220/3*v**3 - 8/3 = 0?
-1/4, 2/5, 1, 2
Let g be (-74)/(-7) + (-14442)/1450 + (-16)/400. Factor -g*z**2 - 2/7*z**4 + 10/7*z**3 - 16/7*z + 0.
-2*z*(z - 4)*(z - 2)*(z + 1)/7
Let t = 14812 - 14808. Let u(d) be the first derivative of 9 - 2/45*d**3 + 2/15*d**2 + 0*d - 1/30*d**t. Suppose u(o) = 0. What is o?
-2, 0, 1
Let v(c) be the first derivative of -c**6/10 - 2*c**5/3 + 3*c**4/2 + 8*c**3/3 + 39*c**2 + 76. Let j(q) be the second derivative of v(q). Solve j(p) = 0 for p.
-4, -1/3, 1
Let d = 25173723/57376 - 3/57376. Solve -d*j**3 - 105*j + 657/2*j**2 + 1701/8*j**4 + 12 = 0.
2/7, 4/9, 2/3
Suppose -6*a = -a - 30, -2*u + 40 = 6*a. Factor 0*z**3 + 0 - 2/3*z**4 + 0*z**u + 2/3*z**5 + 0*z.
2*z**4*(z - 1)/3
Let i(q) be the third derivative of 0*q - 196*q**2 + 1/12*q**4 + 1/30*q**5 - 1/3*q**3 - 1/60*q**6 + 0. Determine s, given that i(s) = 0.
-1, 1
Let a(c) be the third derivative of -c**6/30 - 68*c**5/15 - 128*c**4/3 - 432*c**2 - 2*c. Determine r, given that a(r) = 0.
-64, -4, 0
Let j(s) be the first derivative of -s**3/3 - 195*s**2/2 + 216*s + 108. Let n(f) = -96*f + 108. Let g(w) = 3*j(w) - 5*n(w). Determine a, given that g(a) = 0.
-36, 1
Factor 334/15 + 2/15*v**2 - 112/5*v.
2*(v - 167)*(v - 1)/15
Let n(l) be the first derivative of 3*l**4/4 + 14*l**3 + 171*l**2/2 + 216*l - 288. Determine f, given that n(f) = 0.
-8, -3
Let o be (-161 + 177)*((0/8)/(-9) + 4/14). Factor -8/7*y**2 - 88/7*y + o + 22/7*y**3.
2*(y - 2)*(y + 2)*(11*y - 4)/7
Let x(c) be the third derivative of -1/60*c**6 + 6*c**3 - 7 + 0*c - 2*c**2 + 8/15*c**5 + 35/12*c**4. Find q such that x(q) = 0.
-1, 18
Suppose -31 - 12 = -43*d. Suppose 4*a - y - 3 = 0, 4 = 3*a - 6*a + 2*y. What is h in -d + 4 - a*h**2 + 6*h - 7 = 0?
1, 2
Let z(o) = 2*o. Let r(i) = -i. Let d(j) = 4*j**2 + 112*j + 1296. Let m(x) = -d(x) - 16*r(x). Let n(c) = m(c) - 24*z(c). Factor n(k).
-4*(k + 18)**2
Let r(i) be the second der