 - 1)*(3*m + 2)/5
Factor -465*k + 216225/2 + 1/2*k**2.
(k - 465)**2/2
Let g(z) be the first derivative of -z**6/30 - 61*z**5/25 - 117*z**4/10 - 346*z**3/15 - 229*z**2/10 - 57*z/5 - 215. Factor g(x).
-(x + 1)**4*(x + 57)/5
Determine s so that -110*s**2 - 5*s**3 - 120 + 15*s**5 - 6*s**3 + 224*s + 8*s**3 - 3*s**3 + 14*s**4 - 17*s**5 = 0.
-3, 1, 2, 5
Factor 863 - 648*x + 1054 + 535628*x**2 - 535625*x**2.
3*(x - 213)*(x - 3)
Let h(x) be the third derivative of -x**5/12 + 265*x**4/8 + 805*x**3/3 + 2508*x**2. Factor h(u).
-5*(u - 161)*(u + 2)
Factor 346/5*u + 204 + 2/5*u**2.
2*(u + 3)*(u + 170)/5
Let n(f) be the third derivative of -2209/6*f**3 - 1/60*f**5 + 0 - 47/12*f**4 - 17*f + 7*f**2. Suppose n(s) = 0. What is s?
-47
Let d(l) = 1201*l - 87673. Let x be d(73). What is h in 19*h**2 + x + 15/2*h**3 + 1/2*h**4 + 12*h = 0?
-12, -2, -1, 0
Let w(j) be the second derivative of -j**4/4 - j**3 + 9*j**2/2 - 96*j. Factor w(h).
-3*(h - 1)*(h + 3)
Factor -l**3 - 33*l**2 + 56*l**2 + 4*l - 15*l**2 - l**3 + 48 - 18*l**2.
-2*(l - 2)*(l + 3)*(l + 4)
Factor 1/11*k**2 - 1688/11 - 842/11*k.
(k - 844)*(k + 2)/11
Suppose -55 = -38*c + 43*c, -q + 3*c = 4*c + 11. Factor 94/7*v**3 - 132/7*v**4 + 0 + q*v - 16/7*v**2 - 18/7*v**5.
-2*v**2*(v + 8)*(3*v - 1)**2/7
Let p(r) be the third derivative of -r**6/1080 - r**5/120 - r**4/36 + 7*r**3 + 7*r**2 + 3. Let s(f) be the first derivative of p(f). Factor s(m).
-(m + 1)*(m + 2)/3
Let t be 10/75 - 3232/(-60). Let q be 0 + (-34)/(-72) + t/(-216). Factor -q*h**2 - 4/9*h + 2/3.
-2*(h - 1)*(h + 3)/9
Let l = 22464 - 22460. Suppose 2/21*q**5 + 0*q**2 + 0 + 4/21*q**l + 2/21*q**3 + 0*q = 0. Calculate q.
-1, 0
Let n(x) be the third derivative of -x**5/420 - 3*x**4 - 1512*x**3 - x**2 + 334*x. Suppose n(w) = 0. What is w?
-252
Suppose -37 = 34*s + 31. Let x be (232/(-1015))/(s/625 + 0). Factor 0 - 300/7*t**2 - 4/7*t**4 + x*t + 60/7*t**3.
-4*t*(t - 5)**3/7
Determine j, given that -4/5*j**2 - 856/5*j + 1728/5 = 0.
-216, 2
Let c(s) be the third derivative of -s**6/660 + 2*s**5/11 + s**4/132 - 20*s**3/11 - 72*s**2 + 2*s. Solve c(x) = 0 for x.
-1, 1, 60
Let y(w) be the third derivative of 71*w**2 + 0*w + 0 + 1/300*w**6 - 1/15*w**4 + 0*w**5 + 0*w**3. Determine b, given that y(b) = 0.
-2, 0, 2
Let n(b) be the third derivative of -2 - 1/2*b**3 - 3/40*b**6 - 7/20*b**5 + 0*b + 27*b**2 - 5/8*b**4. Factor n(c).
-3*(c + 1)**2*(3*c + 1)
Let d = 6 + -20. Let n = 4 - d. Factor -4*m - n*m**3 + 12 - 12 + 7*m**4 + 14*m**2 + 3*m**4 - 2*m**5.
-2*m*(m - 2)*(m - 1)**3
Suppose 3*h - 44 = -8. Solve -27*b**3 + 14*b**3 + b**3 + h*b**2 + 3*b**4 = 0.
0, 2
Factor 5/2*r**4 + 14520*r**2 - 212960*r + 0 - 330*r**3.
5*r*(r - 44)**3/2
Factor 942/17*s + 2/17*s**2 + 940/17.
2*(s + 1)*(s + 470)/17
Let z(p) be the first derivative of p**5/210 - 5*p**4/42 + 6*p**2 + 2*p - 22. Let w(q) be the second derivative of z(q). What is g in w(g) = 0?
0, 10
Let u(p) be the first derivative of -3*p**5/10 + 21*p**4 - 419*p**3 + 1134*p**2 - 2187*p/2 - 1165. Factor u(z).
-3*(z - 27)**2*(z - 1)**2/2
Let w(m) be the second derivative of -m**5/70 - 211*m**4/42 + 425*m**3/21 - 213*m**2/7 + 47*m - 25. Solve w(x) = 0 for x.
-213, 1
Let q(s) = 6*s**2 - 518*s + 512. Let a(n) = 4*n**2 - 518*n + 514. Let c(x) = 4*a(x) - 3*q(x). Factor c(p).
-2*(p - 1)*(p + 260)
Let q(h) be the second derivative of -h**4/24 + 2*h**3 - 20*h**2 + 462*h. Factor q(i).
-(i - 20)*(i - 4)/2
Suppose 42*y = -2331 + 2457. Factor -45/2*q - 3/2*q**2 + 27/2 + 5/2*q**y.
(q - 3)*(q + 3)*(5*q - 3)/2
Let f(d) be the first derivative of d**3/6 - 885*d**2/2 + 783225*d/2 - 1152. What is t in f(t) = 0?
885
Suppose 0 = 3*a + 4*c - 20, 5*a - 3*c = -c + 42. Suppose 0 = -7*n + 8*n - 3. Factor -3*p**n + 15*p + p**3 + 45 - 25*p**2 + a*p**3 - p**3.
5*(p - 3)**2*(p + 1)
Let d(c) = 14*c + 23 - c**2 - 1 + 15*c - 98. Let k be d(3). Find r, given that -1/2*r**3 - 1/2*r**k + 0*r + 0 = 0.
-1, 0
Let g(r) be the third derivative of -55*r**8/48 - 130*r**7/21 - 173*r**6/24 + 83*r**5/6 + 245*r**4/6 + 100*r**3/3 - 13503*r**2. Suppose g(j) = 0. Calculate j.
-2, -1, -2/7, 10/11
Suppose -2*p - p - 9 = -2*w, p = -2*w + 29. Factor 20*q - 11 - 5 - w + 3 + 5*q**2.
5*(q - 1)*(q + 5)
Suppose -380*v = 3*o - 381*v + 4, -o - 5*v + 52 = 0. Find d, given that 16/17 + 12/17*d**o - 24/17*d - 2/17*d**3 = 0.
2
Suppose -5*r = -2*n + 3, -97*n - 6*r = -92*n - 26. Let t(q) be the second derivative of 5/19*q**3 - 22*q - 2/19*q**2 + 0 - 9/38*q**n. Let t(v) = 0. Calculate v.
2/9, 1/3
Let d(w) = -9*w - 1. Let i be d(-1). Let a be (-11)/(-88) - (-15)/i. What is j in -72/5*j**3 + 0 - 39/5*j**a - 6/5*j - 27/5*j**4 = 0?
-2, -1/3, 0
Let d(h) = 17*h**3 - 59*h**2 + 127*h - 43. Let t(w) = 32*w**3 - 119*w**2 + 252*w - 88. Let m(f) = -11*d(f) + 6*t(f). Let m(o) = 0. What is o?
1, 11
Solve 5054/3 - 62/3*b**2 + 190/3*b + 2/3*b**3 = 0 for b.
-7, 19
Let c(k) be the second derivative of k**5/20 + 97*k**4/12 - 197*k**3/6 + 99*k**2/2 - 640*k + 2. Let c(r) = 0. Calculate r.
-99, 1
Let z(j) = j**3 + 4*j**2 - 5*j + 2. Let r be z(-5). Let s(w) = 4*w**3 + 2*w**2 - 3*w + 2. Let l be s(1). Factor 82*d - 80 + 38*d - 28*d**2 + l*d**3 - 17*d**r.
5*(d - 4)**2*(d - 1)
Suppose 30*g + 3 = 31*g. Suppose -4*w**g - 14*w**2 + 23*w**2 + 23*w**2 = 0. Calculate w.
0, 8
Let i(n) be the first derivative of -22*n**5/5 + 3*n**4/2 + 50*n**3/3 - 3*n**2 - 28*n - 813. Solve i(m) = 0.
-1, 1, 14/11
Let m be (-3396)/1415*4/(-3). Factor -12/5*g**2 + 2/5*g**3 + 0 + m*g.
2*g*(g - 4)*(g - 2)/5
Let r(q) = 3 - q + 11 - 14 - q**2. Let d be (-2)/(-9) - (-352)/36. Let c(t) = 20*t**3 - 50*t**2 + 55*t. Let i(n) = d*r(n) + c(n). Factor i(j).
5*j*(2*j - 3)**2
Suppose 0 = 4*m - 3*a - 7979, 0 = -3*a - 10 + 7. Suppose m = 3*o + 1982. Factor 0 + 16/3*z**o + 8*z**3 + 4/3*z + 16/3*z**2 + 4/3*z**5.
4*z*(z + 1)**4/3
Let o(d) = 3*d**2 + 24*d - 120. Let r(g) = -4*g**2 - 24*g + 118. Let k(c) = -5*o(c) - 4*r(c). Determine f, given that k(f) = 0.
8, 16
Let h(f) be the first derivative of 4*f**2 - 20*f**3 + 73 - 44/5*f**5 + 24*f**4 + 0*f. Factor h(s).
-4*s*(s - 1)**2*(11*s - 2)
Let w(l) be the second derivative of l**7/504 + 5*l**6/144 + l**5/6 - l**4/3 - l**3 + 2*l + 53. Let m(n) be the third derivative of w(n). Solve m(z) = 0.
-4, -1
Find o such that -32*o + 192*o**3 - 72*o**2 + 0*o**5 - 196*o**3 + 42*o**4 - 9*o**5 = 0.
-2/3, 0, 2, 4
Factor 326/3*o**2 - 26569/3*o - 1/3*o**3 + 0.
-o*(o - 163)**2/3
Let o(x) be the second derivative of -140*x + 3/20*x**5 + 1/6*x**3 + 1/4*x**4 + 0*x**2 + 0 + 1/30*x**6. What is q in o(q) = 0?
-1, 0
Solve 23/5*t**3 + 1/5*t**4 + 191/5*t**2 + 180 + 137*t = 0 for t.
-9, -5, -4
Let v be 9*((2 - -3) + (1 - 5)). Let k(u) be the first derivative of -v + u - 1/6*u**3 + 1/4*u**2. Factor k(m).
-(m - 2)*(m + 1)/2
Let t(i) be the second derivative of i**5/20 - 65*i**4/3 - 523*i**3/6 - 131*i**2 + 480*i. Let t(v) = 0. What is v?
-1, 262
Let y be (0 - (0 - 1)) + (12 - 11). Solve 2*h - 14 - 4*h**y - h**2 + 67 + 47 + 3*h = 0 for h.
-4, 5
Determine c, given that -7 + 19*c**2 + 144*c + 134*c**2 - 12*c**2 + 10 = 0.
-1, -1/47
Let d(j) be the second derivative of j**7/210 - 61*j**6/150 + 1017*j**5/100 - 2639*j**4/60 + 841*j**3/15 - 553*j - 3. Determine a, given that d(a) = 0.
0, 1, 2, 29
Suppose 103*v - 2260 = -334*v - 693*v. Suppose 40/7 + 32/7*r**v + 4/7*r**3 - 76/7*r = 0. What is r?
-10, 1
Suppose 0 = -5*f + 3*s - 8, 3*f + 31 = 4*s + 13. Let j(o) be the first derivative of -5 + 0*o + f*o**3 + 3/2*o**2 + 3/4*o**4. What is z in j(z) = 0?
-1, 0
Let h = -61197 + 61253. Factor -24*s - 28/3*s**4 - 122/3*s**3 - 2/3*s**5 + 0 - h*s**2.
-2*s*(s + 1)**2*(s + 6)**2/3
Let u(c) be the second derivative of -c**7/399 - 17*c**6/285 - c**5/10 + 433*c**4/114 - 880*c**3/57 + 484*c**2/19 - 109*c. Determine j, given that u(j) = 0.
-11, 1, 2
Suppose -10*n + 6*n + t = 5*t - 12, t = 3. Factor n - 75*x - 5/2*x**2.
-5*x*(x + 30)/2
Let b = 84 + 33. Let g = -113 + b. Factor -80*r**2 + g*r**5 + 72*r**3 + 474*r - 8*r**4 - 20*r**4 - 442*r.
4*r*(r - 2)**3*(r - 1)
Let g = -115012 - -345041/3. Let -2*f + g + 1/3*f**2 = 0. What is f?
1, 5
Let s = -98 + 146. What is l in 48 + 12*l**3 - s*l**2 + 9*l**4 - 3*l**5 + 59544*l - 59544*l = 0?
-2, -1, 2
Let f(k) = k**2 + 485*k + 1451. Let i be f(-3). Suppose 0 = -2*x - 2*x + 40. Factor -5*t**5 + 2*t**2 - 7*t**4 + 14*t**3 - x*t**2 + 11*t**5 - 5*t