5
Let l(g) be the first derivative of -g**8/336 - g**7/56 - g**6/24 - g**5/24 - 25*g**3/3 + 88. Let m(k) be the third derivative of l(k). Factor m(a).
-5*a*(a + 1)**3
Let g(y) = 20*y**4 - 326*y**3 + 1424*y**2 - 1917*y + 821. Let l(j) = 7*j**4 - 109*j**3 + 475*j**2 - 639*j + 274. Let z(u) = 4*g(u) - 11*l(u). Factor z(p).
3*(p - 30)*(p - 3)*(p - 1)**2
Let g(n) be the third derivative of 11*n**5/630 - 115*n**4/252 + 82*n**3/21 - 541*n**2. Factor g(w).
2*(w - 3)*(11*w - 82)/21
Let d(u) be the second derivative of 0 + 1/3*u**4 - 79*u - 8*u**2 - 1/5*u**5 + 8/3*u**3. What is f in d(f) = 0?
-2, 1, 2
Let v(u) = -u. Let p be v(-2). Suppose -15*s**p + 5*s**4 - 5*s**3 + 25*s**2 - 10*s**2 = 0. Calculate s.
0, 1
Factor 375/8*p**3 + 0 - 1488*p**2 - 3/8*p**4 + 2883/2*p.
-3*p*(p - 62)**2*(p - 1)/8
Let j = -243 - -152. Let n = j - -96. Let 3*y + n*y + 25*y**2 - 5*y + 7*y = 0. What is y?
-2/5, 0
Let i(b) = b**3 - b**2 + b + 6. Let s(x) = -2*x**4 + 46*x**3 - 204*x**2 + 310*x - 164. Let w(u) = 4*i(u) + 2*s(u). Factor w(t).
-4*(t - 19)*(t - 2)**2*(t - 1)
Let j = 75395 + -376903/5. Factor -12/5 - j*o - 33/5*o**2.
-3*(o + 2)*(11*o + 2)/5
Let o(k) be the first derivative of -k**3/12 + 59*k**2/8 - 55*k + 1144. Factor o(i).
-(i - 55)*(i - 4)/4
Let l(t) be the third derivative of -t**6/360 - 3257*t**5/180 - 294487*t**4/8 + 294849*t**3/2 + 13248*t**2. Find p such that l(p) = 0.
-1629, 1
Let z be 24/22*27/(-6)*(-44)/36. Suppose 0 = -3*a - 1 + 10. Let z*u**a + u**2 - 3*u**4 + 1632 + 5*u**2 - 1635 - 3*u**5 - 3*u = 0. What is u?
-1, 1
Let i = -181 + 296. Factor 100*u + 4*u**3 + 177 - i - 110 - 56*u**2.
4*(u - 12)*(u - 1)**2
Suppose -4*x + 4 = -4*h, 2*x = 3*x + 1. Let d be (h/(-10))/((-19)/(7315/(-28))). Let -5/4*k - k**3 - 1/2 + d*k**2 = 0. What is k?
-1/4, 1, 2
Let o = 4294 - 4292. Let s(w) be the first derivative of -15*w + 5 - 5*w**o + 5/3*w**3. Factor s(f).
5*(f - 3)*(f + 1)
Let h = -142580 + 712922/5. Solve 0*v**3 + 0 - h*v**2 + 4/5*v + 56/5*v**5 + 82/5*v**4 = 0.
-1, 0, 1/4, 2/7
Let a(z) be the first derivative of -5/2*z**2 + 5/4*z**4 - 25/3*z**3 + 25*z - 94. Factor a(m).
5*(m - 5)*(m - 1)*(m + 1)
Let z be (21 - 20)/(2/(-26)). Let k be (-2)/5*(z + (-510)/(-45)). Determine i so that -1/6*i**5 + 0 - 2/3*i**4 + 0*i**2 + 0*i - k*i**3 = 0.
-2, 0
Factor -192*h**2 + 73839/5*h + 478242/5 + 3/5*h**3.
3*(h - 163)**2*(h + 6)/5
Factor -15*y + 0*y - 605*y**2 + 607*y**2 - 2728 - 11*y.
2*(y - 44)*(y + 31)
Let f(k) be the third derivative of -k**6/360 - 31*k**5/60 - 961*k**4/24 + 34*k**3 - 4*k**2. Let i(q) be the first derivative of f(q). Factor i(t).
-(t + 31)**2
Suppose -12*s = -4 - 32. Let u(c) be the second derivative of -1/42*c**s - 10*c + 0 + 1/28*c**4 - 1/7*c**2. Suppose u(b) = 0. What is b?
-2/3, 1
Let y be 100/26 + (-16)/(-104) - 1. Let g(a) be the second derivative of -1/11*a**2 - 1/66*a**4 + 2/33*a**y + 15*a + 0. Factor g(q).
-2*(q - 1)**2/11
Let t be (-3 - 1) + (-45)/(-15). Let n = 7 + t. Factor -2*z - 2 - 4 + 26*z**2 - 36*z**3 + 9*z**4 + n*z**5 - 7*z**4 + 10*z**2.
2*(z - 1)**3*(z + 3)*(3*z + 1)
Suppose 6*y - 11*y + 2*j + 4 = 0, -j = -3. Factor -8*k**y + 276*k**5 - 141*k**5 - 137*k**5 + 6*k**4.
-2*k**2*(k - 2)**2*(k + 1)
Let h(q) = q**3 + 7*q**2 - q - 7. Let k be h(-5). Suppose -5*m + 122 = 42. Factor -m + k + 4*j**2 + 32*j + 32.
4*(j + 4)**2
Let v(d) be the second derivative of -d**5/5 - 124*d**4/3 - 2478*d**3 + 15876*d**2 + 2815*d. Factor v(c).
-4*(c - 2)*(c + 63)**2
Let t(m) = 30*m**2 + 681*m - 207. Let a be t(-23). Solve -2/9*i**5 + 0*i**3 + 0*i + 8/9*i**2 - 2/3*i**4 + a = 0 for i.
-2, 0, 1
Let y = 141028/14427 - -4/1603. Let v = y + -82/9. Let -4/3*x**2 + v*x**3 + 0 + 2/3*x = 0. What is x?
0, 1
Let y(z) be the second derivative of -z**6/225 - 118*z**5/75 - 47*z**4/18 + 1597*z. Let y(d) = 0. Calculate d.
-235, -1, 0
Let b(y) be the second derivative of -1/4*y**4 - 5/6*y**3 - 10*y + 1/30*y**6 - y**2 - 8 + 1/20*y**5. Factor b(a).
(a - 2)*(a + 1)**3
Let s(m) be the third derivative of m**9/272160 - m**8/30240 + m**7/11340 - 29*m**5/30 - 21*m**2. Let q(a) be the third derivative of s(a). Solve q(h) = 0.
0, 1, 2
Let b(j) = -2*j**4 + 352*j**3 - 10*j**2 - 292*j - 24. Let l(y) = -y**4 + 211*y**3 - 6*y**2 - 176*y - 14. Let d(u) = 7*b(u) - 12*l(u). Factor d(v).
-2*v*(v - 1)*(v + 1)*(v + 34)
Find a, given that -1/3*a**5 - 24332/3*a**2 + 49928/3*a - 8426*a**3 - 317/3*a**4 + 0 = 0.
-158, -2, 0, 1
Let p = 41989/136 + -2469/8. Let c(x) be the second derivative of -p*x**2 + 0 - 1/255*x**6 + 1/34*x**4 - 1/51*x**3 + 1/170*x**5 + 23*x. Solve c(v) = 0 for v.
-1, 1, 2
Let v(g) be the third derivative of -g**5/30 + 83*g**4/12 + 170*g**3/3 + 5417*g**2. Solve v(i) = 0.
-2, 85
Let a be 5/((-2860)/952) - -2. Let p = a + -2/13. Factor -10/11 - 12/11*s - p*s**2.
-2*(s + 1)*(s + 5)/11
Let t = -390138 - -2340829/6. Factor -1/6*s**3 + 0*s + 0 + t*s**4 - s**2.
s**2*(s - 3)*(s + 2)/6
Let l be 259640/228 + 2/(-19). Let a = -1138 + l. Solve 8/9*v + 2/9*v**2 + a = 0 for v.
-3, -1
Let t be (10/75*15)/(7/(84/8)). Let r(h) be the first derivative of 1/2*h**2 + 15 + 1/12*h**t + 0*h. Factor r(d).
d*(d + 4)/4
Let z(f) be the third derivative of 0*f + 5/4*f**3 - 41/32*f**4 + 119*f**2 + 1/20*f**5 + 0. Factor z(d).
3*(d - 10)*(4*d - 1)/4
Let c(x) = 4*x**2 - 1. Let s be c(1). Suppose 3*y = 3 + 12, -y = -s*l + 106. Find q, given that -31*q**3 + 5*q**4 - 5*q**2 + l*q**3 - 26*q**3 + 20*q**5 = 0.
-1, -1/4, 0, 1
Factor 303*v + 0 + 3/2*v**2.
3*v*(v + 202)/2
Let w(q) be the first derivative of 21*q + 1/6*q**4 + 27 + 2/3*q**3 + 0*q**2. Let v(h) be the first derivative of w(h). Find g such that v(g) = 0.
-2, 0
Suppose 306 = 78*f + 24*f. Suppose -f*u = -2*k - k - 12, -2*u - 5*k + 1 = 0. Factor 0 + 1/7*g - 2/7*g**2 + 1/7*g**u.
g*(g - 1)**2/7
Let -1041*k + 246016 - 680*k + 697*k + 4*k**2 - 960*k = 0. What is k?
248
Suppose 6*u + 10 = 22. Let 2*b**3 + 1 - 8 + 7 - 14*b**u + 30*b - 18 = 0. Calculate b.
1, 3
Let t(h) be the second derivative of h**5/50 + h**4/10 - 24*h**3/5 + 176*h**2/5 + 2*h - 217. Determine a, given that t(a) = 0.
-11, 4
Let v be (-27 - -21)*(-2)/(-4) - (-10 - -1). Let a(w) be the first derivative of -42/5*w**3 - 49/20*w**4 - 8/5*w + 3 - v*w**2. Factor a(i).
-(i + 2)*(7*i + 2)**2/5
Factor 1328/13*i + 2/13*i**2 + 0.
2*i*(i + 664)/13
Let o(v) be the second derivative of -v**4/12 - 2024*v**3/3 - 2048288*v**2 - 2*v + 12. Find x such that o(x) = 0.
-2024
Let w(g) be the second derivative of g**7/126 + g**6/9 - 29*g**5/30 - 4*g**4/9 + 59*g**3/6 + 21*g**2 + 27*g - 27. Solve w(p) = 0.
-14, -1, 3
Let d(s) be the first derivative of -3*s**5/40 + 111*s**4/32 + 189*s**3/8 - 37179*s**2/16 + 812. Determine o so that d(o) = 0.
-17, 0, 27
Let -15*r**5 - 38439 + 38149 + 400*r**4 - 434*r + 1000*r**3 + 9*r + 450*r**2 = 0. What is r?
-1, 2/3, 29
Let j(g) be the second derivative of -g**9/7560 + g**8/3360 + g**7/1260 - g**6/360 + 23*g**4/2 - 84*g. Let y(l) be the third derivative of j(l). Factor y(z).
-2*z*(z - 1)**2*(z + 1)
Let 12784005/2 + 5/2*v**2 + 7995*v = 0. What is v?
-1599
Let s(z) = 8*z**2 - 14*z + 42. Let r(c) = -c**2 + 1. Suppose 3*f = 5*a - a - 51, -6 = 2*a. Suppose -9*o - 15 = 12. Let x(j) = f*r(j) + o*s(j). Factor x(k).
-3*(k - 7)**2
Let n(v) be the second derivative of -v**6/2700 - v**5/50 - 11*v**3/2 - v**2 + 14*v + 2. Let o(x) be the second derivative of n(x). Factor o(p).
-2*p*(p + 18)/15
Suppose 1/4*w**4 - 15*w - 25/4*w**2 - 9 + 0*w**3 = 0. What is w?
-3, -2, -1, 6
Let c = -51 - -89. Let v be (4 + -8 + c)/1. Solve 14*j**4 - v*j**4 + 4*j**2 + 16*j**4 = 0 for j.
-1, 0, 1
Let d be (-722)/(-95) - 4/(-10). What is n in -5*n**2 - d*n**2 + 6*n - 2*n**5 - 3*n**2 + 12*n**3 + 7*n**2 - 7*n**2 = 0?
-3, 0, 1
Factor -4*o**2 - 304325 - 794672 + 4968*o + 183730 + 152382 - 779679.
-4*(o - 621)**2
Let u(x) be the first derivative of x**3/2 + 117*x**2 - 2612. Factor u(h).
3*h*(h + 156)/2
Let n(q) be the third derivative of -q**7/840 - q**6/96 + 19*q**5/120 + 11*q**4/8 - 15*q**3 + 6*q**2 + 120. Let n(f) = 0. What is f?
-6, 2, 5
Let l(q) be the third derivative of 1/5*q**3 + 0*q - 7/30*q**4 + 68*q**2 + 0 - 1/30*q**5. Factor l(t).
-2*(t + 3)*(5*t - 1)/5
Let u be 14*(187/(-357) + -1*12/(-18)). Suppose -1/2*m**u - 1/2*m + 1 = 0. What is m?
-2, 1
Let v(j) = -1. Let f(g) = -2*g + 16. Let n(k) = -f(k) - 2*v(k). Let t be n(8). Factor -7*