9)*(g + 1)**3
Let h(o) be the first derivative of -o**6/18 + o**5/6 - o**4/12 - 2*o**3/9 + o**2/3 - o/6 - 1278. Suppose h(c) = 0. What is c?
-1, 1/2, 1
Let l(w) be the first derivative of -w**6/8 - 3*w**5/5 - 3*w**4/16 + 3*w**3/2 - 6358. Find r, given that l(r) = 0.
-3, -2, 0, 1
Let q(x) be the third derivative of -x**7/70 + 11*x**6/40 + 3*x**5/5 - 2451*x**2. Factor q(b).
-3*b**2*(b - 12)*(b + 1)
Let m(a) be the first derivative of a**4/4 - 16*a**3/3 + 55*a**2/2 + 2301. Determine g, given that m(g) = 0.
0, 5, 11
Let i = 61451 - 61424. Factor i + 21/2*z - 3/2*z**2.
-3*(z - 9)*(z + 2)/2
Suppose -29131 = -27*g - 29050. Let h(x) be the second derivative of 42*x - 8/3*x**g + 0*x**2 + 1/30*x**6 - 9/20*x**5 + 0 + 2*x**4. Let h(q) = 0. What is q?
0, 1, 4
Let t(z) be the first derivative of -z**5/140 - z**4 - 56*z**3 + 67*z**2/2 + 105. Let f(j) be the second derivative of t(j). Factor f(n).
-3*(n + 28)**2/7
Let v(h) be the first derivative of 4/5*h**5 - 8/3*h**3 + 0*h + 0*h**2 + h**4 + 18. Factor v(r).
4*r**2*(r - 1)*(r + 2)
Let t(u) = 114*u**4 - 125*u**3 + 3*u**2 - 4*u. Let f(k) = -113*k**4 + 125*k**3 - 6*k**2 + 3*k. Let g(a) = 4*f(a) + 3*t(a). Factor g(r).
-5*r**2*(r - 1)*(22*r - 3)
Let k = -607 - -612. Let l(x) be the first derivative of -8 + 0*x**2 + 4/15*x**3 + 0*x + 9/25*x**k + 3/5*x**4. Factor l(n).
n**2*(3*n + 2)**2/5
Let o be (2 - 6) + (-14)/(-2). Factor 6*c**2 - 213*c + 213*c - 2*c**o.
-2*c**2*(c - 3)
Let u(g) be the second derivative of g**6/180 - g**5/15 - 5*g**4/12 + 59*g**3/6 - 71*g. Let x(o) be the second derivative of u(o). Factor x(s).
2*(s - 5)*(s + 1)
Suppose -4*y = -z - 60 - 102, 2*y = -3*z + 102. Let x(h) be the first derivative of 3/4*h + y + 1/4*h**3 + 3/4*h**2. Factor x(m).
3*(m + 1)**2/4
Let a(k) be the third derivative of k**6/30 - 29*k**5/45 + 19*k**4/9 + 32*k**3/9 - 479*k**2. Find f, given that a(f) = 0.
-1/3, 2, 8
Let q(r) be the third derivative of 0*r + 171*r**2 - 19/12*r**4 - 1/120*r**6 + 0 + 4*r**3 + 1/4*r**5. Let q(w) = 0. What is w?
1, 2, 12
Suppose r + 4 = k, -5*k + 4*k + 4 = 3*r. Suppose -5*m - 3*d - 9 + k = 0, m + 8 = -2*d. Let -1/7*t**3 + 0 - 3/7*t**m + 4/7*t = 0. What is t?
-4, 0, 1
Let p = 936 - 934. Factor -35*y + 7 + 8*y**p + 5*y**2 + 9*y**3 + y**2 + 5.
(y - 1)*(y + 3)*(9*y - 4)
Let w be (7 - (-592)/(-84))/((-313)/17528). Factor 2/9*b**3 - w*b - 16/9*b**2 + 0 + 2/9*b**4.
2*b*(b - 3)*(b + 2)**2/9
Suppose 5*h + 2*i = 73, -3*i = 11 - 23. Let q be h - ((-4 - -7) + 4). Find b, given that 9/4*b**5 + 0 + 3/4*b**3 - 3*b - 6*b**4 + q*b**2 = 0.
-1, 0, 2/3, 1, 2
Let h(y) = 663*y - 46408. Let x be h(70). Factor -5/3*g - 1/3*g**x + 8.
-(g - 3)*(g + 8)/3
Let t(h) = -9*h**3 - 432*h**2 + 4. Let k(y) = 125*y**3 + 6055*y**2 - 55. Let f(u) = -4*k(u) - 55*t(u). Factor f(w).
-5*w**2*(w + 92)
Let a(n) be the first derivative of 2*n**3/15 - 8*n**2/5 + 2208. Factor a(s).
2*s*(s - 8)/5
Factor 41064*g**2 - 2256*g + 41098*g**2 + 2240 - 81586*g**2 - 4*g**3.
-4*(g - 140)*(g - 2)**2
Let m(i) be the second derivative of -i**5/10 - 139*i**4/6 - 269*i**3 - 1197*i**2 - 1817*i. Factor m(b).
-2*(b + 3)**2*(b + 133)
Let v = 535/258 - 121/86. Let t(d) be the second derivative of v*d**3 - 3 - 2*d - 5/3*d**2 - 1/18*d**4. Factor t(y).
-2*(y - 5)*(y - 1)/3
Let r = 13 - 8. Factor 12*w**4 - r - 6*w**2 - 1 + 12*w**3 + 6370*w + 3*w**5 - 6385*w.
3*(w - 1)*(w + 1)**3*(w + 2)
Let m(c) be the first derivative of -22/3*c**3 - 31 + 16*c + c**4 + 10*c**2. Factor m(v).
2*(v - 4)*(v - 2)*(2*v + 1)
Let h(f) be the third derivative of 2*f**7/945 - 13*f**5/135 - 2*f**4/9 - 10*f**2 + 13*f. Factor h(b).
4*b*(b - 4)*(b + 1)*(b + 3)/9
Let f(a) be the second derivative of 5/6*a**4 - 2/3*a**3 + 0*a**2 - 2/5*a**5 - 74*a + 1/15*a**6 + 0. Determine p, given that f(p) = 0.
0, 1, 2
Let z(t) = -t**2 - t - 1. Let f(q) = -7*q**2 - 2*q - 2. Let a(p) = -f(p) + 4*z(p). Let u be a(-2). Solve -2*s**2 + s**2 - s**2 + 8*s - u*s = 0 for s.
-3, 0
Let p = 14987/3 + -29969/6. Factor -10/3*y**2 + 0*y + 0 - p*y**3.
-5*y**2*(y + 4)/6
Let l = 385 + 275. Let h be ((-2)/12*1)/((-6)/l). Solve 4 + 25/3*s**3 - 56/3*s + h*s**2 = 0.
-3, 2/5
Let a(j) be the first derivative of j**6/30 - 102*j**5/25 + 2601*j**4/20 - 182. Suppose a(z) = 0. Calculate z.
0, 51
Factor 288*j - 12*j**3 - 579*j**2 - 1500*j + 35*j**2 - 344.
-4*(j + 2)*(j + 43)*(3*j + 1)
Suppose 13*p = 9*p + 84. Suppose -5*w = -w - 3*c - p, -5*c = -25. Suppose 13 - w*t - 8 + 7*t**3 - 4*t**3 - 11 = 0. What is t?
-1, 2
Let p(q) be the second derivative of -q**7/42 + 3*q**5/20 - q**4/6 + 1803*q. Let p(x) = 0. What is x?
-2, 0, 1
Let o(u) be the second derivative of 2*u**7/7 + 12*u**6/5 - 201*u**5/20 - 17*u**4/4 + 27*u**3 - 24*u**2 + 65*u - 4. Solve o(l) = 0.
-8, -1, 1/2, 2
Let a = 3277 + -2286. Let w = a - 14861/15. Factor 0 + 2/15*n**3 - 2/5*n - w*n**2.
2*n*(n - 3)*(n + 1)/15
Let y be (28/12 - 1)*(-9)/(-6). Let u(q) = q**3 - 2*q**2 + 9*q - 18. Let d be u(y). Determine i so that 12/7 - 3/7*i**2 + d*i = 0.
-2, 2
Let m(q) be the first derivative of 2*q**6/3 + 4*q**5/5 - 15*q**4 - 12*q**3 + 108*q**2 + 5932. Factor m(k).
4*k*(k - 3)*(k - 2)*(k + 3)**2
Let l be 0*(-10 + (-124)/(-12)). Let r be 611/117 - 10/2. Factor r*j + l - 2/9*j**2.
-2*j*(j - 1)/9
Let m(s) be the third derivative of -s**8/420 - 54*s**7/175 - 293*s**6/25 - 4798*s**5/75 - 1547*s**4/10 - 1014*s**3/5 - 849*s**2 + s. Factor m(x).
-4*(x + 1)**3*(x + 39)**2/5
Suppose 0 = y + 4*y - 15, 2*p - 11 = y. Let r be (-26)/455*p + 44/10. Solve 4/7 + 2/7*a**r - 6/7*a**2 - 2/7*a**3 + 2/7*a = 0.
-1, 1, 2
Let v(n) be the third derivative of n**6/48 - 23*n**5/4 + 450*n**4 + 12960*n**3 + 11*n**2 + 2*n - 43. Factor v(z).
5*(z - 72)**2*(z + 6)/2
Let v(o) = 2*o**3 - o. Let i(n) = 5*n**3 + 1050*n**2 - 367503*n + 42875000. Let b(z) = 4*i(z) - 12*v(z). Determine p, given that b(p) = 0.
350
Factor 141/2 - 1/2*u**4 + 210*u**2 - 211*u - 69*u**3.
-(u - 1)**3*(u + 141)/2
Let d = 73481/2 - 36738. Let n be (2/(-2))/(2/(-4)). Suppose 10 + 10*b + d*b**n = 0. What is b?
-2
Let t = -1336 + 1338. Let -21/4*c**t + c**3 + 5/4*c + 0 = 0. Calculate c.
0, 1/4, 5
Let a(p) be the third derivative of -p**6/360 + 2*p**5/45 + p**4/18 - 16*p**3/9 + p**2 + 4*p + 98. Suppose a(u) = 0. Calculate u.
-2, 2, 8
Let h(n) be the first derivative of n**4/20 + 1523*n**3/5 + 6958587*n**2/10 + 3532642667*n/5 + 4588. Factor h(w).
(w + 1523)**3/5
Let g(d) = 11*d**3 - 115*d**2 + 222*d - 113. Let c = 430 - 432. Let i(l) = -5*l**3 + 58*l**2 - 111*l + 56. Let y(b) = c*g(b) - 5*i(b). Factor y(n).
3*(n - 18)*(n - 1)**2
Let f = 78 - -104. Let u be f/(-455) + (-24)/(-10) + 0. Factor -2*i**4 + 7*i**5 + 14*i**2 - 6*i**5 - i - 12*i**u.
i*(i - 1)**3*(i + 1)
Let h(s) be the first derivative of 2*s**3/3 + 136*s**2 + 270*s - 1939. Factor h(v).
2*(v + 1)*(v + 135)
Suppose -3*s - 4*g = 10, 4 = -166*g + 165*g. Suppose -s*y = 4*h - 6, 15*y - 13*y = -h. Let 24/11*d + 8/11*d**h + 18/11 = 0. What is d?
-3/2
Let m = -68 - -50. Let k = m - -24. Let 4*d**3 - k*d**3 + 0 + 9*d - 3*d - 4 = 0. What is d?
-2, 1
Determine q so that 260*q - 177274 + 667324 - 2641*q + 401*q + 2*q**2 = 0.
495
Let q = 1428808 - 2857595/2. Solve -15/2*l**2 + q*l + 3/2*l**3 - 9/2 = 0.
1, 3
Let a(x) be the first derivative of x**2 - 8*x - 2. Let d be a(5). Let 6*o**5 + 2*o**2 - 8*o**5 - 2*o**4 - d*o**3 + 4*o**3 + 0*o**2 = 0. What is o?
-1, 0, 1
Let n(d) be the second derivative of -3*d**5/100 - 19*d**4 + 763*d**3/10 - 573*d**2/5 - 3030*d. Factor n(u).
-3*(u - 1)**2*(u + 382)/5
Find b, given that -34 - 8*b**3 + 93 + 105*b**2 - 22*b**3 - 73 + 614 + 730*b - 5*b**4 = 0.
-6, -4, -1, 5
Factor -72*a**2 - 327*a**3 + 179*a**2 + 18*a**4 + 145*a**2 - 30*a**4 + 0*a**4.
-3*a**2*(a + 28)*(4*a - 3)
Let z = 9591 - 172637/18. Let w(d) be the third derivative of -z*d**4 + 0 + 1/60*d**6 + 0*d + 7/180*d**5 + 8*d**2 - 5/18*d**3. Factor w(r).
(r + 1)**2*(6*r - 5)/3
Let d(u) be the third derivative of -u**5/12 - 200*u**4 - 192000*u**3 + 3767*u**2. Determine c, given that d(c) = 0.
-480
What is w in -2/3*w + 0 - 14/9*w**2 + 4/3*w**5 + 26/9*w**3 + 46/9*w**4 = 0?
-3, -1, -1/3, 0, 1/2
Factor -11 + 17329*i - 126*i**3 - 372*i**2 - 28 - i**4 - 17699*i - 84.
-(i + 1)**3*(i + 123)
Let u be (-10)/25 - (-664)/10. Factor -10*w**2 + 39*w - 7*w + 98 + 16 + 43*w + u - 5*w**3.
-5*(w - 4)*(w + 3)**2
Let q(o) be the third derivative of -7/