t s(m) = m**3 - 281*m**2 + 3481*m + 804. Let g be s(268). Factor 2/21*w**5 + 6/7*w**3 + g*w - 8/21*w**2 - 4/7*w**4 + 0.
2*w**2*(w - 4)*(w - 1)**2/21
Suppose -830*k + 1873 - 213 = 0. Let m(l) be the first derivative of 5/12*l**4 + 37 + 10/9*l**3 - 5/6*l**k - 10/3*l. Factor m(j).
5*(j - 1)*(j + 1)*(j + 2)/3
Let u(q) be the third derivative of 1/180*q**6 - 1/36*q**5 + 0*q + 0 + 127*q**2 + 0*q**3 + 1/630*q**7 - 1/12*q**4. Factor u(o).
o*(o - 2)*(o + 1)*(o + 3)/3
Let x(f) be the third derivative of 3/4*f**3 + 0*f + 1/240*f**5 + 0 - 19/96*f**4 - 70*f**2. Suppose x(i) = 0. What is i?
1, 18
Let x(b) be the second derivative of b**4/30 + 407*b**3/15 - 2*b - 210. Factor x(s).
2*s*(s + 407)/5
Suppose 111*o = 23 + 52 + 147. Find p, given that o*p**2 + 8/5*p**3 + 4/5*p + 2/5*p**4 + 0 = 0.
-2, -1, 0
Let u(m) be the first derivative of m**3/15 - 47*m**2 - 517. Find v, given that u(v) = 0.
0, 470
Let x(o) = -o**2 + 13*o - 26. Let b(a) = -3*a**2 + 26*a - 52. Let v(p) = -2*b(p) + 5*x(p). Let m be v(-15). Factor 9*h**2 + 6*h**3 + 5*h + h - 17*h**3 - m*h**3.
-3*h*(h - 1)*(5*h + 2)
Let n be (-2 - 167992/(-5)) + 50 + -46. Let f = n + -33442. Factor -484/5*r**4 - 148/5*r**2 - 16/5 - 144/5*r + f*r**3.
-4*(r - 1)**2*(11*r + 2)**2/5
Let f be (50/(-125))/(28/(-120)). Solve -5*u**3 + 109/7*u**2 - 8/7*u - f = 0.
-2/7, 2/5, 3
Let m = 16183 - 323659/20. Let i(s) be the second derivative of 2 + 1/16*s**4 + 16*s - m*s**5 + 1/24*s**3 + 0*s**2. Factor i(z).
-z*(z - 1)*(4*z + 1)/4
Suppose -29*w = -69*w + 200. Let l(t) be the third derivative of -1/60*t**w + 0*t**3 + 0*t - 7/24*t**4 + 3*t**2 + 0. Factor l(b).
-b*(b + 7)
Suppose 3*p + 5*d = -0*d + 4, 0 = p - 2*d - 5. Let v(a) = 7*a**2 + 6*a - 1. Let r(n) = -4*n**2 - 3*n + 1. Let t(i) = p*v(i) + 5*r(i). Solve t(y) = 0 for y.
-2, -1
Let b be 0 - 119/12 - (16 + -26). Let w(a) be the first derivative of 5/32*a**4 - 5/16*a**2 - b*a**3 + 1/4*a + 9. Factor w(g).
(g - 1)*(g + 1)*(5*g - 2)/8
Let g(r) be the first derivative of r**7/840 - r**6/96 + 7*r**5/240 - r**4/32 + 21*r**2 + 71. Let h(t) be the second derivative of g(t). Factor h(f).
f*(f - 3)*(f - 1)**2/4
Suppose 15312 = -5*f + 15452. Let q be (-2334)/(-20) + (-42)/f. Find d, given that -512/15 - 54/5*d**4 + 288/5*d**3 - q*d**2 + 512/5*d = 0.
4/3
Suppose -1152/5 + 12/5*n**3 - 3344/5*n + 68*n**2 = 0. Calculate n.
-36, -1/3, 8
Factor 0 + 19041/2*s**3 + 2450*s - 9730*s**2 + 2*s**5 + 278*s**4.
s*(s + 70)**2*(2*s - 1)**2/2
Let a(b) = 2*b**2 - 3. Let s be a(-4). Suppose 0 = -5*h + 5*p + 45, h = 3*p + 2*p + s. Let 45*w**2 - 77*w**h - 9*w**3 - 3*w + 62*w**4 - 9 - 9 = 0. What is w?
-2, -3/5, 1
Let j(q) be the third derivative of -q**5/510 + 91*q**4/204 + 686*q**3/51 + 103*q**2 + 21*q + 1. Factor j(a).
-2*(a - 98)*(a + 7)/17
Let s(u) be the third derivative of u**7/420 - 11*u**6/240 - u**5/3 - 7*u**4/12 + 1423*u**2. Determine y so that s(y) = 0.
-2, -1, 0, 14
Suppose 33*m - 83*m = 0. Suppose -4/7*g - 5/7*g**3 + 8/7*g**2 + m + 1/7*g**4 = 0. What is g?
0, 1, 2
Let s(b) = -245*b**2 - 276*b - 3. Let z be s(-1). Find g, given that -1408/5*g + z*g**2 + 3072/5 - 4/5*g**3 = 0.
3, 16
Let m(h) = -72*h**2 - 96*h - 315. Let j(f) = -95*f**2 - 97*f - 312. Let g(t) = -3*j(t) + 4*m(t). What is i in g(i) = 0?
-27, -4
Suppose 2/9*w**5 - 2*w**4 - 8*w + 0 - 2/3*w**2 + 46/9*w**3 = 0. Calculate w.
-1, 0, 3, 4
Let q(n) be the second derivative of n**5/15 + n**4/9 - 32*n**3/9 + 40*n**2/3 + 1494*n. Factor q(x).
4*(x - 2)**2*(x + 5)/3
Let i(z) be the second derivative of z**10/15120 - z**9/1890 - 29*z**4/12 + 93*z. Let j(m) be the third derivative of i(m). Find k such that j(k) = 0.
0, 4
Factor 76*x**2 - 154*x**3 - 15*x**4 + 31*x**2 + 448*x**3 - 199*x**3 + 3*x**2.
-5*x**2*(x + 1)*(3*x - 22)
Let k = 6 - 0. Suppose -11*j + 13*j = k. Solve 10*g**2 - 3*g**j - g**3 - 29*g + 5*g**2 + 33*g = 0.
-1/4, 0, 4
Let a(x) be the second derivative of 0*x**3 - 2 - 30*x - 3/100*x**5 + 1/10*x**4 + 0*x**2. Factor a(b).
-3*b**2*(b - 2)/5
Let p(u) be the second derivative of 0 + 101*u - 6*u**2 + 32/3*u**3 - 26/15*u**6 + 6*u**5 - 32/3*u**4 + 4/21*u**7. Factor p(s).
4*(s - 3)*(s - 1)**3*(2*s - 1)
Let a be (13*9/117)/((-2)/(-6)). Factor 214375/4 - 5/4*d**a + 525/4*d**2 - 18375/4*d.
-5*(d - 35)**3/4
Let z(t) be the second derivative of -t**6/30 - 13*t**5/5 + 37*t**4/4 + 27*t**3 - 37*t - 1. Solve z(x) = 0 for x.
-54, -1, 0, 3
Suppose 0 = 2*a + 5*g + 13, -10 = -g - 9. Let q be a + (-408)/(-80) + 4. Factor 2/5 + q*w**3 - 1/10*w**2 - 2/5*w.
(w - 2)*(w - 1)*(w + 2)/10
Let f(p) be the third derivative of 286*p**2 - 5/18*p**4 + 0*p - 1/5*p**5 + 2/315*p**7 + 0*p**3 - 1/30*p**6 + 0. Factor f(u).
4*u*(u - 5)*(u + 1)**2/3
Let y be (-90)/126 - (-10)/14. Let b(j) be the third derivative of 0 + 8*j**2 - 1/15*j**3 + y*j + 1/40*j**4 - 1/300*j**5. Let b(l) = 0. Calculate l.
1, 2
Let a = -1390 + 1334. Let q be -3 - 150/a - 28/(-49). Factor x - q*x**2 - 1.
-(x - 2)**2/4
Let i = 29 + -35. Let c(j) = -j**3 - 5*j**2 + 5*j - 4. Let n be c(i). Find y, given that 12*y**5 + y**4 - n*y**4 + y**2 - 8*y**5 - y**3 - 3*y**5 = 0.
-1, 0, 1
Find s such that -92/17*s**3 + 144/17*s**2 + 0 + 2/17*s**5 + 0*s + 6/17*s**4 = 0.
-9, 0, 2, 4
Let v = 1 - -1. Suppose 3368*m = 3292*m. Suppose -1/3*u**v + m - 2/3*u = 0. Calculate u.
-2, 0
Let b(w) = w**2 + 2*w - 1. Let u(m) = 6*m**2 + 816*m - 160808. Let x(r) = -7*b(r) + u(r). Solve x(f) = 0.
401
Let q = 145323/2 - 72661. Factor -q*v**3 - 3*v - 7/2*v**2 + 0.
-v*(v + 1)*(v + 6)/2
Let a(f) be the third derivative of f**5/20 - 635*f**4/24 + 211*f**3/3 - 769*f**2. Factor a(c).
(c - 211)*(3*c - 2)
Let l(r) = -5*r**3 + 6*r**2 + 6*r**2 - 11 - 7*r + 9 + 29*r. Let i(u) = 2*u**3 - 6*u**2 - 11*u. Let p(o) = 7*i(o) + 3*l(o). Suppose p(c) = 0. What is c?
-3, -2, -1
Suppose 9*k - 170 = 127. Factor -7*r + k*r + 4*r**2 - 18 + 2*r - 14.
4*(r - 1)*(r + 8)
Let n = 1453 + -1464. Let w be 156/(-858) + -1 + (-46)/n. Factor -15*p**2 - 15/2*p**4 - 3/2*p**5 - 3/2 - 15/2*p - 15*p**w.
-3*(p + 1)**5/2
Let r(p) be the first derivative of -p**4/12 - 346*p**3/3 + 1039*p**2/6 + 11272. Solve r(s) = 0 for s.
-1039, 0, 1
Let t(o) be the first derivative of -2*o**2 + 1/3*o**3 - 1/48*o**4 - 4 - 11*o. Let g(w) be the first derivative of t(w). Find a such that g(a) = 0.
4
Let t(s) be the second derivative of -s**6/15 + 3*s**5/10 + 18*s**4 - 220*s**3/3 - 51*s - 1. Factor t(p).
-2*p*(p - 11)*(p - 2)*(p + 10)
Let r(g) be the first derivative of g**4/10 + 104*g**3/15 - 431*g**2/5 - 2124*g/5 - 5277. Factor r(z).
2*(z - 9)*(z + 2)*(z + 59)/5
Let u be (2 - -7 - 5) + -1 + 4. Let m(n) = -n**2 + 5*n + 16. Let z be m(u). Factor -g - 15 - 7*g + 15 + 4*g**z.
4*g*(g - 2)
Let v(h) be the third derivative of -3/40*h**6 - 1/210*h**7 + 1/336*h**8 - 11/60*h**5 + 10 - 1/6*h**4 + 4*h**2 + 0*h**3 + 0*h. Let v(n) = 0. Calculate n.
-1, 0, 4
Let g = 45 + -43. Suppose -g = d, -3*d = -5*h + 21 - 5. Let 17*p + 2 - 23*p + 6*p**3 - 6 + 2*p**2 + h*p**4 = 0. Calculate p.
-2, -1, 1
Suppose 0 = a + 2*r - 43, r + 22 = 26. Suppose 1 = -p, a*z + p - 19 = 30*z. Determine v so that -3*v**3 + 9/2*v**z + 0*v**2 - 3/2*v**5 + 0 + 0*v = 0.
0, 1, 2
Let p(v) = 94*v - 46. Let t be p(-3). Let q = 330 + t. Let -7/5*d - 4/5*d**q + 2/5 = 0. Calculate d.
-2, 1/4
Let c(y) be the third derivative of y**6/585 + 23*y**5/780 - y**4/26 - 19*y**3/3 - y**2 + 4*y. Let z(l) be the first derivative of c(l). Factor z(r).
2*(r + 6)*(4*r - 1)/13
Suppose 0*z = -3*z + 5*t - 18, 0 = -2*z - t + 1. Let m be (3/(-6))/(z/252). Solve 6*q - 129*q**2 + m*q**2 + 18 - 3*q = 0.
-2, 3
Let n(c) be the first derivative of -5*c**2/2 - 35*c - 78. Let m be n(-7). Suppose -4/9*z**2 + m + 0*z = 0. Calculate z.
0
Find m, given that 83*m**3 - 39*m**3 - 41*m**3 - 16 + 264*m - 7*m**2 + 58*m**2 + 448 = 0.
-9, -4
Factor 436*t**2 + 890*t - 880*t**2 + 449*t**2.
5*t*(t + 178)
Let p = -8142/131 - -47522/655. Factor p*r + 2/5*r**2 + 10.
2*(r + 1)*(r + 25)/5
Factor -3/2*m**2 - 873 + 879/2*m.
-3*(m - 291)*(m - 2)/2
Suppose 3/2*f**5 - 336*f - 921*f**2 - 39*f**4 + 669/2*f**3 + 960 = 0. Calculate f.
-1, 1, 8, 10
Suppose -1449 = 1547*v - 1550*v. Let f = 2418/5 - v. Determine n, given that f*n**4 - 9/5*n + 3/5*n**2 + 9/5*n**3 - 6/5 = 0.
-2, -1, 1
Factor -204*k**2 - 12980*k + 302*k**2 + 18407488 + 2652562 - 96*k**2.
2*(k - 3245)**2
Suppose 4*r - 19*r + 750 = 0. Factor 47*p**3 +