
Suppose 4*x + 12 = 0, 5*x + 10 = 4*g - 5*g. Suppose 4*i - 2*o = 2, 0*i = -g*i + 4*o - 5. Factor 6*q**3 - 2*q**3 - 3 + i.
4*q**3
Let r(k) be the second derivative of k**7/70 + 3*k**6/25 - 12*k**5/25 - 1036*k. Factor r(l).
3*l**3*(l - 2)*(l + 8)/5
Let b(j) = j**2 + 21*j + 41. Let g be b(-19). Suppose g*o = -0*o - 2*p + 12, 5*o - 5*p - 45 = 0. Factor -5*f + f + f - o*f**2 - 16 + 3*f**3 + 22.
3*(f - 2)*(f - 1)*(f + 1)
Let s = 92 + -89. Suppose -166*k - 2 + 48*k**2 + 20*k**4 + 30*k**4 + 34 + 38*k + 160*k**s = 0. Calculate k.
-2, 2/5
Suppose -12*i - 18*i + 90 = 0. Let n be (-6)/4*4/(-3). Solve 31*y**3 - 12*y**4 + 17*y**i - 16*y**3 - 8*y**5 - 8*y**n - 4*y**2 = 0.
-3, 0, 1/2, 1
Let g be (5 + -6)/(6/33)*18/(-8). Factor 27/2 - g*y + 15/4*y**2 - 3/8*y**3.
-3*(y - 4)*(y - 3)**2/8
Let i(c) be the first derivative of -225*c**4 + 2320*c**3/3 - 602*c**2 - 392*c - 733. Factor i(j).
-4*(5*j - 7)**2*(9*j + 2)
Let j(h) = -h**3 + 2*h**2 + 2*h + 1. Let m be j(-1). Let o = -26 + 29. Factor 6*x**o + 9*x**3 - m*x**2 - 6*x**2 - 4*x**2 - 3*x.
3*x*(x - 1)*(5*x + 1)
Let r(n) be the third derivative of -n**6/10 + 5*n**5/9 + n**4/3 - 622*n**2. Solve r(f) = 0 for f.
-2/9, 0, 3
Let w(p) = 6*p**2 - 724*p + 742. Let t(g) = -8*g**2 + 722*g - 744. Let c(d) = 4*t(d) + 5*w(d). Factor c(b).
-2*(b - 1)*(b + 367)
Let z(m) be the second derivative of -m**4/36 + 4*m**3/3 - 21*m**2/2 + 4887*m. Determine t, given that z(t) = 0.
3, 21
Let x = 235/34 - -191/238. Suppose -16/7*q**3 - x*q**2 - 8/7 - 38/7*q + 8/7*q**4 = 0. What is q?
-1, -1/2, 4
Let o(x) be the first derivative of 2*x**3/3 + 1704*x**2 + 3406*x + 5905. Factor o(f).
2*(f + 1)*(f + 1703)
Let d be ((-6 - -21) + -15)/(1 + 4/(-2)). Let v(h) be the first derivative of d*h + 34 - 2/3*h**2 - h**3 - 1/6*h**4. Factor v(u).
-u*(u + 4)*(2*u + 1)/3
Let u be (-531)/36 + (-1)/4. Let d be -1 + 1 + (u - -3)/(-4). Solve -3*w**2 - w**2 + 6*w - d*w**5 + 4 + 4*w**5 - 8*w**3 + w**5 = 0 for w.
-1, 1, 2
Let g(d) be the first derivative of -d**6/90 + d**5/3 - 3*d**4/2 + 41*d**3/3 + 81. Let f(a) be the third derivative of g(a). Let f(v) = 0. Calculate v.
1, 9
Let b be ((-1)/4 - 286/104) + 1659/316. Solve 0 + b*l - 1/4*l**2 = 0.
0, 9
Let y(a) = 124*a - 392. Let u be y(3). Let q be (u/16)/(330/(-176)). What is s in 4*s**3 + 8/3 + q*s**4 + 8*s + 26/3*s**2 = 0?
-2, -1
Factor -10208*l**4 + 1248*l - 594*l**2 - 13 + 75*l**3 + 1933 + 10205*l**4.
-3*(l - 10)*(l - 8)**2*(l + 1)
Let t be -1 - (-34)/18 - 0/(-3306). Suppose 0*r + 0 - 2/9*r**4 - t*r**2 - 8/9*r**3 = 0. Calculate r.
-2, 0
Let m = -2681 - -2693. Let q(a) be the third derivative of -2/33*a**3 - 1/660*a**6 + 1/165*a**5 + 0 + m*a**2 + 1/132*a**4 + 0*a. Factor q(r).
-2*(r - 2)*(r - 1)*(r + 1)/11
Let x = 62726/39 - 20900/13. Determine y so that 7/3*y**2 + x*y**3 + y + 0 = 0.
-3, -1/2, 0
Let c(t) = t**3 - 2*t**2 - 18*t - 7. Let w be c(6). Let q be (-434)/(-294) - (w/7 - 4). Factor -4/3*o + q*o**2 + 0 - 1/3*o**3.
-o*(o - 2)**2/3
Let n(a) be the second derivative of a**5/80 - 25*a**4/48 - a**3/6 + 25*a**2/2 + 218*a. Determine f, given that n(f) = 0.
-2, 2, 25
Suppose 418 = x - 3*q - 355, -4*q + 2306 = 3*x. Let d = 1541/2 - x. Suppose -d*f**4 + 0*f + 0*f**2 + 0*f**3 + 1/2*f**5 + 0 = 0. What is f?
0, 1
Let w(g) be the second derivative of -g**7/84 - 523*g**6/60 - 33797*g**5/20 + 102965*g**4/12 - 206981*g**3/12 + 69169*g**2/4 + 11*g - 5. Factor w(l).
-(l - 1)**3*(l + 263)**2/2
Let a(b) = -b**3 - 99*b**2 + 210*b - 4. Let d(l) = 5*l**3 + 494*l**2 - 1052*l + 22. Let t(j) = 11*a(j) + 2*d(j). Factor t(x).
-x*(x - 2)*(x + 103)
Let w(q) be the first derivative of -43 - 1/5*q**2 + 1/10*q**4 - 1/15*q**3 + 1/25*q**5 + 0*q. Suppose w(z) = 0. What is z?
-2, -1, 0, 1
Let h = 609/235 + -9/47. Let u be 750/(-875) + 33*28/735. Factor -1/5*p**4 - u*p**3 - 14/5*p + 1 + h*p**2.
-(p - 1)**3*(p + 5)/5
Let z = -72 + 72. Suppose 2*m = -z*m + 90. Factor 224*i**2 + 192*i**3 - 5*i**5 + 6*i**5 + 469*i**2 + 432*i - m*i**2 - 1296 + 23*i**4.
(i - 1)*(i + 6)**4
Let s(o) = 4*o**2 + o - 1. Let i be s(1). Let y be i/(-2) - 34*-1. Factor y*h**5 - 30*h**4 - 10*h**3 + 32*h**5 + 5*h**4 - 29*h**5.
5*h**3*(h - 1)*(7*h + 2)
Suppose 4*j + n + 25 - 1 = 0, -4*j - 24 = -2*n. Let f = 2 - j. Factor 3*s**3 - 2*s**4 + f*s**2 - s**5 + 4*s - 59 + 33 + 26.
-s*(s - 2)*(s + 1)**2*(s + 2)
Suppose -2342 - 2414 = 74*f - 49*f - 1214*f. Suppose -22/5*i**3 - 6/5*i**2 + 16/3*i - 4/3*i**f + 8/5 = 0. Calculate i.
-2, -3/10, 1
Let l(p) be the third derivative of 0 + 0*p + 77*p**2 + 2/3*p**3 + 1/30*p**5 + 1/4*p**4. Factor l(w).
2*(w + 1)*(w + 2)
Suppose -2*d - 3*d + 160 = 0. Suppose -8*q + d - 8 = 0. Factor -2*l - q*l + 6*l**2 - l - 9*l**2.
-3*l*(l + 2)
Let i be (-42)/4*1848/(-96). Let x = i + -202. Find y, given that -x*y**4 - 1/8*y**5 + 1/8*y**3 + 0 + 0*y + 1/8*y**2 = 0.
-1, 0, 1
Let u(w) be the second derivative of w**7/90 + w**6/15 - 2*w**5/15 - w**4/6 - 61*w. Let c(q) be the third derivative of u(q). Determine d so that c(d) = 0.
-2, 2/7
Let g(f) = f - 3. Let o be g(5). Suppose 4*b - 4 = 0, -152*r + 20 = -147*r + 5*b. Factor -3*y**3 + 21*y - y**2 + 6*y**r + 9 + 16*y**o.
3*(y + 1)**2*(y + 3)
Let n(o) = -920*o**3 + 4095*o**2 + 13505*o + 3100. Let k(q) = -45*q**3 - 1. Let f(c) = 20*k(c) - n(c). Factor f(p).
5*(p - 208)*(p + 3)*(4*p + 1)
Suppose -5/3*n**3 - 115/3*n + 15*n**2 + 25 = 0. Calculate n.
1, 3, 5
Let s(y) be the third derivative of y**5/330 + 95*y**4/22 + 7576*y**2. Let s(f) = 0. Calculate f.
-570, 0
Let m(g) be the first derivative of -8/15*g**5 + 206/9*g**3 + 22 - 31/3*g**2 - 10*g - 53/6*g**4. Determine s, given that m(s) = 0.
-15, -1/4, 1
Let y(a) = 18*a**3 + 41*a**2 + 180*a + 216. Let p(m) = 10*m**3 + 20*m**2 + 90*m + 108. Suppose -90 = -20*r + 50. Let l(j) = r*p(j) - 4*y(j). Solve l(c) = 0.
-6, -3
Factor 1702*q**2 + 220/3*q**3 + 111392/3 - 51920/3*q + 2/3*q**4.
2*(q - 4)**2*(q + 59)**2/3
Determine x, given that 1/7*x**3 + 883/7*x**2 - 883/7 - 1/7*x = 0.
-883, -1, 1
Let z = -337/14 - -908861/37758. Let h = 21542/45849 - z. Factor -6/17 - h*f - 2/17*f**2.
-2*(f + 1)*(f + 3)/17
Let g = -299 + 339. Let 0 + 15*i**2 + 0 - 12*i - 8*i**3 - 55*i**2 - g*i**3 - 4*i**5 - 24*i**4 = 0. Calculate i.
-3, -1, 0
Let y(j) = -2*j**3 + 3*j**2 + 14*j + 16. Let k be y(-2). Let f(a) be the first derivative of -22*a**2 + 16 + 34/3*a**3 - 3/2*a**4 + k*a. Factor f(b).
-2*(b - 4)*(b - 1)*(3*b - 2)
Suppose 972 + 378 = -9*l. Let o be ((-20)/l*-10)/(10/(-13)). Find t, given that 14/15*t**2 + o*t**4 + 0 - 8/15*t**5 - 2*t**3 - 2/15*t = 0.
0, 1/4, 1
Let o = -193 + 191. Let s(y) = -y**3 - y**2 - y. Let b(j) = 2*j**4 - 8*j**3 - 4*j**2 + 4*j. Let q(f) = o*b(f) + 4*s(f). Factor q(k).
-4*k*(k - 3)*(k - 1)*(k + 1)
Let m = -86364 - -431822/5. Find x such that m*x**4 - 21/5*x**3 + 42/5*x**2 - 16/5*x + 0 = 0.
0, 1/2, 2, 8
Suppose 4*w + 202 = -5*u, 30 - 180 = 3*w + 3*u. Let j = 51 + w. What is a in 8 - 13*a**4 - 2*a**4 - 14*a**2 - 8*a**4 - 2*a**j + 2*a**5 + 29*a**4 = 0?
-2, -1, 1
Suppose 0 = 2*w + 33 - 31. Let s(q) = -2*q**3 + 18*q**2 + 8*q - 6. Let a(p) = 2*p**2 - 1. Let u(h) = w*s(h) + 6*a(h). Factor u(j).
2*j*(j - 4)*(j + 1)
Let i be -5 + 1 - 3136/(-441) - (-6)/(-54). Find s such that -24/7*s**i - 3/7*s**2 + 0*s + 0 = 0.
-1/8, 0
Let g(u) be the third derivative of 3*u**8/28 - 16*u**7/15 - 17*u**6/10 + 14*u**5/15 - 781*u**2. Find x, given that g(x) = 0.
-1, 0, 2/9, 7
Let i(s) be the third derivative of s**5/15 + 23*s**4/2 + 268*s**3/3 - 849*s**2 - s. Factor i(v).
4*(v + 2)*(v + 67)
Let s(z) be the third derivative of -z**7/70 + 19*z**6/8 + 303*z**5/20 - 887*z**4/8 + 245*z**3 + 4709*z**2 + 2*z. Factor s(m).
-3*(m - 98)*(m - 1)**2*(m + 5)
Suppose 2*q = 2*s + 24, 5*s + 13*s + 174 = -3*q. Factor -2*m + 1/2*m**q - 6.
(m - 6)*(m + 2)/2
Let n(a) = 5*a**4 - 2*a**3 + 2*a**2 - 1. Let c(i) = -92*i**4 - 4*i**3 - 36*i**2 + 18. Let z(b) = 2*c(b) + 36*n(b). Suppose z(p) = 0. What is p?
-20, 0
Let o(r) be the second derivative of r**7/21 + r**6/30 - 9*r**5/10 - 3*r**4/4 + 256*r - 8. Factor o(c).
c**2*(c - 3)*(c + 3)*(2*c + 1)
Suppose -5*l + 130 = -2*w + 3*w, -4*w - 74 = -2*l. Let a = 29 - l. Factor -17*u**2 + 8*u + a*u**3 + 13*u**2 - 6*u**3.
-4*u*(u - 1)*(u + 2)
Let v(x) = 25*x**2 + x + 4. Let m be v(0). Let y(t) = -t + 3. Let i be y(3). Factor 0 + 8/9*s**2 - 2/9*s**m + 0*s + i*s**3.
-2*s**2*(s - 2)*(s + 2)/9
Let 