
Let i(t) be the second derivative of -8*t**7/105 + 7*t**6/30 - t**5/5 + 61*t**2/2 - 80*t. Let n(l) be the first derivative of i(l). Factor n(x).
-4*x**2*(x - 1)*(4*x - 3)
Let q(y) be the first derivative of -3*y**4/4 + 9*y**3 + 54*y**2 - 1592. Suppose q(z) = 0. Calculate z.
-3, 0, 12
Let a(q) be the second derivative of q**6/60 + 41*q**5/120 + 115*q**4/72 + 47*q**3/36 - 5*q**2/2 - 964*q. Solve a(c) = 0 for c.
-10, -3, -1, 1/3
Let b = 94302 + -94302. Solve -n**2 + 0 + b*n - 1/3*n**3 = 0 for n.
-3, 0
Factor 103005*r**2 - 109 - 155*r - 103010*r**2 - 181.
-5*(r + 2)*(r + 29)
Suppose 8*h = 39 + 1. Suppose c - 5*c + 2*a = -32, 3*a = h*c - 38. Solve 35*l**2 + 2 + 8 + 1 - c*l**3 - 1 - 35*l = 0.
1/2, 1, 2
Let k(x) = 22*x**2 - x + 3. Let u(t) = -436*t**2 - 576*t + 2260. Let i(w) = 20*k(w) + u(w). Factor i(m).
4*(m - 145)*(m - 4)
Let y(p) be the third derivative of p**6/144 - 299*p**5/180 - 845*p**4/144 - 121*p**3/18 - 1418*p**2. Factor y(n).
(n - 121)*(n + 1)*(5*n + 2)/6
Let a(n) be the first derivative of -4*n**3/3 + 1376*n**2 - 473344*n - 2306. Find d, given that a(d) = 0.
344
Let j(d) be the first derivative of -d**4/90 - 14*d**3/45 + d**2 - d + 30. Let x(m) be the first derivative of j(m). Factor x(z).
-2*(z - 1)*(z + 15)/15
Let k be 36/(-63) - -25*3/21. Find y, given that -2*y**4 - 12*y**k + 152*y**2 - 152*y**2 = 0.
-6, 0
Let q(b) be the first derivative of b**3/15 - 3*b**2/10 - 4*b/5 - 479. Factor q(k).
(k - 4)*(k + 1)/5
Let d(s) be the first derivative of s**6/340 - 11*s**5/510 + s**4/17 - 4*s**3/51 + 35*s**2/2 + 16. Let l(y) be the second derivative of d(y). Factor l(k).
2*(k - 2)*(k - 1)*(3*k - 2)/17
Let l(x) be the third derivative of x**4/6 - 3*x**3 + 16*x**2. Let u be l(5). Solve -10*n**2 + 14*n**2 - n - u*n**3 - n = 0 for n.
0, 1
Let a(j) be the second derivative of 3*j**4/20 + 52*j**3/5 - 21*j**2/2 + 2*j - 9. Factor a(u).
3*(u + 35)*(3*u - 1)/5
Let v = -735 - -732. Let i be 42/(-28)*1/v. Let 0 + 0*c**2 - i*c**4 - 1/4*c**5 + 0*c + 0*c**3 = 0. Calculate c.
-2, 0
Let i(t) be the second derivative of -3*t**5/10 + 11*t**4/12 - 5*t**3/6 + 725*t. Factor i(j).
-j*(j - 1)*(6*j - 5)
Let h(x) = -x**2 + 232*x - 13229. Let z be h(101). Factor -1/4*n**z + 3/2*n + 0.
-n*(n - 6)/4
Let g be ((-3392)/(-2968))/((864/784)/(3/14)). Find a, given that 8/9*a**2 + 8 + 82/9*a - g*a**3 = 0.
-4, -1, 9
Let y be -104*(-15)/600 - (8/(-1 + -1))/10. Factor -972/5 - 3/5*l**y + 21*l**2 - 864/5*l.
-3*(l - 18)**2*(l + 1)/5
Let p(r) be the first derivative of r**4 - 64*r**3/3 + 26*r**2 + 120*r + 1722. Determine s so that p(s) = 0.
-1, 2, 15
Solve 1/6*d**2 - 88 - 41/3*d = 0 for d.
-6, 88
Let h(d) = -151*d**2 - 12*d - 14. Let b be h(-2). Let q = b + 601. Factor 49/2 + q*n + 1/2*n**2.
(n + 7)**2/2
Let n(l) = 2*l**4 + l. Let k(v) = -21*v**4 - 2*v**3 - 9*v - 1. Let m(o) = -4*k(o) - 44*n(o). Factor m(a).
-4*(a - 1)**3*(a + 1)
Let k(g) be the third derivative of -2*g**7/105 - 2*g**6/5 - 17*g**5/15 + 5*g**4 - g**2 + 378. Factor k(d).
-4*d*(d - 1)*(d + 3)*(d + 10)
Let n(x) be the third derivative of x**6/450 - 7*x**5/150 + x**4/5 + 37*x**3/6 + 12*x**2 + 4. Let f(d) be the first derivative of n(d). Factor f(o).
4*(o - 6)*(o - 1)/5
Let p(i) be the first derivative of -i**6/10 + 21*i**4/4 - 6*i**3 - 48*i**2 - 288*i/5 + 806. Suppose p(v) = 0. What is v?
-6, -1, 4
Let i(c) be the first derivative of 2*c**6/27 - 2*c**5/45 - 17*c**4/18 + 38*c**3/27 + 5*c**2/3 - 4*c - 483. Suppose i(q) = 0. Calculate q.
-3, -1, 1, 3/2, 2
Let h(q) = -q + 17. Let n be h(13). Let t be n*((-1)/5)/((-16)/40). Determine x so that -8*x**t + 0 + 0 + 24*x**2 + 4*x**3 = 0.
-4, 0
Let h(o) = 23*o**2 + 505*o + 2282. Let b(n) = -215*n**2 - 4715*n - 21300. Let t(q) = -8*b(q) - 75*h(q). Factor t(l).
-5*(l + 6)*(l + 25)
Let w be 3/(-21)*(50/150)/(6/(-54)). Factor -12/7*j**3 - 6/7*j + w*j**4 + 0 + 15/7*j**2.
3*j*(j - 2)*(j - 1)**2/7
Let r(s) be the second derivative of 0*s**3 - 1/330*s**5 - 13*s + 1/660*s**6 - s**2 + 0 - 1/66*s**4. Let f(p) be the first derivative of r(p). Factor f(q).
2*q*(q - 2)*(q + 1)/11
Let j(i) be the first derivative of 2*i**7/21 + 2*i**6/5 + 2*i**5/5 + 108*i - 10. Let y(k) be the first derivative of j(k). Suppose y(a) = 0. What is a?
-2, -1, 0
Let k(q) = 3*q**4 - 90*q**3 + 9*q**2 + 303*q + 30. Let p(y) = y**4 - 23*y**3 + 2*y**2 + 76*y + 8. Let s(h) = 4*k(h) - 15*p(h). Factor s(d).
-3*d*(d - 2)*(d + 3)*(d + 4)
Let h(c) = c**2 + 15*c + 188. Let f(z) = 5*z**2 + 61*z + 939. Let g(d) = -4*f(d) + 22*h(d). Suppose g(t) = 0. Calculate t.
-38, -5
Suppose -5*z + 4*z = -2*c + 4, -5*c = 3*z - 10. Suppose -a - c*d = -1, 2*a + 2*d - 29 = -3*a. Solve a*q**2 - 7*q**2 - 4*q - 8 + 4*q**2 = 0.
-1, 2
Factor 2/9*t**2 - 226/9*t + 148/3.
2*(t - 111)*(t - 2)/9
Let s(c) = -3*c**2 - 43*c - 10. Let a be s(-14). Factor h**5 + 16*h + 15*h**3 - 5*h**3 - 32*h**2 - 8*h**a + 14*h**3.
h*(h - 2)**4
Let g(o) be the second derivative of -45/4*o**4 - 15*o**3 + 0*o**2 - 1/6*o**6 - 5/2*o**5 - o + 0. Let g(w) = 0. What is w?
-6, -3, -1, 0
Let -2304*r**2 + 291 + 2300*r**2 + 963*r - 235*r + 441 = 0. Calculate r.
-1, 183
Let j(r) be the first derivative of 2*r + 1/16*r**4 + 49 - 5/12*r**3 + 1/4*r**2. Let j(v) = 0. What is v?
-1, 2, 4
Suppose -5*p - 4*h + 5 = -4, -p = -4*h - 21. Suppose -2*q - 3*i + p = 0, -4*q + i = -3*i. Factor q + 4*b**2 - 2*b - 2*b + 9*b.
(b + 1)*(4*b + 1)
Let p(y) = -3*y**2 - 75*y - 63. Let g(t) = 12*t + 21*t + t**2 + 16 - 14*t. Suppose -53 = 6*l + 1. Let a(c) = l*g(c) - 2*p(c). Factor a(m).
-3*(m + 1)*(m + 6)
Let k(d) = 7 + d + 0 - 4. Let h be k(-1). Let g(u) = 5*u**2 + 8*u + 7. Let x(y) = -110*y**2 - 175*y - 155. Let n(c) = h*x(c) + 45*g(c). What is w in n(w) = 0?
-1
Let c(a) be the first derivative of a**7/21 - a**6/5 - a**5/10 + a**4/2 - 124*a - 199. Let n(d) be the first derivative of c(d). Find y such that n(y) = 0.
-1, 0, 1, 3
Let u(t) = -19*t**4 - 24*t**3 - 95*t**2 - 6*t + 6. Let f(l) = -16*l**4 - 24*l**3 - 95*l**2 - 5*l + 5. Let w(r) = 6*f(r) - 5*u(r). Factor w(n).
-n**2*(n + 5)*(n + 19)
Let j(t) = -t**2 + 23*t - 11. Let n be j(12). Factor -10*h**4 - 38*h**3 - 57*h + 59*h**5 - n*h**5 - 68*h**2 - 18 + 61*h**5.
-(h + 1)**2*(h + 2)*(h + 3)**2
Let l = -123105 + 123105. Let -32/5*u**2 + 0*u + 2/5*u**4 + 12/5*u**3 + l = 0. What is u?
-8, 0, 2
Suppose 2*h + 4*k = 88, 0 = -2*k - 3 + 7. Factor x**3 - 24*x - 4*x**4 - 5*x**3 - 96 + h*x + 40*x**2.
-4*(x - 2)**2*(x + 2)*(x + 3)
Factor 5*z**3 - 6*z**4 + z**4 - 476*z - 550*z**2 - 67*z**3 - 33*z**3 - 524*z.
-5*z*(z + 4)*(z + 5)*(z + 10)
Suppose -3*s = -5*k - 16, 3*s - 2*k = 34 - 15. Suppose 0 = -s*g - 579 + 635. Factor 4*x - g*x**2 - 2/3 - 2*x**4 + 20/3*x**3.
-2*(x - 1)**3*(3*x - 1)/3
Let o(h) be the third derivative of 0 - 8/5*h**3 + h + h**4 - 1/4*h**5 - 3*h**2. Factor o(m).
-3*(5*m - 4)**2/5
Let c(p) be the third derivative of -1/20*p**5 + 2*p + 1/40*p**6 + 0*p**3 - 3/2*p**4 + 0 - 2*p**2. Solve c(r) = 0.
-3, 0, 4
Let p(v) = v**2 + 7. Let z be p(-5). Let k = z - 24. Factor 2*s**2 + 10 - 45*s - k*s**3 + 13*s**2 + 18*s**3 + 10*s**3.
5*(s - 1)*(s + 2)*(4*s - 1)
Suppose -19*n + 7410 = -0*n. Suppose 0 = n*a - 376*a. Factor t**2 + a - 1/2*t**3 + 0*t.
-t**2*(t - 2)/2
Suppose 1640*q - 1604*q = 0. Let h(z) be the third derivative of 9*z**2 - 1/1008*z**8 + 0*z**3 + 0*z**7 + 0 + 0*z**5 + 0*z + q*z**4 + 1/360*z**6. Factor h(w).
-w**3*(w - 1)*(w + 1)/3
Let h(w) = w**2 - w - 1. Let k(i) be the third derivative of i**5/20 - 11*i**4/24 + i**3 - i**2 - 20. Let g(o) = 2*h(o) - k(o). Factor g(v).
-(v - 8)*(v - 1)
Let x(f) be the first derivative of -68 - 1/6*f + 1/4*f**2 + 1/24*f**4 - 1/6*f**3. Factor x(j).
(j - 1)**3/6
Let l(b) be the first derivative of b**7/14 + b**6/6 - b**5/3 - 67*b**2/2 + 30. Let f(c) be the second derivative of l(c). Factor f(j).
5*j**2*(j + 2)*(3*j - 2)
Solve 1053*a - 13*a**2 - 4*a**3 - 10*a**3 - 9*a**2 + 16 - 512*a + 2*a**5 + 6*a**4 - 529*a = 0 for a.
-4, -1, 1, 2
Let -121*h - 703 - 333*h + 54*h + 703 + 4*h**2 = 0. Calculate h.
0, 100
Let i(k) = 9*k**3 + 960*k**2 + 46969*k + 90246. Let z(h) = 17*h**3 + 1920*h**2 + 93952*h + 180493. Let q(y) = -7*i(y) + 4*z(y). Factor q(p).
5*(p + 2)*(p + 95)**2
Let s(b) be the first derivative of 0*b + 0*b**2 - 8/27*b**3 - 48 + 0*b**4 + 2/45*b**5. Factor s(l).
2*l**2*(l - 2)*(l + 2)/9
Suppose 5*u + 62 = 6*z, -31*z + 30*z = 2*u - 16. 