 s**7/1680 + s**6/1440 + 4*s**3 + 6. Let k(f) be the third derivative of h(f). Suppose k(m) = 0. What is m?
-1, 0
Let b(i) be the second derivative of 21*i**5/20 + 23*i**4/4 - 60*i**3 - 54*i**2 + 191*i. Factor b(w).
3*(w - 3)*(w + 6)*(7*w + 2)
Suppose 0 = 31*m - 94*m. Factor 0*y**2 - 16/7*y + 12/7*y**3 + 4/7*y**4 + m.
4*y*(y - 1)*(y + 2)**2/7
Let g(x) = 2*x**2 + 12*x + 16. Let s be g(-2). Let c(i) be the first derivative of 3*i**4 + 21/2*i**6 - 3 + 0*i**3 + 0*i - 12*i**5 + s*i**2. Factor c(h).
3*h**3*(3*h - 2)*(7*h - 2)
Let f = 819/1642 + 1/821. Factor 1/4*d**4 + 0*d + 0*d**3 - f*d**2 + 1/4.
(d - 1)**2*(d + 1)**2/4
Let w(z) be the second derivative of z**6/50 - 18*z**5/25 + 21*z**4/2 - 392*z**3/5 + 3087*z**2/10 - 3*z + 32. Find u, given that w(u) = 0.
3, 7
Let a = 4486/9 - 498. Solve -14/9*p - 2/9*p**4 - 2*p**2 - 10/9*p**3 - a = 0 for p.
-2, -1
Let n = 7319 - 7319. Suppose 0 + 6/7*i**3 - 2/7*i**5 - 4/7*i**2 + n*i**4 + 0*i = 0. What is i?
-2, 0, 1
Let z(y) be the third derivative of y**8/1680 + y**7/210 + y**6/60 + y**5/30 - y**4/2 - y**2. Let h(g) be the second derivative of z(g). Factor h(s).
4*(s + 1)**3
Let o(r) be the second derivative of r**6/24 + 5*r**5/12 + 5*r**4/3 + 10*r**3/3 + 8*r**2 - 27*r. Let y(a) be the first derivative of o(a). Factor y(s).
5*(s + 1)*(s + 2)**2
Let n be (-1)/(4/(-44)*1). Let l be (-8)/16 - n/(-10). Factor -1/5*k**2 + 4/5*k - l.
-(k - 3)*(k - 1)/5
Find i, given that -45/2 + 7*i - 1/2*i**2 = 0.
5, 9
Let x(k) be the third derivative of -k**5/330 + 10*k**4/33 - 400*k**3/33 + k**2 + 41*k. Suppose x(f) = 0. What is f?
20
Let f(m) = -m + 5. Let r(y) = y - 4. Let t(i) = -4*f(i) - 5*r(i). Let s be t(0). Suppose -1/2*w**2 - 1/6*w**4 - 1/6*w + s - 1/2*w**3 = 0. What is w?
-1, 0
Let r(d) be the second derivative of d**8/17920 - d**7/2240 + d**6/640 - d**5/320 - 5*d**4/6 - 3*d. Let x(u) be the third derivative of r(u). Factor x(l).
3*(l - 1)**3/8
Let u be 18/30 + 903/70. What is r in -21/4*r**3 - 15*r + u*r**2 + 3/4*r**4 + 6 = 0?
1, 2
Let n be 3/(6/46) + -3. Let x be (n/40)/((-2)/(-2)). Suppose x*f - 1 + 1/2*f**2 = 0. Calculate f.
-2, 1
Let k = -1562 + 7816/5. Factor -9/5*d**3 + 0 - k*d**4 - 3/5*d**2 + 0*d.
-3*d**2*(d + 1)*(2*d + 1)/5
Let c = -640 - -649. Let f(j) be the second derivative of 4/105*j**6 - c*j + 1/7*j**2 - 1/14*j**4 + 0 - 2/35*j**5 + 2/21*j**3. Solve f(v) = 0.
-1/2, 1
Let f(o) be the third derivative of -13*o**6/40 + 19*o**5/10 - 23*o**4/8 - o**3 - 178*o**2 - o. Let f(v) = 0. Calculate v.
-1/13, 1, 2
Let q(j) be the third derivative of j**6/60 + j**5/15 - 8*j**4/3 - 32*j**3 + j**2 - 18*j. Find s, given that q(s) = 0.
-4, 6
Suppose -18*o = -o - 102. Let p(d) be the first derivative of -1/3*d**3 - 1/6*d**6 - 3/4*d**4 + o + 0*d**2 + 0*d - 3/5*d**5. Determine t, given that p(t) = 0.
-1, 0
Let d = 90 - 88. Find b, given that -22*b**2 + 4*b + 45*b**2 - 27*b**d = 0.
0, 1
Let l = 118/45 - 12/5. Let z = l + 8/45. Factor -1/5*x**4 + 0*x + 0*x**3 + z*x**2 - 1/5.
-(x - 1)**2*(x + 1)**2/5
Let j be -2*3/(-6)*6. Let z be ((-6)/9)/((-2)/j). What is o in -4/7 + 2/7*o + 2/7*o**z = 0?
-2, 1
Let x = 7249 - 21746/3. Determine f, given that -f + x*f**2 - 4/3 = 0.
-1, 4
Let g(o) = o + 15. Let i be g(-3). Determine l, given that 9*l - l**2 - i + 15*l + 3*l**4 - 6*l**3 - 8*l**2 = 0.
-2, 1, 2
Let d(o) be the second derivative of -o**4/18 - 29*o**3/9 - 26*o**2 + 6*o + 13. Factor d(m).
-2*(m + 3)*(m + 26)/3
Let p(x) be the third derivative of 0 - 32*x**2 + 1/33*x**4 + 1/660*x**5 + 0*x + 0*x**3. Suppose p(i) = 0. Calculate i.
-8, 0
Let u(o) = 3*o**2 + 33*o + 3. Let t(b) = -3*b**2 - 33*b - 4. Let m(f) = 3*t(f) + 4*u(f). Factor m(v).
3*v*(v + 11)
Let d be (-88)/(-90) + (-4)/(-18). Let j be (-32)/(-30) - (-326)/(-489). Let -6/5*i**2 + 2/5*i + d*i**3 + 0 - j*i**4 = 0. Calculate i.
0, 1
Let f(s) be the first derivative of s**3 - 24*s**2 + 84*s - 180. What is v in f(v) = 0?
2, 14
Suppose -y - 1 - 3 = -p, 2*y = -p - 5. Suppose -2*c + 4*i + 2 = 6, -i = 4*c - p. Solve 0 + 0*o + 4/9*o**3 + 2/9*o**4 + c*o**2 = 0 for o.
-2, 0
Let l be (-1 - 313/(-315))/((-56)/21). Let r(d) be the third derivative of 0*d**3 + 0 - d**2 - 1/105*d**5 - l*d**6 - 1/84*d**4 + 0*d. Factor r(s).
-2*s*(s + 1)**2/7
Let o(q) be the first derivative of 49*q**5 + 875*q**4/4 - 670*q**3 - 670*q**2 - 200*q + 119. Factor o(g).
5*(g - 2)*(g + 5)*(7*g + 2)**2
Let m(u) = -u**3 + 14*u**2 + 33*u - 26. Let g be m(16). Let l be (g/25)/((-7)/25). Factor -6/7 - 2/7*c**2 + 2/7*c**3 - l*c.
2*(c - 3)*(c + 1)**2/7
Let z(d) be the second derivative of -1/48*d**4 - 1/8*d**3 - 7*d + 0 + 1/2*d**2. Factor z(t).
-(t - 1)*(t + 4)/4
Let x = 35027/24237 + -2/2693. Let p = x + -73/63. Suppose -p*c - 2/7 + 4/7*c**2 = 0. Calculate c.
-1/2, 1
Let z = -16/65 + 373/195. Let p(u) be the first derivative of 6 - 5/3*u**2 + z*u + 5/9*u**3. What is s in p(s) = 0?
1
Let w(b) be the first derivative of -b**5/160 - b**4/24 - b**3/12 + 21*b - 4. Let f(x) be the first derivative of w(x). Solve f(s) = 0.
-2, 0
Let a(v) = 3*v. Let i be a(0). Factor i*u**4 - 9*u**2 - 3*u**3 - 9*u**3 + 12*u + 12 - 3*u**4.
-3*(u - 1)*(u + 1)*(u + 2)**2
Suppose -15*d + 5 = -25. Let s(v) be the second derivative of -9/2*v**d + 6*v - 3/10*v**5 + v**3 - 1/10*v**6 + 0 + v**4. Factor s(h).
-3*(h - 1)**2*(h + 1)*(h + 3)
Let h(c) be the first derivative of c**3/9 + 7*c**2/6 - 6*c + 71. Determine y so that h(y) = 0.
-9, 2
Let k = 507 - 214. Let f = -871/3 + k. Let 0 + 4/3*o**2 + f*o = 0. Calculate o.
-2, 0
Let d be 2 + -1 + 2 + 1 + 0. Suppose 0 = -o - y + 2, -5*o + d*y + 4 = -3*o. What is u in -2/5*u + 4/5*u**o - 2/5 = 0?
-1/2, 1
Solve 2*o**3 + 2*o - 6*o**2 + 4*o - 32*o + 18*o = 0.
-1, 0, 4
Let h be 20/42 - (-312)/(-702). Let r(a) be the second derivative of 0*a**2 + 0 + 0*a**5 + 1/15*a**6 - 7*a + 0*a**3 - 1/18*a**4 - h*a**7. Factor r(i).
-2*i**2*(i - 1)**2*(2*i + 1)/3
Let k(x) be the second derivative of -x**9/11340 + x**8/1680 - x**7/630 + x**6/540 - 2*x**4/3 - 6*x. Let b(l) be the third derivative of k(l). Factor b(v).
-4*v*(v - 1)**3/3
Suppose 5*y + 15 = 0, 4*o - y = y - 18. Let m be (-5)/40*o*4. Factor 2/9*c**2 + 0*c - 2/3*c**m + 0 - 2/9*c**5 + 2/3*c**4.
-2*c**2*(c - 1)**3/9
Let m(h) be the second derivative of 3*h**5/16 - 3*h**4/2 - 75*h**3/8 - 21*h**2/4 - 7*h - 11. Factor m(v).
3*(v - 7)*(v + 2)*(5*v + 1)/4
Let g be ((-555)/(-25) + -22)/((-6)/(-10)). Determine p, given that 2*p + 3 + g*p**2 = 0.
-3
Let v(a) = a - 4. Let u be v(10). Factor -10*t**2 + u*t**2 - 12*t - 20*t - 28.
-4*(t + 1)*(t + 7)
Let j(u) be the third derivative of -u**10/6048 + u**8/1344 - u**4/6 + 16*u**2. Let f(t) be the second derivative of j(t). Factor f(o).
-5*o**3*(o - 1)*(o + 1)
Factor -1/2 - 1/2*i**2 - i.
-(i + 1)**2/2
Suppose 12 = 4*u, -5*u - 16 + 49 = -3*p. Let o(i) = 4*i + 26. Let r be o(p). Factor 2/3*h**r + 1/3*h**3 + 0 + 1/3*h.
h*(h + 1)**2/3
Let z be (4 - -1) + (1 + -6 - -2). Solve -3*n**2 + 46 - 52 + z*n**3 - 7*n**2 + 14*n = 0 for n.
1, 3
Let f(w) = -1. Let q(k) = k**2 + k + 5. Let m(s) = -s**2 - 4. Let r(g) = -7*m(g) - 6*q(g). Let j(a) = -35*f(a) + 5*r(a). Factor j(h).
5*(h - 5)*(h - 1)
Let r(w) = -w**3 - 4*w**2 - 20*w - 12. Let i(c) = -2*c**3 - 4*c**2 - 20*c - 12. Let f(m) = 5*i(m) - 6*r(m). Factor f(u).
-4*(u - 3)*(u + 1)**2
Let j(b) be the second derivative of -3*b**5/80 + b**4/8 + b**3/8 - 3*b**2/4 + 2*b - 13. What is n in j(n) = 0?
-1, 1, 2
Let d = 1993/5 - 395. Let p(x) be the first derivative of -4 + 0*x + 0*x**2 + d*x**5 + x**3 + 5/4*x**6 + 27/8*x**4. Determine w so that p(w) = 0.
-1, -2/5, 0
Let l be ((-24)/40)/(2/10). Let g be (-27)/(-6)*(-2)/l. Factor -2/11*h**2 + 0 - 4/11*h**g - 2/11*h**4 + 0*h.
-2*h**2*(h + 1)**2/11
Let k(t) = 21*t + 170. Let j be k(-8). Factor -j*i + 3/2*i**2 + 3/4 + 0*i**3 - 1/4*i**4.
-(i - 1)**3*(i + 3)/4
Let j = 57 + -55. Factor -3*k**2 + 27*k - j*k - 30 - 2*k**2.
-5*(k - 3)*(k - 2)
Let j = 1138 - 1138. Let q = 342/5 - 68. Let j + 2/5*s**2 + q*s = 0. What is s?
-1, 0
Let d(m) be the first derivative of 3/10*m**4 - 3/25*m**5 + 21 + 0*m - 1/5*m**3 + 0*m**2. Determine z so that d(z) = 0.
0, 1
Let b(g) be the third derivative of 3*g**8/784 - 227*g**7/1470 + 997*g**6/420 - 564*g**5/35 + 752*g**4/21 - 512*g**3/21 - 58*g**2. What is k in b(k) = 0?
2/9, 1, 8
Let l(v) be the first derivative of v**6/14 - 81*v**5/35 + 423*v**4/14 - 20