 1/4*s**d + 1/24*s**4. Factor p(x).
x*(x + 1)*(x + 3)/6
Suppose 6 + 2 = -4*c, 4*h + c = -14. Let a(z) = z**3 - 5*z**2 - 9*z - 3. Let o(t) = -6*t**2 - 9*t - 3. Let d(u) = h*a(u) + 4*o(u). Factor d(w).
-3*(w + 1)**3
Let v(g) be the second derivative of g**5/70 + 2*g**4/21 - g**3/7 - 18*g**2/7 + 61*g. Determine f so that v(f) = 0.
-3, 2
Let q(d) be the third derivative of 0*d**3 - 1/30*d**5 + 1/168*d**8 - 1/35*d**7 + 0*d + 16*d**2 + 0 + 0*d**4 + 1/20*d**6. Factor q(i).
2*i**2*(i - 1)**3
Let o(j) = -3*j**2 - 23*j - 4. Let c(r) = -r**2 - 3*r - 1. Let g(q) = -4*c(q) + o(q). Factor g(l).
l*(l - 11)
Suppose -10*y + 108 = -11*y - 4*u, -4*y + 4*u = 472. Let f = -579/5 - y. What is b in -16/5 + 7/5*b**2 - 8/5*b - f*b**3 = 0?
-1, 4
Suppose 2*k**2 + 44448*k - 44396*k - k**2 = 0. Calculate k.
-52, 0
Let p(i) be the third derivative of i**6/1020 - 11*i**5/170 + 21*i**4/68 - 31*i**3/51 + 942*i**2. What is l in p(l) = 0?
1, 31
Let v(q) be the second derivative of -1/3*q**4 + 0 - 23*q + 14/3*q**3 - 12*q**2. Factor v(f).
-4*(f - 6)*(f - 1)
Let l(z) = 12*z**2 - 58*z - 6. Let f be l(5). Let c(r) be the third derivative of -1/7*r**3 + 0*r - 11*r**2 + 3/56*r**f - 1/140*r**5 + 0. Factor c(b).
-3*(b - 2)*(b - 1)/7
Let j(s) = -2 + 40*s**2 - 2 - 39*s**2 + 5*s. Let o be j(-6). Factor -7*m - 3*m + 4*m + 3*m**2 - m**o.
2*m*(m - 3)
Let w be (-6)/33 - (-70)/22. Suppose -c = w*c + c. Factor 1/2*q**2 - q + c.
q*(q - 2)/2
Let t(b) be the first derivative of -2*b**5/45 + 16*b**3/27 - 32*b/9 + 109. What is o in t(o) = 0?
-2, 2
Let x(m) be the third derivative of m**8/84 + 26*m**7/105 + 2*m**6 + 112*m**5/15 + 32*m**4/3 + m**2 - 34*m. Factor x(q).
4*q*(q + 1)*(q + 4)**3
Factor 2/9*o**5 - 512/9 + 0*o + 320/9*o**2 + 10/3*o**4 + 160/9*o**3.
2*(o - 1)*(o + 4)**4/9
Let z be (6 - 0)/(24/60). Factor 2 + s - z*s**2 + 7*s**2 + 7*s**2.
-(s - 2)*(s + 1)
Let g(b) be the third derivative of 7*b**2 - 1/48*b**6 - 1/420*b**7 + 5/48*b**4 + 0*b - 1/40*b**5 + 1/3*b**3 + 0. Solve g(a) = 0 for a.
-4, -1, 1
Factor -7/4*h - 1/2*h**2 + 1/4*h**3 - 1.
(h - 4)*(h + 1)**2/4
Let v(i) = 15*i**2 - 3240*i + 74100. Let s(n) = 2*n**2 - 463*n + 10586. Let r(k) = 20*s(k) - 3*v(k). Solve r(t) = 0 for t.
46
Let a be (-1)/((-7)/2 + 3). Suppose 5*t + 0 = -4*i - a, t - 8 = -5*i. Find h such that 1/2*h**i + 0 - h + 1/2*h**3 = 0.
-2, 0, 1
Suppose -44 = -4*b - 36. Let 2*i - 11*i - 3*i**b + 2 + 9*i**2 + 2 - i**3 = 0. Calculate i.
1, 4
Let h(t) be the first derivative of t**4/6 - 4*t**3/3 + 3*t**2 + 4*t + 2. Let s(r) be the first derivative of h(r). Factor s(n).
2*(n - 3)*(n - 1)
Let a(u) be the third derivative of -5*u**8/42 - 13*u**7/42 + u**6/4 + 4*u**5/3 + 5*u**4/12 - 5*u**3/2 + 258*u**2. Solve a(c) = 0 for c.
-1, 3/8, 1
Let y be (2 + 0)*780/520. Let -40/3*n - 20/3 - 25/3*n**2 - 5/3*n**y = 0. What is n?
-2, -1
Let q(g) be the second derivative of 1/21*g**2 + 41/105*g**5 + 5*g + 17/63*g**3 + 53/315*g**6 + 29/63*g**4 + 13/441*g**7 - 5. Factor q(u).
2*(u + 1)**4*(13*u + 1)/21
Let s be (2/(-30)*1)/(15/(-120)). Let 0 - 2/15*q**3 + s*q**2 + 2/3*q = 0. What is q?
-1, 0, 5
Suppose -6/5*h - 4/15 + 22/15*h**2 = 0. What is h?
-2/11, 1
Let y(n) = 3*n**2 + 5*n + 2. Suppose -k - 2 = -5*z, 3*z = -z + 4*k - 8. Let d(i) = -5 - z - 9*i**2 + 0 - 1 - 16*i. Let j(l) = -4*d(l) - 11*y(l). Factor j(u).
3*(u + 1)*(u + 2)
Let p(x) be the second derivative of -3*x**5/20 + 3*x**3/2 + 3*x**2 - 12*x - 2. Suppose p(f) = 0. What is f?
-1, 2
Find v, given that -4*v**2 + 0*v - 5476 - 334*v + 38*v = 0.
-37
Suppose 2*v + 3*z - 20 = 0, 0 = -3*v + z + 1 + 7. Factor v*l + 15*l**2 - 30 - 19*l + 4*l - 24*l.
5*(l - 3)*(3*l + 2)
Let k(q) be the third derivative of q**5/120 - q**3/12 - 15*q**2 + 2. Factor k(n).
(n - 1)*(n + 1)/2
Let l = -198 + 189. Let z be (-495)/22*1/l. Determine d, given that -5 - 5/2*d**4 - z*d + 5/2*d**3 + 15/2*d**2 = 0.
-1, 1, 2
Let z(m) = 27*m + 9. Let j be z(-4). Let d be (-22)/j - 32/(-18). Factor -18*i**2 + 27*i**2 - d*i + 5*i**3 + 6*i**3.
i*(i + 1)*(11*i - 2)
Let j be 1*(4/2)/(-4)*-2. Let v be 117/81 - (2 - j). Find q, given that -v*q + 2/9*q**2 + 0 = 0.
0, 2
Let z = 106/9 + -524/45. Let t = z + 8/15. Determine k so that -1/3*k + t - 1/3*k**2 = 0.
-2, 1
Let a = -2537/7 + 364. Let v(p) be the first derivative of -a*p**3 + 3/7*p**4 + 15/14*p**2 + 5 + 6/7*p. Factor v(d).
3*(d - 2)*(d - 1)*(4*d + 1)/7
Let p(b) = b + b**3 - 3 + 1 + 0*b**3 + 0*b**3. Let f(v) = -3*v**3 - v**2 - 3*v + 5. Let s(c) = 2*f(c) + 5*p(c). Factor s(x).
-x*(x + 1)**2
Let n(i) be the third derivative of 1/12*i**4 + 1/300*i**6 + 0*i + 0 + 2/15*i**3 + 16*i**2 + 2/75*i**5. Factor n(p).
2*(p + 1)**2*(p + 2)/5
Let j(f) be the third derivative of f**10/75600 - f**9/37800 - f**8/8400 - 5*f**4/24 + 29*f**2. Let i(c) be the second derivative of j(c). Factor i(g).
2*g**3*(g - 2)*(g + 1)/5
Let u(q) = -q**3 + q**2 + 1. Let z(l) = -2*l**3 - 3*l**2 - 8*l + 7. Let b(n) = 3*u(n) - z(n). Let x be b(7). Factor 3/4*g**2 + x*g**3 - 3*g - 3/4.
3*(g - 1)*(g + 1)*(4*g + 1)/4
Let n(y) be the third derivative of -y**5/40 + y**4/4 - 3*y**3/4 - 461*y**2. Factor n(j).
-3*(j - 3)*(j - 1)/2
Let y(o) be the third derivative of 3*o**7/14 + 37*o**6/8 + 7*o**5/3 - 125*o**4/6 - 40*o**3 - 177*o**2. Suppose y(w) = 0. Calculate w.
-12, -2/3, 1
Let m be 8/54*(-945)/(-630). Let -m*z**3 + 2/3*z**2 - 2/9*z**4 - 4/9 + 2/9*z = 0. What is z?
-2, -1, 1
Suppose 5*k - 3*k = 0. Let v(s) be the third derivative of -1/240*s**5 + 0*s - 1/210*s**7 - 1/96*s**6 + 0*s**3 + 0*s**4 + 2*s**2 + k. Let v(y) = 0. Calculate y.
-1, -1/4, 0
Suppose -2 = d - 5. Suppose -t = 3*j + 1, 0*t + t - 17 = d*j. Factor 31*i - 12*i**3 - t*i**2 - i**5 - 6*i**4 - 31*i.
-i**2*(i + 2)**3
Let m(i) = -i**3 - 7*i**2 - i - 7. Let g(c) = -4*c**3 - 29*c**2 - 4*c - 28. Let q(k) = 2*g(k) - 9*m(k). Let v be q(-5). Solve -4*z**2 + 5*z**v + 2*z**2 = 0.
0
Let h(c) be the third derivative of c**9/45360 - c**8/3360 + c**7/840 - c**6/540 - c**4/3 + 14*c**2. Let n(q) be the second derivative of h(q). Solve n(a) = 0.
0, 1, 4
Suppose 8 = -4*q - 5*a, 23 = -0*q + q - 5*a. Determine u, given that 4*u**2 - 3*u**3 - 4*u**3 + 7*u**q - 4*u**3 = 0.
0, 1
Let a(s) = 348*s + 2788. Let t be a(-8). Factor -48*n - t*n**3 + 24*n**2 + 2/9*n**4 + 0.
2*n*(n - 6)**3/9
Let g be 136/(-612)*6/(-16). Let m(l) be the first derivative of 1/3*l**2 + 0*l + 1/9*l**3 + 4 - g*l**4. Factor m(d).
-d*(d - 2)*(d + 1)/3
Factor -3/4*o**2 - 48 - 12*o.
-3*(o + 8)**2/4
Suppose 0 = -4*s - 5*i + 23, 0 = s - 4*s + 3*i - 3. Suppose 0 = -4*m + 5*x - 10, -s*m + x + 6 = 8. Determine k, given that m*k + 1/5*k**2 + 0 = 0.
0
Factor 90*i**2 - 44*i**3 + 17*i**4 - 12*i**4 - i**3.
5*i**2*(i - 6)*(i - 3)
Suppose 2*l = 6*l - 16. Let s(f) be the second derivative of 0*f**2 + 1/15*f**3 + 2*f - 1/30*f**l + 0. Factor s(x).
-2*x*(x - 1)/5
Find d such that 32/5*d**3 + 18/5*d**4 - 4/5*d + 2*d**2 + 0 = 0.
-1, 0, 2/9
Let d = -9 + 8. Let r be 6*d*(-4)/8. Suppose r*n**2 - 80 + 80 = 0. Calculate n.
0
Let x(v) be the second derivative of v**5/60 + 7*v**4/12 - 92*v. Factor x(w).
w**2*(w + 21)/3
Let r(d) be the second derivative of -1/10*d**6 - 1/10*d**5 + 0 + 1/4*d**4 + 0*d**2 - 15*d + 1/3*d**3. Let r(f) = 0. What is f?
-1, -2/3, 0, 1
Let s be ((-42)/5)/((-93)/15 + 6). Suppose s - 16 - 3*k**3 + 9*k + 28 - 12*k**2 = 0. Calculate k.
-3, 2
Let k(y) be the second derivative of -15*y + 0 + 0*y**2 + 1/24*y**3 + 7/96*y**4 + 9/160*y**5 + 1/336*y**7 + 1/48*y**6. Factor k(m).
m*(m + 1)**3*(m + 2)/8
Suppose -62 = -2*y - 4. Let h = y - 29. Determine s so that 0*s - 2/3*s**3 + h + 4/3*s**2 = 0.
0, 2
Let j(r) be the third derivative of 0*r + 0 + 19*r**2 - 1/270*r**5 + 2/27*r**4 - 16/27*r**3. Suppose j(b) = 0. What is b?
4
Suppose -15 = -2*l - 3*l. Suppose b - l*b = -10. Factor t**5 - 7*t**5 + t**5 + 6*t**4 - 3*t**3 + 2*t**b.
-3*t**3*(t - 1)**2
Let l = -58 - -62. Find k such that l - 1 + 4*k - k**2 - 7 + 1 = 0.
1, 3
Let m(d) = 2*d**2 + 196*d + 210. Let y(t) = -t**2 - 131*t - 140. Let n(k) = -5*m(k) - 8*y(k). Suppose n(o) = 0. What is o?
-1, 35
Let b be (-5)/95*-1*3. Let c = b - 1/247. Suppose c*w**2 - 4/13*w + 0 = 0. Calculate w.
0, 2
Let w(o) = -11*o**2 - 18*o - 19. Let s(k) = -41*k**2 - 70*k - 75. Let y(t) = -3*s(t) + 11*w(t). Solve y(z) = 0 for z.
-4, -2
Let n(m) be the second derivative of m**6/30 + m**5/3 + 4*m**4/3 + 8*m**3/3 - 13*m**2/2 - 8