m = 0, q + 3*q + 4*m - 8 = 0. Factor -4*u**3 - 6*u**4 + u**5 + q*u**5 + 4*u**3 + 3*u**3.
3*u**3*(u - 1)**2
Suppose 236*l - 38 = 237*l + 5*z, -28 = 2*l + 4*z. Factor -18/5*b**3 - 2*b**5 + 0*b - 4/5*b**l - 24/5*b**4 + 0.
-2*b**2*(b + 1)**2*(5*b + 2)/5
Let z(c) be the third derivative of 1/12*c**4 + 0 - 17*c**2 + 2/3*c**3 - 1/30*c**5 + 0*c. Factor z(p).
-2*(p - 2)*(p + 1)
Let w(y) be the first derivative of -y**6/1260 - 2*y**5/105 - 4*y**4/21 + y**3 + 12. Let q(g) be the third derivative of w(g). Determine a so that q(a) = 0.
-4
Let k(i) = -2*i**2. Let o(t) = -9*t**2 - 20*t + 100. Let v(a) = -15*k(a) + 3*o(a). Determine p so that v(p) = 0.
10
Factor 168 - 138 - 120*j**3 + 40*j**4 - 121*j - 5*j**5 + 170*j**2 + 6*j.
-5*(j - 3)*(j - 2)*(j - 1)**3
Let z(i) be the third derivative of i**6/24 + 4*i**5/3 + 25*i**4/8 - 449*i**2. Find k such that z(k) = 0.
-15, -1, 0
Let x = 58 + -44. Let s be 39/6 - 1/2. Factor -2*i - i - i + x*i**2 - s*i**4 - 4*i**3.
-2*i*(i - 1)*(i + 2)*(3*i - 1)
Let z(h) be the second derivative of 3*h**5 + 575*h**4/12 + 160*h**3/3 + 45*h**2/2 - 115*h. Suppose z(u) = 0. Calculate u.
-9, -1/3, -1/4
Let g(l) = 3*l**2 + l - 2. Let r(c) = -7*c**2 - 2*c + 4. Let k(s) = s**2 + 1. Let t be k(3). Let u(m) = t*g(m) + 4*r(m). Factor u(d).
2*(d - 1)*(d + 2)
Let y(h) be the second derivative of 0*h**3 + 0 - 1/5*h**2 + 11*h + 1/30*h**4. Find i such that y(i) = 0.
-1, 1
Let n(r) be the third derivative of r**6/240 - r**5/60 - r**4/16 + 4*r**2 + 10. Let n(p) = 0. Calculate p.
-1, 0, 3
Determine c, given that -7/6*c**2 + 3*c - 11/6 = 0.
1, 11/7
Let u(y) be the first derivative of -2*y**3/21 + 15*y**2/7 - 4*y - 27. Factor u(m).
-2*(m - 14)*(m - 1)/7
Let n(q) = -49*q**3 - 505*q**2 + 301*q - 47. Let d(s) = -98*s**3 - 1008*s**2 + 601*s - 95. Let h(u) = -3*d(u) + 7*n(u). Factor h(t).
-(t + 11)*(7*t - 2)**2
Let s(u) be the second derivative of -u**6/15 + u**5 + 23*u**4/6 + 4*u**3 + 13*u. Let s(i) = 0. What is i?
-1, 0, 12
Let q(x) = -x**4 + 5*x**3 + 17*x**2 + 19*x + 4. Let b(i) = 5*i**4 - 20*i**3 - 70*i**2 - 75*i - 15. Let v(j) = -4*b(j) - 15*q(j). Solve v(p) = 0 for p.
-1, 0, 3
Let g be 38/10 + 30/150. Let p be (7 - g) + -6 - (-48)/14. Factor 1/7*z**2 + 0 - z**3 + p*z - 5/7*z**4.
-z*(z + 1)**2*(5*z - 3)/7
Let l = 8 - 37. Let i = -23 - l. Factor -12*h**3 - 14*h - 3*h**4 + 32*h + 11*h**4 - 19*h + i*h**2.
h*(2*h - 1)**3
Let j(y) be the second derivative of -y**7/1680 + y**6/60 - 7*y**5/80 - 13*y**4/12 - 24*y. Let p(c) be the third derivative of j(c). Factor p(u).
-3*(u - 7)*(u - 1)/2
Let i = -28 - -31. Factor 33*c**3 - 4*c**4 - 21*c**3 - 20*c**i.
-4*c**3*(c + 2)
Let j = -992 + 29761/30. Let c(q) be the second derivative of 1/150*q**5 + 0 - 1/9*q**3 + 2/15*q**2 + j*q**4 + 14*q - 1/225*q**6. Let c(o) = 0. What is o?
-2, 1
Let w(k) = -k**3 - 15*k**2 - 7*k - 103. Let t be w(-15). Factor 4/3*n - 2/3 + 2/3*n**4 - 4/3*n**3 + 0*n**t.
2*(n - 1)**3*(n + 1)/3
Let c(w) be the second derivative of w**4/3 + 4*w**3 - 32*w**2 - 8*w. Suppose c(d) = 0. What is d?
-8, 2
Let r(u) be the second derivative of -1/50*u**5 + 1/15*u**4 + 0 - 13*u + 0*u**2 + 0*u**3. Let r(w) = 0. What is w?
0, 2
Let x(z) = 3*z + 1. Let b be x(1). Suppose -8*o = -b*o - 16. Factor -5*c**o + 2*c**4 - c**4 + 3*c**3 + c**4.
-3*c**3*(c - 1)
Let v(o) = -6*o**2 - 318*o - 6406. Let a(q) = -13*q**2 - 635*q - 12815. Let t(h) = 2*a(h) - 5*v(h). Factor t(m).
4*(m + 40)**2
Let c(h) be the second derivative of -h**7/42 + 4*h**6/15 - 23*h**5/20 + 7*h**4/3 - 2*h**3 - 50*h + 1. Solve c(x) = 0 for x.
0, 1, 2, 3
Let c(k) be the second derivative of -k**4/21 - 14*k**3 + 296*k**2/7 + 2*k - 71. Factor c(s).
-4*(s - 1)*(s + 148)/7
Let -168*j**2 + 50*j**2 - 144*j**3 - 3*j**5 - 74*j**2 + 40*j**4 + 5*j**4 = 0. What is j?
-1, 0, 8
Suppose 7*u = 12*u + 15, u + 3 = -3*x. Factor 0*f + x + 1/3*f**5 + 0*f**2 - 1/3*f**3 + 0*f**4.
f**3*(f - 1)*(f + 1)/3
Solve -23 + 315*y**2 + 3 - 9874*y + 312*y**3 - 35*y**4 + 64*y**2 + 9886*y = 0.
-1, -2/7, 1/5, 10
Suppose -4*x = 13*x - 51. Suppose -4*s - 5*r = -8*r, -s - 9 = -x*r. Factor -2/7*c + 0 - 8/7*c**4 - 2/7*c**5 - 12/7*c**s - 8/7*c**2.
-2*c*(c + 1)**4/7
Let t(d) be the first derivative of -49*d**6/10 - 21*d**5/2 + 13*d**4 - 4*d**3 - 13*d - 21. Let n(h) be the first derivative of t(h). Factor n(p).
-3*p*(p + 2)*(7*p - 2)**2
Let t be 4*((-4)/12 - 13/(-12)). Suppose 3*i - 13 = 4*s, -s + 3 = i - 6. Factor -6*m**4 - i*m**3 + 5*m**3 + 4*m**t.
-2*m**3*(3*m - 1)
Let q(n) be the second derivative of -n**7/4200 + n**6/900 + n**5/600 - n**4/60 + n**3/6 + 7*n. Let g(x) be the second derivative of q(x). Factor g(l).
-(l - 2)*(l - 1)*(l + 1)/5
Let a(l) be the third derivative of -l**6/180 + 49*l**5/90 - 95*l**4/36 + 47*l**3/9 + 266*l**2. Factor a(f).
-2*(f - 47)*(f - 1)**2/3
Let j = -76 + 82. Let m(y) be the third derivative of 1/540*y**j + 0*y + 0 + 0*y**3 + 1/27*y**4 + 2/135*y**5 + 6*y**2. Solve m(p) = 0 for p.
-2, 0
Suppose 5*h = 35 - 5. Suppose -h*x = -x - 15. Factor -b**2 - 27*b - b**2 + 31*b - b**x + 8.
-(b - 2)*(b + 2)**2
Let l(i) be the third derivative of 8/3*i**3 - 1/30*i**6 - 18*i**2 + 0*i - 1/5*i**5 + 0*i**4 + 0. Factor l(r).
-4*(r - 1)*(r + 2)**2
Suppose -5*m - j = -24 + 3, m + 15 = -5*j. Suppose 0 = m*o - o - 32. Suppose 2 + 3*z**2 + 3*z - o + 6 = 0. Calculate z.
-1, 0
Let n(h) = -36*h**2 - 645*h + 58. Let r be n(-18). Find d, given that -1/2*d**2 - 7/2*d + r = 0.
-8, 1
Let u(v) be the third derivative of 4*v**6/15 - 19*v**5/15 + 7*v**4/3 - 2*v**3 + 48*v**2 - 1. Let u(y) = 0. Calculate y.
3/8, 1
Let f = 2937151/45 + -65275. Let w = f + 26/5. Factor -250/9 - 10/3*z**2 + w*z**3 + 50/3*z.
2*(z - 5)**3/9
Let s(w) be the first derivative of 4*w**3/15 - 2*w**2 + 24*w/5 + 8. Solve s(h) = 0 for h.
2, 3
Let z(j) be the third derivative of -j**8/576 + 13*j**7/1260 - j**6/72 - j**5/90 + 99*j**2. Solve z(s) = 0 for s.
-2/7, 0, 2
Suppose 4*g = 2*s + 4, 2*g - 75*s + 72*s = 6. Factor 3/4*z + 3/4*z**2 + g.
3*z*(z + 1)/4
Let g(t) be the first derivative of -31 + 7/6*t**4 - 8/9*t**3 + 0*t - 4/15*t**5 + 0*t**2 - 1/9*t**6. Let g(i) = 0. What is i?
-4, 0, 1
Let p(v) = -3*v + 80. Let s be p(26). Let i be (s/5)/((-2)/(-5)). Solve 3/2*n - 1/2*n**3 - i + 0*n**2 = 0 for n.
-2, 1
Let j(u) be the second derivative of u**4/24 - u**3/12 - u**2/2 - 3*u - 20. Let j(g) = 0. What is g?
-1, 2
Let y(b) be the first derivative of 7*b**4/6 + 20*b**3/3 + 8*b**2/3 - 920. Determine m so that y(m) = 0.
-4, -2/7, 0
Let k(w) be the second derivative of 5*w**4/12 + 5*w**3/6 - 50*w**2 - w + 49. Let k(q) = 0. Calculate q.
-5, 4
Let w(z) be the second derivative of z**4/16 + 5*z**3/8 - 9*z**2/4 - 4*z + 5. Factor w(l).
3*(l - 1)*(l + 6)/4
Suppose 0*c - 16 = -4*c. Factor -6 - 4*k - k**2 - k**2 + c*k**2.
2*(k - 3)*(k + 1)
Solve 10*t**2 + 0*t - 6*t**3 + 0 - 18/5*t**4 - 2/5*t**5 = 0.
-5, 0, 1
Let i(j) = -162*j**3 - 72*j**2 - 11*j + 3. Let g(h) = -h + 1. Let a(d) = 3*g(d) - i(d). Suppose a(l) = 0. Calculate l.
-2/9, 0
Let 358*z**3 + 357*z**3 - 706*z**3 - 3*z**2 = 0. What is z?
0, 1/3
Let h(q) be the third derivative of q**6/60 - 21*q**5/5 + 441*q**4 - 24696*q**3 + 8*q**2 - 6*q. Determine l, given that h(l) = 0.
42
Suppose -l - 1 = -f, -3*l + l = 3*f - 13. Factor 3*c**l + c**2 + 0*c + 2*c + 2*c.
4*c*(c + 1)
Let s(k) be the third derivative of -k**6/24 - k**5/3 + 5*k**4/6 + 40*k**3/3 + 10*k**2. Factor s(w).
-5*(w - 2)*(w + 2)*(w + 4)
Let z be 2 + 6*(-2)/9 + 0. Factor 14/9*p**3 + 0 + 10/9*p**4 + z*p**2 + 2/9*p**5 + 0*p.
2*p**2*(p + 1)**2*(p + 3)/9
Let m = -8879/8 - -1110. Let i(p) be the third derivative of 0*p + 3/40*p**5 + 1/12*p**3 - 5*p**2 + 0 + m*p**4. Factor i(t).
(3*t + 1)**2/2
Let h(u) = -2*u**3 + 14*u**2 + 8*u + 4. Let c = 57 + -48. Let z(k) = 5*k**3 - 29*k**2 - 16*k - 9. Let y(t) = c*h(t) + 4*z(t). Factor y(a).
2*a*(a + 1)*(a + 4)
Let d be 0 + 150/24 - 6. Solve -d*r**3 + 0 - 1/4*r + 1/2*r**2 = 0.
0, 1
Let q(s) be the third derivative of s**5/60 - 29*s**4/12 + 19*s**3/2 - 22*s**2. What is z in q(z) = 0?
1, 57
Let i(r) be the first derivative of r**3/3 - 6*r**2 + 20*r - 41. Factor i(o).
(o - 10)*(o - 2)
Let f(l) be the third derivative of -l**6/30 + l**5/15 + l**4/3 + 330*l**2. Factor f(z).
-4*z*(z - 2)*(z + 1)
Let z(n) be the third derivative of 0 + 5*n**2 - 7/30*n**5 + 2*n**3 - 1/12*n**4 + 0*n. Let z(k) = 0. What is k?
-1, 6/7
Factor 