8 - (-2)/(-2). Let v = x + 3/248. Factor 3*g**3 - 3/2 - v*g**5 - 3/2*g + 3*g**2 - 3/2*g**4.
-3*(g - 1)**2*(g + 1)**3/2
Let f(l) be the second derivative of 2*l**6/75 - 66*l**5/25 + 1021*l**4/15 + 1496*l**3/5 + 2312*l**2/5 + 2*l - 142. Find b, given that f(b) = 0.
-1, 34
Let n = -50664/139 + 729/2. Let r = 1689/1946 - n. Determine z so that -6/7*z**3 + 3/7*z + 12/7*z**2 + 3/7*z**5 - r*z**4 - 6/7 = 0.
-1, 1, 2
Let l(p) = p**2 - 29*p + 58. Let u be l(27). Suppose 0*n = -n - u*n. Factor 2/7*h + n + 4/7*h**3 + 6/7*h**2.
2*h*(h + 1)*(2*h + 1)/7
Let t(i) be the first derivative of i**3/15 + i**2 + 21*i/5 + 279. Solve t(j) = 0.
-7, -3
Let y be -12*-1*4/12. Suppose 0 = -u + y*t, -2*u = 2*t - t - 9. Find j such that -3*j**2 + 0*j**2 + u*j - j = 0.
0, 1
Let m(f) = 35 - 7 + 14 - f**2 + 6*f. Let d be m(10). Solve -4/7 - 6/7*z - 2/7*z**d = 0.
-2, -1
Let t(n) = -18*n**3 - 29*n**2. Let p(s) = -s**3. Let d(f) = 5*p(f) + t(f). Let x(h) = 4*h**3 + 5*h**2. Let w(m) = 6*d(m) + 34*x(m). Solve w(i) = 0 for i.
-2, 0
Let s(p) be the second derivative of -3/10*p**2 + 1/5*p**3 + 0 - 5*p - 1/20*p**4. Factor s(q).
-3*(q - 1)**2/5
Let i(c) be the third derivative of 3*c**6/8 + c**5/3 - 15*c**4/8 - 10*c**3/3 + 12*c**2 + 5. Factor i(p).
5*(p - 1)*(p + 1)*(9*p + 4)
Let j(i) be the third derivative of i**8/56 + 13*i**7/15 + 263*i**6/20 + 1513*i**5/30 + 84*i**4 + 196*i**3/3 + 8*i**2 - 15. Determine x, given that j(x) = 0.
-14, -1, -1/3
Let u be ((-1)/21)/(170/(-3060)). Suppose u*t**2 - 6/7*t**3 + 0 + 2/7*t**4 - 2/7*t = 0. Calculate t.
0, 1
Let j = 24 + -20. Let i be (j/(-8))/(1/(-2)). Factor -3 - n**2 + 5*n - n + 1 - i.
-(n - 3)*(n - 1)
Let z(g) be the first derivative of 28/5*g**5 + 32*g + 4 - 88*g**2 - 37*g**4 + 88*g**3. Determine r so that z(r) = 0.
2/7, 1, 2
Let y be -15*14/40 + 0 + 6. Let -5/4*g + 1/2 - g**2 + y*g**3 = 0. What is g?
-1, 1/3, 2
Let d(u) = 7*u**4 + 15*u**3 + 11*u**2 + 13*u. Let x be (30/(-12))/(1/2). Let a(q) = -4*q**4 - 8*q**3 - 5*q**2 - 7*q. Let i(c) = x*a(c) - 3*d(c). Factor i(z).
-z*(z + 1)*(z + 2)**2
Let z(k) be the first derivative of k**6/10 + 129*k**5/25 + 879*k**4/10 + 414*k**3 - 3645*k**2/2 + 2025*k - 29. Let z(r) = 0. What is r?
-15, 1
Let h = 313/690 - -11/138. Let l(y) be the first derivative of 26/25*y**5 - h*y**3 - 1/3*y**6 + 0*y + 0*y**2 - 6 - 2/5*y**4. Solve l(o) = 0.
-2/5, 0, 1, 2
Determine d, given that 124*d - 23*d**2 + 2*d**3 + 25*d**2 - 128*d = 0.
-2, 0, 1
Determine y so that 50 - 18*y**2 - 590/3*y + 18*y**3 + 8/3*y**4 = 0.
-5, 1/4, 3
Let f(d) be the second derivative of 2*d**3 + 5*d - 16*d**2 + 1/10*d**5 + 3/2*d**4 + 0. Factor f(a).
2*(a - 1)*(a + 2)*(a + 8)
Factor -2*v**2 + 19*v - 87*v + 7*v**2 + 155 - 92*v.
5*(v - 31)*(v - 1)
Let y(w) be the first derivative of w**9/1512 - w**8/525 - w**7/525 + 8*w**3/3 - 5. Let n(u) be the third derivative of y(u). Factor n(o).
2*o**3*(o - 2)*(5*o + 2)/5
Suppose -5*l + l = p + 9, 3*l = 4*p + 17. Let t be (l/(-3))/((-4)/(-3)). Factor -1/4*b + 1/4*b**2 + t*b**3 - 1/4.
(b - 1)*(b + 1)**2/4
Suppose 6 = 10*t - 9*t. Let t*p**4 + 359 - 69*p - 41*p**3 - 350 + 18*p + 85*p**2 = 0. What is p?
1/3, 1/2, 3
Let j = 4135 - 4132. Factor 1/2*x**2 - 1/4*x**j - 1/4*x + 0.
-x*(x - 1)**2/4
Let a(v) = -2*v**4 - 20*v**3 - 3*v**2 + 123*v + 216. Let n(f) = -4*f**4 - 42*f**3 - 5*f**2 + 245*f + 432. Let b(w) = 7*a(w) - 3*n(w). Factor b(t).
-2*(t - 3)*(t + 3)**2*(t + 4)
Suppose -80 - 106*v**4 + 604*v**2 + 444*v**3 - 130*v**4 + 126*v**5 - 186*v**5 - 96*v = 0. Calculate v.
-5, -1, -1/3, 2/5, 2
Suppose -3*o + 15 = -3*f, -f - 4*f - 25 = -2*o. Let z(p) be the second derivative of -1/72*p**4 + 9*p + 1/36*p**3 + 1/6*p**2 + o. Let z(t) = 0. What is t?
-1, 2
Let w(h) = -10*h**3 - 62*h**2 - 130*h - 66. Let j(s) = -8*s**3 - 61*s**2 - 128*s - 65. Let v(o) = 6*j(o) - 5*w(o). What is b in v(b) = 0?
-1, 30
Suppose -3*u - 11 = -3*q - 14, 2*q - 13 = -3*u. Factor 2/7*n**u + 48/7*n - 18/7*n**2 - 32/7.
2*(n - 4)**2*(n - 1)/7
Let r(c) be the third derivative of -c**7/1680 + c**6/160 + 7*c**5/480 + 2*c**2 + 88. Suppose r(d) = 0. What is d?
-1, 0, 7
Suppose -83*l + 165 = 109 - 193. Factor 0*j + 0*j**2 + 2/21*j**4 - 2/21*j**l + 0.
2*j**3*(j - 1)/21
Let f(h) = 15*h**4 - 17*h**3 - 53*h**2 - 21*h. Let t(z) = 16*z**4 - 16*z**3 - 52*z**2 - 20*z. Let s(r) = 4*f(r) - 5*t(r). Find l such that s(l) = 0.
-1, -2/5, 0, 2
Let y(p) be the third derivative of -1/315*p**7 + 0*p**3 + 1/2016*p**8 + 1/120*p**6 + 0 + p**2 + 1/144*p**4 + 0*p - 1/90*p**5. Factor y(z).
z*(z - 1)**4/6
Let c(m) = 6*m**2 - 68*m - 15. Let o(f) = 24*f**2 - 340*f - 76. Let p(r) = 16*c(r) - 3*o(r). Factor p(s).
4*(s - 3)*(6*s + 1)
Suppose 78*k + 7 = 81*k - 2*y, -y = -1. Let q(w) be the first derivative of -6 + 0*w + 2/27*w**k - 1/3*w**2. Suppose q(z) = 0. What is z?
0, 3
Let c(w) be the second derivative of 0*w**2 + 0 + 1/10*w**5 + 1/27*w**3 - 1/9*w**4 + 6*w. Factor c(j).
2*j*(3*j - 1)**2/9
Suppose w + 1 - 18 = -5*y, 4 = -4*w + 4*y. Factor -7*t**3 - 3*t**w + t**3 - 4*t**4 + t**4.
-3*t**2*(t + 1)**2
Let b(n) be the third derivative of 0*n + 0*n**3 + 1/42*n**7 + 5/3*n**4 - 1/3*n**5 - 1/4*n**6 + 2*n**2 + 0 + 5/336*n**8. Factor b(h).
5*h*(h - 2)*(h - 1)*(h + 2)**2
Let y(o) = -o**3 - 177*o**2 + 332*o - 159. Let c(q) = 2*q**3 + 530*q**2 - 996*q + 478. Let a(j) = 5*c(j) + 14*y(j). Factor a(f).
-4*(f - 41)*(f - 1)**2
Let b be -8*(-5)/40*2. Let 2*k**3 + 53*k**5 + 6*k**4 + 5*k**2 - 11*k**b - 50*k**5 - 5*k**3 = 0. What is k?
-2, -1, 0, 1
Let r(n) = -2*n. Let p be r(-1). Let o be (6/(-5) - 0)/((-45)/300). Factor -2*u**2 - 9 - o*u**2 - 15*u**p - 30*u.
-(5*u + 3)**2
Let h(k) be the second derivative of -k**5/45 + 11*k**4/54 + 23*k**3/27 - 14*k**2/9 - 677*k. Factor h(i).
-2*(i - 7)*(i + 2)*(2*i - 1)/9
Let y(g) = -g**3 - g**2. Let p(b) = -6*b**4 - 8*b**3 + b**2 + 3*b. Let t be (5/4)/((-19)/(-76)). Let z(o) = t*y(o) - p(o). Factor z(x).
3*x*(x - 1)*(x + 1)*(2*x + 1)
Suppose -5*t = -5*k, 0*t = 2*k + 2*t - 8. Determine m, given that 28*m**3 - 36 - 224*m - 196*m**k - 92 - 2*m**4 + 130*m**2 = 0.
-1, 8
Let a(c) be the third derivative of c**7/70 + 49*c**6/360 + 83*c**5/180 + 55*c**4/72 + 2*c**3/3 - 118*c**2. What is v in a(v) = 0?
-3, -1, -4/9
Solve 510*m**3 - 470*m**3 + m**4 - 312*m**2 - 1936 - 2*m**4 - 845*m - 915*m = 0 for m.
-2, 22
Factor 11*p**4 + 5*p**4 - 7880*p + 16*p**2 + 24*p**3 + 7884*p + 4*p**5.
4*p*(p + 1)**4
Suppose -12*n = -5*n - 56. Let v be n/(-6) + 760/399. Factor 0 + 6/7*f**3 - 8/7*f - v*f**4 - 2/7*f**5 + 8/7*f**2.
-2*f*(f - 1)**2*(f + 2)**2/7
Let g(t) = -t**3 + 5*t**2 + 7*t - 35. Let q be g(5). Find b such that 10/9*b**3 + 0*b**4 + q + 0*b**2 - 8/9*b - 2/9*b**5 = 0.
-2, -1, 0, 1, 2
Let n = -427/3 - -143. Let r(b) be the second derivative of 0 + 4/3*b**2 + 1/60*b**5 + 1/6*b**4 - b + n*b**3. Find g such that r(g) = 0.
-2
Find y such that 45*y - 9*y + 108*y - 69*y**2 + 129*y + 3*y**3 + 1521 = 0.
-3, 13
Let w(i) be the third derivative of i**6/1380 - 7*i**4/276 - 2*i**3/23 - 6*i**2 - 14. Factor w(h).
2*(h - 3)*(h + 1)*(h + 2)/23
Let i(j) be the first derivative of 3/10*j**4 + 0*j + 1/5*j**2 - 2/25*j**5 - 2/5*j**3 + 7. Let i(w) = 0. What is w?
0, 1
Suppose -8 = -2*r + 2*w - 0, 5*r - 21 = 4*w. Let u(o) be the third derivative of 0 + 1/32*o**4 - 8*o**2 + 1/160*o**6 + 1/40*o**r + 0*o + 0*o**3. Factor u(f).
3*f*(f + 1)**2/4
Determine v, given that 5/4*v**3 + 0*v + 0 - 15/4*v**4 - 5/4*v**5 + 15/4*v**2 = 0.
-3, -1, 0, 1
Suppose -7 = -a + 1. Suppose 4*l = a*l - 12. Find y, given that -y**2 + 3*y**2 - 10*y**3 + 2*y**5 - l*y**4 + 7*y**3 = 0.
-1, 0, 1/2, 2
Let r(j) be the third derivative of -j**5/150 + j**4/5 + 13*j**3/15 + j**2 + 131. Factor r(f).
-2*(f - 13)*(f + 1)/5
Let v be -2 + 0 - (-208)/91. Let q be 20/(-5) + (-136)/(-28). Factor -v*n**2 + q*n - 4/7.
-2*(n - 2)*(n - 1)/7
Let t(y) be the third derivative of 0*y + 0*y**3 + 5*y**2 + 1/300*y**5 + 0 - 1/1200*y**6 + 0*y**4. Factor t(q).
-q**2*(q - 2)/10
Let s(i) = 42*i - 252. Let o be s(6). Find g, given that -3/7*g**4 + o*g**2 + 3/7 - 6/7*g**3 + 6/7*g = 0.
-1, 1
Let b be -6*(1/(-3))/1. Suppose -h - 16 = 5*u, 2*h + 4*u = -b*h. Factor m**4 + 16*m - 5*m**2 + h*m**2 - 18*m + 2*m**3.
m*(m - 1)*(m + 1)*(m + 2)
Let b = 10806/11 + -980. Find f, given that 12/11 - 6/11*f**3 + 54/11*f**2 - b*f**4 - 46/11*f + 12/11*f**5 = 0.
-3/2, 2/3, 1
Let m = -34 + 103/3. Let b(d