- 2/(-8)*2. Find c such that 4/3 + 2/3*c - 2/3*c**o = 0.
-1, 2
Let p(f) be the third derivative of 1/40*f**6 + 0*f + 1/8*f**5 + 0 - 7*f**2 + 0*f**3 - 3/16*f**4. Let p(z) = 0. Calculate z.
-3, 0, 1/2
Let y = -197699/300 - -659. Let u(m) be the third derivative of -2/75*m**5 + 0*m - 1/12*m**4 - y*m**6 + 4*m**2 + 0 - 2/15*m**3. Factor u(l).
-2*(l + 1)**2*(l + 2)/5
Let h = -6 + 9. Suppose -61 = 2*q - 69. Factor -2*s**q - h*s - s**4 + 3*s - 3*s**2 - 6*s**3.
-3*s**2*(s + 1)**2
Let p(h) be the third derivative of 0*h**4 + 0*h**3 + 0*h**5 + 0*h - 11/42*h**7 - 1/12*h**6 + 19*h**2 + 0. Suppose p(x) = 0. Calculate x.
-2/11, 0
Let x = 5731/2 - 2864. Factor x*q**2 + 3/2 - 3*q.
3*(q - 1)**2/2
Let y(k) = k + 14. Let l be y(-12). Suppose 5*t = -q + 20, l*t = -0*q + q + 8. Suppose -6*m + 36 - 7*m - 11*m + t*m**2 = 0. Calculate m.
3
Let j(r) = -5*r**2 + 300*r + 7508. Let q(o) = 3*o**2 - 200*o - 5005. Let g(w) = 5*j(w) + 8*q(w). Let g(v) = 0. What is v?
-50
Let c be 232/(-1232)*-4 - 4/22. Find b such that -2/7*b**3 + 2/7*b**5 + 4/7*b**4 + 0*b + 0 - c*b**2 = 0.
-2, -1, 0, 1
Let k = -45 - -63. Factor -177*y + k*y**2 - 21*y**4 + 177*y - 57*y**3.
-3*y**2*(y + 3)*(7*y - 2)
Let w = -11 - -12. Suppose 4 + w = 5*h, b + 2*h - 27 = 0. Factor -3*z**2 - 12*z**3 + 5*z**2 + 0*z**3 + b*z**2 - 6*z.
-3*z*(z - 2)*(4*z - 1)
Suppose 0 = -4*o - 4*w, 5*o + 1 - 4 = -2*w. Let p be (12/(-9) + 2)*o. Find u such that p*u**3 + 0*u**2 + 0 + 2/3*u**5 + 0*u - 4/3*u**4 = 0.
0, 1
Let i = 65 + -50. Factor -31*k**2 - 34*k**2 - i*k - 6*k + 68*k**2.
3*k*(k - 7)
Let q(p) be the third derivative of -p**7/336 + 11*p**6/480 - p**5/40 + 17*p**4/24 - 15*p**2. Let l(c) be the second derivative of q(c). Factor l(g).
-3*(g - 2)*(5*g - 1)/2
Let i be (-66)/126 - (-3 + 2). Let c = i + -12/35. Factor 0 + 2/15*v - 4/15*v**2 + c*v**3.
2*v*(v - 1)**2/15
Find n, given that 84*n - 212*n - 1440 - 16*n + 144 - 4*n**2 = 0.
-18
Let q(j) = -23*j + 50. Let f be q(2). Let h(n) be the first derivative of -19/2*n**f - n**2 + 1 + 4*n - 14/5*n**5 - 10*n**3. Factor h(b).
-2*(b + 1)**3*(7*b - 2)
Let d be 0/(32/(6 + 10)). Factor 0 + 12/17*y**2 + 2/17*y**4 + 14/17*y**3 + d*y.
2*y**2*(y + 1)*(y + 6)/17
Let s(q) be the first derivative of 3*q**4/16 - 27*q**3 + 1458*q**2 - 34992*q + 162. Find i, given that s(i) = 0.
36
Determine f, given that -3/2*f**2 - 171/2 - 87*f = 0.
-57, -1
Let i = -1449 - -65207/45. Let z(o) be the first derivative of 2/15*o**2 - i*o**3 - 2/15*o + 8. Factor z(f).
-2*(f - 1)**2/15
Let y(g) be the second derivative of -2*g**6/15 + 7*g**5 - 915*g. Factor y(p).
-4*p**3*(p - 35)
Let y(q) = -7*q**4 - 38*q**3 + 398*q**2 - 2*q - 2. Let u(c) = -18*c**4 - 75*c**3 + 795*c**2 - 5*c - 5. Let r(d) = 2*u(d) - 5*y(d). What is w in r(w) = 0?
0, 20
Let z(g) be the first derivative of -5*g**4/4 + 30*g**3 - 405*g**2/2 - 87. Determine s so that z(s) = 0.
0, 9
Let t(f) be the third derivative of -f**6/48 + 31*f**5/24 - 25*f**4/8 - 15*f**2. Factor t(b).
-5*b*(b - 30)*(b - 1)/2
Let h = -50 + 52. Determine j, given that 24*j**4 - 48*j**4 + 30*j**h - 6 + 9*j - 7*j**5 + j**5 - 3*j**5 = 0.
-2, -1, 1/3, 1
Let q(x) be the first derivative of -6*x**3/19 - 16*x**2/19 - 62. Factor q(i).
-2*i*(9*i + 16)/19
Let b(n) be the second derivative of -n**4/3 - 4*n**3 + n + 62. Factor b(s).
-4*s*(s + 6)
Let b(o) be the first derivative of -o**5/40 - o**4/12 + o**3/12 + o**2/2 - 2*o + 6. Let p(n) be the first derivative of b(n). Factor p(j).
-(j - 1)*(j + 1)*(j + 2)/2
Factor 15*o - 10*o + 12 + 2*o**2 + 6*o + 3*o.
2*(o + 1)*(o + 6)
Let u(f) = f**2 - 2*f + 1. Let a be u(-3). What is q in -a*q**2 + 8/3 - 28/3*q**3 - 4*q = 0?
-1, 2/7
Suppose 23*j = 63*j. Let q(p) be the second derivative of j*p**4 + 0*p**2 + 0 + 0*p**5 - 10*p - 1/135*p**6 + 0*p**3 - 1/189*p**7. Factor q(u).
-2*u**4*(u + 1)/9
Let v(q) be the third derivative of q**6/1980 - 7*q**5/660 + 5*q**3/3 - 12*q**2. Let x(w) be the first derivative of v(w). Factor x(o).
2*o*(o - 7)/11
Factor -8*t**4 - 12*t + 0*t**4 + 4*t**5 - 29*t**3 + 17*t**3 + 32*t**2 - 4*t.
4*t*(t - 2)*(t - 1)**2*(t + 2)
Suppose -11*n + 12*n = -1. Let b be (n - 0)/((-5)/3). Let 0*u + 3/5*u**2 - b = 0. What is u?
-1, 1
Let m(r) be the first derivative of -r**4/32 - 17*r**3/24 - 31*r**2/16 - 15*r/8 - 47. Factor m(q).
-(q + 1)**2*(q + 15)/8
Suppose -4*x + 8 = 2*u, 5*u - 38 = -3*x - 18. Factor x + 5/2*k + 12*k**2 + 15/2*k**3 - 2*k**4.
-k*(k - 5)*(k + 1)*(4*k + 1)/2
Factor -23/2*j**2 - 5*j - 5/2*j**3 + 4.
-(j + 1)*(j + 4)*(5*j - 2)/2
Let q(o) = -2*o**3 - 18*o**2 - 3*o + 3. Let l(v) = -10*v**3 - 90*v**2 - 14*v + 14. Let x(j) = 6*l(j) - 28*q(j). Factor x(d).
-4*d**2*(d + 9)
Let a(l) = -l - 1. Suppose 3*g - 6 = -s, -12 = -2*s + 4*g + 10. Let b(h) = -3*h**3 - 6*h**2 - 12*h - 9. Let x(i) = s*a(i) - b(i). Factor x(d).
3*d*(d + 1)**2
Let v(s) be the first derivative of -2/9*s**3 - 2 - 6*s + 2*s**2. Determine g so that v(g) = 0.
3
Let l(r) be the first derivative of -r**3/2 + 135*r**2/4 - 66*r + 396. Factor l(y).
-3*(y - 44)*(y - 1)/2
Suppose -6*u = -2*u, -2*t - u + 20 = 0. Factor t*i - 4*i**2 - 11*i**2 - 12*i**3 + 17*i**3.
5*i*(i - 2)*(i - 1)
Let n(f) be the third derivative of -f**5/480 + 5*f**4/64 + 276*f**2. Factor n(a).
-a*(a - 15)/8
Let d be (6/(-8))/((-34)/8). Let v = 64/119 + d. Factor v*o**4 + 2/7*o**5 - 4/7*o**2 + 2/7*o**3 - 1/7 - 4/7*o.
(o - 1)*(o + 1)**3*(2*o + 1)/7
Let o be -1 + -3*(-112)/144. Solve -256/3 - o*p**2 + 64/3*p = 0 for p.
8
Suppose s + 4 = 6. Factor h**2 + 3*h**2 + h**s.
5*h**2
Let b(u) be the second derivative of 5/2*u**2 + 0 - 3*u + 1/60*u**5 + 0*u**3 - 1/12*u**4. Let i(t) be the first derivative of b(t). Factor i(k).
k*(k - 2)
Let l = 1053/2 + -525. Suppose 3/8*i**2 + 15/8*i + l = 0. What is i?
-4, -1
Let c be ((-3)/(-2))/((-2)/(-4)). Let t be (-2 - 10)*c/(-21). Let 4/7 + 2/7*x - t*x**2 = 0. Calculate x.
-1/2, 2/3
Let d(k) be the second derivative of k**7/6 + k**6/15 - 7*k**5/20 - k**4/6 + 194*k. Find f, given that d(f) = 0.
-1, -2/7, 0, 1
Suppose 0 = 10*k - 6*k + 5 - 5. Factor k + 1/3*a**4 + 1/6*a - 11/12*a**3 + 5/12*a**2.
a*(a - 2)*(a - 1)*(4*a + 1)/12
Let d(w) be the first derivative of w**8/112 + w**7/70 - w**6/40 - w**5/20 - w**2 - 5. Let m(c) be the second derivative of d(c). Factor m(n).
3*n**2*(n - 1)*(n + 1)**2
Factor -15082 + 15122 + 4*p**3 + 12*p - 6*p**2 - 18*p**2.
4*(p - 5)*(p - 2)*(p + 1)
Let p(b) = -5*b + 17*b - 9*b**2 - 3*b - 21 + 24*b**3. Let c(q) = -6*q**3 + 2*q**2 - 2*q + 5. Let x(y) = -21*c(y) - 5*p(y). Find z, given that x(z) = 0.
-1, 0, 1/2
Let c(n) be the third derivative of 0*n + 1/20*n**6 - 2/105*n**7 - 16*n**2 + 0*n**3 + 1/24*n**4 + 0 + 1/336*n**8 - 1/15*n**5. Find g such that c(g) = 0.
0, 1
Let l = -6347/25 + 254. Let n = l - -29/175. Factor n*h**3 - 4/7*h - 2/7*h**2 + 0.
2*h*(h - 2)*(h + 1)/7
Let y = 1 - -44. Let w = y - 403/9. Factor 4/9 - 2/9*u**2 - w*u.
-2*(u - 1)*(u + 2)/9
Let u = 83/156 - 11/39. Let q(g) be the first derivative of -7 - g + 3/2*g**2 + u*g**4 - g**3. Factor q(c).
(c - 1)**3
Let p = -14 - -22. Suppose 0 = -n + a - 0 + 2, -4*n - 5*a + p = 0. Find x, given that x**3 + 2*x**2 - n*x**4 + 2*x - 3*x**3 + 0*x**3 = 0.
-1, 0, 1
Let f(s) be the third derivative of 0*s**4 + 0 - 1/30*s**5 + 0*s**3 - 1/180*s**6 + 8*s**2 + 0*s. Factor f(l).
-2*l**2*(l + 3)/3
Factor -14/5 - 2/15*o**2 - 44/15*o.
-2*(o + 1)*(o + 21)/15
Let b(j) be the second derivative of -j**5/170 - 7*j**4/102 - 5*j**3/17 - 9*j**2/17 + 132*j - 2. Factor b(v).
-2*(v + 1)*(v + 3)**2/17
Determine j so that 10/3*j - 4 + 4/3*j**2 - 2/3*j**3 = 0.
-2, 1, 3
Let v be 7/2*14/245. Let q(z) be the second derivative of 0 + 2*z - 2/3*z**4 + 0*z**2 + 0*z**3 - v*z**5. Factor q(g).
-4*g**2*(g + 2)
Suppose 11*v = 15*v + 44. Let b be v - -8 - (-4 + 1). Factor 4/7*g + 2/7*g**2 + b.
2*g*(g + 2)/7
Let i be 9/2 + (-21)/(-28). Factor i*n**2 - 45/4*n + 27/4 - 3/4*n**3.
-3*(n - 3)**2*(n - 1)/4
Let 17*k - 11*k**2 - 41*k - 4*k**4 - 11*k**2 + 16*k**3 + 18*k**2 = 0. Calculate k.
-1, 0, 2, 3
Let n(m) = 74*m + 222. Let f be n(-3). Solve -1/5*h**4 + 2/5*h**3 + f*h + 0 - 1/5*h**2 = 0 for h.
0, 1
Let x(a) be the first derivative of a**4/6 - a**3/3 - 2*a**2 + 17*a - 9. Let w(s) be the first derivative of x(s). Determine q so that w(q) = 0.
-1, 2
Let n(p) be the first derivative of 0*p**3 + 1/4*p**4 - 3/2*p**2 - 2*p + 3. Solve n(a) = 0.
-1, 2
Let w(u)