) be the second derivative of -p**7/6300 + p**6/450 - 5*p**4/12 + 54*p. Let q(o) be the third derivative of y(o). Let q(w) = 0. What is w?
0, 4
Let w(d) be the third derivative of -32*d**7/21 + 6*d**6 + 35*d**5 - 7105*d**4/24 + 1715*d**3/2 - 254*d**2. Factor w(z).
-5*(z + 3)*(4*z - 7)**3
Let -2/3*t**2 + 0*t + 2*t**3 + 0 + 2/3*t**5 - 2*t**4 = 0. Calculate t.
0, 1
Let i(v) be the third derivative of v**8/1680 - v**6/180 + v**4/4 + 2*v**2. Let g(f) be the second derivative of i(f). Factor g(c).
4*c*(c - 1)*(c + 1)
Let m(l) = -1836*l + 3674. Let u be m(2). Let 3/2*v**3 + 15/2 - 3/2*v - 15/2*v**u = 0. Calculate v.
-1, 1, 5
Let f(z) be the first derivative of -5*z**4/12 + 5*z**2/2 - 45*z - 45. Let c(m) be the first derivative of f(m). Factor c(n).
-5*(n - 1)*(n + 1)
Let k = -6392 + 44748/7. Suppose 4/7*j**2 - 4/7*j**3 + k*j - 4/7 = 0. Calculate j.
-1, 1
Suppose 8*z = -40 + 64. Let d(k) be the second derivative of -1/5*k**z + 1/20*k**4 + 0 + 0*k**2 - 7*k. Factor d(w).
3*w*(w - 2)/5
Suppose 19*j**2 - 5*j + j**2 - 5*j**3 - j - 4*j - 5*j = 0. Calculate j.
0, 1, 3
Let z(j) be the second derivative of 1/10*j**5 + 0*j**2 + 0*j**3 + 12*j - 1/6*j**4 + 0. Let z(m) = 0. What is m?
0, 1
Suppose 3*o + 3*d - 36 = -2*o, -4*d - 39 = -3*o. Let a(j) be the first derivative of 3/7*j**2 - 2/7*j + 1/14*j**4 - 2/7*j**3 - o. Factor a(i).
2*(i - 1)**3/7
Let u(m) be the third derivative of m**8/336 - 4*m**7/105 - m**6/60 + 4*m**5/15 + m**4/24 - 4*m**3/3 + 640*m**2. Factor u(r).
(r - 8)*(r - 1)**2*(r + 1)**2
Let t(s) be the third derivative of -121*s**6/90 + 11*s**5/15 - s**4/6 - 10*s**3/3 - 34*s**2. Let j(r) be the first derivative of t(r). Factor j(m).
-4*(11*m - 1)**2
Let u(k) be the first derivative of -4*k + 0*k**2 - 2/3*k**3 + 2/3*k**4 + 19/20*k**5 + 9 + 7/30*k**6. Let h(s) be the first derivative of u(s). Factor h(d).
d*(d + 1)*(d + 2)*(7*d - 2)
Suppose -t + 3*t + 40 = -4*h, -5*t = 4*h + 94. Let v = -3 - t. Factor 1 + 3*s**4 - 21*s**5 - 1 + v*s**5.
-3*s**4*(2*s - 1)
Let r = -2926/15 - -5867/30. Factor r*w**2 - 1/6 + 1/3*w.
(w + 1)*(3*w - 1)/6
Let l = 305 - 548. Let b = l + 245. Factor 3*o + 3/4 + 9/2*o**b + 3*o**3 + 3/4*o**4.
3*(o + 1)**4/4
Factor 1800*g**4 - 1140*g**3 + 121/2*g**2 + 38*g + 2.
(5*g - 2)**2*(12*g + 1)**2/2
Let v be 4/14 - (-6)/(-21). Suppose -3*c + 5*t = t - 34, -t - 11 = -2*c. Determine x, given that -2/3*x**5 + 4/3*x**c + 0 - 4/3*x**4 + 2/3*x + v*x**3 = 0.
-1, 0, 1
Let i(c) = c**2 - 17*c. Let w be i(17). Let s(m) be the first derivative of 1/5*m**5 + 3 + 1/2*m**4 + w*m**2 + 0*m**3 - 1/6*m**6 + 0*m. Factor s(v).
-v**3*(v - 2)*(v + 1)
Let w be 1486/26 - 2/13. Let q = w - 57. Let 0 + 0*z**2 + q*z - 2/3*z**5 + 4/15*z**3 + 2/5*z**4 = 0. Calculate z.
-2/5, 0, 1
Suppose 3*r = 2*f - 4*f + 9, -3*f = -3*r + 9. Let x(a) = -a**2 + 5*a + 8. Let u be x(6). Factor -5*b**u + 13*b**2 - 31*b - 4*b**r + 27*b.
-4*b*(b - 1)**2
Let s(q) = 9*q**3 - 101*q**2 + 412*q - 450. Let a(u) = -15*u**3 + 168*u**2 - 687*u + 750. Let z(b) = 7*a(b) + 12*s(b). Find g, given that z(g) = 0.
2, 5
Let t(o) be the first derivative of o**3/2 - o**2/4 - o/3 + 90. Factor t(u).
(3*u - 2)*(3*u + 1)/6
Let m = -8783/9 - -979. Let d(z) be the first derivative of -12 - 4/5*z**5 - 16/3*z + m*z**3 + 4/3*z**4 - 8/3*z**2. Let d(c) = 0. What is c?
-1, -2/3, 1, 2
Let p be 1/((-1)/(-3) + 0/(-10)). Determine h, given that 9*h - 25 + 90*h**2 + h**p + 6*h + 100*h**2 - 181*h**2 = 0.
-5, 1
Let r(x) be the first derivative of x**3/3 + 83*x**2/2 + 82*x - 8. Factor r(j).
(j + 1)*(j + 82)
Let g(p) = -19*p**3 - p**2 + p + 1. Let f be g(-1). Find o such that f*o - 68*o**2 + o**3 + 8 + 60*o**4 - 15*o + 3*o**3 - 7*o = 0.
-1, -2/5, 1/3, 1
Let g = -230 + 3452/15. Let o(y) be the first derivative of 8 + g*y**3 - 8/15*y + 1/30*y**4 + 0*y**2. Factor o(k).
2*(k - 1)*(k + 2)**2/15
Find u, given that 2/3*u**4 - 4/3*u**3 + 2 + 4/3*u - 8/3*u**2 = 0.
-1, 1, 3
Let c(o) be the first derivative of -1/12*o**3 + 4 + 5/4*o**2 - 25/4*o. Determine f so that c(f) = 0.
5
Let d(y) be the first derivative of -y**5 + 145*y**4/4 - 90*y**3 + 527. Suppose d(a) = 0. Calculate a.
0, 2, 27
Let t(c) be the third derivative of c**5/15 + 14*c**4/3 + 104*c**3/3 + 194*c**2. Factor t(a).
4*(a + 2)*(a + 26)
Factor -12/7*a**2 - 48/7 - 64/7*a + 4/7*a**3.
4*(a - 6)*(a + 1)*(a + 2)/7
Let g(y) be the third derivative of y**7/210 - 3*y**6/20 + 9*y**5/5 - 119*y**4/12 + 49*y**3/2 + 142*y**2. Suppose g(i) = 0. What is i?
1, 3, 7
Suppose -54/11 - 774/11*g**2 + 200*g**4 - 1060/11*g**3 + 2000/11*g**5 + 432/11*g = 0. Calculate g.
-1, 3/10
Let r(c) be the third derivative of 7*c**5/18 - 29*c**4/36 - 2*c**3/3 - 187*c**2. Find l, given that r(l) = 0.
-6/35, 1
Suppose 4*c + r = -16, 4*r - 20 = 4*c + c. Let y be 2 + (-9)/12*c. Factor -2 + 36*m**3 - m**2 - 1 + 9*m**2 - 36*m - y.
4*(m - 1)*(m + 1)*(9*m + 2)
Let c(i) be the first derivative of -i**3 - 3*i**2/2 + 18*i + 163. Suppose c(j) = 0. What is j?
-3, 2
Let p(d) = -35*d**3 + 20*d**2 + 15*d + 5. Let q(n) = 10*n**2 + 5*n - 2*n + 5*n + 2 - n - 17*n**3. Let a(k) = 2*p(k) - 5*q(k). Find g such that a(g) = 0.
-1/3, 0, 1
Let f be (10/8)/5 - (-16044)/(-10224). Let z = 1/71 - f. Factor -z*n + 2/3*n**2 + 0.
2*n*(n - 2)/3
Let c be (-6 - -2 - -9)*1. Factor -c*g + 15*g + 15*g**3 + 4*g**2 - 29*g**2.
5*g*(g - 1)*(3*g - 2)
Let d = -97 + 99. Suppose -d*w + 8 - 8 = 0. Factor -x**2 + 0 + 1/2*x**5 - 3/2*x**3 + w*x**4 + 0*x.
x**2*(x - 2)*(x + 1)**2/2
Suppose w - 5 = -3*j - 0*j, j + 2 = -4*w. Factor 89*k - k**4 - 184*k - j*k**3 + 95*k - k**2.
-k**2*(k + 1)**2
Let w(p) be the second derivative of -p**8/40320 + p**6/4320 + 11*p**4/6 + 3*p. Let m(k) be the third derivative of w(k). Factor m(g).
-g*(g - 1)*(g + 1)/6
Let n(m) be the third derivative of m**8/840 + 272*m**7/525 + 2312*m**6/25 + 628864*m**5/75 + 5345344*m**4/15 - 245*m**2. Solve n(p) = 0 for p.
-68, 0
Find u such that -18/7*u**5 - 48/7*u**4 - 26/7*u**3 + 0 + 0*u - 4/7*u**2 = 0.
-2, -1/3, 0
Let y(w) be the first derivative of -w**4/6 + 2*w**3/3 - 16*w + 18. Let o(q) be the first derivative of y(q). Suppose o(s) = 0. What is s?
0, 2
Factor -35 - 2*h**2 + 7*h**2 + 9*h - h - 38*h.
5*(h - 7)*(h + 1)
Let f(p) be the third derivative of 2/105*p**7 - 15*p**2 - 1/168*p**8 + 0*p**3 + 0 + 0*p**4 + 0*p + 0*p**6 + 0*p**5. Factor f(r).
-2*r**4*(r - 2)
Let n(g) = 11*g**2 + 704*g + 43200. Let s(o) = -4*o**2 - 234*o - 14400. Let r(m) = -3*n(m) - 8*s(m). Factor r(z).
-(z + 120)**2
Let j(i) = -10*i + 62. Let n be j(6). Factor -838 + 33*k**2 - 27*k**3 - n*k - 4*k + 838.
-3*k*(k - 1)*(9*k - 2)
Let l(b) be the first derivative of 1/3*b**3 + 25*b + 22 - 5*b**2. Determine p so that l(p) = 0.
5
Let a(h) = -2*h**3 + 2*h**2 + 18*h - 28. Let w be a(2). Factor w*u + 1/4*u**2 + 0.
u**2/4
Suppose 8 = -7*r + 9*r. Factor -24*z**3 - 41*z**4 - 37*z - 52*z**2 + 37*z**r - 11*z - 16.
-4*(z + 1)**2*(z + 2)**2
Let x be 1/(-36)*1*(8 + -11). Let l(f) be the second derivative of 1/6*f**3 - 3*f + 0*f**2 + x*f**4 + 0. Find t such that l(t) = 0.
-1, 0
Factor 1/5*f**3 - 1 + f**2 - 1/5*f.
(f - 1)*(f + 1)*(f + 5)/5
Let n(j) = -5*j + 53. Let w be n(12). Let h be (-63)/27*16/w. Factor 4/3*m + 0 + 7*m**3 + 3*m**4 + h*m**2.
m*(m + 1)*(3*m + 2)**2/3
Let o(n) be the second derivative of 2*n**6/15 - 9*n**5/5 + 9*n**4 - 18*n**3 - 55*n. Factor o(g).
4*g*(g - 3)**3
Let i(h) be the third derivative of 1/240*h**6 + 0*h - 1/120*h**5 - 12*h**2 + 0 + 1/420*h**7 - 1/48*h**4 + 0*h**3. Factor i(o).
o*(o - 1)*(o + 1)**2/2
Let r be -17 - 6*(-4)/8. Let p = r + 19. Let 486*h**2 + 12 - 729*h**3 + 1 - p - 108*h = 0. What is h?
2/9
Let m(d) = -4*d - 53. Let z be m(-14). Let t(n) be the first derivative of 2/15*n**z + 5 - 2/5*n + 1/5*n**2 - 1/10*n**4. Solve t(w) = 0.
-1, 1
Let y(q) be the third derivative of q**6/60 - q**4/3 + 64*q**2. Factor y(o).
2*o*(o - 2)*(o + 2)
Factor 1/5*x**5 + 117/5*x - 88/5*x**2 - 44/5 + 2/5*x**3 + 12/5*x**4.
(x - 1)**3*(x + 4)*(x + 11)/5
Let z(u) be the second derivative of u**7/70 - u**6/20 + u**4/4 - u**3/2 + 7*u**2 - u. Let c(x) be the first derivative of z(x). Factor c(d).
3*(d - 1)**3*(d + 1)
Let k(f) be the second derivative of -f**6/240 - f**5/40 + f**4/48 + f**3/4 + 2*f**2 + 24*f. Let y(a) be the first derivative of k(a). Factor y(c).
-(c - 1)*(c + 1)*(c + 3)/2
Let l be (((-104060)/(-40))/(-43))/(-1). Factor -l - 1/2*v