e the second derivative of -1/2*z**3 + 5*z**2 - 1/12*z**4 + 54*z + 0. Factor o(p).
-(p - 2)*(p + 5)
Let y(g) = -12*g - 10. Let b be y(-1). Let t(a) be the second derivative of 7*a + 0 + 0*a**5 + 0*a**3 - 1/24*a**4 + 1/60*a**6 + 0*a**b. Factor t(v).
v**2*(v - 1)*(v + 1)/2
Let n(b) be the second derivative of b**4/12 - 19*b**3/6 + 3*b**2/2 + 8*b. Let s be n(19). Factor -2/5*g**s + 0*g**4 + 0*g**2 + 1/5*g + 1/5*g**5 + 0.
g*(g - 1)**2*(g + 1)**2/5
Suppose 18 - 18 = 59*i + 32*i. Factor -1/6*x**2 + i + 0*x + 1/6*x**3.
x**2*(x - 1)/6
Let l(g) be the second derivative of 3*g**5/20 + 47*g**4/4 + 67*g**3 + 132*g**2 - 190*g. Factor l(b).
3*(b + 1)*(b + 2)*(b + 44)
Let u(d) be the third derivative of -d**7/840 - d**6/120 - 19*d**4/24 - 30*d**2. Let r(s) be the second derivative of u(s). Solve r(a) = 0.
-2, 0
Let i(x) be the second derivative of -x**6/120 - x**5/20 - x**4/8 - 2*x**3/3 + 19*x. Let w(u) be the second derivative of i(u). Factor w(a).
-3*(a + 1)**2
Factor 14568*m**3 + 0*m**4 + m**4 - 14573*m**3 + 7*m**2 - 3*m.
m*(m - 3)*(m - 1)**2
Let u be (-1)/((2/3)/(12/(-9))). Let c be u/8*(-2 + (-28)/(-2)). Factor -1/8*g + 1/8*g**c - 1/8 + 1/8*g**2.
(g - 1)*(g + 1)**2/8
Let q(d) = -5*d**3 + 54*d**2 - 41*d - 28. Let j(b) = 2*b**3 - 56*b**2 + 42*b + 28. Let u(l) = -5*j(l) - 4*q(l). Determine k so that u(k) = 0.
-7, -2/5, 1
Let h(k) be the third derivative of k**6/660 + 17*k**5/330 + 8*k**4/11 + 60*k**3/11 + 15*k**2 - 2. Determine j so that h(j) = 0.
-6, -5
Let q(h) = h**2 - 19*h + 81. Let f be q(13). Let d(y) be the first derivative of -5/12*y**4 + 0*y + 1/3*y**f + 1/3*y**2 + 4. Factor d(o).
-o*(o - 1)*(5*o + 2)/3
Let s(o) = -5*o**3 + 4*o**2 + 20*o - 40. Let w(y) = -10*y**3 + 7*y**2 + 40*y - 80. Let k(t) = -13*s(t) + 6*w(t). Determine p, given that k(p) = 0.
-2, 2
Determine p, given that 41*p**2 + 0*p**3 - 3*p**3 - 35*p**2 - 3*p**4 = 0.
-2, 0, 1
Let l(f) = 12*f**2 + 13*f + 11*f - 18*f**2 - 24. Let p(z) = -3*z**2 + 12*z - 12. Let j(s) = 4*l(s) - 9*p(s). Find d such that j(d) = 0.
2
Let k(l) be the third derivative of l**8/168 - l**7/35 - l**6/15 + 8*l**5/15 - 16*l**3/3 + 2*l**2 - 110*l. Factor k(m).
2*(m - 2)**3*(m + 1)*(m + 2)
Let n be 3 + ((-56)/20)/1. Solve 0*u + 0 - 1/10*u**3 - n*u**2 = 0 for u.
-2, 0
Let a(i) be the third derivative of 2*i**4/3 - 40*i**3/3 - 32*i**2. Let x be a(5). Factor 4/5*b**3 + 0*b + x + 14/5*b**4 + 0*b**2.
2*b**3*(7*b + 2)/5
Let l(x) be the second derivative of x**9/756 - 3*x**8/280 + x**7/35 - x**6/45 + 17*x**3/6 - 22*x. Let v(b) be the second derivative of l(b). Solve v(z) = 0.
0, 1/2, 2
Let z = -94 + 225. Let y = z + -652/5. Let -y*v + 2/5 + 1/5*v**2 = 0. What is v?
1, 2
Let g(f) be the first derivative of -f**4/20 - 118*f**3/5 - 20886*f**2/5 - 1643032*f/5 - 100. Determine x, given that g(x) = 0.
-118
Let r(k) = -4*k**3 + 4*k**2 + 4*k - 12. Let w(q) = 3*q**3 - 3*q**2 - 3*q + 8. Let x(o) = 5*r(o) + 8*w(o). Let x(p) = 0. Calculate p.
-1, 1
Suppose 5 + 3 = 5*x - 4*u, 4*x - 4 = 2*u. Let r(i) be the second derivative of -1/66*i**4 + 2/33*i**3 - 7*i - 1/11*i**2 + x. Find b such that r(b) = 0.
1
Let r(n) be the second derivative of -n**5/70 - 10*n**4/21 + 53*n. Suppose r(y) = 0. Calculate y.
-20, 0
Determine j, given that 2*j**3 + j + 16*j**2 - 6*j**3 - 2*j**3 + 10*j**3 + 11*j = 0.
-3, -1, 0
Let q be -5 - (377/957)/((-14)/(-15) - 1). Factor -1/11*w**3 + 0 - q*w**2 - 25/11*w.
-w*(w + 5)**2/11
Let n(b) be the third derivative of -b**6/150 + 12*b**5/25 - 19*b**4/2 - 1444*b**3/15 + 2*b**2 - 44*b. Find z, given that n(z) = 0.
-2, 19
Let f(u) = u**2 - 5*u - 11. Let j be f(7). Determine l so that 4*l**4 + 14*l**2 - 17*l**3 - 2*l**j - 16*l - l**3 + 18*l**2 = 0.
0, 1, 2
Let z(x) be the second derivative of -x**4/24 + x**2/4 - 18*x + 2. Suppose z(a) = 0. Calculate a.
-1, 1
Let b be ((-84)/((-434)/31))/(12/10). Suppose -1/4*z**b + 0*z**3 + 0 + 1/4*z + 1/2*z**2 - 1/2*z**4 = 0. Calculate z.
-1, 0, 1
Let j(s) = 2*s**3 - 4*s**2 + 2*s + 1. Let g be j(2). Solve g*m**3 - 36*m + 85*m + 20*m**2 - 29*m = 0 for m.
-2, 0
Let l(b) be the first derivative of -b**4/20 - 4*b**3/5 - 29*b**2/10 - 18*b/5 + 53. Suppose l(h) = 0. What is h?
-9, -2, -1
Let o be 272/18*12/80. Let i = o - 21/10. Factor -1/3*d**2 + i*d**5 + 1/3 - 2/3*d**3 + 1/2*d + 0*d**4.
(d - 2)*(d - 1)*(d + 1)**3/6
Suppose -9*k**2 + 211*k + 4*k**2 - 151*k = 0. Calculate k.
0, 12
Let w(i) be the third derivative of i**5/15 - i**4/2 + 4*i**3/3 + 41*i**2 - 1. Factor w(s).
4*(s - 2)*(s - 1)
Let l = -34/113 + 8273/27120. Let w(v) be the third derivative of 0*v**3 + 0*v + 0*v**4 + 0*v**5 + 1/672*v**8 + 10*v**2 - 1/210*v**7 + 0 + l*v**6. Factor w(m).
m**3*(m - 1)**2/2
Let w = 149 - 144. Let l(p) be the first derivative of 1/21*p**3 + 2/7*p**2 + 4/7*p + w. Factor l(i).
(i + 2)**2/7
Let f be 1 + (52 - 53) + (-2)/(-9)*3. Factor -1/6*v**3 - 1/3 - f*v**2 - 5/6*v.
-(v + 1)**2*(v + 2)/6
Let n(c) be the second derivative of -c**6/90 - 19*c**5/30 - 128*c. Factor n(q).
-q**3*(q + 38)/3
Suppose -7*q + 55*q = 0. Let v(g) be the second derivative of 1/5*g**5 + q*g**3 + 0*g**2 + 0 + 5/3*g**4 - 14*g. Factor v(y).
4*y**2*(y + 5)
Let o(h) be the second derivative of h**5/100 - 7*h**4/60 + h**3/2 - 9*h**2/10 - h - 12. Factor o(c).
(c - 3)**2*(c - 1)/5
Suppose 2*g - 10 = 2*x, g - 2*g + 11 = -3*x. Let m(y) be the third derivative of -4/33*y**3 - 10*y**g + 0*y + 1/330*y**5 + 1/44*y**4 + 0. Factor m(u).
2*(u - 1)*(u + 4)/11
Factor 4/3 - 1/3*i**2 - 2/3*i**3 + 8/3*i.
-(i - 2)*(i + 2)*(2*i + 1)/3
Let o(m) = -7*m - 10. Let j be o(-2). Factor 0*v**3 - v**j - v**3 - 2*v**3 + 59*v**2 - v - 62*v**2.
-v*(v + 1)**3
Let a(j) be the third derivative of -j**6/60 + 79*j**5/15 + j**4/12 - 158*j**3/3 - 190*j**2 + 2*j. What is k in a(k) = 0?
-1, 1, 158
Let w = 16638 + -16638. Factor w*y - 12*y**4 + 8/3*y**2 + 0 - 28/3*y**3.
-4*y**2*(y + 1)*(9*y - 2)/3
Let g be (-1 - 3)*(-5)/10. Let r be ((-10)/25)/(g/(-120)). Let -16*y**5 + 3*y**2 + r*y**4 - 9*y**5 - 23*y**5 + 21*y**3 = 0. Calculate y.
-1/4, 0, 1
Let q(n) be the first derivative of -n**4/4 + n**2/2 + 209. Factor q(s).
-s*(s - 1)*(s + 1)
Solve 0 + 1/2*p + 1/4*p**2 = 0 for p.
-2, 0
Factor -246*w + 17*w**2 + 494*w - 266*w + w**3.
w*(w - 1)*(w + 18)
Suppose 7 - 11*n**3 - 11*n**4 - 27*n**2 - 14*n**3 - 5*n - 5 - 6*n**3 = 0. Calculate n.
-1, 2/11
Suppose 2*h - 17 = -17. Let s(v) be the first derivative of -1/15*v**3 + 1/5*v + 3 + h*v**2. Find g such that s(g) = 0.
-1, 1
Find v, given that 2 + 2*v**2 - 6*v + 7 - 6 + 1 = 0.
1, 2
Suppose -5*k - 35 = -12*k. Let u be (-456)/(-90) + -4 - 2/k. Let 0 - u*j - 2/3*j**3 - 4/3*j**2 = 0. What is j?
-1, 0
Let p(t) be the second derivative of 0*t**2 - 1/3*t**4 + 0 - 24*t - 2/3*t**3. Factor p(w).
-4*w*(w + 1)
Suppose -3*c + 8 = v, 0 = c + 4*v + v - 12. Factor -10*n**3 + 15*n**4 - 5 - 5*n**5 + 0*n + 15*n - 9*n**c + 0*n**3 - n**2.
-5*(n - 1)**4*(n + 1)
Let 1/9*h**2 - 1/3*h + 0 = 0. What is h?
0, 3
Let f = -38507/2994 - -14/499. Let l = 599/42 + f. Determine y so that -2/7*y**5 + 0 - l*y**3 - 8/7*y**4 + 0*y - 4/7*y**2 = 0.
-2, -1, 0
Let b(m) = m**2 - m + 1. Let w(f) = -12*f**2 + 18*f - 14. Suppose -2*d + 140 = -7*d. Let k(n) = d*b(n) - 2*w(n). Factor k(i).
-4*i*(i + 2)
Suppose 5 - 21 = -8*v. Suppose v*q - 5*f - 39 = -15, -4*f - 14 = q. Find j, given that 2/5 + 2/5*j**q - 4/5*j = 0.
1
Let i(n) = -23*n**2 - 3*n. Let f be i(-1). Let c = f + 25. Factor -y**c - 8/3*y**4 - 2*y**3 + 0*y**2 + 0 + 1/3*y.
-y*(y + 1)**3*(3*y - 1)/3
Let u(n) be the first derivative of 3*n**5/20 + 21*n**4/16 + 3*n**3/2 + 158. Factor u(b).
3*b**2*(b + 1)*(b + 6)/4
Let j(b) be the second derivative of -2*b**7/21 + 4*b**6/15 + 3*b**5/5 - 4*b**4/3 - 8*b**3/3 + 34*b. Solve j(o) = 0 for o.
-1, 0, 2
Let m(g) = 2*g**2 - 3*g - 4. Let y be m(3). Suppose -y*u = -9*u + 64. Factor u + 12*a**2 - 7*a**3 + 8*a**3 + 24*a + a**3.
2*(a + 2)**3
Suppose 5/2*p**2 + 195/2*p + 0 = 0. What is p?
-39, 0
Let w = 160/9 - 976/63. Let i be (-17)/(714/(-36)) + (216/63 - 4). Factor i*p**2 + 32/7 - w*p.
2*(p - 4)**2/7
Let m be 14/(-70) - 66/(-5). Suppose -5*s - 20 = 5*n, -m = 2*n + 4*s + 3. Let n*q**3 + 3*q**2 - 19*q**2 - 6*q**3 - 16*q + 2*q**3 = 0. Calculate q.
-2, 0
Let p be (-42)/(-12) - 4 - (-270)/60. Solve 2/21*s**p + 0 + 0*s - 20/21*s**3 + 50/21*s**2 = 0.
0, 5
Let t(i) be the first derivative of 6 + 0*i + 1/30*i**5 + 0*i**