be the second derivative of 0*u**2 + 1/27*u**3 + 1/54*u**4 + u + 0. Factor p(j).
2*j*(j + 1)/9
Let q(t) be the first derivative of 0*t + 0*t**2 + 1/8*t**4 - 1/3*t**3 + 0*t**5 - 1/120*t**6 - 1. Let p(n) be the third derivative of q(n). Factor p(y).
-3*(y - 1)*(y + 1)
Let f = -23 + 20. Let o = 1 - f. Suppose o*t**3 - 4*t**3 + 2*t**4 + 4*t**3 + 3*t**5 - 5*t**5 = 0. What is t?
-1, 0, 2
Suppose -3*b = 2*k - 36, -5*b + 4*k + 38 = -0*k. Let 16*c - 7*c + c**2 - b*c = 0. What is c?
0, 1
Factor -1/3*d**2 + 2 - 1/3*d.
-(d - 2)*(d + 3)/3
Let v(w) be the second derivative of w**9/1008 - 3*w**8/560 + 3*w**7/280 - w**6/120 + 4*w**3/3 + 12*w. Let s(q) be the second derivative of v(q). Factor s(k).
3*k**2*(k - 1)**3
Let b(s) be the first derivative of 1/4*s**4 + 8 + 0*s + 2/3*s**3 - 2*s**2. Let l(u) = u**2. Let j(z) = 3*b(z) - 6*l(z). Factor j(v).
3*v*(v - 2)*(v + 2)
Let h be (6 - -1) + -10 + 5. Factor -m**5 - 2*m**4 + m + 3*m**2 - 7*m**2 + 6*m**h + 0*m**4.
-m*(m - 1)*(m + 1)**3
Suppose 9*z**2 - 6*z + 3/2 - 6*z**3 + 3/2*z**4 = 0. What is z?
1
Let p(o) = 7*o**3 - o**2 - o - 1. Let x(y) = -48*y**3 + 20*y**2 - 23*y + 7. Let l(s) = -14*p(s) - 2*x(s). Let l(h) = 0. What is h?
-15, 0, 2
Let s(n) be the second derivative of -n**6/720 + n**5/72 - n**4/36 - 35*n**2/2 - 4*n - 4. Let j(x) be the first derivative of s(x). Find z, given that j(z) = 0.
0, 1, 4
Let n(p) be the third derivative of -p**6/420 + p**5/14 - 3*p**4/4 + 27*p**3/7 - p**2 + 2. Solve n(s) = 0.
3, 9
Let a be ((-585)/(-525))/((-4)/(-28)). Let -18/5*h**3 - a*h**2 - 36/5*h - 3/5*h**4 - 12/5 = 0. Calculate h.
-2, -1
Suppose -d - 6*d = 0. What is y in d*y + 0 + y**3 - 2/3*y**2 = 0?
0, 2/3
Let l = 9237/2 + -4618. Factor -1/8*x**5 + 0 - 1/2*x**4 - 3/4*x**3 - l*x**2 - 1/8*x.
-x*(x + 1)**4/8
Let x(r) be the third derivative of -1/30*r**4 + 1/105*r**7 + 0*r**3 + 7/150*r**5 - 3/100*r**6 + 0*r - 1/840*r**8 + 0 + 32*r**2. Find b such that x(b) = 0.
0, 1, 2
Let r(c) be the second derivative of -c**5/90 + 31*c**4/27 + 127*c**3/27 + 64*c**2/9 + 44*c. Let r(f) = 0. What is f?
-1, 64
Let a be 16/(-28)*(-15)/2 + -4. Suppose 5*p = -5*l - 5, 3*p + p = l + 1. Factor 4/7*d**2 + p*d + 0 - a*d**3.
-2*d**2*(d - 2)/7
Let l(q) be the third derivative of q**9/28350 + q**8/10080 + q**7/18900 + q**4/4 - 10*q**2. Let v(c) be the second derivative of l(c). Factor v(u).
2*u**2*(u + 1)*(4*u + 1)/15
Suppose 0 = 2*c + 2*h - 8, -2*c - h = c - 8. Factor -2*q + 32 + c*q**2 + 15*q - 3*q + 6*q.
2*(q + 4)**2
Factor 15/8*d**3 - 13/8*d**2 + 7/4 - 1/8*d**4 - 15/8*d.
-(d - 14)*(d - 1)**2*(d + 1)/8
Let i(k) = -k**4 - 20*k**3 + 5*k**2 + 72*k + 50. Let w(a) = -2*a**4 - a**3 + a**2 + 1. Let c(j) = i(j) - 2*w(j). Solve c(o) = 0 for o.
-1, 4
Suppose -2*n = 8, 0*n + 2*n = 4*x + 88. Let h be 128/(-48)*x/2. Factor -h*g - 35*g**2 + 38*g**2 + 25*g**2 - 4*g**3 - 64.
-4*(g - 4)**2*(g + 1)
Let a(g) be the second derivative of -g**2/2 - 3*g. Let d(u) be the first derivative of -2*u**3/3 - 2*u**2 - 5*u - 28. Let o(z) = 5*a(z) - d(z). Factor o(f).
2*f*(f + 2)
Let l = -8321 - -24965/3. Find i, given that -6 - l*i**2 - 4*i = 0.
-3
Let q(z) be the third derivative of -5*z**8/112 + 2*z**7/5 - 7*z**6/10 - 4*z**5/5 + 11*z**2 - 3*z. Find f such that q(f) = 0.
-2/5, 0, 2, 4
Let m(s) = -5*s**2 - 30*s + 27. Let n(p) = -p**2 - 7*p - 2. Let j(k) = m(k) - 4*n(k). Determine a so that j(a) = 0.
-7, 5
Suppose -23*c + 21*c = -25*c + 46. Let -32/15*r**c + 32/15*r + 2/5*r**4 - 8/15*r**3 + 32/15 = 0. What is r?
-2, -2/3, 2
Let u = 7 - 3. Suppose -2*x = -0*t + t, -u*x = t + 2. Factor 9/2 - 3*h + 1/2*h**t.
(h - 3)**2/2
Suppose 4 = i, 2*z - i = -1 - 1. Suppose g = 5*x - z, -5*g - x + 5 + 16 = 0. Factor -2*y**2 + 4*y**2 - g*y + 0*y**2.
2*y*(y - 2)
Let g(m) = -9*m**2 - 25*m + 9. Let d(c) = 5*c**2 + 11*c - 4. Let x(h) = -5*d(h) - 2*g(h). Let x(y) = 0. Calculate y.
-1, 2/7
Suppose 0 = -0*w + 3*w. Let q be 5 - (2 + w + 1). Solve -x + 4*x**2 - x**q - 4*x**2 = 0 for x.
-1, 0
Factor -9/4*l**2 - 33/4*l + 3/2*l**3 + 9/2.
3*(l - 3)*(l + 2)*(2*l - 1)/4
Let v be ((-2)/(-20))/(-1*11/(-88)). Factor -2/5*u**2 + v + 2/5*u.
-2*(u - 2)*(u + 1)/5
Let p(x) = 27*x + 29. Let j be p(-1). Let a(g) be the second derivative of 0*g**j + 0 - 4/3*g**3 - 5/3*g**4 + 2/3*g**6 - 4*g + 2/5*g**5. Factor a(o).
4*o*(o - 1)*(o + 1)*(5*o + 2)
Factor 12*z**3 - 8*z**2 + 13*z**5 + 11*z**5 - 5*z**5 - 23*z**5.
-4*z**2*(z - 1)**2*(z + 2)
Let k(y) = 5*y**3 - 32*y**2 - 3*y + 3. Let x(z) = -15*z**3 + 97*z**2 + 8*z - 8. Suppose -7*f - 88 = 4*f. Let j(a) = f*k(a) - 3*x(a). Solve j(i) = 0.
0, 7
Determine x, given that 60*x**4 + 6*x + 59*x**4 + 12*x**2 + 58*x**4 - 9 - 6*x**3 + 57*x**4 - 237*x**4 = 0.
-3, -1, 1
Let r(z) = z**2 - z - 2. Let d(g) = -g**2 + 2*g + 1. Let w(i) = 5*d(i) + 4*r(i). Let y be w(5). Factor 8*k**4 - 3*k - k - 11*k**2 + 4*k**5 + 2*k**y + k**2.
4*k*(k - 1)*(k + 1)**3
Solve -2904 + d**2 - 24*d**3 + 1214*d + 26*d**3 - 45*d**2 + 18*d - 50*d**2 = 0 for d.
3, 22
Let s be 23 - 19 - (2 + -4). Find z, given that -51*z**2 - s*z - 35 - 39 + 74 = 0.
-2/17, 0
Let k(m) be the first derivative of -9*m**5/20 + 5*m**4/2 - 9*m**3/2 + 3*m**2 - 18*m - 2. Let x(j) be the first derivative of k(j). Factor x(p).
-3*(p - 2)*(p - 1)*(3*p - 1)
Factor 3/7*c**2 - 1/7*c**4 - 5/7*c + 2/7 + 1/7*c**3.
-(c - 1)**3*(c + 2)/7
Suppose 5547/5*l**4 - 4104/5*l + 86691/5*l**2 + 48/5 + 44118/5*l**3 = 0. Calculate l.
-4, 1/43
Determine s so that -2*s**3 + 4*s**3 + 32*s - 34*s - 116*s**2 + 16 - 236*s - 136 = 0.
-1, 60
Let d(a) be the third derivative of a**6/420 - a**5/21 - 61*a**4/84 + 10*a**3/3 - 403*a**2. Factor d(b).
2*(b - 14)*(b - 1)*(b + 5)/7
Suppose 29*z = 22*z - 14. Let r be (-16)/6 - z - 4/(-6). Factor 2/3*m + r - m**2 + 1/3*m**3.
m*(m - 2)*(m - 1)/3
Let a(b) be the third derivative of 0*b**3 + 7*b**2 - 1/12*b**5 + 0 + 0*b - 25/24*b**4. Let a(h) = 0. What is h?
-5, 0
Suppose -8 = -3*b - b. Suppose 2*s = 4, 0 = -b*k - 0*k - 4*s + 12. Solve 8*u + 0 + k*u**2 - 6*u**2 + 0 = 0.
0, 2
Find o, given that 0 + 3*o + 1/2*o**2 = 0.
-6, 0
Let g(n) be the third derivative of 0 + 2*n - 1/15*n**5 + 0*n**4 - 2*n**2 + 2/105*n**7 + 0*n**6 + 0*n**3. Factor g(y).
4*y**2*(y - 1)*(y + 1)
Let g = -23/26 - -44/13. Factor -4*q - 2 - g*q**2 - 1/2*q**3.
-(q + 1)*(q + 2)**2/2
Let s(n) = -3*n**2 + 40*n - 78. Let v(t) = -15*t + 21 + 56 - 40*t + 15*t + 2*t**2. Let y(j) = 3*s(j) + 2*v(j). Factor y(r).
-5*(r - 4)**2
Let z(y) = -31*y**4 - 249*y**3 - 463*y**2 - 275*y - 38. Let x(d) = 123*d**4 + 996*d**3 + 1851*d**2 + 1101*d + 153. Let s(h) = 4*x(h) + 15*z(h). Factor s(k).
3*(k + 1)**2*(k + 7)*(9*k + 2)
Let x be (-7 - (-2 + -3)) + 7 + -3. Factor 7/2*o + 5/2*o**x + 1.
(o + 1)*(5*o + 2)/2
Let c(u) = -14*u**2 + 36*u + 26. Let x(j) = 16*j**2 - 37*j - 25. Let z(m) = 7*c(m) + 6*x(m). Let z(s) = 0. Calculate s.
-1, 16
Let t(f) be the second derivative of -f**5/5 - f**4 + 8*f**3/3 - 339*f. Find l such that t(l) = 0.
-4, 0, 1
Let n(k) = -k**2 + 9*k - 18. Let d be n(4). Factor -18*g**3 - 45*g - 32*g**3 - 120*g**d + 4*g**3 - 34*g**3.
-5*g*(4*g + 3)**2
Let d = 16392 - 16388. Find g such that 1/5*g**3 - 1/5*g - 2/5*g**2 + 2/5*g**d + 0 = 0.
-1, -1/2, 0, 1
Find r such that 14/3*r**3 + 0*r - 2/3*r**4 - 4*r**2 + 0 = 0.
0, 1, 6
Let 8/9*a + 0 + 4/9*a**3 - 4/3*a**2 = 0. Calculate a.
0, 1, 2
Solve 10/17*c**4 - 2/17*c**5 + 0*c + 0 + 6/17*c**2 - 14/17*c**3 = 0 for c.
0, 1, 3
Let i(p) be the first derivative of 0*p + 0*p**2 + 5 - 2/3*p**3 + 0*p**4 - 1/90*p**6 - 1/60*p**5. Let h(k) be the third derivative of i(k). Factor h(j).
-2*j*(2*j + 1)
Let f = 35 - 32. Let l be ((-75)/45)/((-1)/f). Factor -a**l - 3*a**3 + 3*a**4 - 3*a**2 + 5*a**2 - 5*a**2 + 2*a + 2*a**3.
-a*(a - 2)*(a - 1)**2*(a + 1)
Suppose h - 28 = -h. Factor -h*x**2 - 6*x + 13*x**4 - 7*x**4 - 10*x**3 - 8*x**4.
-2*x*(x + 1)**2*(x + 3)
Let h(r) be the first derivative of -7*r**6/90 - r**5/9 + r**4/9 - 5*r**2 + 10. Let d(c) be the second derivative of h(c). Let d(v) = 0. Calculate v.
-1, 0, 2/7
Determine s, given that -3/2*s**4 - 1/2*s**3 + 0 + s - 1/2*s**5 + 3/2*s**2 = 0.
-2, -1, 0, 1
Let z(r) be the second derivative of -2*r**7/105 - r**6/10 - r**5/15 + r**4/2 + 4*r**3/3 - 4*r**2 - 4*r. Let b(h) be the first derivative of z(h). Factor b(k).
-4*(k - 1)*(k + 1)**2*(k + 2)
Let y(u) be the third derivative of u**5/100 + 27*u**4/10 + 1458*u**3/5 + 2*u**2 + 