-4 - -7). Let u(t) be the second derivative of -4/27*t**3 + 0 - 4/9*t**y - 1/54*t**4 - 5*t. Factor u(k).
-2*(k + 2)**2/9
Let -234*j**3 - 106*j**3 - 164*j**2 + 318*j**2 + 10*j**5 + 46*j**4 + 334*j**2 - 144*j = 0. Calculate j.
-9, 0, 2/5, 2
Factor 3/2*l**2 - 9*l + 0.
3*l*(l - 6)/2
Let q(s) be the second derivative of s**6/30 + s**5/15 - 3*s**2/2 + 12*s. Let k(w) be the first derivative of q(w). Factor k(p).
4*p**2*(p + 1)
Let n = 329/8 + -3491/88. Let g(s) = s**2 - 12*s - 26. Let a be g(14). Factor 8/11 + n*w + 6/11*w**a.
2*(w + 2)*(3*w + 2)/11
Let b(q) be the second derivative of q**6/30 + 52*q**5/5 + 1352*q**4 + 281216*q**3/3 + 3655808*q**2 + 94*q. Factor b(c).
(c + 52)**4
Let y(f) be the second derivative of -2*f**6/45 + 11*f**5/90 + f**4/27 - 11*f**3/27 + 4*f**2/9 - 184*f. Let y(u) = 0. Calculate u.
-1, 1/2, 1, 4/3
Factor 4*o**2 - 210 + 0*o**2 + 427 - 29*o**2 + 15*o - 207.
-5*(o - 1)*(5*o + 2)
Let b(t) be the second derivative of -t**5/10 + t**4/6 + 10*t**3/3 + 8*t**2 - 109*t. Factor b(y).
-2*(y - 4)*(y + 1)*(y + 2)
Let y(w) = -w**3 - 14*w**2 + 13*w - 27. Let t be y(-15). Factor -5*z**4 + 6*z - 9*z**2 - 16*z + 2*z + 10*z + 12*z**t.
-z*(z - 1)**2*(5*z - 2)
Factor -729/4*x**2 - 2187*x + 69/4*x**4 + 3/4*x**5 + 0 + 405/4*x**3.
3*x*(x - 4)*(x + 9)**3/4
Let m = 543691/111705 - 1539/677. Let w = m + 4/55. Factor w*f - 8/3 - 2/3*f**2.
-2*(f - 2)**2/3
Let c(b) = 422*b**2 - 7*b + 3. Let n(i) = 422*i**2 - 8*i + 4. Let t(f) = -4*c(f) + 3*n(f). Determine s, given that t(s) = 0.
0, 2/211
Let j = -15 - -19. Let y = 8 - j. Let -5*f**2 + 0*f**2 + y*f**4 - 3*f**2 + 8*f - 4*f**2 = 0. Calculate f.
-2, 0, 1
Let w(d) be the second derivative of d**8/84 - 2*d**7/35 + d**6/15 + 4*d**2 + 21*d. Let u(n) be the first derivative of w(n). Suppose u(v) = 0. What is v?
0, 1, 2
Let v(g) be the third derivative of -1/420*g**6 + 0*g + 1/105*g**5 - 25*g**2 + 1/28*g**4 + 0 + 0*g**3. Let v(w) = 0. What is w?
-1, 0, 3
Let t(b) be the first derivative of 2*b**7/21 + 4*b**6/15 + b**5/5 + 5*b + 26. Let f(h) be the first derivative of t(h). Suppose f(p) = 0. What is p?
-1, 0
Suppose 0 = 297*q - 295*q. Let g(h) be the second derivative of q + 5*h + 1/24*h**4 + 0*h**2 + 1/12*h**3. Factor g(d).
d*(d + 1)/2
Factor 72/7*i**2 + 112 + 4/7*i**3 + 60*i.
4*(i + 4)*(i + 7)**2/7
Suppose 0*o**2 + 9/2*o**3 + 0*o - 21/4*o**4 + 0 = 0. Calculate o.
0, 6/7
Let r(x) be the first derivative of 5*x**4/2 + 25*x**3 + 60*x**2 - 80*x - 13. Let r(o) = 0. Calculate o.
-4, 1/2
Find a such that 1/2*a**3 - 3*a**2 + 5/2*a + 0 = 0.
0, 1, 5
Let d(h) be the first derivative of -8 + h**2 + 0*h + 0*h**3 - 1/2*h**4. Find m, given that d(m) = 0.
-1, 0, 1
Let o(f) be the second derivative of f**7/1470 - 2*f**6/315 + 2*f**5/105 + 2*f**3 - 3*f. Let j(n) be the second derivative of o(n). Let j(k) = 0. What is k?
0, 2
Suppose -25*a = 2*a - 108. Suppose -a*r = -5*r - r. Suppose 0*b**2 - 3/2*b - 3/2*b**5 + 0*b**4 + r + 3*b**3 = 0. What is b?
-1, 0, 1
Let v(n) = -10*n**2 + 76*n - 69. Let f(x) = 28*x**2 - 228*x + 208. Let d(o) = 3*f(o) + 8*v(o). Find j, given that d(j) = 0.
1, 18
Let c(b) = -3*b**2 + 14*b + 9. Let s(o) = -10*o**2 + 55*o + 35. Let n(a) = 15*c(a) - 4*s(a). Factor n(q).
-5*(q + 1)**2
Let j(r) be the third derivative of -r**8/3360 - r**7/630 - r**6/360 + 23*r**4/24 + 2*r**2. Let f(k) be the second derivative of j(k). Factor f(t).
-2*t*(t + 1)**2
Suppose -20 = 12*n - 56. Let g(q) be the first derivative of -12*q**2 + 11/2*q**4 - 5/3*q**6 - 5 + 24/5*q**5 + 16*q - 52/3*q**n. Suppose g(a) = 0. What is a?
-1, 2/5, 2
Let k = -23 + 26. Determine n so that -2*n**2 + 4*n - 6*n + n - n**k = 0.
-1, 0
Find x, given that -55*x**3 - 7*x**2 + x**4 - 34*x + 24 + 4*x**2 + 114*x**3 - 47*x**3 = 0.
-12, -2, 1
Let v(h) be the third derivative of h**8/8400 + h**7/4200 - h**6/1800 - h**5/600 + 4*h**3/3 - 13*h**2. Let s(f) be the first derivative of v(f). Factor s(m).
m*(m - 1)*(m + 1)**2/5
Let i(c) be the first derivative of 2/21*c**6 - 1/7*c**5 - 1/14*c**2 + 0*c - 3/28*c**4 - 7 + 5/21*c**3. Suppose i(n) = 0. What is n?
-1, 0, 1/4, 1
Suppose 0 = v - 5*t - 12, t = 2*v + 4*t - 24. Factor -8 - 3*c**3 + 63*c**2 + v*c + 29*c**2 - 45*c**3.
-4*(c - 2)*(3*c + 1)*(4*c - 1)
Let x = -1420 + 1420. Let k(b) be the first derivative of -7 + 0*b**3 + x*b + 0*b**2 - 1/16*b**4. Factor k(t).
-t**3/4
Let u(z) = 2*z**2 - 16*z - 1. Let l(q) = -q**2 + 9*q + 2. Let s(g) = g. Let p(n) = -l(n) - 6*s(n). Let i(m) = 5*p(m) - 4*u(m). Factor i(f).
-(f + 3)*(3*f + 2)
Suppose 46*y - 53*y + 42 = 0. Let p(q) be the third derivative of 3/10*q**5 + 0 + 1/40*q**y + 4*q**2 + 3/2*q**4 + 0*q + 4*q**3. Solve p(g) = 0.
-2
Suppose 4*h = -3*q - 0*h + 22, -35 = -5*q - 5*h. Suppose q = 3*g - g. Factor -r - 39*r**2 + 45*r**2 - 3*r - 2*r**g.
-2*r*(r - 2)*(r - 1)
Solve -30*g + 145*g**2 + 68 + 40 - 147*g**2 = 0 for g.
-18, 3
Let l(c) be the first derivative of 2*c**5/5 + 9*c**4/2 + 26*c**3/3 - 9*c**2 - 28*c + 54. Let l(j) = 0. Calculate j.
-7, -2, -1, 1
Let f be (6/3 + 0)/((-3)/(-6)). Factor x**5 - x**3 + 0*x - 773*x**4 + 769*x**4 + 0*x + f*x**2.
x**2*(x - 4)*(x - 1)*(x + 1)
Let f(c) be the third derivative of -c**8/840 + c**7/525 + c**6/100 - c**5/30 + c**4/30 - 4*c**2 + 3. Factor f(b).
-2*b*(b - 1)**3*(b + 2)/5
Suppose 0 - 2/3*k**2 + 26/3*k = 0. Calculate k.
0, 13
Let w(x) = -4*x - 67. Let r be w(-17). Let k be r*1/1*0. Factor -4/3*d**2 + k - 16/3*d.
-4*d*(d + 4)/3
Let f = 37 + -38. Let h be (3 - 3)*f/(-3). Factor h + 0*v**2 - 2/5*v**4 + 1/5*v - 3/5*v**3.
-v*(v + 1)**2*(2*v - 1)/5
Let u(g) be the third derivative of g**6/480 + g**5/24 + g**4/3 + 4*g**3/3 + 156*g**2. Let u(v) = 0. Calculate v.
-4, -2
Let j be 1*(-1)/((-3)/12). Suppose -x - j = -3*x. Factor -2*m**2 + 0*m**3 + m**x - 3*m**3.
-m**2*(3*m + 1)
Let b be (-28)/(-8) - (-7)/(-2). Let -15*r**3 + 10*r**4 - 5/2*r**5 + b + 10*r**2 - 5/2*r = 0. What is r?
0, 1
Suppose 4*a + 109 = 3*x, -a + 2*a - 69 = -2*x. Factor 0 - x*m**2 - 5*m**3 - 7 - 70*m - 38 - 5*m.
-5*(m + 1)*(m + 3)**2
Let f(i) be the first derivative of -2*i**5/95 + 3*i**4/19 - 6*i**3/19 - 35. Factor f(k).
-2*k**2*(k - 3)**2/19
Suppose 3*t + 4*k - 13 = -12, 4*k + 5 = -t. Factor -2/3 - 4/3*p**4 + 2*p**2 - 4/3*p**t + p**5 + 1/3*p.
(p - 1)**3*(p + 1)*(3*p + 2)/3
Let h(f) be the third derivative of -f**6/24 - 95*f**5/6 + 1915*f**4/24 - 160*f**3 - 846*f**2. Factor h(k).
-5*(k - 1)**2*(k + 192)
Let n(f) be the third derivative of 0*f**4 + 0 + 0*f**3 + 1/588*f**8 + 1/105*f**5 + 0*f + 1/70*f**6 + 2/245*f**7 + 9*f**2. Solve n(d) = 0 for d.
-1, 0
Let b(g) be the third derivative of -g**8/5040 - 11*g**7/17640 - g**6/1260 + 3*g**5/20 + 15*g**2. Let l(x) be the third derivative of b(x). Factor l(i).
-2*(2*i + 1)*(7*i + 2)/7
Determine p, given that 3/5*p**5 + 0*p**2 + 24/5*p**4 + 54/5*p**3 + 0 - 81/5*p = 0.
-3, 0, 1
Let u(q) be the first derivative of q**8/840 + q**7/140 + q**6/90 - 25*q**3/3 + 15. Let y(a) be the third derivative of u(a). Factor y(m).
2*m**2*(m + 1)*(m + 2)
Let v(q) be the third derivative of 0*q + 0 + 6*q**2 + 0*q**5 - 1/2*q**4 - 4/3*q**3 + 1/30*q**6. Find t such that v(t) = 0.
-1, 2
Let g(z) be the second derivative of z**4/24 + 37*z**3/12 + 9*z**2 - z + 11. Find i such that g(i) = 0.
-36, -1
Let q = 167/330 - 1/165. Factor -t + 0 + 1/2*t**3 - q*t**2.
t*(t - 2)*(t + 1)/2
Let x be (4/10)/(2/10). Let l = 12528 - 162860/13. Find b, given that -2/13*b**3 + 2/13*b - 4/13*b**x + l = 0.
-2, -1, 1
Factor 1/4*t**2 + 1 - 5/4*t.
(t - 4)*(t - 1)/4
Let t(b) be the second derivative of b**6/3240 - b**4/216 + b**3/6 - 15*b. Let p(a) be the second derivative of t(a). Find s, given that p(s) = 0.
-1, 1
Factor -60*l - 200*l**2 + 35*l**3 + 5519 - 5519.
5*l*(l - 6)*(7*l + 2)
Factor -5/6*y**3 + y**2 + 0 + 0*y + 1/6*y**4.
y**2*(y - 3)*(y - 2)/6
Let a = -16 - -31. Determine i so that 4 + i + 8*i**3 - a*i + 6*i**2 - 3*i - i = 0.
-2, 1/4, 1
Let b(u) = -22*u**3 - 6*u**2 + 30*u - 14. Let a(p) = -p**3 + p**2 - p - 1. Let z(n) = 6*a(n) - b(n). Suppose z(j) = 0. Calculate j.
-2, 1/4, 1
Suppose -185 = -5*u + 210. Let q = u + -75. Suppose 0 + 4/3*f**3 + 8/3*f - q*f**2 = 0. Calculate f.
0, 1, 2
Let t(m) be the third derivative of m**7/105 + m**6/16 + 7*m**5/40 + 13*m**4/48 + m**3/4 - 18*m**2 + 2. Let t(z) = 0. What is z?
-1, -3/4
Let k(p) = -5*p**4 + 10*p**3 - 8*p**2 + 4*p - 8. Let f(q) = 4*q**4 