o - 1)**3*(o + 1)
Let s(u) be the third derivative of 5*u**8/336 - u**7/42 - u**6/8 + u**5/12 + 5*u**4/12 + 51*u**2. Factor s(a).
5*a*(a - 2)*(a - 1)*(a + 1)**2
Let r be (-2)/((-10)/(-4) + -3). Let k(b) be the second derivative of -1/12*b**6 + 0 - 1/84*b**7 - 1/4*b**2 - 5/12*b**3 - 1/4*b**5 - 5/12*b**r - b. Factor k(i).
-(i + 1)**5/2
Suppose -2*u + 7*u + o = 15, 0 = -u - o + 7. Let d(l) = -l + 6. Let s be d(3). Factor -5 - 6*c - 2*c**s - 3*c**2 - 3*c**u + 3.
-2*(c + 1)**3
Suppose -5*y - 9 = 3*q, -2*q - 2 = -4*y - 18. Factor -3*k**q + k**3 + 3 + 3*k - 4*k**3 + 0*k**3.
-3*(k - 1)*(k + 1)**2
Let q = 237 + -235. Determine t, given that 2/5*t**q + 4/5*t + 0 - 12*t**3 + 56/5*t**5 - 2/5*t**4 = 0.
-1, -1/4, 0, 2/7, 1
Suppose -2*f + 3*x = -4, -3*x - 8 - 2 = -5*f. Suppose 0*a**4 - f*a**2 - 7*a**4 + 9*a**4 = 0. What is a?
-1, 0, 1
Let r = 558/355 - -2/71. Determine f, given that r*f**5 + 8/5*f - 16/5*f**3 - 2/5*f**4 + 4/5*f**2 - 2/5 = 0.
-1, 1/4, 1
Let x(n) be the first derivative of n**7/14 - 3*n**6/10 + 9*n**5/20 - n**4/4 + 3*n + 3. Let g(s) be the first derivative of x(s). Solve g(z) = 0 for z.
0, 1
Let y = 2/191 + 931/2292. Let h(m) be the second derivative of 0 + m - 1/3*m**3 - y*m**4 + 0*m**2. Factor h(i).
-i*(5*i + 2)
Factor 2/5*f**2 + 36/5*f + 162/5.
2*(f + 9)**2/5
Suppose -10 = -0*m - 5*m. Determine o, given that 5*o - 3*o + o**2 - m*o**2 + o = 0.
0, 3
Let n = 21 + -18. Let 22*b**4 - 10*b**2 - 2*b - 12*b**4 - 3*b**3 - n*b**3 + 8*b**5 = 0. What is b?
-1, -1/4, 0, 1
Let p(c) = -2*c. Let y(f) = f**2 + f. Let d = 6 + -7. Let m(q) = d*p(q) - y(q). Solve m(l) = 0 for l.
0, 1
Suppose -3/5*l**2 + 0*l**3 + 2/5*l + 0 + 1/5*l**4 = 0. What is l?
-2, 0, 1
Let j(t) be the second derivative of t**5/150 + t**4/10 + 3*t**3/5 + 9*t**2/5 - 2*t. Solve j(w) = 0 for w.
-3
Let w(k) be the third derivative of -k**6/360 - k**5/30 - k**4/6 - k**3/3 - 3*k**2. Let i(n) be the first derivative of w(n). Factor i(j).
-(j + 2)**2
Factor 0*j + 8/5*j**2 - 4/5*j**3 + 0.
-4*j**2*(j - 2)/5
Let s(v) be the first derivative of 1/105*v**5 + 0*v**4 + 0*v**3 + 0*v - 4 - v**2 + 1/420*v**6. Let i(d) be the second derivative of s(d). Factor i(h).
2*h**2*(h + 2)/7
Let u = 4 + 17. Let q(a) = 5*a**5 + a**4 - 2*a**2 - 2*a. Let d(g) = -51*g**5 - 9*g**4 + 21*g**2 + 21*g. Let l(o) = u*q(o) + 2*d(o). Factor l(z).
3*z**4*(z + 1)
Factor 5/6*y**3 + 7/6*y - 1/6*y**4 - 3/2*y**2 - 1/3.
-(y - 2)*(y - 1)**3/6
Let u be ((-12)/8)/(4/(-8)). Suppose -q**3 + 3*q**u - 4*q**4 - 3*q**5 + 5*q**5 = 0. Calculate q.
0, 1
Let d = -44 + 133/3. Factor d*s**5 - 1/3*s**3 + 0 + 0*s**2 + 0*s**4 + 0*s.
s**3*(s - 1)*(s + 1)/3
Let v(l) be the second derivative of -l**7/840 + l**6/80 - 5*l**4/12 + l. Let x(t) be the third derivative of v(t). Let x(h) = 0. What is h?
0, 3
Let g be 1*1/(2 - 1). Let j be 6/2 - (0 + g). Factor 24*z + 45*z**j + z**3 + 4 + 24*z**3 + 0*z**3.
(z + 1)*(5*z + 2)**2
Let n be (-444)/(-184) + 30/345. Factor 3/2*y**2 - 1/2*y**3 + 1 + n*y - 1/2*y**4.
-(y - 2)*(y + 1)**3/2
Factor 9/5*y**3 + 7/5*y**4 + 1/5*y + 0 + 2/5*y**5 + y**2.
y*(y + 1)**3*(2*y + 1)/5
Let v(f) be the second derivative of 1/40*f**5 + f - 1/720*f**6 + 0*f**2 + 0 - 3/16*f**4 - 2/3*f**3. Let w(i) be the second derivative of v(i). Factor w(q).
-(q - 3)**2/2
Solve 0 + 5*i + 5*i**2 + 5/4*i**3 = 0 for i.
-2, 0
Factor -6*s**3 + 0 - 4*s - 58/3*s**2.
-2*s*(s + 3)*(9*s + 2)/3
Let b = 4933/780 - 82/13. Let x(d) be the third derivative of 0 - b*d**6 + 0*d**4 - 4*d**2 + 0*d - 1/30*d**5 + 0*d**3. What is t in x(t) = 0?
-1, 0
Let k = 1 - -3. Let n be (k/10)/((-8)/(-10)). Factor -n*c + 0 + 1/2*c**2.
c*(c - 1)/2
Suppose -w + 16 = -0*w. Let j(y) = y**4 + y**3 - 9*y**2 - 17*y - 8. Let s(h) = 4*h**4 + 4*h**3 - 44*h**2 - 84*h - 40. Let b(a) = w*j(a) - 3*s(a). Factor b(t).
4*(t - 2)*(t + 1)**3
Let z = 2 + 1. Suppose j - 4 = -o, 8 = z*o - j + 3*j. Factor -1/3*m + o - 1/3*m**2.
-m*(m + 1)/3
Let m(l) be the first derivative of l**8/448 - l**7/120 + l**6/160 + l**5/80 - l**4/48 + 3*l**2/2 - 2. Let j(u) be the second derivative of m(u). Factor j(g).
g*(g - 1)**3*(3*g + 2)/4
Suppose 0 = 2*a - r - 6, -15 = -8*a + 3*a - 2*r. Solve -3*z**4 - 3 + 9/4*z**2 + 33/4*z**a - 12*z = 0 for z.
-1, -1/4, 2
Factor 1/5*u**4 + 0 + 0*u**3 + 2/5*u - 3/5*u**2.
u*(u - 1)**2*(u + 2)/5
Let o = -2 + 5. Suppose -3*m + 6*m - u - 9 = 0, -2*u = o*m. Factor 0*g**4 - 3*g**4 + m*g**4.
-g**4
Suppose i = 4*j - 8, -3*i - 5 + 32 = 5*j. Factor -j*p**2 + 0*p**4 - 2*p**3 + p**4 + 4*p**2.
p**2*(p - 1)**2
Let s(u) be the first derivative of -2*u**5/5 - u**4 + 2*u**2 + 2*u + 9. Solve s(v) = 0.
-1, 1
Let l be (-1 + 4/5)*-1. Let h = -1/8 + 29/40. Suppose h*g - 1/5 + l*g**3 - 3/5*g**2 = 0. What is g?
1
Let u(o) be the second derivative of -o**5/40 - o**4/24 + o**3/6 - 19*o. Suppose u(c) = 0. Calculate c.
-2, 0, 1
Suppose 0*l = l - 3. Let n = 8 - l. Factor 0 - 2/5*a + 8/5*a**4 - 2/5*a**n + 8/5*a**2 - 12/5*a**3.
-2*a*(a - 1)**4/5
Let s be (-2)/(-3)*(-3 - 96/(-28)). Factor -4/7*n**2 + s*n**4 + 0*n + 0*n**3 + 2/7.
2*(n - 1)**2*(n + 1)**2/7
Let g(a) = a**2 + 4*a + 3. Let i be g(-4). Factor -b**3 + 4*b + 2*b**i + b**3 - 6*b**2.
2*b*(b - 2)*(b - 1)
Suppose 2*s - 2*g - 7 = -3*g, 3*s = g + 13. Factor -f**4 + 0*f**s - 6 + 6 - f**5.
-f**4*(f + 1)
Let v(g) be the second derivative of 7*g + 0*g**2 + 0 + 1/12*g**3 - 1/48*g**4. Factor v(y).
-y*(y - 2)/4
Suppose -8 = 4*x - 2*z - 2*z, 4*x + 4 = 3*z. Factor 1 - 5 - 4*n**2 - x*n - 6*n.
-4*(n + 1)**2
Let u(i) be the third derivative of i**6/480 - i**5/120 - i**4/96 + i**3/12 + 29*i**2. Factor u(g).
(g - 2)*(g - 1)*(g + 1)/4
Let y(d) be the third derivative of 0*d**3 + 0 + 1/18*d**4 + 0*d + 2*d**2 + 1/90*d**5. Determine i so that y(i) = 0.
-2, 0
Let k(r) = -3 + r**2 + 2*r - 4*r**2 + 3 + 1. Let w(d) = 7*d**2 - 5*d - 2. Let v(u) = -9*k(u) - 4*w(u). Factor v(f).
-(f - 1)**2
Let g(c) be the first derivative of -c**3/24 - c**2/4 - c/2 + 27. Solve g(n) = 0.
-2
Let c be -1*(2 + -1)*(-19)/76. Let c*d**3 + 0 + 1/4*d**2 - 1/4*d**4 - 1/4*d = 0. What is d?
-1, 0, 1
Let t(d) be the second derivative of d**4/12 + 5*d**3/6 - 3*d**2 + 10*d - 2. Factor t(j).
(j - 1)*(j + 6)
Factor -i**2 - 1/2*i + 1 + 1/2*i**3.
(i - 2)*(i - 1)*(i + 1)/2
Let v(i) be the second derivative of -1/105*i**7 + 0*i**5 + 0*i**4 - 1/75*i**6 + 0*i**2 + 0*i**3 + 0 - 4*i. Let v(z) = 0. What is z?
-1, 0
Let r = -3 - -8. Suppose r*s - s = 8. Factor -1 + 2 + v + 3*v - 3*v**2 + v**4 - s*v**3 + 3.
(v - 2)**2*(v + 1)**2
Let g(i) = -4*i - 24. Let w be g(-6). Let u(x) be the third derivative of 1/24*x**4 + 1/240*x**5 + 4*x**2 + w*x + 1/6*x**3 + 0. Factor u(a).
(a + 2)**2/4
Factor 8*f**2 + 14*f + 4 - 50*f**2 - 52*f.
-2*(f + 1)*(21*f - 2)
Let x(i) = -2*i - 7. Let n be x(-6). Suppose g + 8 = n*g. Factor 0*f + 0*f**3 + 2/7*f**4 + 0 + 0*f**g.
2*f**4/7
Let r(o) = -8*o**3 - 12*o**2 - 6*o - 6. Let q(u) = u**3 + u**2 + u + 1. Let x(p) = -6*q(p) - r(p). Suppose x(l) = 0. Calculate l.
-3, 0
Let w(u) = 3*u**4 + 25*u**3 + 40*u**2 + 11*u - 7. Let b(y) = -y**4 - 8*y**3 - 13*y**2 - 4*y + 2. Let i(d) = 21*b(d) + 6*w(d). Solve i(o) = 0 for o.
-3, -2, -1, 0
What is x in -x**4 + 0*x + 0 + 1/3*x**5 - 1/3*x**2 + x**3 = 0?
0, 1
Suppose -d = 2*d - 9. Suppose 2*b + b + 0*b = 0. Factor 2/5*v**2 + b*v + 0 + 2/5*v**d.
2*v**2*(v + 1)/5
Let h be -7*(164/280*-6 + 3). Suppose 42/5*z**2 - 32/5*z - h*z**3 + 8/5 = 0. What is z?
2/3, 1
Let d(s) = 1 + 2*s + 0 - 7. Let h be d(5). Factor 2*u - 3 + h + 0 - 2*u**3 - u**4.
-(u - 1)*(u + 1)**3
Let d(u) = -u**2 - 14*u. Let o be d(0). Factor 0*m + o - 1/4*m**2 - 1/2*m**3 - 1/4*m**4.
-m**2*(m + 1)**2/4
Let q(k) be the second derivative of 2/21*k**3 + k - 1/12*k**4 + 1/70*k**5 + k**2 + 0. Let f(l) be the first derivative of q(l). Solve f(r) = 0 for r.
1/3, 2
Let r = 2359/2 - 1206. Let m = 27 + r. Factor 0 - 3/2*j**2 + j + m*j**3.
j*(j - 2)*(j - 1)/2
Let n(a) be the first derivative of 3/2*a**2 - 4 - 1/3*a**3 + 0*a. Factor n(i).
-i*(i - 3)
Let z(v) be the third derivative of 0 + 0*v - 1/15*v**5 + 0*v**3 - 9*v**2 - 1/2*v**4. Find n such that z(n) = 0.
-3, 0
Let g(f) = 45*f**5 + 30*f**4 + 20*f**2 + 20*f + 20. Let t(m) = -m**5 - m**4 - m**2 - m - 1. Let n(q) = -g(q) - 20*t(q). Factor n(k).
-5*k**4*(5*k + 2)
Suppose 4*h = -3*v + 14, -6 = -5*v - 2*h + 4*h. Let 0 - 3/2*b**v + 0*b + 3/4*b**3 = 0. What is b?
0, 2
Let h(n) be the first der