 n.
-1, 0, 1/4
Let t(p) be the first derivative of -1/240*p**5 + 0*p + 0*p**4 - 3 + 1/24*p**3 + 1/2*p**2. Let g(i) be the second derivative of t(i). Factor g(x).
-(x - 1)*(x + 1)/4
Let u(y) be the second derivative of -y**6/60 - y**5/20 + y**3/6 + y**2/4 - 5*y. Find o, given that u(o) = 0.
-1, 1
Let y be (-8)/12 + 19/(-3). Let f(b) = -b**3 - 7*b**2 + 2. Let k be f(y). Factor -2*d**5 - k*d**5 + d**3 + d**4 + 3*d**5 - d**2.
-d**2*(d - 1)**2*(d + 1)
Let n(k) be the third derivative of 1/180*k**5 + 0*k**4 + 0 + 1/720*k**6 + 0*k**3 + 0*k - 2*k**2. Factor n(y).
y**2*(y + 2)/6
Let k(x) = -x**5 + 4*x**4 - 16*x**3 + 2*x**2 + 13*x - 6. Let w(u) = -u**5 + u**4 - u**3 - u**2 + u. Let m(q) = -k(q) + 4*w(q). Factor m(i).
-3*(i - 1)**3*(i + 1)*(i + 2)
Suppose 0*v + 2 = v. Suppose -v*m = 2*w - 2, -6*w - 5*m - 1 = -3*w. Solve -2*b**5 + 2*b**3 + 4*b**4 - 4*b**w + 0*b**5 = 0.
0, 1
Let i = 10 + -8. Suppose -3*h - i*z - 4 = -0, -33 = -4*h + 5*z. Factor -v**h + 2*v + 3*v**2 - 1 + 1.
2*v*(v + 1)
Let s = 90 + -87. Find c such that -c**2 + 7/5*c**5 + 0 - 9/5*c**s + c**4 + 2/5*c = 0.
-1, 0, 2/7, 1
Factor 3/2*d**3 + 0 + 0*d + 3/2*d**2.
3*d**2*(d + 1)/2
Let c be ((-3)/12)/((-4)/48). Factor -r + r**2 - 1/3*r**c + 1/3.
-(r - 1)**3/3
Let b = 7 - 13/3. Let j(o) be the first derivative of 0*o + 1/2*o**4 - 2 - b*o**3 + 4*o**2. Factor j(w).
2*w*(w - 2)**2
Let r(o) be the first derivative of o**8/2800 - o**6/600 - 5*o**3/3 - 3. Let f(i) be the third derivative of r(i). Factor f(c).
3*c**2*(c - 1)*(c + 1)/5
Let n(i) be the first derivative of i**5/30 - i**4/2 + 3*i**3 - i**2 - 3. Let l(k) be the second derivative of n(k). Let l(c) = 0. What is c?
3
Let i be 2/(-16)*2 + (-28)/(-48). Factor 1/3*t - i*t**3 - 1/3*t**2 + 1/3.
-(t - 1)*(t + 1)**2/3
Let t = 98 - 96. Let p(a) be the second derivative of 13/105*a**6 + 1/6*a**4 + 1/21*a**3 + t*a + 0 + 3/14*a**5 + 4/147*a**7 + 0*a**2. Let p(q) = 0. Calculate q.
-1, -1/4, 0
Let i(r) be the first derivative of r**7/2520 - r**6/1080 + 2*r**3/3 - 4. Let u(o) be the third derivative of i(o). What is b in u(b) = 0?
0, 1
Suppose 4*z - 38 = 2*z + 3*y, 0 = 5*z - 4*y - 95. Suppose z = 2*u + 5*k, -k - k = 3*u - 12. Factor 3*p**u - p**4 - 2*p**2 + 0*p**2.
-p**2*(p - 1)*(p + 1)
Let n(u) = u**3 + 6*u**2 + 6. Let y be n(-6). Factor y*a - 3*a**2 + 5 + 3 + 1.
-3*(a - 3)*(a + 1)
Suppose 4/13*u + 2/13*u**2 + 0 = 0. Calculate u.
-2, 0
Suppose 4*m - 32 = 4*d - 0, 4*d = 2*m - 26. Let -1 + 0*y**2 - 3*y + 2 - y**2 - m = 0. What is y?
-2, -1
Determine j, given that 9*j**4 - 2*j**3 + 0*j**3 - 2*j**2 + 9*j**3 = 0.
-1, 0, 2/9
Let o = 24 + -38. Let x be 4/o + 6/21. Suppose -2/3*s**2 + 5/3*s**3 + x*s - 5/3*s**5 + 0 + 2/3*s**4 = 0. Calculate s.
-1, 0, 2/5, 1
Suppose -4*a - 2 = -6*a + 2*k, 3*a = 4*k + 1. Factor 1/2*v**2 - 1/2 + 1/4*v - 1/4*v**a.
-(v - 2)*(v - 1)*(v + 1)/4
Let u(y) be the second derivative of -y**9/252 - y**8/80 - y**7/140 + y**6/120 - y**3 - 2*y. Let s(z) be the second derivative of u(z). Let s(c) = 0. What is c?
-1, 0, 1/4
Let x(t) be the second derivative of 3*t**5/20 + t**4/2 + t**3/2 + 49*t. Factor x(y).
3*y*(y + 1)**2
Suppose 16/9 - 4/3*s - 4/9*s**2 = 0. What is s?
-4, 1
Let l(r) be the second derivative of r**6/90 - r**5/30 + r**3/9 - r**2/6 - 5*r. Factor l(u).
(u - 1)**3*(u + 1)/3
Let y(s) be the third derivative of s**7/70 + s**6/20 + 8*s**2. Factor y(v).
3*v**3*(v + 2)
Let r(b) be the second derivative of b**5/20 - 17*b**4/60 + 8*b**3/15 - 2*b**2/5 - 7*b. Suppose r(u) = 0. Calculate u.
2/5, 1, 2
Let p(z) be the third derivative of -z**5/12 + 5*z**4/12 + 5*z**3/2 - 4*z**2. Let p(s) = 0. Calculate s.
-1, 3
Let y(f) be the second derivative of -f**9/1680 - f**8/1120 + 5*f**4/12 + 2*f. Let n(v) be the third derivative of y(v). Determine d, given that n(d) = 0.
-2/3, 0
Let t(h) = -3*h**3 - h**2 - h. Let y be t(-1). Determine z, given that -z**3 - 11 + 11 + 4*z**y - 3*z**2 = 0.
0, 1
Let w(r) be the first derivative of -r**6/18 - r**5/5 - r**4/6 + 2*r**3/9 + r**2/2 + r/3 - 2. Determine m, given that w(m) = 0.
-1, 1
Let j(g) = -5*g - 45. Let f be j(-9). Let k(q) be the first derivative of 0*q - 2/5*q**5 - 1/2*q**2 - 1 + 3/4*q**4 + f*q**3. Suppose k(m) = 0. Calculate m.
-1/2, 0, 1
Let h(s) = -51*s + 8 + 37*s**2 + 10*s - 4*s**2. Suppose -4*b + 6*b - 4 = 0. Let n(d) = 16*d**2 - 20*d + 4. Let y(k) = b*h(k) - 5*n(k). Let y(x) = 0. What is x?
2/7, 1
Let f(c) be the third derivative of -1/100*c**6 + 8*c**2 - 1/1680*c**8 + 0*c**3 + 0*c - 1/120*c**4 - 2/525*c**7 + 0 - 1/75*c**5. Factor f(m).
-m*(m + 1)**4/5
Let g be (80/(-30) - -3)*9. Factor 0*l + 4/3*l**4 + 0*l**2 - 4/3*l**g + 0.
4*l**3*(l - 1)/3
Let m(r) be the first derivative of -2*r**6/3 + 2*r**4 - 2*r**2 - 17. Solve m(u) = 0 for u.
-1, 0, 1
Factor 3 - 3*g**2 + 3*g**2 + 0*g**2 - 3*g**2.
-3*(g - 1)*(g + 1)
Let i(j) be the third derivative of 1/42*j**7 - 2*j**2 + 0*j**3 - 1/168*j**8 + 0*j - 1/60*j**5 + 0 + 1/24*j**4 - 1/40*j**6. Find g such that i(g) = 0.
-1/2, 0, 1
Let d(s) = s - 12. Let j be d(9). Let a be 9/18 - j/2. Determine g, given that 0*g + 2*g**5 + 6*g**2 - 2*g - a*g**2 - 4*g**4 = 0.
-1, 0, 1
Suppose 6*m - 4 = 4*m. Factor -2*q**2 + 4*q - 2*q - m*q - 2*q**3.
-2*q**2*(q + 1)
Solve 1/5*n**4 + 0 - 1/10*n + 2/5*n**3 - 1/5*n**2 - 3/10*n**5 = 0.
-1, -1/3, 0, 1
Suppose p = v - 2*v + 19, 92 = 5*v + 4*p. Solve -48*m**2 - 178*m**3 - 22*m**2 + v*m - 48*m**3 - 218*m**4 - 70*m**5 + 8 = 0 for m.
-1, -2/5, 2/7
Let d = 8 - 2. Suppose 5*b + d = 21. Suppose -3*w**3 - w**b + 0*w**2 + 5*w**3 - w**2 = 0. Calculate w.
0, 1
Let d be (-14 + -4)/(-3) + -2. Factor -3 - 6*a**4 - 16*a + 16*a**3 + 10*a**d - 9 + 8*a**2.
4*(a - 1)*(a + 1)**2*(a + 3)
Suppose -5*d + 4*m = -2, 0 = 3*d + 4*m - 6*m. Let z = d + 2. Factor z - 2*v**2 + 8 - 7 + v**4.
(v - 1)**2*(v + 1)**2
Suppose 0 = 4*f - 9*f - 5*n, -f = -4*n - 20. Suppose 5/3*i - 4/3*i**3 + 4/3*i**f - 2/3 - 2/3*i**2 - 1/3*i**5 = 0. Calculate i.
-1, 1, 2
Let h(v) be the third derivative of -1/210*v**5 + 0 + 1/84*v**4 + 0*v - 3*v**2 + 0*v**3. Suppose h(k) = 0. Calculate k.
0, 1
Let h = 13 - 10. Suppose -6*v**2 + 3*v**4 - 9*v + 6*v**4 - 2*v**h + 3*v**5 + 5*v**3 + 3*v**3 - 3 = 0. What is v?
-1, 1
Let h be (-1)/5 - 114/(-45). Let z = 113/3 + -37. Factor 3*s + h*s**2 + z.
(s + 1)*(7*s + 2)/3
Let k(v) = -3*v**3 - 15*v**2 - 12*v - 5. Let m(p) = -15*p**3 - 75*p**2 - 60*p - 24. Let w(h) = -24*k(h) + 5*m(h). Solve w(s) = 0 for s.
-4, -1, 0
Let a = -325 - -327. Determine c so that -1/4*c - 1/4*c**3 - 1/2*c**a + 0 = 0.
-1, 0
Let r(j) = -17*j + 5. Let h be r(-3). Let t be (-24)/(-32) + (-26)/h. Factor -t*o**5 + 0*o**4 + 0 + 0*o + 6/7*o**3 - 4/7*o**2.
-2*o**2*(o - 1)**2*(o + 2)/7
Let g(o) be the second derivative of 1/14*o**7 + 0*o**4 + 0 + 0*o**3 + 7*o + 0*o**6 - 3/20*o**5 + 0*o**2. Suppose g(v) = 0. What is v?
-1, 0, 1
Factor -2*r - 8 - 1/8*r**2.
-(r + 8)**2/8
Let q = 17 + -2. Suppose 3*y + 2*m - 12 = -0*m, -3*y + q = 3*m. Factor 3*f + 4*f - 2*f**3 - y*f**2 + 4*f**4 - 5*f - 2*f**4.
2*f*(f - 1)**2*(f + 1)
Let m(u) be the second derivative of -u**8/1260 - u**7/315 - u**6/216 - u**5/360 + 5*u**3/6 - 9*u. Let n(d) be the second derivative of m(d). Factor n(i).
-i*(i + 1)*(2*i + 1)**2/3
Let c(v) be the third derivative of -v**7/3150 + 7*v**6/3600 + v**5/300 + v**4/8 - v**2. Let w(i) be the second derivative of c(i). Factor w(n).
-(n - 2)*(4*n + 1)/5
Let y(l) = 5*l**2 + l - 14. Let k(i) = 2*i**2 - 5. Let n(f) = -8*k(f) + 3*y(f). Factor n(z).
-(z - 2)*(z - 1)
Let v(w) be the second derivative of 3*w**5/20 - 3*w**4/2 - w**3/2 + 9*w**2 - 12*w + 1. Let v(c) = 0. Calculate c.
-1, 1, 6
Let r(p) be the first derivative of -4*p**3/9 - 10*p**2/3 + 13. Factor r(l).
-4*l*(l + 5)/3
Let c(i) be the first derivative of i**5/15 + i**4/24 + i**2 + 1. Let r(m) be the second derivative of c(m). Factor r(s).
s*(4*s + 1)
Let m be 5 + 0 + (-380)/228. Factor 4/3 - m*d - 2/3*d**3 + 8/3*d**2.
-2*(d - 2)*(d - 1)**2/3
Let n be ((-4)/9)/(2/(-9)). Suppose 2*u + n*u = 0. Let u*m + 2/5*m**2 + 0 = 0. What is m?
0
Let v(j) = j**3 + 8*j**2 + 6*j - 5. Let k be v(-7). Let y(z) be the second derivative of 0 - 1/6*z**3 - k*z + 0*z**2 + 1/12*z**4. Determine f so that y(f) = 0.
0, 1
Let y(c) be the first derivative of -4 + 0*c**2 + 7/3*c**3 - 3/4*c**4 - 4*c. Let y(b) = 0. Calculate b.
-2/3, 1, 2
Let k(z) be the first derivative of -2*z**3/