 l(n) be the third derivative of 0 + 0*n + 1/5*n**3 - 1/40*n**4 + 3/200*n**6 - 1/25*n**5 + n**2. Determine u, given that l(u) = 0.
-2/3, 1
Determine y, given that -1/4*y**4 + 1/2*y**3 - 1/2*y + 1/4 + 0*y**2 = 0.
-1, 1
Factor 0*i - 4/9 + 1/3*i**2 - 1/9*i**3.
-(i - 2)**2*(i + 1)/9
Let k = 40 - 61. Let z be -2 - k/(-18)*-2. Solve -z*b**4 - 1/3*b**3 + 1/3*b + 0 + 1/3*b**2 = 0.
-1, 0, 1
Let g(t) be the third derivative of t**8/1260 + t**7/840 - t**6/216 - t**5/120 + t**4/72 + t**3/2 - t**2. Let i(c) be the first derivative of g(c). Factor i(v).
(v - 1)*(v + 1)**2*(4*v - 1)/3
Let t be 90*(-6)/(-84)*1 + -5. Factor -8/7*g**2 - 4/7 + 2/7*g**3 + t*g.
2*(g - 2)*(g - 1)**2/7
Let t(h) be the third derivative of -h**5/15 - h**4/2 - 4*h**3/3 - 5*h**2. Factor t(k).
-4*(k + 1)*(k + 2)
Let x be (12/(-8))/(6/(-56)). Suppose x - 4 = 5*b. Find z, given that -6*z**b - z**3 + 3*z**4 + 9*z**4 + z + 6*z**3 = 0.
-1, 0, 1/4, 1/3
Let n be 2 - (6/(-3) + -1). Suppose 8*q**4 + 1 - n*q**4 - 1 = 0. What is q?
0
Let g(m) be the third derivative of 1/60*m**5 + 0*m + 0*m**4 + 0 + 5*m**2 - 1/40*m**6 + 0*m**3. Factor g(y).
-y**2*(3*y - 1)
Let 6*p**4 + 60*p**3 - 75*p**3 - 10*p**2 + 4*p**4 = 0. What is p?
-1/2, 0, 2
Let k(s) = -13*s**5 + 32*s**3 + 5*s**2 + 5*s. Let o(z) = -20*z**5 + 48*z**3 + 8*z**2 + 8*z. Let b(t) = -8*k(t) + 5*o(t). Factor b(w).
4*w**3*(w - 2)*(w + 2)
Let v = -6 + 9. Let p(c) = -c**3 + 6*c**2 - 4*c - 5. Let o be p(5). Suppose v*x**3 - 2*x**5 - x**3 + o*x**3 = 0. Calculate x.
-1, 0, 1
Let r = 61/105 + -1/105. Let l = r + 2/21. Factor -8/3*c + 0 - l*c**3 + 8/3*c**2.
-2*c*(c - 2)**2/3
Factor -f**3 + 2*f**3 + f**2 + 10 - 10.
f**2*(f + 1)
Suppose -i = 4*i - 25. Suppose i = q + 3. Factor -c**3 - q*c + 0*c**3 + c - 2*c**2.
-c*(c + 1)**2
Let v(p) = 9*p**2 + 9*p - 10. Let z(y) = -17*y**2 - 17*y + 20. Let t(i) = 7*v(i) + 4*z(i). Factor t(n).
-5*(n - 1)*(n + 2)
Let o(f) = -f**3 - 10*f**2 + 9*f - 19. Let d be o(-11). Solve 0*g + 0 + 2/5*g**2 + 2/5*g**d = 0 for g.
-1, 0
Factor -4/3 - 4/3*m**2 + 8/3*m**4 + 2/3*m**5 - 10/3*m + 8/3*m**3.
2*(m - 1)*(m + 1)**3*(m + 2)/3
Let r(c) be the second derivative of c**7/2520 - c**6/450 - c**5/150 + c**4/2 + 7*c. Let y(x) be the third derivative of r(x). Factor y(m).
(m - 2)*(5*m + 2)/5
Let x(h) be the second derivative of 1/10*h**5 - 1/3*h**4 + 0*h**2 - h + 1/3*h**3 + 0. Determine s so that x(s) = 0.
0, 1
Suppose 3*y = -y + 12. Suppose 3 - 12*u + 12*u**y + 5*u**4 - 7 + 4*u**4 - 5*u**2 = 0. Calculate u.
-1, -2/3, 1
What is v in 0 - 7/9*v**3 + 4/9*v - 4/9*v**4 + 1/3*v**5 + 4/9*v**2 = 0?
-1, -2/3, 0, 1, 2
Let y(p) be the first derivative of p**6/18 + p**5/3 + 2*p**4/3 + 4*p**3/9 + 7. Factor y(q).
q**2*(q + 1)*(q + 2)**2/3
Solve 2/3*z**4 + 0 - 2/3*z**3 + 0*z + 0*z**2 + 4/3*z**5 = 0.
-1, 0, 1/2
Let j(z) = 5*z**2 + 7*z - 10. Let h be j(2). Let c(p) be the first derivative of -4 - 18*p**2 - 3/4*p**4 - 6*p**3 - h*p. Factor c(g).
-3*(g + 2)**3
Suppose -h - 2*h + 4*u - 8 = 0, 32 = 3*h + 4*u. Find f, given that 8 + 23*f + h*f**4 + 5*f + 20*f**3 - 13*f**2 + 49*f**2 = 0.
-2, -1
Let y(o) = 6*o**2 - 6*o + 2 - 5*o**2 + o. Let f be y(5). Factor 2*p**3 - 2*p - 2 + f*p**4 + 2*p**3 - 2*p.
2*(p - 1)*(p + 1)**3
Let q(c) be the first derivative of c**6/5 - c**5/2 - c**4/3 + 10*c + 8. Let t(j) be the first derivative of q(j). Solve t(d) = 0 for d.
-1/3, 0, 2
Find l, given that 24 + 0*l**2 + 2*l**2 - 3*l**3 - 24 + l**5 = 0.
-2, 0, 1
Let f(r) be the second derivative of 1/4*r**2 + 1/24*r**4 + 0 - 1/6*r**3 + 6*r. Factor f(w).
(w - 1)**2/2
Let -4/5*r**4 + 0 + 4/5*r**2 + 0*r + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let u(x) be the third derivative of -13/120*x**4 - 23/600*x**6 - 1/150*x**7 - 1/15*x**3 - 9/100*x**5 + 0 + 0*x + 3*x**2. Factor u(h).
-(h + 1)**3*(7*h + 2)/5
Suppose 5*h + i - 480 = 0, -h + 48 = 2*i - 57. Let o = h - 853/9. Factor -4/9*z**2 - 2/9*z + 0 - o*z**3.
-2*z*(z + 1)**2/9
Let m(j) be the third derivative of 3*j**6/40 + j**5/20 - j**4/4 + 8*j**2. Solve m(r) = 0 for r.
-1, 0, 2/3
Let y(q) be the first derivative of 2/15*q**5 - 1 + 0*q - 2/9*q**3 + 1/3*q**2 - 1/6*q**4. Factor y(d).
2*d*(d - 1)**2*(d + 1)/3
Find w such that -2/15*w**2 - 8/15*w - 8/15 = 0.
-2
Let h(a) = 5*a**2 - 17*a + 2*a**3 - a**2 + 2*a**3. Suppose -1 = -4*c + 7. Let i(s) = -s**3 - s**2 + 4*s. Let m(p) = c*h(p) + 9*i(p). Factor m(b).
-b*(b - 1)*(b + 2)
Let o be (-15)/(-2) + (-8)/(-16). Let p be o/6*2/4. Factor 2/3*i**3 - 2/3*i + 2/3 - p*i**2.
2*(i - 1)**2*(i + 1)/3
Let q(z) be the first derivative of -z**3/4 + 3*z/4 + 7. Suppose q(j) = 0. Calculate j.
-1, 1
Let p(h) be the first derivative of -h**6/3 + 2*h**5/5 + h**4/2 - 2*h**3/3 - 9. Find m, given that p(m) = 0.
-1, 0, 1
Suppose -2*n = -3*n + 3. Let a = 1 + n. Factor -13*o**2 + 4*o**2 - 15*o**4 - a*o**2 + 2*o + 26*o**3.
-o*(o - 1)*(3*o - 1)*(5*o - 2)
Let a(l) be the first derivative of 3*l**5/35 - 9*l**4/14 + l**3/7 + 36*l**2/7 + 48*l/7 - 24. Find m, given that a(m) = 0.
-1, 4
Let l be 2/(-4)*2 - -3. Suppose -2*p + 4 = -4. Factor 2 - d**2 - d**l + 2 - 6 - p*d.
-2*(d + 1)**2
Let n(a) be the first derivative of 1/15*a**5 + 0*a - 1/4*a**4 + 1/18*a**6 - 2 + 1/3*a**2 - 1/9*a**3. Solve n(p) = 0 for p.
-2, -1, 0, 1
Let g(i) be the second derivative of 2*i**6/15 - i**4 - 4*i**3/3 - 21*i. Factor g(w).
4*w*(w - 2)*(w + 1)**2
Suppose 0 = 2*g - 5*p + 4, -g + 3*g - 16 = -5*p. Suppose g + 1 = x. Factor -2/3*s**5 - 4/3*s + 0 + 10/3*s**x - 6*s**3 + 14/3*s**2.
-2*s*(s - 2)*(s - 1)**3/3
Let c(n) = 3*n**3 + n - 4. Let v(l) = -3*l**3 - 2*l + 5. Let d be (-23)/5 + 12/(-30). Let w(x) = d*c(x) - 4*v(x). Factor w(s).
-3*s*(s - 1)*(s + 1)
Suppose 0 = 12*n - 18*n + 30. Let o(a) be the third derivative of 5/96*a**4 + a**2 - 1/60*a**n + 0*a - 1/24*a**3 + 0. What is t in o(t) = 0?
1/4, 1
Suppose 3*j = -2*j + 25. Let q(c) = c**2 - 5*c + 4. Let b be q(j). Factor -b*z**2 + 2*z**2 - 2*z**4 - 8*z**3 - 6*z**2.
-2*z**2*(z + 2)**2
Let u = 1 - -4. Suppose -2*w = -0*m - 5*m - 15, u*w = -2*m - 6. Determine h, given that 2*h**4 + 7*h**5 + 0*h**4 - 7*h**3 + w*h**3 - 2*h**2 = 0.
-1, -2/7, 0, 1
Let g be (-6 - 44/(-8))*(2 + -12). What is o in 0*o + 16/5*o**4 - 6/5*o**g + 4/5*o**2 - 14/5*o**3 + 0 = 0?
0, 2/3, 1
Let d be 2/5*(-4 - -5). Factor 13/5*h**4 + 9/5*h**3 + 0 + h**5 - 1/5*h**2 - d*h.
h*(h + 1)**3*(5*h - 2)/5
Let p(w) = -w**2 - 9*w + 5. Let h be p(-9). Let f(x) be the third derivative of x**2 + 0 + 5/84*x**4 + 0*x + 1/105*x**h + 2/21*x**3. Factor f(j).
2*(j + 2)*(2*j + 1)/7
Let j be (-1)/(-3) - 8/(-3). Let z be 39 + -37 + 12/(-7). Factor -4/7*s**j - 2/7 + z*s**4 + 0*s**2 + 4/7*s.
2*(s - 1)**3*(s + 1)/7
Suppose -11 - 26 + j**2 + 57 - 6*j**2 = 0. What is j?
-2, 2
Let x(g) be the third derivative of -g**7/1785 - g**6/1020 + g**5/255 + 2*g**2. Factor x(v).
-2*v**2*(v - 1)*(v + 2)/17
Let w = 10 - 6. Factor 5*r**4 + 20*r**3 + 20*r**2 + w*r**4 + r**4 + 2*r**5 + 10*r + 2.
2*(r + 1)**5
Let a be (-8)/20 - 16/(-15). Let q(h) be the second derivative of 0 + 0*h**2 + 1/10*h**5 + 4/3*h**3 + a*h**4 + 2*h. Find n, given that q(n) = 0.
-2, 0
Let t(b) be the third derivative of b**8/336 + b**7/70 + b**6/60 + 8*b**2. Factor t(z).
z**3*(z + 1)*(z + 2)
Factor 1/5*w + 6/5*w**3 + 1/5*w**5 + 4/5*w**4 + 0 + 4/5*w**2.
w*(w + 1)**4/5
Let s(a) be the third derivative of -a**5/140 + a**4/56 + a**3/7 + 3*a**2. Let s(z) = 0. Calculate z.
-1, 2
Let i(m) be the first derivative of 9*m**5/20 + 5*m**4/24 - 11*m**3/12 + m**2/2 + m + 3. Let n(o) be the first derivative of i(o). Factor n(x).
(x + 1)*(2*x - 1)*(9*x - 2)/2
Let b(x) be the first derivative of -x**4/6 + 2*x**3/3 - x**2 + x + 1. Let u(v) be the first derivative of b(v). Determine s, given that u(s) = 0.
1
Let z be 18*(4 - (-2 + 7)). Let f be z/21*(-21)/12. Factor -f*c**3 - 3/2*c**4 + 0 + 3/2*c + 3/2*c**2.
-3*c*(c - 1)*(c + 1)**2/2
Let j(c) be the second derivative of -c**4/6 + c**2 + 4*c. Suppose j(w) = 0. Calculate w.
-1, 1
Let p(s) be the first derivative of 2*s**5/55 + 6*s**4/11 + 70*s**3/33 - 12*s**2/11 - 72*s/11 + 20. What is b in p(b) = 0?
-6, -1, 1
Let q(f) be the first derivative of f**9/1512 - f**8/210 + f**7/70 - f**6/45 + f**5/60 - f**3 + 2. Let g(w) be the third derivative of q(w). Solve g(z) = 0.
0, 1
Let n = -1 + 4. Suppose a - n*a = 0. Determine z, given that a*z**3 + 4*z**2 - 2*z - 10*z**2 + 8*z**3 = 0.
-1/4, 0, 1
Factor 14*w + 20/3 