the second derivative of n(h). Determine o so that u(o) = 0.
-3, -1
Let o(v) be the second derivative of 5*v**4/6 + 65*v**3/12 + 15*v**2/4 + 18*v. Factor o(u).
5*(u + 3)*(4*u + 1)/2
Factor 0 + 2*s**2 + 2*s - 4 - 6*s + 2*s.
2*(s - 2)*(s + 1)
Let v = -70 + 77. Let z(n) be the second derivative of -1/42*n**v - n - 1/12*n**4 + 0*n**2 - 3/20*n**5 + 0 + 0*n**3 - 1/10*n**6. Let z(x) = 0. Calculate x.
-1, 0
Suppose 2*l = -2*l. Factor -3*v**2 + l*v**2 - 8 + v**2 - 8*v.
-2*(v + 2)**2
Let m be 16/(-7) - 6/(-21). Let g be m/5 + 210/25. Factor 3*y - y - 2*y - 14*y**4 + 24*y**3 + g*y**2.
-2*y**2*(y - 2)*(7*y + 2)
Let u = 76 + -378/5. Factor 2/5*d**3 + 4/5 + u*d**4 - 2/5*d - 6/5*d**2.
2*(d - 1)**2*(d + 1)*(d + 2)/5
Suppose -8 + 1 = i + 3*c, -5*c - 17 = -i. Let 2/11*q**i - 2/11*q - 4/11 = 0. What is q?
-1, 2
Let t(u) be the second derivative of 1/150*u**5 + 0 + 10*u + 2/45*u**4 + 0*u**2 + 4/45*u**3. Suppose t(v) = 0. What is v?
-2, 0
Factor 0 + 0*v + 2/15*v**2 - 2/15*v**3.
-2*v**2*(v - 1)/15
Let l(o) be the first derivative of -3/2*o**2 - 2 + 0*o - o**3. Determine a so that l(a) = 0.
-1, 0
Find r such that 2/15*r**3 + 0 - 8/15*r + 0*r**2 = 0.
-2, 0, 2
Suppose 0 = l - 6 + 1. Let f(b) be the third derivative of 2*b**2 + 1/20*b**l + 0*b**6 + 0*b**3 - 1/210*b**7 + 1/12*b**4 + 0 + 0*b. Factor f(n).
-n*(n - 2)*(n + 1)**2
Let v(n) be the first derivative of n**4 - 2*n**2 + 4. Determine g, given that v(g) = 0.
-1, 0, 1
Factor 0 - 6*y - 4 + 8*y + 2*y**2.
2*(y - 1)*(y + 2)
Factor 6*q**2 - 6*q**2 + 7*q - 8*q + q**3.
q*(q - 1)*(q + 1)
Let q be (-92)/24 + 2*2. Let i(t) be the second derivative of 3*t + q*t**4 + 2/3*t**3 + 0 + t**2. Suppose i(d) = 0. Calculate d.
-1
Let o be (-16 - 6/(-3))*-1. Let q = o + -12. Factor 1/2*w**q + w + 0.
w*(w + 2)/2
Let q = 6 + -3. Factor 0*b**q - b**3 + b**2 - 5*b + 5*b.
-b**2*(b - 1)
Let k = 9661/30 - 322. Let b(r) be the third derivative of 0*r + 1/9*r**3 - 1/180*r**6 + 0 + k*r**5 - 1/12*r**4 - 3*r**2. Suppose b(s) = 0. Calculate s.
1
Let w(l) be the third derivative of -l**8/560 + l**7/350 + l**6/50 - l**5/25 + 47*l**2. Solve w(z) = 0.
-2, 0, 1, 2
Factor 9/5*f + 0 - 3/5*f**3 + 6/5*f**2.
-3*f*(f - 3)*(f + 1)/5
Factor 2 + 3*w + 0*w - w**2 + 8*w**2 - 6*w**2.
(w + 1)*(w + 2)
Let m(t) be the second derivative of t**6/1800 + t**5/150 + t**4/40 + 2*t**3/3 + 4*t. Let d(j) be the second derivative of m(j). Factor d(f).
(f + 1)*(f + 3)/5
Let s(g) = -2*g - 9. Let v be s(-7). Suppose v*f - 30 - 20 = 0. Let -6*c + 24*c**2 - f*c**3 - 8*c**3 + 4*c**3 - 4 + 0*c**3 = 0. What is c?
-2/7, 1
Let v(n) be the first derivative of n**5/20 - n**4/16 - n**3/12 + n**2/8 + 16. Suppose v(b) = 0. Calculate b.
-1, 0, 1
Let v be 2/(2/1)*2. Suppose -v*q = -0*q. Factor 4/9*n**2 + q + 2/9*n**3 + 2/9*n.
2*n*(n + 1)**2/9
Let r(z) be the third derivative of 0*z + 0*z**6 + 0*z**4 + 0*z**5 + 0 + 0*z**3 + 4*z**2 - 1/70*z**7. Find c, given that r(c) = 0.
0
Let p = 43/175 + 1/25. Factor -p*m**3 + 2/7*m + 0*m**2 + 0.
-2*m*(m - 1)*(m + 1)/7
Suppose h + 5*k - 16 = 9, -2*h + 4*k - 20 = 0. Let f(q) be the third derivative of -1/30*q**5 - 2/3*q**3 + 0 - 3*q**2 - 1/4*q**4 + h*q. Factor f(s).
-2*(s + 1)*(s + 2)
Let c(d) = 2*d**3 + 5*d**2 + 9*d + 6. Let r(v) = -v**3 - 2*v**2 - 4*v - 3. Let q(a) = 3*c(a) + 5*r(a). Factor q(o).
(o + 1)**2*(o + 3)
Let j be (-1 + -1)*3/(-6). Let q be ((-4)/(-10))/(j/5). Determine t so that -4*t**2 + q*t**5 + 4*t**3 + 2 + 2*t**4 - 8*t**3 + 0 + 2*t = 0.
-1, 1
Let v = 200/297 - 2/297. Find l, given that 2/3*l**3 + 0 + v*l + 4/3*l**2 = 0.
-1, 0
Let z = 223 - 1113/5. Solve -2/5*x**3 + 6/5*x**2 + z - 6/5*x = 0.
1
Let p(r) be the first derivative of r**5/35 - 3*r**4/28 + 2*r**3/21 - 7. Factor p(l).
l**2*(l - 2)*(l - 1)/7
Let l(g) be the third derivative of 0*g + 1/60*g**4 - 4*g**2 + 0 + 0*g**3 + 1/300*g**5. Factor l(f).
f*(f + 2)/5
What is q in 3*q**3 + 6*q**2 - 6*q**4 + 0*q - 3*q + 0*q**3 = 0?
-1, 0, 1/2, 1
Suppose 4*m = -3*d - 4 + 9, 3 = -3*d. Factor 2/11 + 2/11*u**m - 4/11*u.
2*(u - 1)**2/11
Find y, given that 4*y**4 - 28/5*y**2 - 44/5*y**3 + 8/5 + 16/5*y**5 + 28/5*y = 0.
-2, -1, -1/4, 1
Let l(b) be the second derivative of b**5/5 - 2*b**3 - 4*b**2 + 3*b. Factor l(n).
4*(n - 2)*(n + 1)**2
Factor -399*o**2 - 261*o**2 + 3630*o - 2451 + 1692 + 40*o**3 - 5896.
5*(2*o - 11)**3
Let z(x) be the third derivative of -x**11/831600 + x**10/378000 + x**5/20 - 4*x**2. Let w(m) be the third derivative of z(m). Let w(g) = 0. Calculate g.
0, 1
Let r = 14 - 3. Find v such that v - 4*v - r*v**2 + 14*v**2 = 0.
0, 1
What is j in -6*j - 4*j**4 + 18*j**4 - 2*j + 2*j**3 + 2*j**4 + 6*j**5 - 16*j**2 = 0?
-2, -1, -2/3, 0, 1
Let p = 68/13 + 137/26. Factor -24*c + p*c**2 + 6.
3*(c - 2)*(7*c - 2)/2
Let q(f) be the second derivative of -1/12*f**4 - 2*f - 1/4*f**2 - 5/24*f**3 + 0 - 1/80*f**5. Factor q(v).
-(v + 1)**2*(v + 2)/4
Suppose 2*y - 35 + 35 = 0. Let c(b) be the third derivative of -2*b**2 + 0*b**3 + 1/15*b**5 + y + 1/20*b**6 + 0*b - 1/12*b**4. Factor c(r).
2*r*(r + 1)*(3*r - 1)
Let o(u) = -u**3 + 4*u**2 - 3*u + 2. Let f be o(3). Find b such that -2*b - 3*b**f + 0*b**2 - b = 0.
-1, 0
Let g(x) be the first derivative of 1/27*x**3 - 1/90*x**5 + 2*x + 2 - 1/9*x**2 + 1/54*x**4. Let n(h) be the first derivative of g(h). Find s such that n(s) = 0.
-1, 1
Suppose 0*z = 3*z - 9. Let u(n) = 2*n**2 + 2*n. Let b(w) = 2*w**2 + 2*w. Let f(t) = z*u(t) - 4*b(t). Determine k, given that f(k) = 0.
-1, 0
Let g(m) be the first derivative of m**8/5040 + m**7/1260 + m**6/1080 + 2*m**3/3 + 1. Let t(v) be the third derivative of g(v). Factor t(q).
q**2*(q + 1)**2/3
What is k in 16*k**5 + 4*k**5 + 4*k**3 + 342*k**4 - 374*k**4 + 8*k**2 = 0?
-2/5, 0, 1
Let n(q) be the first derivative of -1 - 5/4*q**2 + 1/2*q**5 - 1/12*q**6 + 1/2*q + 5/3*q**3 - 5/4*q**4. Factor n(r).
-(r - 1)**5/2
Factor 0 - 1/3*q**2 + 2/3*q.
-q*(q - 2)/3
Factor 0*i**2 + 0 - 2/3*i**4 + 1/3*i**5 + 1/3*i**3 + 0*i.
i**3*(i - 1)**2/3
Let x = -197 - -200. What is a in 0 - 6/11*a**x + 8/11*a + 8/11*a**2 + 2/11*a**5 - 4/11*a**4 = 0?
-1, 0, 2
Let w(a) be the third derivative of a**5/75 + a**4/10 + 4*a**3/15 - 13*a**2. Factor w(y).
4*(y + 1)*(y + 2)/5
Let t(v) = -v**2 + 18*v - 7. Let m(o) = 3*o**2 - 63*o + 24. Let x = -7 + 12. Let c(d) = x*m(d) + 18*t(d). Determine u so that c(u) = 0.
1, 2
Let p(z) be the second derivative of -z**10/24192 + z**9/20160 + z**8/13440 - z**4/12 - z. Let h(q) be the third derivative of p(q). Factor h(f).
-f**3*(f - 1)*(5*f + 2)/4
Let h(c) be the third derivative of -2*c**7/105 + c**6/15 + c**5/15 - c**4/3 + 23*c**2. Find f, given that h(f) = 0.
-1, 0, 1, 2
Let j be 15 + -12 - (-1 + 2). Let l(r) be the first derivative of 1/12*r**4 + 1/18*r**6 + 2/15*r**5 + 0*r**2 + 0*r**3 + 0*r + j. Factor l(s).
s**3*(s + 1)**2/3
Let n = -4/65 + 82/65. Suppose n*t + 9/5 + 1/5*t**2 = 0. What is t?
-3
Let h(v) be the third derivative of 0*v + 0*v**3 + 1/24*v**4 + 0 + 1/420*v**7 + 0*v**6 - 1/40*v**5 + 2*v**2. Factor h(f).
f*(f - 1)**2*(f + 2)/2
Let d(a) be the first derivative of 5*a**3/3 - 5*a**2/2 + 20. Factor d(c).
5*c*(c - 1)
Let z be 1*(3 - -73)/4. Let p = z - 19. Find k such that p + k**2 + 1/2*k + 1/2*k**3 = 0.
-1, 0
Let z(l) be the third derivative of l**7/420 - l**5/80 + l**4/48 + l**3/2 + 5*l**2. Let t(x) be the first derivative of z(x). What is g in t(g) = 0?
-1, 1/2
Let t(z) be the first derivative of 0*z**2 - 9/28*z**4 - 11 - 1/14*z**6 + 9/35*z**5 + 1/7*z**3 + 0*z. What is x in t(x) = 0?
0, 1
Suppose -3*m + 14 = p, -4*m - m = -3*p - 28. Suppose -2*c - m*x = -7*c + 35, 5*c + 3*x = -5. Factor -14*s**3 + 8*s + 24*s**c - 4 + 4.
-2*s*(s - 2)*(7*s + 2)
Let i = 3 - -1. Suppose -5 + d**i + 5 - d**3 + 2*d**3 = 0. What is d?
-1, 0
Let l = 82 + -78. Let c(h) be the first derivative of -44/21*h**3 - 8/7*h**2 - 18/35*h**5 - 3 - 2/7*h - 12/7*h**l. Suppose c(a) = 0. Calculate a.
-1, -1/3
Let g(q) be the second derivative of q**7/126 - q**6/90 - q**5/30 + q**4/18 + q**3/18 - q**2/6 - 5*q. Suppose g(b) = 0. What is b?
-1, 1
Let z = -2/45 - -17/45. Let s(o) = o**3 + 11*o**2 - 13*o - 12. Let u be s(-12). Solve u - 2/3*q**3 + z*q**2 - q**4 + 0*q = 0.
-1, 0, 1/3
Find z, given that 11/3*z**4 + 1 - z**5 - 2/3*z**3 - 14/3*z**2 + 5/3*z = 0.
-1, -1/3, 1, 3
Let s(x) = -105*x**3 + 281*x**2 - 144*x - 41. Let u(z) = -26*z**3 + 70*z**2 - 36*z - 10. Let l(r) = 