ative of r**8/2016 + r**7/1260 - r**6/540 + r**4/12 - 8*r**2. Let y(j) be the second derivative of v(j). Find x such that y(x) = 0.
-1, 0, 2/5
Suppose 8*a**3 - 15*a**4 - 25*a**2 + 12*a**3 + 10*a**4 + 9*a + a = 0. What is a?
0, 1, 2
Factor 2/3*i - 5/6*i**2 + 0 + 1/6*i**3.
i*(i - 4)*(i - 1)/6
Find a such that -1/4*a**4 + 2*a + 1/4*a**2 + 0 - 2*a**3 = 0.
-8, -1, 0, 1
Suppose -k + 1 = -2*w - 2*k, 3*k = -3*w - 3. Factor -4*n**3 + w*n + 6*n - 3*n**2 + n**3.
-3*n*(n - 1)*(n + 2)
Solve -41 - 2*x**3 + 7*x + 4 + 5 - 55*x - 18*x**2 = 0 for x.
-4, -1
Let s(u) be the third derivative of 1/15*u**3 + 1/300*u**6 - 1/150*u**5 - 1/60*u**4 + 0*u + 0 + u**2. Suppose s(t) = 0. Calculate t.
-1, 1
Let d(s) = 2*s - 2. Suppose -5*c + 10*c - 15 = 0. Let p be d(c). Let 0 - 1/4*z**2 - 1/4*z**p + 0*z + 1/2*z**3 = 0. Calculate z.
0, 1
Let q = -30 - -33. Factor 0*c**q + 0 + 1/2*c**4 - 1/2*c**2 + 0*c.
c**2*(c - 1)*(c + 1)/2
Let c = 41 - 34. Let l(b) be the second derivative of -5/168*b**c + 1/12*b**3 + 1/48*b**4 + 0*b**2 - 9/80*b**5 - 13/120*b**6 + 0 + 3*b. Solve l(r) = 0.
-1, 0, 2/5
Suppose -14*f + 11*f = -15. Factor 0*j + 21/4*j**4 + 3/2*j**3 + 0*j**2 + 15/4*j**f + 0.
3*j**3*(j + 1)*(5*j + 2)/4
Let r(x) = -2*x**2 - 6*x - 4. Let y(s) = -10*s**2 - 30*s - 20. Let z(m) = 14*r(m) - 3*y(m). Factor z(f).
2*(f + 1)*(f + 2)
Suppose 8*d = 5*d + 9. Let m(i) be the second derivative of 0 + i + 1/5*i**2 - 1/30*i**4 + 0*i**d. Suppose m(u) = 0. What is u?
-1, 1
Let v(j) be the first derivative of j**4/4 - 11*j**3 + 363*j**2/2 - 1331*j - 44. Let v(b) = 0. What is b?
11
Let s(q) be the second derivative of q**6/90 - q**5/60 - q**4/36 + q**3/18 - 14*q. Factor s(t).
t*(t - 1)**2*(t + 1)/3
Let w(x) = x**3 + 2*x**2 - 2*x - 2. Let v be w(-2). Determine b, given that 3*b**v + 2*b + b - 3*b + 3 + 6*b = 0.
-1
Let c(y) = y**3 + 5*y**2 + y + 5. Let t be c(-5). Let w(d) be the third derivative of -1/6*d**3 - 1/60*d**5 + t*d + 0 + 1/12*d**4 - 2*d**2. Factor w(h).
-(h - 1)**2
Let j(t) be the third derivative of 0 - t**2 + 0*t + 1/11*t**3 + 1/66*t**4 - 1/330*t**5. Factor j(r).
-2*(r - 3)*(r + 1)/11
Let u(t) be the third derivative of -t**8/33600 + t**7/4200 - t**6/1800 - 5*t**4/24 + 2*t**2. Let i(j) be the second derivative of u(j). Solve i(g) = 0.
0, 1, 2
Let -13/3*q - 2/3*q**3 - 4/3 - 11/3*q**2 = 0. What is q?
-4, -1, -1/2
Determine b, given that 0 + 2/5*b**5 + 3*b**4 + 0*b - 16/5*b**2 + 24/5*b**3 = 0.
-4, 0, 1/2
Let q(t) = -t - 1 + 0*t - 3*t + 2*t - t**2. Suppose 0*z + 20 = -5*z. Let f(w) = w**2 + 2*w + 1. Let s(i) = z*q(i) - 3*f(i). Factor s(b).
(b + 1)**2
Let o(p) = 13*p**5 - 19*p**4 + 19*p**3 - 8*p**2 - 5*p. Let q(z) = 32*z**5 - 48*z**4 + 48*z**3 - 20*z**2 - 12*z. Let r(u) = 12*o(u) - 5*q(u). Factor r(i).
-4*i**2*(i - 1)**3
Let p be 20/(-4) + 2 + 44/10. Let g = -583/5 + 117. Factor -l**2 - p*l - g.
-(l + 1)*(5*l + 2)/5
Let r(j) be the second derivative of -j**7/7560 + j**6/2160 + j**5/180 - j**4/12 - 5*j. Let n(o) be the third derivative of r(o). Factor n(m).
-(m - 2)*(m + 1)/3
Let f(p) be the third derivative of p**8/56 - 3*p**7/70 - p**6/5 + 13*p**5/20 - 2*p**3 + 10*p**2. Find k, given that f(k) = 0.
-2, -1/2, 1, 2
Solve 0 + 2/7*f**3 + 4/7*f**2 + 2/7*f = 0 for f.
-1, 0
Let z(m) = 3*m + 50. Let o be z(-16). Let 6/11*y - 2/11*y**o - 4/11 = 0. Calculate y.
1, 2
Factor -2/3 - 8/3*u**2 + 8/3*u.
-2*(2*u - 1)**2/3
Let f(b) be the first derivative of -b**5/240 - b**4/16 - 3*b**3/8 - b**2/2 + 7. Let x(a) be the second derivative of f(a). Factor x(j).
-(j + 3)**2/4
Factor -432/11*q - 72/11*q**2 + 0 + 60/11*q**3 - 6/11*q**4.
-6*q*(q - 6)**2*(q + 2)/11
Let b(g) be the second derivative of -g**5/60 + g**3/18 - 10*g. Suppose b(q) = 0. Calculate q.
-1, 0, 1
Let w(t) = -t**2 - 2*t. Let k be w(-2). Factor 8/11*n + 0 + 2/11*n**4 - 6/11*n**3 + k*n**2.
2*n*(n - 2)**2*(n + 1)/11
Let x = 1/314 - -625/942. Determine i so that -x*i**2 + 1/3*i**5 + 2/3*i**4 - 1/3*i + 0 + 0*i**3 = 0.
-1, 0, 1
Let m(n) be the second derivative of -n**8/672 + n**7/210 - n**5/60 + n**4/48 - n**2/2 - n. Let q(f) be the first derivative of m(f). Factor q(r).
-r*(r - 1)**3*(r + 1)/2
Let r(h) be the first derivative of -h**7/840 + h**6/240 - h**5/240 + 2*h**2 - 5. Let n(m) be the second derivative of r(m). Determine o, given that n(o) = 0.
0, 1
Suppose 0 = u + 4 - 5. Let l be u + -1 - (-2 + 0). What is t in -3*t**3 + t**l + t**2 + 4*t**5 - t**2 = 0?
-1, 0, 1/2
Let y = 1 - 1. Suppose y = -0*c + 4*c - 16, 3*c - 15 = -l. Suppose 0*t**4 + l*t**4 - t**4 - 2*t**2 = 0. What is t?
-1, 0, 1
Let l(y) be the second derivative of -2/33*y**4 - 2/55*y**5 + 0*y**2 - 1/165*y**6 + y + 0*y**3 + 0. Solve l(m) = 0 for m.
-2, 0
Determine l, given that -1/3*l**4 + 0*l - 1/6*l**3 + 0*l**2 + 0 - 1/6*l**5 = 0.
-1, 0
Let a = -1211/9 - -134. Let h = 1/9 - a. Factor -1/3*p**2 + h*p + 0.
-p*(p - 2)/3
Let k(q) be the first derivative of 2/5*q**3 + 0*q + 3 + 0*q**2 - 1/10*q**4. Determine v so that k(v) = 0.
0, 3
Suppose 3*v - 4 = 5. What is k in 0*k**2 - 3*k**4 - 2*k**2 - 8*k**v - 3*k**4 = 0?
-1, -1/3, 0
Let u(g) be the third derivative of -g**8/10080 + g**7/630 - g**6/90 + g**5/20 - 2*g**2. Let q(a) be the third derivative of u(a). Find s, given that q(s) = 0.
2
Let v be (24/(-16))/(2/(-4)). Let m = 1/19 + 15/76. Factor 1/4 + 1/4*n**v - 1/4*n - m*n**2.
(n - 1)**2*(n + 1)/4
Let u = 63 - 251/4. Factor u*d**3 - 1/4*d**2 - 1/4*d + 1/4*d**4 + 0.
d*(d - 1)*(d + 1)**2/4
Factor -1/3*p**3 - 2*p**2 - 8/3 - 4*p.
-(p + 2)**3/3
Suppose 5*b - 2*b - 36 = 0. Solve 5*a**3 + 14*a + 10*a - 15*a**2 - 2*a**3 - b = 0.
1, 2
Let x(a) be the first derivative of 4*a**3/3 + 2*a**2 - 13. Solve x(c) = 0.
-1, 0
Let z(g) = 2*g**2 + 8*g - 6. Let f be z(-5). Factor 8/5*d**3 - 2/5*d**f - 12/5*d**2 + 8/5*d - 2/5.
-2*(d - 1)**4/5
Let d(j) be the third derivative of j**7/315 + j**6/90 - j**5/90 - j**4/18 - 20*j**2. Suppose d(y) = 0. What is y?
-2, -1, 0, 1
Let y be 36/10 - 4/(-10). Let m(x) = 2*x**2 + 2. Let j(b) = 3*b**2 - 8*b**2 - 6 + 2 - 1 + b. Let u(r) = y*j(r) + 11*m(r). Factor u(w).
2*(w + 1)**2
Let u(v) = v**4 + v**2 - v + 1. Let z(k) = 20*k**4 + 18*k**3 + 10*k**2 - 6*k + 6. Let h(m) = -12*u(m) + 2*z(m). What is y in h(y) = 0?
-1, -2/7, 0
Let x(y) be the first derivative of -2*y**3/21 - 10*y**2/7 - 50*y/7 + 2. Find m, given that x(m) = 0.
-5
Suppose -2*l**2 + 212*l - 212*l = 0. Calculate l.
0
Let c = 15 + -15. Let g(s) be the first derivative of 0*s**2 + 1/4*s**4 + 1/5*s**5 + 0*s + c*s**3 - 2. Solve g(k) = 0.
-1, 0
Let g(w) be the first derivative of 3*w**5/5 - 9*w**4/4 + 6*w**2 - 32. Factor g(d).
3*d*(d - 2)**2*(d + 1)
Let i be (9/6)/((-9)/(-30)). Factor -6*r**3 + 2*r**5 + 4*r**i - 3*r**5 + 3*r.
3*r*(r - 1)**2*(r + 1)**2
Let y(v) = 6*v**4 - 6*v**3 - 3*v - 3. Let u(a) = -11*a**4 + 12*a**3 - a**2 + 5*a + 5. Let f(q) = 3*u(q) + 5*y(q). Factor f(k).
-3*k**2*(k - 1)**2
Let k(f) be the first derivative of -4*f**5/5 - f**4 + 4*f**3/3 + 2*f**2 - 6. Factor k(p).
-4*p*(p - 1)*(p + 1)**2
Let p = 34 + -21. Suppose 2*c = c + p. Solve -12*q**2 + 6*q + 16*q**5 + 18*q**3 - 12*q**4 - 3*q - c*q**5 = 0.
0, 1
Suppose -5*i + 19 = -2*r, 2*i + i + r = 18. Determine j, given that -2*j**2 - 4*j**i + 2*j**3 + 3*j**5 + 2*j**5 - 4*j**3 + j + 1 + j**4 = 0.
-1, 1
Let k(t) be the third derivative of 3*t**2 + 1/6*t**5 + 4/15*t**3 + 0 + 0*t + 1/3*t**4. Factor k(h).
2*(5*h + 2)**2/5
Let x(r) be the second derivative of r**6/45 + r**5/30 - r**4/18 - r**3/9 + 6*r. Determine i so that x(i) = 0.
-1, 0, 1
Let h = 5 + 0. Factor 6*l**5 + 72*l**3 + l**h + 42*l + l**5 - 78*l**2 - 2*l**5 - 9 - 33*l**4.
3*(l - 1)**4*(2*l - 3)
Let x(m) be the first derivative of -2*m**5/5 + 5*m**4/8 + 23*m**3/6 - 3*m**2/2 - 37. Let x(y) = 0. Calculate y.
-2, 0, 1/4, 3
Let g be 2/(3 - 1) + 15/(-27). Factor -10/9*c + 2/3*c**2 - g.
2*(c - 2)*(3*c + 1)/9
Solve 18/17*h + 78/17*h**2 - 38/17*h**4 + 8/17*h**5 + 0 + 14/17*h**3 = 0.
-1, -1/4, 0, 3
Let r(n) be the second derivative of n**7/13860 + n**6/3960 + n**4/3 - 5*n. Let s(g) be the third derivative of r(g). Factor s(a).
2*a*(a + 1)/11
Let a = 1757 - 6993/4. Suppose -3*v - 2 = -5*v. Factor -a*m**2 + m + v.
-(5*m - 2)*(7*m + 2)/4
Let a(l) be the second derivative of l**4/54 - 3*l. Determine x so that a(x) = 0.
0
Suppose 10*x - 25 = 5*x. Factor x*c - 4*c - c**2 - 3*c - 2 - c.
-(c + 1)*(c + 2)
Let f(y) be the first d