Let g(n) = n + 6. Let r be g(0). Let y(u) be the second derivative of -2*u + 1/12*u**4 + 1/6*u**3 - 1/20*u**5 + 0*u**2 - 1/30*u**r + 0. Let y(j) = 0. What is j?
-1, 0, 1
Let w(y) be the second derivative of -y**7/63 + 2*y**6/45 + y**5/15 - 2*y**4/9 - y**3/9 + 2*y**2/3 - 8*y. Determine p so that w(p) = 0.
-1, 1, 2
Let y(m) be the first derivative of 1/6*m**4 + 0*m - 2 - 1/9*m**6 + 0*m**2 + 2/9*m**3 - 2/15*m**5. Determine n, given that y(n) = 0.
-1, 0, 1
Suppose q = -2, 5*k - 2*q + q = 2. Find v such that -1/6*v**5 + 0*v - 1/6*v**4 + k*v**2 + 0 + 0*v**3 = 0.
-1, 0
Let c(f) = -f**2 - 10*f - 13. Let v(j) = -j - 1. Let m(q) = q**3 + q + 4. Let w be m(0). Let r(d) = w*v(d) - c(d). Factor r(y).
(y + 3)**2
Let t(h) be the third derivative of h**5/15 + h**4/3 + 3*h**2. Find k, given that t(k) = 0.
-2, 0
Suppose -5*b - 58 = -13. Let u = b + 12. Find k such that 0 + 49/4*k**5 - 77/4*k**4 - k**2 + 8*k**u + 0*k = 0.
0, 2/7, 1
Let t(n) be the third derivative of n**5/30 + 4*n**2. Factor t(l).
2*l**2
Let k be -2 - 0*1/(-2). Let o(j) = 4*j**2 - 6*j + 8. Suppose -27*h + 32*h = -35. Let z(x) = -13*x**2 + 17*x - 24. Let n(b) = h*o(b) + k*z(b). Factor n(d).
-2*(d - 2)**2
Let f be 1/((-2 - -4)/(-10)). Let w be f/(-6) + (-2)/6. Factor -w*h**2 + 3/2*h - 1.
-(h - 2)*(h - 1)/2
Let t(f) = -4 + 12*f**2 + 4. Let x(b) = b**2. Suppose 0 = -4*r - 4*d - 4, 3*r + 10 = 4*d - 0. Let c(q) = r*t(q) + 22*x(q). What is l in c(l) = 0?
0
Factor -1/2*h - 1/2*h**2 + 3.
-(h - 2)*(h + 3)/2
Suppose -4*u - 16 = 0, -p + 4*p - 4*u - 28 = 0. Let o(f) be the third derivative of 0*f**5 + 1/120*f**6 - 1/24*f**p + 0 + 0*f - 2*f**2 + 0*f**3. Factor o(m).
m*(m - 1)*(m + 1)
Let x(f) = 5*f**2 + 9*f + 2. Let q be x(-2). Factor -1/5*z + 0 - 3*z**3 - 7/5*z**2 - 9/5*z**q.
-z*(z + 1)*(3*z + 1)**2/5
Let o(d) be the first derivative of -2*d**5/25 + d**4/5 - 2*d**3/15 + 7. What is b in o(b) = 0?
0, 1
Let i(l) be the second derivative of 2*l**7/63 - 4*l**6/45 + 2*l**4/9 - 2*l**3/9 - 8*l. Let i(w) = 0. Calculate w.
-1, 0, 1
Let h(r) be the second derivative of -r**4/6 - 2*r**3/3 + 20*r. Factor h(x).
-2*x*(x + 2)
Let u(y) = 5*y**3 - 8*y**2 - 5*y + 2. Let s(g) = 27*g**3 - 41*g**2 - 24*g + 11. Let h(a) = 6*s(a) - 33*u(a). Factor h(d).
-3*d*(d - 7)*(d + 1)
Find z such that -4*z**2 + 8*z**4 - 6*z**3 + z**5 - 5*z + 10*z**5 - 3*z**5 + 7*z = 0.
-1, 0, 1/2
Let -10*x - 12 + x**2 - 4*x**2 - 2*x = 0. What is x?
-2
Let s(a) be the first derivative of 4*a**5/5 - 3*a**4 + 4*a**3/3 + 6*a**2 - 8*a - 22. Suppose s(i) = 0. What is i?
-1, 1, 2
Let h(n) be the second derivative of -5*n**4/12 - 5*n**3/3 - 5*n**2/2 - 3*n. Factor h(c).
-5*(c + 1)**2
Let k = -452 - -1388/3. Factor 0 + 16/3*p**3 + k*p**4 + 0*p + 2/3*p**2.
2*p**2*(4*p + 1)**2/3
Let v(b) = -3*b**3 - 2*b**2 - 3*b + 4. Let t(y) = -2*y**3 - 2*y**2 - 3*y + 3. Let z(p) = -4*t(p) + 3*v(p). Factor z(d).
-d*(d - 3)*(d + 1)
Factor -13*b**2 + 54*b**4 + 16*b**2 - 50*b**4 + 16*b**3 + 13*b**2.
4*b**2*(b + 2)**2
Let q(l) be the second derivative of 5*l + 0*l**3 + 1/70*l**5 - 1/14*l**4 + 0*l**2 + 0. Factor q(b).
2*b**2*(b - 3)/7
Let j(c) be the second derivative of -4/9*c**4 + 25/42*c**7 - 2/9*c**3 + c + 0*c**2 + 10/9*c**6 + 13/60*c**5 + 0. Find a, given that j(a) = 0.
-1, -2/5, -1/3, 0, 2/5
Let b(w) be the first derivative of 3*w**4/28 - 2*w**3/7 - 3*w**2/14 + 6*w/7 + 4. Solve b(i) = 0 for i.
-1, 1, 2
Let b(g) = -g**3 - 2*g**2 - g - 2. Let o be b(-2). Suppose -5*q = -q - 3*n - 12, o = -q + 5*n + 3. Factor -r**q + 0*r**3 + 0*r**3.
-r**3
Let w(h) = -h**3 - 2*h**2 - h - 2. Let b be w(-3). Suppose -2*m + 0*m + b = 0. Factor -2/7*g + 2/7*g**m - 4/7*g**2 + 0*g**3 + 0 + 4/7*g**4.
2*g*(g - 1)*(g + 1)**3/7
Let k be (-12)/(-10) + -2 + 336/120. Determine x, given that 0*x + 0 + 2/3*x**k = 0.
0
Let g = 0 + 0. Factor 5 + x**2 - 5 - x + g*x**2.
x*(x - 1)
Let h(i) be the second derivative of i**7/8 + 11*i**6/24 + 7*i**5/40 - 7*i**4/12 - i**3/3 + 9*i. Solve h(c) = 0 for c.
-2, -1, -2/7, 0, 2/3
Let l(i) be the first derivative of -4*i**3 - i**2 - 32. Solve l(j) = 0.
-1/6, 0
Let k(x) = -x + 4. Let r be k(2). Let y(v) be the second derivative of 0 + 0*v**4 + 1/105*v**6 + 0*v**3 - 2*v - 1/147*v**7 + 0*v**r + 0*v**5. Factor y(o).
-2*o**4*(o - 1)/7
Let j = 31/105 - 2/21. Find l such that 0*l + j*l**4 + 0*l**3 + 0 - 1/5*l**2 = 0.
-1, 0, 1
Solve -2/5*i**2 - 8/5*i - 6/5 = 0 for i.
-3, -1
Suppose 4*z + 8 = 2*s, 2*z + 7 = s - 3*z. Determine r, given that -12/5*r**s + 12/5 - 32/5*r = 0.
-3, 1/3
Let j(y) be the third derivative of -y**6/360 - y**5/60 - y**4/36 + 17*y**2. Find i, given that j(i) = 0.
-2, -1, 0
Let n(r) = -10*r**2 + 14*r + 2. Let a(m) = 19*m**2 - 27*m - 3. Let p(i) = -6*a(i) - 11*n(i). Find j, given that p(j) = 0.
1
Suppose 6 = 3*f - 12. Let s be f/(-4)*6/(-3). Factor -2*y - 2*y**2 - 3*y**4 + 2*y**s + 5*y**4 + 0*y**4.
2*y*(y - 1)*(y + 1)**2
Let l = 5525/21 - 263. Let x(q) be the first derivative of -1/14*q**4 + l*q**3 - 2/7*q + 1/7*q**2 - 2. Factor x(g).
-2*(g - 1)**2*(g + 1)/7
Let k(h) = 14*h**5 - 22*h**4 - 4*h**2 + 4*h. Let j(r) = -r**4 - r**3 - r**2 + r. Let l(a) = -4*j(a) + k(a). Factor l(p).
2*p**3*(p - 1)*(7*p - 2)
Let r be 3*-1 - 40/(-12). Find v, given that -v - r*v**3 - 1/3 - v**2 = 0.
-1
Factor 28*o**4 - 28*o**2 - 1019*o**3 + 21*o + 1007*o**3 - 9*o.
4*o*(o - 1)*(o + 1)*(7*o - 3)
Let j(m) = m**2 - 2. Let q be 10*(-1 + (-6)/(-5)). Let i be j(q). Factor -1/3 - d + d**3 + 1/3*d**i.
(d - 1)*(d + 1)*(3*d + 1)/3
Let n(c) = -c**2 - 3*c + 4. Suppose 6*s - 4*g = 3*s, -4*s - 3*g = 25. Let z be n(s). Factor -8/5*q + 24/5*q**2 + z + 14/5*q**3.
2*q*(q + 2)*(7*q - 2)/5
Suppose 0 = o - 0 - 6. Let i(n) be the third derivative of 0 - 1/105*n**7 + 0*n**3 - 1/20*n**o + 0*n - 1/10*n**5 - 1/12*n**4 + 2*n**2. Factor i(a).
-2*a*(a + 1)**3
Let m(a) be the first derivative of -a**5/180 + a**4/72 + a**3/9 - 2*a**2 - 3. Let h(p) be the second derivative of m(p). Let h(o) = 0. Calculate o.
-1, 2
Let n be 2 + 2 + (-3)/((-12)/(-16)). Let l(h) be the second derivative of 0 + n*h**3 + 0*h**2 - 1/6*h**4 - 2*h. Factor l(o).
-2*o**2
Let l(c) be the first derivative of c**5/40 + 3*c**4/32 + c**3/8 + c**2/16 - 15. Suppose l(s) = 0. Calculate s.
-1, 0
Let v(b) be the second derivative of -3*b**5/80 + b**4/2 - 2*b**3 + 11*b + 2. Solve v(p) = 0 for p.
0, 4
Suppose -2*t = t - 5*q - 10, 3*t - 17 = -2*q. Factor -4/11*f - 10/11*f**2 + 2/11*f**t - 6/11*f**3 + 0 + 2/11*f**4.
2*f*(f - 2)*(f + 1)**3/11
Let p be 4/(-14) - 69/(-21). Find z, given that 11 + 4*z**p - 5*z + 2*z**4 - 3*z - 6*z**2 - 3 = 0.
-2, 1
Let p(c) be the first derivative of 21*c**4/4 + 5*c**3 - 24*c**2 + 12*c + 16. Factor p(u).
3*(u - 1)*(u + 2)*(7*u - 2)
Let f(b) be the third derivative of 0*b + 1/336*b**8 + 1/60*b**5 - 1/120*b**6 - 1/210*b**7 + 0*b**3 + 0*b**4 + 0 + 7*b**2. Let f(z) = 0. What is z?
-1, 0, 1
Let g = -32/3 + 11. Let y(a) be the first derivative of -a**2 + g*a**3 + a + 1. What is s in y(s) = 0?
1
Suppose 0*s - 2/3*s**3 - 2/9*s**4 + 0*s**2 + 0 = 0. Calculate s.
-3, 0
Let u(g) be the third derivative of -g**9/30240 - g**8/8064 - g**7/10080 + g**5/15 + 3*g**2. Let b(l) be the third derivative of u(l). What is s in b(s) = 0?
-1, -1/4, 0
Let l(y) be the second derivative of y**7/8820 - y**6/1260 + y**5/420 + y**4/3 + y. Let u(g) be the third derivative of l(g). Factor u(d).
2*(d - 1)**2/7
Let b(r) be the third derivative of 0*r - 1/40*r**6 + 7*r**2 + 0 - 1/2*r**3 - 3/8*r**4 - 3/20*r**5. Suppose b(c) = 0. Calculate c.
-1
Let q(k) be the third derivative of 0*k + 0*k**5 + 0 - 1/189*k**7 - 1/216*k**8 + 1/270*k**6 + 0*k**4 + 0*k**3 - 7*k**2. Factor q(b).
-2*b**3*(b + 1)*(7*b - 2)/9
Let a(u) be the second derivative of u**7/420 - u**6/90 + u**5/60 + u**3/3 - 2*u. Let z(w) be the second derivative of a(w). Factor z(y).
2*y*(y - 1)**2
Suppose -8*j = -3*j - 210. Let y be (-12)/j + 24/35. Suppose y*z**4 + 0 + 0*z**2 + 0*z + 2/5*z**3 = 0. What is z?
-1, 0
Let l(z) be the third derivative of -1/30*z**4 + z**2 - 1/105*z**7 + 0 + 0*z**3 + 1/30*z**5 + 0*z + 1/150*z**6. Find x, given that l(x) = 0.
-1, 0, 2/5, 1
Let z(t) be the third derivative of t**5/510 + t**4/68 + 2*t**3/51 - 9*t**2. Determine x, given that z(x) = 0.
-2, -1
Let s(n) be the second derivative of -n**5/4 + 35*n**4/12 - 20*n**3/3 - 40*n**2 - 3*n. Factor s(t).
-5*(t - 4)**2*(t + 1)
Let u = -71 + 356/5. 