-12. Let w(p) be the first derivative of 2/5*p**5 + 1/2*p**4 - x*p**3 - p**2 + 0*p - 2. Let w(o) = 0. What is o?
-1, 0, 1
Factor 1/2*h**2 + 1/2 - h.
(h - 1)**2/2
Let r(o) = -o**2 + 6. Let n be r(0). Solve 7*b**3 - 2*b**5 + n*b**4 + 4*b - 9*b**3 - 5*b**2 - b**2 = 0.
-1, 0, 1, 2
Let x(n) be the first derivative of n**3/3 + 2*n**2 + 2*n + 1. Let g be x(-4). Find c such that 4/3*c**4 + 0*c + 0 - 14/3*c**3 + 14/3*c**5 - 4/3*c**g = 0.
-1, -2/7, 0, 1
Let r(n) be the second derivative of -7*n - 1/60*n**4 + 0 - 1/10*n**2 - 1/15*n**3. Let r(p) = 0. What is p?
-1
Factor -3*u**5 - 340*u**3 + 6*u**2 + 16*u**4 - 4*u**4 + 325*u**3.
-3*u**2*(u - 2)*(u - 1)**2
Let k(s) be the third derivative of 4*s**7/105 - s**6/15 - s**5/10 + s**4/3 - s**3/3 + 3*s**2. Factor k(c).
2*(c - 1)*(c + 1)*(2*c - 1)**2
Let i(f) be the third derivative of -f**8/420 + f**7/420 + f**6/180 - f**3/2 - 4*f**2. Let k(o) be the first derivative of i(o). Factor k(x).
-2*x**2*(x - 1)*(2*x + 1)
Let h(g) = g**2 - 6*g + 8. Let f be h(5). Factor 3*i**2 - 3*i**3 - f + 3.
-3*i**2*(i - 1)
Let y(w) = w + 3 - 4 + 5. Let t be y(0). Factor t*r**2 - 3*r**2 + 2*r - r.
r*(r + 1)
Let m = -594 - -599. Factor -16/3*g**2 - 4/3*g**m + 0 - 16/3*g + 4*g**3 + 8/3*g**4.
-4*g*(g - 2)**2*(g + 1)**2/3
Let x = -1031/5 + 3098/15. Solve -x*b**2 - b - 2/3 = 0 for b.
-2, -1
Let a(v) be the second derivative of 1/12*v**4 + 2*v + 1/2*v**3 + 0 + v**2. Factor a(y).
(y + 1)*(y + 2)
Let b(g) = g**2 + 8*g + 8. Let t be b(-8). Suppose -2 = -2*m + t. Suppose -7/3*o**m + 4/3*o**2 + 14/3*o**3 - 7/3*o - 2/3*o**4 - 2/3 = 0. Calculate o.
-1, -2/7, 1
Find o, given that 7*o**2 - 9*o**3 + 15*o**4 - 10*o**4 + 9*o**5 - 10*o**5 - 2*o = 0.
0, 1, 2
Let l = 17/26 + -2/13. Let l + 3/4*m**2 - 5/4*m = 0. Calculate m.
2/3, 1
Let v(f) = f**3 - f - 1. Let j(m) = -5*m**3 + 12*m**2 - 41*m + 54. Let g(u) = -j(u) - 4*v(u). Suppose g(b) = 0. Calculate b.
2, 5
Let j(v) be the first derivative of -2/33*v**3 + 2 + 1/11*v**2 + 4/11*v. Factor j(l).
-2*(l - 2)*(l + 1)/11
Let a(c) be the third derivative of c**8/1176 + 2*c**7/245 + 13*c**6/420 + 2*c**5/35 + c**4/21 - 2*c**2. Factor a(v).
2*v*(v + 1)**2*(v + 2)**2/7
Find q, given that 12*q**2 + 4 + 21*q**4 + 28*q - 10*q**3 - 96*q**4 + 41*q**2 = 0.
-2/5, -1/3, 1
Let m(h) be the third derivative of h**5/480 - h**4/192 - h**3/24 + 3*h**2. Suppose m(w) = 0. What is w?
-1, 2
Let m(h) = h**2 - 8*h + 1. Let g(w) = -2*w**2 + 15*w - 1. Let o(i) = 4*g(i) + 7*m(i). Let y be o(4). What is z in -8*z**y - 2*z**2 - 1 + 5*z**3 + 1 = 0?
-2/3, 0
Suppose -3*q + 8 + 4 = 0. Suppose -q*k = -k. Find c, given that -c**3 + c**2 + k*c**3 + 0*c**3 = 0.
0, 1
Let b be 6/(-9)*(-3)/2. Let u = 3 + b. Factor -f**2 + u + 0*f**2 - 5 + 2*f.
-(f - 1)**2
Suppose 0 = j - 2*t + 19, -3*j + 34 = 5*t + 124. Let m = j - -25. Find z such that -2*z**4 - 1/2*z**3 + m*z + 0 + 0*z**2 = 0.
-1/4, 0
Let c(s) be the first derivative of -s**4 + 0*s**3 - 2/5*s**5 - 4 + 2*s**2 + 2*s. Find t, given that c(t) = 0.
-1, 1
Let t(b) be the third derivative of -b**9/141120 + b**8/47040 + b**5/60 - 2*b**2. Let i(o) be the third derivative of t(o). Factor i(a).
-3*a**2*(a - 1)/7
Let k be 2/13 + 977/(-13). Let n be 80/k*15/(-6). Determine m, given that 14/9*m**5 - 4/9*m**2 + 0*m + n*m**4 + 2/3*m**3 + 0 = 0.
-1, 0, 2/7
Let g be (1 - 3/6)*-4. Let z(h) = h**2 - 6*h + 4. Let x(n) = -n. Let o(s) = g*x(s) + z(s). Determine a so that o(a) = 0.
2
Let c = 5644 - 28333/5. Let z = c + 23. Solve 4/5*n**3 + 0*n**2 - 4/5*n + z - 2/5*n**4 = 0.
-1, 1
Let t(x) be the third derivative of -x**8/336 - x**7/21 - 11*x**6/40 - 2*x**5/3 - 2*x**4/3 + 14*x**2. Let t(y) = 0. Calculate y.
-4, -1, 0
Let u = 33/2360 + -1/177. Let l(d) be the third derivative of d**2 - 1/60*d**5 + 0*d**4 + 0 + 0*d + 0*d**3 + u*d**6. Factor l(o).
o**2*(o - 1)
Suppose o = 1 + 1. Factor -1 + g - g**3 + 3 - o.
-g*(g - 1)*(g + 1)
Suppose 7*g = 4*g + 9. Let n(s) be the first derivative of -g + 2/21*s**3 + 2/7*s + 2/7*s**2. Factor n(l).
2*(l + 1)**2/7
Suppose -z = 3*z - 28. Let m(b) = -b + 7. Let o be m(7). Find d such that -z*d**3 + o*d**2 - 2*d**4 + 2*d**2 + 24*d**5 - 19*d**3 + 2*d = 0.
-1, -1/4, 0, 1/3, 1
Let z(i) be the first derivative of -3/10*i**4 + 0*i**3 + 2/25*i**5 + 4/5*i**2 - 1 + 0*i. Factor z(v).
2*v*(v - 2)**2*(v + 1)/5
Suppose y + 0*y + 2 = 0. Let c be (y/2 + -2)*-1. Find r such that -2*r**c - 6/5*r**4 + 0 + 2/5*r + 8/5*r**5 + 6/5*r**2 = 0.
-1, -1/4, 0, 1
Let q(p) be the third derivative of p**9/60480 - p**8/6720 + p**7/1680 - p**6/720 + p**5/20 - 4*p**2. Let l(n) be the third derivative of q(n). Factor l(k).
(k - 1)**3
Let b(r) be the second derivative of -r**6/180 + r**5/20 - r**4/6 - r**3/6 + 2*r. Let g(t) be the second derivative of b(t). Factor g(d).
-2*(d - 2)*(d - 1)
Solve 22*v**4 + 14/3*v**5 + 14/3*v**2 - 4*v + 0 + 26*v**3 = 0 for v.
-3, -1, 0, 2/7
Factor -1/3*q**2 + 1/3*q**3 + 0 - 2/3*q.
q*(q - 2)*(q + 1)/3
Let j(x) be the first derivative of -3*x**4/4 + x**3 + 10. Factor j(t).
-3*t**2*(t - 1)
Let d = 6 + 3. Let o = -2 - -4. Suppose -2*a**o + 2*a**3 - d + 9 = 0. Calculate a.
0, 1
Let k be 16/6 + 2/(-1). Let c(r) be the first derivative of -1 + 0*r**2 + 0*r + 3/4*r**4 - k*r**3. Factor c(q).
q**2*(3*q - 2)
Let t = -4 - -4. Suppose 4*k + t = 8. Let 2*y**k + y**3 - y + 0*y**3 - 2*y**3 = 0. What is y?
0, 1
Let u = -59/10 - -32/5. What is q in 3/4*q**4 - 3/4*q - 1/4 + 1/2*q**3 - u*q**2 + 1/4*q**5 = 0?
-1, 1
Let m(f) be the second derivative of -f**7/189 - f**6/135 + f**5/18 + f**4/54 - 8*f**3/27 + 4*f**2/9 - 7*f. Factor m(b).
-2*(b - 1)**3*(b + 2)**2/9
Let t(z) be the second derivative of -z**6/120 - z**5/40 - z**4/48 - 7*z. Factor t(w).
-w**2*(w + 1)**2/4
Let m(s) be the first derivative of -1 + 4/5*s**5 - 2*s**4 + 3/2*s**3 - 2*s - 1/2*s**2. Let a(o) be the first derivative of m(o). Let a(v) = 0. What is v?
1/4, 1
Let h(i) = -i**3 + 3*i**2 + i - 3. Let g(v) = -3*v**3 + 2*v + 9*v**2 + 4*v - 4*v - 4 - 4. Suppose -27 = -3*u + 6. Let r(m) = u*h(m) - 4*g(m). Factor r(d).
(d - 1)**3
Determine u, given that -9*u**3 + 36*u + 6*u**3 - 15*u - 18 = 0.
-3, 1, 2
Let l(a) = -2*a**2 + 2*a - 12. Let x(r) = r**2 - r + 8. Let f(b) = -5*l(b) - 8*x(b). Factor f(o).
2*(o - 2)*(o + 1)
Let o(l) = -l**2 - 8*l. Let j be o(-6). Factor j - 4 - 26*h + 2*h + 10*h**2.
2*(h - 2)*(5*h - 2)
Factor -2*l**3 + 4 - 78*l**2 + l**3 + l + 74*l**2.
-(l - 1)*(l + 1)*(l + 4)
Let l be -3*-1*(-6)/(-9). Let r(o) = o. Let b be r(l). Factor b*c - 4*c**3 + 0*c**4 - 6*c - 1 + 0*c**4 - 6*c**2 - c**4.
-(c + 1)**4
Suppose 2*q - 4*u + 94 = 0, 283 = -5*q - 6*u + 4*u. Let o = -273/5 - q. Factor o*k + 4/5*k**2 - 4/5*k**3 - 2/5*k**4 - 2/5 + 2/5*k**5.
2*(k - 1)**3*(k + 1)**2/5
Let u be 71/(-3)*6/8. Let h = 18 + u. Factor 1/4*l**3 + 1/4*l**2 + 0 - 1/4*l - h*l**4.
-l*(l - 1)**2*(l + 1)/4
Let o be ((-2)/5)/(34/(-170)). Factor -4/5*p + 6/5 + 2/15*p**o.
2*(p - 3)**2/15
Suppose 0*c + 2*c = 4. Suppose -2*g - 2*i + 11 = -5*i, -3*g - c*i = -10. Solve -k**g - 2*k - k**2 + 2*k**2 + 2*k = 0.
-1, 0, 1
Let d = 873 + -1252. Let s = -1883/5 - d. Determine k, given that 3/5*k**2 + 0*k + 0 + 3*k**4 - 6/5*k**5 - s*k**3 = 0.
0, 1/2, 1
Let l(d) be the third derivative of -1/4*d**4 + 0 + 0*d - 1/2*d**3 - 2*d**2 - 1/20*d**5. Factor l(m).
-3*(m + 1)**2
Suppose 4*i - i + 2 = u, i - 8 = -4*u. Factor 3*g + 2 + g - u*g**2 - 4*g.
-2*(g - 1)*(g + 1)
Let y(h) be the third derivative of h**5/60 - h**4/6 + h**3/2 + h**2. Factor y(m).
(m - 3)*(m - 1)
Let u(y) be the first derivative of -35*y**6/6 + 26*y**5 - 135*y**4/4 + 20*y**3/3 + 10*y**2 + 18. Suppose u(v) = 0. What is v?
-2/7, 0, 1, 2
Let c = 0 - -3/2. Let s(u) be the first derivative of -u**3 - u + 1/4*u**4 + c*u**2 - 1. Factor s(f).
(f - 1)**3
Let w be 3/(-8)*11/(-33). Let u(r) be the first derivative of -1/6*r**3 + 0*r - 2 + 0*r**2 - w*r**4. Factor u(m).
-m**2*(m + 1)/2
Suppose -4*l + 1 = -15. Let g(y) = 4*y**2 - 1. Let i be g(1). Solve -1/5*b**i - 1/5*b**2 + 1/5*b**l + 1/5*b + 0 = 0 for b.
-1, 0, 1
Let r(z) be the first derivative of -1/2*z**4 - 1/3*z**2 + 2/15*z**5 + 0*z - 3 + 2/3*z**3. Factor r(t).
2*t*(t - 1)**3/3
Factor 0*x - x**2 - 19/10*x**3 - 4/5*x**4 + 0 + 1/10*x**5.
x**2*(x - 10)*(x + 1)**2/10
Let d(w) = -7*w**4 - 20*w**3 - 19*w**2 - 4*w. Let x(h) = h**4 + h**2. Let l(a) = -d(a) - x(a). Factor l(g).
2*g*(g + 1)*(g + 2)*(3*g + 1)
Fact