**5 - 1/105*j**6 + 0*j**3 - 2*j + 0*j**2 - 1/42*j**4. Factor k(p).
-2*p**2*(p - 1)**2/7
Let z = -18 + 30. Let 3 - r - 5 - 3*r**4 - 7*r**4 + z*r**2 + r**3 = 0. Calculate r.
-1, -2/5, 1/2, 1
Suppose 5*c - 4*n - 30 = 0, 0 = -6*c + c - n + 5. Factor 19*h**c - 8 - 4*h**3 + 3*h + h - 11*h**2.
-4*(h - 2)*(h - 1)*(h + 1)
Let h(q) = -11*q**3 + 2*q**2 - 8*q. Let p(s) = 4*s**3 - s**2 + 3*s. Let y(b) = -3*h(b) - 8*p(b). Suppose y(o) = 0. What is o?
-2, 0
Let q(a) = 7*a + 191. Let t be q(-27). Determine j, given that -j**3 + 0*j**t + j + 1/2 - 1/2*j**4 = 0.
-1, 1
Let f(z) = -2*z**2 + 10*z - 2. Let r(o) = 7*o**2 - 29*o + 6. Let i(d) = 8*f(d) + 3*r(d). Determine h, given that i(h) = 0.
2/5, 1
Let q = 3 + -1. Suppose 0 = -6*r + 4*r + q. Find p such that -1/2*p**3 + 1/2*p - r + p**2 = 0.
-1, 1, 2
Suppose 1 - 1/4*r**2 - 3/4*r = 0. Calculate r.
-4, 1
Suppose -11*g + 7*g = -16. What is t in 0*t + 0 + t**g + 0*t**2 - 3/2*t**5 + 1/2*t**3 = 0?
-1/3, 0, 1
Let s be (-10)/5 - 7/(-3). Let u = s - -1/6. What is n in 0*n + 0 - u*n**3 + 1/2*n**2 = 0?
0, 1
Let w(a) be the first derivative of 5*a**4/4 - 25*a**3/3 + 20*a**2 - 20*a - 20. Find j such that w(j) = 0.
1, 2
Suppose 15*w**2 - 2*w**2 + w**2 + 4*w + 2*w**5 + 16*w**4 + 18*w**3 - 6*w**4 = 0. What is w?
-2, -1, 0
Suppose -16/9*z**4 + 4/9*z**2 + 0 + 0*z - 2/9*z**3 - 10/9*z**5 = 0. What is z?
-1, 0, 2/5
Let s(q) be the third derivative of q**8/20160 + q**4/6 + 3*q**2. Let f(a) be the second derivative of s(a). Suppose f(n) = 0. Calculate n.
0
Let y(k) be the second derivative of k**4/10 - k**3/15 + 23*k. Find f such that y(f) = 0.
0, 1/3
Let u(h) be the first derivative of -h**4/36 + h**3/27 + h**2/9 - 14. Factor u(g).
-g*(g - 2)*(g + 1)/9
Let y = 15 + -11. Suppose -2*r = 2*m - m - y, -28 = -4*r + 3*m. Solve g**2 + 11*g**2 - 1 + 8*g**3 - 2*g - 6*g**5 - 8*g**r - 3 = 0 for g.
-1, 2/3, 1
Let m(j) = j + 1. Let q be m(0). Let l = q + 1. Let -2/5 - 2/5*o**3 + 2/5*o + 2/5*o**l = 0. Calculate o.
-1, 1
Let j = 12081 + -471097/39. Let i = j + -12/13. Solve 0 + 0*x + 0*x**2 + i*x**4 + 0*x**3 = 0.
0
Let y = -40 - -43. Factor 12/5*r**y + 0 + 2/5*r**5 + 2/5*r - 8/5*r**4 - 8/5*r**2.
2*r*(r - 1)**4/5
Let y(x) = 64*x**4 + 104*x**3 + 56*x**2 + 4*x - 4. Let g(b) = -65*b**4 - 104*b**3 - 57*b**2 - 3*b + 5. Let w(n) = -4*g(n) - 5*y(n). Let w(j) = 0. What is j?
-1, -2/5, -1/3, 0
Determine a so that -40/9 + 2/9*a**3 - 32/9*a - 2/9*a**2 = 0.
-2, 5
Let p(u) be the third derivative of u**8/672 - u**7/140 + u**6/240 + u**5/40 - u**4/24 - u**2. Factor p(n).
n*(n - 2)*(n - 1)**2*(n + 1)/2
Factor 0 + 0*g - 2/3*g**3 + 0*g**2.
-2*g**3/3
Let p(g) be the first derivative of 7*g**9/1080 - g**8/150 + g**7/525 + 2*g**3/3 - 3. Let y(o) be the third derivative of p(o). Factor y(q).
2*q**3*(7*q - 2)**2/5
Let g(b) = 3*b - 3. Let t be g(-6). Let j = t + 31. Solve 5*p**4 + 8*p**5 - 2*p**5 - j*p**3 - 2*p**4 + 4*p - p**4 - 2*p**2 = 0 for p.
-1, 0, 2/3, 1
Let o be (-2)/(-4) - (-6)/4. Let u be (-14)/(-10) + (1 - o). Factor 0*q + 0 + 2/5*q**4 - 2/5*q**2 + 2/5*q**5 - u*q**3.
2*q**2*(q - 1)*(q + 1)**2/5
Suppose 4 = -31*v + 33*v. Let x(s) be the second derivative of 1/45*s**6 - s + 0*s**3 + 0*s**5 + 1/3*s**v + 0 - 1/9*s**4. Factor x(o).
2*(o - 1)**2*(o + 1)**2/3
Let c be 7/(-7) - (24/(-10) + 1). Find d such that 0 + 1/5*d + c*d**2 + 1/5*d**3 = 0.
-1, 0
Let g(a) be the first derivative of 2*a**3/15 + 4*a**2/5 + 6*a/5 - 12. Factor g(o).
2*(o + 1)*(o + 3)/5
Let l(a) = 3*a**2 + 2*a. Let b be l(-2). Suppose -4 = 2*w - b. Factor -6/7*d**3 + 0 + 6/7*d**4 + 2/7*d**w - 2/7*d**5 + 0*d.
-2*d**2*(d - 1)**3/7
Let k(m) be the third derivative of m**7/42 + m**6/8 - m**5/4 - 35*m**4/24 + 5*m**3 - 19*m**2. Find b such that k(b) = 0.
-3, -2, 1
Suppose -2*a = a - 6. Let m = 1 + a. Factor x**4 - x**2 - 3*x**2 + m*x**2 + x**3 - x**5.
-x**2*(x - 1)**2*(x + 1)
Let g(v) be the first derivative of -7*v**3/3 - 15*v**2/2 - 8*v - 3. Let s(y) = -3*y**2 - 7*y - 4. Let k(f) = 3*g(f) - 5*s(f). Solve k(u) = 0 for u.
-1, -2/3
Let c be (-2)/12 - (-258)/36. Solve c*v**4 - 4*v**4 - 3*v**5 + 0*v**4 = 0 for v.
0, 1
Let y(a) be the first derivative of -a**4/16 + a**3/12 + a**2/8 - a/4 - 10. Factor y(c).
-(c - 1)**2*(c + 1)/4
Let r(v) be the second derivative of -v**4/42 + 8*v**3/21 - 16*v**2/7 + 3*v. Factor r(z).
-2*(z - 4)**2/7
Let m(l) be the third derivative of 3*l**3 - 6*l**2 + 1/30*l**5 + 1/2*l**4 + 0*l + 0. Factor m(z).
2*(z + 3)**2
Suppose 3*i - 30 = -7*i. Let h(y) be the second derivative of -1/2*y**i + 0 - 3/20*y**5 + 0*y**2 + 1/2*y**4 - 3*y. Find d such that h(d) = 0.
0, 1
Let h(k) be the second derivative of -2/15*k**3 + 2*k + 0*k**2 + 0*k**4 + 1/25*k**5 + 0. Let h(u) = 0. Calculate u.
-1, 0, 1
Let i = 481/8 + -60. Let h(a) be the first derivative of 2 + 1/12*a**3 + i*a**2 + 0*a. Factor h(d).
d*(d + 1)/4
Suppose 4/3*w - 2/3 - 2/3*w**2 = 0. What is w?
1
Suppose -2*f + 3*b = 0, 0 = -2*f - 3*f + b. Let c = 2 - f. Factor -2*s + 0*s + c*s**2 + 0*s.
2*s*(s - 1)
Let u(o) = 14*o**2 - 20*o + 50. Let m(l) = 2*l**2 - 3*l + 7. Let c(t) = -44*m(t) + 6*u(t). Find q, given that c(q) = 0.
1, 2
Suppose -5*q - 3*s + 22 = 0, -4*s = -2*q + s - 16. Suppose q*x = -2*x + 8. Factor -3/2*b**3 - 1 + 1/2*b**4 + 1/2*b**x + 3/2*b.
(b - 2)*(b - 1)**2*(b + 1)/2
Let c(y) be the second derivative of -y**7/5040 - y**6/1440 + y**5/120 + y**4/6 - 3*y. Let r(i) be the third derivative of c(i). Solve r(p) = 0.
-2, 1
Let o = -1709/8 + 214. Let b = o - -1/8. What is v in b*v**2 + 0 + 0*v = 0?
0
Factor -53*j + 3*j - 13*j**2 + 14*j**3 - 12 - 11*j**2.
2*(j - 3)*(j + 1)*(7*j + 2)
Let y(n) be the second derivative of n**6/1080 + n**5/360 + 2*n**3/3 + 4*n. Let k(m) be the second derivative of y(m). Factor k(q).
q*(q + 1)/3
Suppose -6*v + v = w - 12, 6 = -2*v + 5*w. Suppose -c - 5 = -2*d - 15, 4*d - 4 = -4*c. Factor -a**2 - v*a - 3*a**3 - c*a**2 + 0*a**3.
-a*(a + 1)*(3*a + 2)
Let a(u) be the third derivative of 4/15*u**5 + 0*u**4 + 0*u - 25/84*u**8 - 4/5*u**6 + 0*u**3 + 6/7*u**7 + 0 - 9*u**2. Factor a(v).
-4*v**2*(v - 1)*(5*v - 2)**2
Let a(f) be the second derivative of 17*f**4/12 - 11*f**3/6 - 4*f. Let z(r) = 9*r**2 - 6*r. Let b(i) = 6*a(i) - 11*z(i). Solve b(u) = 0.
0
Let v be (3/18)/((21/(-3))/(-14)). Determine a, given that -v*a**2 + 0*a - 1/3*a**3 + 0 = 0.
-1, 0
Let g(y) = -y + 7. Let p be g(6). Factor p - 2 - 2*w**2 - w**2 + 3*w + 0*w**3 + w**3.
(w - 1)**3
Suppose 4*i = 14 - 2. Let -5/2*o**i + 0 + 7/2*o**4 + 0*o - o**2 = 0. What is o?
-2/7, 0, 1
Suppose -5*w = -12 - 3. Factor w*v**2 + v**2 - 3*v**2 - 2*v**2 + v + 2.
-(v - 2)*(v + 1)
Determine x, given that -3*x**2 + 0*x - 5*x**2 - 13*x**2 - 3*x**4 - 9*x - 15*x**3 = 0.
-3, -1, 0
Let c(g) be the third derivative of -g**7/42 - 11*g**6/24 - 9*g**5/4 - 125*g**4/24 - 20*g**3/3 - 2*g**2. Suppose c(y) = 0. What is y?
-8, -1
Factor 4/9*w**4 + 8/9*w + 8/3*w**2 + 2*w**3 + 0.
2*w*(w + 2)**2*(2*w + 1)/9
Suppose -4*w + w = -5*k, 2*k + 4*w = 26. Suppose -20*r**4 + 4*r**2 + 2*r - 7*r**k + 8*r**5 - 6*r + 19*r**3 = 0. Calculate r.
-1/2, 0, 1
Let f(r) be the second derivative of 0 + 1/3*r**2 + 1/36*r**4 - 5*r - 1/6*r**3. Factor f(g).
(g - 2)*(g - 1)/3
Factor 1/3*h**2 + 0 + 0*h.
h**2/3
Suppose 0 = -2*p + 4 + 2. Suppose 0 = p*t - 148 + 16. Factor -c**5 + 14*c + 2 + 26*c**4 + 36*c**2 + 0*c**5 + t*c**3 + 7*c**5.
2*(c + 1)**4*(3*c + 1)
Let s(m) = -m**3 + 5*m**2 - 4*m - 1. Let c be s(4). Let b be -5*(-3)/(-15)*c. Factor -b + o + 4*o + 3 + o - 8*o**2.
-2*(o - 1)*(4*o + 1)
Let f = -20 + 28. Suppose -4*c + 8*c = f. Factor -c*y**3 + y**3 + y**5 + 0*y**3 - y**2 + 3*y**4 - 2*y**4.
y**2*(y - 1)*(y + 1)**2
Let n(s) be the first derivative of -s**4/48 - s**3/24 + s**2/4 + 2*s - 3. Let l(c) be the first derivative of n(c). Factor l(j).
-(j - 1)*(j + 2)/4
Let k(y) be the second derivative of -y**6/300 - y**5/150 + y**4/60 + y**3/15 + 5*y**2/2 + 6*y. Let a(q) be the first derivative of k(q). Factor a(n).
-2*(n - 1)*(n + 1)**2/5
Suppose i = -4*k + 5*i, -4*k - 3*i = -28. Let r(h) be the first derivative of 2/3*h**3 - h**k + 2/5*h**5 + 0*h + 1 + 0*h**2. Factor r(v).
2*v**2*(v - 1)**2
Let h be 0 + 1 - (4 + -7). Let q(i) = -2 + 3*i**2 + 1 + 2*i - 4. Let s(m) = 4*m**2 + 3*m - 6. Let f(o) = h*s(o) - 5*q(o). Factor f(v).
(v + 1)**2
Factor -9/7*l**3 - 3/7*l**4 + 0 + 9/7*l + 3/7*l**2.
-3*l*(l - 1)*(l + 1)*(l + 3)/7
Let p(i) = -i. Let