i be ((-2)/(-6))/(3/(-18)). Let w(a) = -a**2 - 2*a + 1. Let n(t) = -4*t**2 - 7*t + 4. Let u(z) = i*n(z) + 7*w(z). Factor u(b).
(b - 1)*(b + 1)
Let v = -4 + 5. Let w(s) = -5*s**3 - 5*s**2 + 6*s + 6. Suppose -3*x = -4*x + 6. Let t(n) = n**3 + n**2 - n - 1. Let b(i) = v*w(i) + x*t(i). Factor b(u).
u**2*(u + 1)
Let p(h) = h**2 - 12*h + 32. Let i be p(3). Factor -1/3 - 1/3*f**i - 1/3*f**4 + 2/3*f**2 + 2/3*f**3 - 1/3*f.
-(f - 1)**2*(f + 1)**3/3
Let y(j) be the first derivative of j**6/18 + j**5/15 - 5*j**4/6 - 4*j**3/9 + 4*j**2 + 39. Suppose y(p) = 0. What is p?
-3, -2, 0, 2
Let a(w) be the second derivative of 0*w**2 - 1/9*w**3 + 0 + 4*w + 7/36*w**4. Factor a(k).
k*(7*k - 2)/3
Let s(u) = -12*u**2 + 6*u - 9. Let n(p) = p**2 - p + 1. Let w(h) = -9*n(h) - s(h). Solve w(a) = 0.
-1, 0
Let x = -47 + 47. Suppose x + 0*s - 1/2*s**2 = 0. What is s?
0
Let m = 3 + -6. Let w = m - -3. Factor 1/3*s**2 + 0*s + 4/3*s**3 + w.
s**2*(4*s + 1)/3
Solve -6/7*j**3 + 2/7 + 6/7*j + 2/7*j**2 - 4/7*j**4 = 0.
-1, -1/2, 1
Factor 10/3 + 5/3*b**2 + 5*b.
5*(b + 1)*(b + 2)/3
Let m = -3 + -2. Let f = -1 - m. Let f*p**4 + 2*p**2 + 0*p**4 - 6*p**4 = 0. Calculate p.
-1, 0, 1
Let u(y) be the first derivative of -y**4/20 - y**3/15 + y**2/5 - 4. Find b such that u(b) = 0.
-2, 0, 1
Let v = 1/16 + 3/16. Let l(b) be the first derivative of 1/2*b**2 + 1/3*b**3 - b - v*b**4 + 3. Find w, given that l(w) = 0.
-1, 1
Let k(z) be the second derivative of z**4/60 + z**3/6 + 2*z**2/5 + 22*z. Factor k(j).
(j + 1)*(j + 4)/5
Let u(j) be the third derivative of -j**6/180 - j**5/12 - j**4/3 - 2*j**3/3 + 10*j**2. Let t(q) be the first derivative of u(q). Find s, given that t(s) = 0.
-4, -1
Suppose -53 = -18*x + 19. Find h, given that 4/5*h**3 + 0 + 2/5*h**x + 2/5*h**2 + 0*h = 0.
-1, 0
Factor 2*l**5 - 6*l + 10*l + 4*l**4 - 4*l**2 - 6*l.
2*l*(l - 1)*(l + 1)**3
Let 6/23 + 2/23*r**2 + 8/23*r = 0. What is r?
-3, -1
Solve -3/2*u**2 - 9*u + 0 = 0 for u.
-6, 0
Let p(s) be the third derivative of -s**5/30 + 7*s**4/12 + 7*s**2. Factor p(a).
-2*a*(a - 7)
Suppose 4*c - 4 = -4*f, f - c - 2*c = -3. Solve 2/3*h**4 + f*h - 2/3*h**2 + 0*h**3 + 0 = 0 for h.
-1, 0, 1
Let a(v) = -v + 5. Let y be a(3). Factor o - 27 + 17*o + 25*o**2 - 28*o**y.
-3*(o - 3)**2
Let h(w) be the second derivative of -1/36*w**4 + w + 0 + 1/3*w**2 - 1/18*w**3. Factor h(v).
-(v - 1)*(v + 2)/3
Suppose 0*k = 2*k - 2. Let f be 6 + -3 + (-3)/k. Factor 0*m + f - 2/9*m**2 + 2/9*m**3.
2*m**2*(m - 1)/9
Let t(u) be the third derivative of u**5/20 + u**4/2 + 2*u**3 - 16*u**2. What is a in t(a) = 0?
-2
Let n(z) = z + 21. Let o be n(-7). Suppose 0 = 5*c + o - 34. Suppose 0 - 1/4*f**c - 5/4*f**3 - f - 2*f**2 = 0. What is f?
-2, -1, 0
Suppose 2/19*v**4 - 20/19*v**3 + 26/19*v**2 + 72/19 + 120/19*v = 0. Calculate v.
-1, 6
Let d(q) be the third derivative of -q**8/504 + q**7/315 + q**6/36 - q**5/18 - q**4/9 + 4*q**3/9 + 24*q**2. Find w such that d(w) = 0.
-2, -1, 1, 2
Let u(f) = -12*f**2 + 26*f - 18. Let j(w) = -w**3 - 12*w**2 + 27*w - 19. Let y(a) = 2*j(a) - 3*u(a). Let y(p) = 0. What is p?
2
Let r(d) be the third derivative of -d**8/224 + d**7/35 - d**6/16 + d**5/20 + 6*d**2. Factor r(p).
-3*p**2*(p - 2)*(p - 1)**2/2
Let a(x) be the third derivative of -x**5/300 + x**4/60 + 3*x**2. Factor a(t).
-t*(t - 2)/5
Suppose 0 = -9*h + 8*h. Determine j, given that 1/4 - 1/2*j + 1/2*j**3 - 1/4*j**4 + h*j**2 = 0.
-1, 1
Let b(n) be the second derivative of 2*n**6/15 - 3*n**5/4 + 4*n**4/3 - n**3/2 - n**2 - 12*n - 1. Factor b(g).
(g - 2)*(g - 1)**2*(4*g + 1)
Suppose 3*a = -4*i + 14, a + 5*i = -3*a + 18. Let g(d) be the second derivative of -1/7*d**3 + 0 - 2/7*d**a - 1/42*d**4 + 3*d. Factor g(y).
-2*(y + 1)*(y + 2)/7
Solve 3*q**3 - q - 4*q + 2*q**3 + 0*q = 0.
-1, 0, 1
Let n be 20/6 + (-3)/9. Let m(j) be the second derivative of 0 + 7/3*j**6 + 7/3*j**4 + 0*j**2 + 2/3*j**n + 69/20*j**5 + 2*j + 25/42*j**7. Factor m(a).
a*(a + 1)**2*(5*a + 2)**2
Let t(p) be the second derivative of p**9/30240 - p**8/13440 + p**4/12 - 3*p. Let v(y) be the third derivative of t(y). Suppose v(b) = 0. Calculate b.
0, 1
Let f be 1 - 1/((-1)/1). Let p = 33 - 33. Factor -s + p*s**f + s**2 + 2*s.
s*(s + 1)
Let a be 1/(1/2) + 4. Factor -34*o + 33*o - o**2 - 4 + a.
-(o - 1)*(o + 2)
Let v(m) = -4*m**2 + 4 - 2*m**2 + 6*m + 4*m**2 + 4*m**2. Let l(n) = -6*n**2 - 18*n - 12. Let f(a) = -5*l(a) - 16*v(a). Let f(b) = 0. What is b?
-2, -1
Suppose -b = 2*x - 11, -x - 3 = -2*b - 1. Let -h**b + 0*h**4 + 1/2*h + 0 + 1/2*h**5 + 0*h**2 = 0. What is h?
-1, 0, 1
Let q(u) be the third derivative of -7*u**8/96 + u**7/6 + u**6/80 - u**5/6 - u**4/12 - 8*u**2. Factor q(n).
-n*(n - 1)**2*(7*n + 2)**2/2
Let k = -261 - -265. Factor -12*u**k + 45/4*u**2 - 18*u**3 - 3/2*u + 0.
-3*u*(u + 2)*(4*u - 1)**2/4
Let s(n) be the third derivative of 2*n**7/735 + n**6/60 + 3*n**5/70 + 5*n**4/84 + n**3/21 - 7*n**2. Factor s(w).
2*(w + 1)**3*(2*w + 1)/7
Let m(b) = 3*b + b - 3*b - 1. Let r be m(3). Suppose -3*l - r - l**2 + 0*l**2 + 0 = 0. Calculate l.
-2, -1
Suppose 0 = 4*d - 3*t - 12, 1 = -t - 3. Suppose 4*b - 3*a + 5 = -2, 5*b + a - 15 = d. Suppose -4/5 + 6/5*i**3 - 6/5*i + 4/5*i**b = 0. Calculate i.
-1, -2/3, 1
Suppose 0*o + 12 = -5*o - 4*p, 9 = -4*o - 3*p. Solve 2/3*u**4 - 2/3*u**5 + o + 0*u + 4/3*u**3 + 0*u**2 = 0 for u.
-1, 0, 2
Let r(l) = -6*l. Let g be r(-1). Suppose -6*v + 4*v**3 - 3*v**2 + 2*v**5 - v**2 + g*v**4 + 0*v**2 - 2 = 0. Calculate v.
-1, 1
Let u(d) be the second derivative of -d**4/3 - 8*d**3/3 - 8*d**2 - 5*d. Factor u(x).
-4*(x + 2)**2
Let q(z) be the second derivative of -z**8/11200 + z**6/1200 - z**4/12 + z. Let t(d) be the third derivative of q(d). Factor t(n).
-3*n*(n - 1)*(n + 1)/5
Let k(z) be the first derivative of 3/2*z**2 + 1/24*z**4 + 0*z + 1 + 1/120*z**6 + 0*z**3 - 1/30*z**5. Let u(a) be the second derivative of k(a). Factor u(n).
n*(n - 1)**2
Let i = -645/4 - -162. Determine d, given that 1/2*d**2 + 0 - 1/4*d**3 + 0*d - i*d**4 = 0.
-1, 0, 2/3
Let b(k) be the second derivative of -3*k - 2/3*k**3 + 7/6*k**4 + 0*k**2 + 0. Solve b(g) = 0.
0, 2/7
Let p(f) be the third derivative of -1/84*f**4 + 0*f - 3*f**2 + 0*f**3 + 1/210*f**5 + 0. Determine j so that p(j) = 0.
0, 1
Let g(z) be the first derivative of -z**3/15 - z**2/5 - z/5 + 27. Factor g(d).
-(d + 1)**2/5
Let g be ((-6)/15)/((-24)/(-15))*-8. Let y(b) be the first derivative of 0*b - g*b**2 - 2/3*b**3 - 1. Determine f, given that y(f) = 0.
-2, 0
Suppose 4*p = -0*p - 16, -68 = -5*l - 3*p. Suppose -4/7*j + 0 - 32/7*j**5 + l*j**4 + 38/7*j**2 - 114/7*j**3 = 0. Calculate j.
0, 1/4, 1, 2
Suppose n = -4*n + 2*z + 29, 0 = -2*z + 6. Let c = n - 5. Factor -2*t**3 + 3*t - 3*t**2 + 7*t**c - 2*t - 3*t.
-2*t*(t - 1)**2
Let g(f) be the third derivative of -1/150*f**5 + 1/300*f**6 + 0*f**3 + 2*f**2 - 1/60*f**4 + 0*f + 1/525*f**7 + 0. Factor g(v).
2*v*(v - 1)*(v + 1)**2/5
Factor 20 - 40*c + 0*c**2 + 2*c**2 - 120 - 6*c**2.
-4*(c + 5)**2
Let o(m) be the second derivative of -7*m**8/120 + m**7/20 + 2*m**6/15 + m**5/15 + m**3/6 + 2*m. Let g(w) be the second derivative of o(w). Factor g(d).
-2*d*(d - 1)*(7*d + 2)**2
Let n(k) be the third derivative of k**6/40 + k**5/10 + k**4/8 - k**2. Determine i so that n(i) = 0.
-1, 0
Suppose -4*g + i = -6, -2*i = -5*g - 6 + 15. Suppose h - 3 - g = 0. Factor -3*y**3 - 3*y - 10*y**h - 3*y**2 + 6*y**3 + 13*y**4.
3*y*(y - 1)*(y + 1)**2
Let z be 7/(70/(-18) + 4). Let g be ((-9)/6)/(z/(-24)). Factor 2/7*w**2 + 2/7*w - g.
2*(w - 1)*(w + 2)/7
Let r(h) be the third derivative of 0*h - 1/12*h**6 - 7/12*h**4 - 3/10*h**5 + 6*h**2 - 1/105*h**7 - 2/3*h**3 + 0. Suppose r(j) = 0. Calculate j.
-2, -1
Let x(z) = -4*z + 4. Let l(j) = 9*j - 8. Let i(w) = 3*l(w) + 7*x(w). Let n be i(2). Solve 0 + 4/7*b**4 + 0*b + 6/7*b**5 - 6/7*b**3 - 4/7*b**n = 0 for b.
-1, -2/3, 0, 1
Suppose -3*o - 16 = o. Let a(u) = u**2 + 3*u - 4. Let w be a(o). Factor 0*z**3 - 1/3*z**5 + w - 2/3*z**2 + 2/3*z**4 + 1/3*z.
-z*(z - 1)**3*(z + 1)/3
Let v(z) be the third derivative of -z**8/320 - z**7/315 + z**6/180 + z**4/4 + 9*z**2. Let b(r) be the second derivative of v(r). Solve b(s) = 0.
-2/3, 0, 2/7
Let k(q) = q + 7. Let s be k(-7). Suppose s = -6*n + 3*n. Factor n*h - 2/7*h**2 + 4/7*h**3 + 0 - 2/7*h**4.
-2*h**2*(h - 1)**2/7
Let y(k) be the third derivative of k**8/840 - k**7/630 + k**6/1440 + k**4/