
Let m(y) be the third derivative of y**8/6720 - y**6/720 - y**4/12 - 2*y**2. Let k(t) be the second derivative of m(t). Suppose k(c) = 0. What is c?
-1, 0, 1
Factor -4/11*t**2 + 2/11*t + 0*t**3 + 4/11*t**4 - 2/11*t**5 + 0.
-2*t*(t - 1)**3*(t + 1)/11
Let d(k) = k**2 - 2*k. Let f be d(2). Let j(t) be the first derivative of f*t**4 + 2/9*t**3 - 2/45*t**5 + 2/9*t**2 + 0*t + 2. Factor j(b).
-2*b*(b - 2)*(b + 1)**2/9
Let d(y) be the third derivative of y**6/360 - y**5/30 + y**4/8 - 3*y**2. Factor d(u).
u*(u - 3)**2/3
Let p = -74/153 + 12/17. Factor 0 + p*a**3 + 2/9*a + 4/9*a**2.
2*a*(a + 1)**2/9
Suppose 2*f - 6 = -0*f. Let d(i) be the first derivative of -f + 0*i**2 + 1/4*i**3 - 3/4*i. Factor d(t).
3*(t - 1)*(t + 1)/4
Suppose -8 = -5*x + f - 27, 0 = x - 4*f. Let m be -1 + x/(28/(-73)). Let -2/7*a + 0 - 32/7*a**5 - 20/7*a**2 - 80/7*a**4 - m*a**3 = 0. What is a?
-1, -1/4, 0
Let w(n) = -n**2 - 4*n + 12. Let p be w(-6). Let d(u) be the second derivative of -1/30*u**5 - 1/36*u**4 + 0*u**2 - 2*u - 1/90*u**6 + p + 0*u**3. Factor d(r).
-r**2*(r + 1)**2/3
Suppose -1 = -3*z + 2*y - 12, 4*z + 10 = -2*y. Let t be z/(-21) + (-51)/(-84). Find w, given that -3/4 + 3/4*w**2 - 3/4*w**3 + t*w = 0.
-1, 1
Let t(h) = 1. Let q(u) = -5*u**2 - 15*u + 5. Let y(l) = -q(l) + 5*t(l). Factor y(i).
5*i*(i + 3)
Let b(n) = 8*n**2 - 2*n + 1. Let y(u) = -u**2. Let r be (1 - -1)*(-21)/(-2). Let g = -1 - -4. Let a(q) = g*b(q) + r*y(q). What is i in a(i) = 0?
1
Suppose n - 20 = -9*n. Find i such that 0*i - 2/9*i**4 + 0 - 2/9*i**3 + 0*i**n = 0.
-1, 0
Let d(l) be the first derivative of l**3 - 3/2*l**2 + 3 - 6*l. Factor d(x).
3*(x - 2)*(x + 1)
Let i(s) = 4*s**3 - 2*s + 0 - 1 + 1. Let b(l) = -9*l**3 + l**2 + 5*l. Let j(d) = -2*b(d) - 5*i(d). Suppose j(g) = 0. What is g?
-1, 0
Let b(f) be the first derivative of -f**4/4 + f**3 + 3*f - 1. Let u be b(3). Factor -1/4*v**2 + 0 + 0*v - 1/4*v**u.
-v**2*(v + 1)/4
Let i(n) = -n**3 - 14*n**2 - 15*n - 6. Let k be i(-13). Let j be -2 + 8/k + 2. Determine p, given that -4/5 - j*p**4 + 2/5*p**3 - 2/5*p + 6/5*p**2 = 0.
-1, 1, 2
Let q(y) be the first derivative of 1/5*y**5 - 1 + y + 0*y**6 + 0*y**2 - 1/21*y**7 + 0*y**4 - 1/3*y**3. Let v(a) be the first derivative of q(a). Factor v(d).
-2*d*(d - 1)**2*(d + 1)**2
Let n(v) be the first derivative of 9/4*v**4 - 1/2*v**6 + 2 + 3*v**2 + 3/5*v**5 + 0*v - 5*v**3. Factor n(g).
-3*g*(g - 1)**3*(g + 2)
Let r be 1 - (-2)/(-2)*-2. Factor -4*a**2 - 7*a + a**2 + 2 + a**2 + 7*a**r.
(a - 1)*(a + 1)*(7*a - 2)
Let j be 3 - 2*(-1 - 0). Let 6*q**4 + q**j - 8*q**4 + q**3 + 4*q**4 = 0. Calculate q.
-1, 0
Let p be (-1)/9*(-3 - -4). Let u = p + 13/36. Find x, given that -u*x**2 + 1/2 - 1/4*x = 0.
-2, 1
What is x in 0 + 8/7*x**2 + 2/7*x**5 + 8/7*x - 6/7*x**3 - 4/7*x**4 = 0?
-1, 0, 2
Suppose -5*q + 0*g - 18 = -2*g, -3*g = 3. Let j(c) = -c**3 + c - 1. Let s(b) = 6*b**3 + 2*b**2 - 4*b + 4. Let o(p) = q*j(p) - s(p). Factor o(r).
-2*r**2*(r + 1)
Let c = -1/155 - -47/2480. Let r(n) be the second derivative of c*n**5 + 1/12*n**4 + 0 + 5/24*n**3 - 4*n + 1/4*n**2. Suppose r(x) = 0. Calculate x.
-2, -1
Let o(x) be the second derivative of x**7/84 + 7*x**6/240 + x**5/60 + x**2 + x. Let l(f) be the first derivative of o(f). Factor l(z).
z**2*(z + 1)*(5*z + 2)/2
Let f(y) = -1. Let w(s) = -s**3 + 2*s**2 + s + 1. Let d(h) = 3*f(h) + w(h). Factor d(p).
-(p - 2)*(p - 1)*(p + 1)
Suppose -3*a + 4 = -8. Let u = a + 1. Factor -z + z**2 + 3*z**3 - z**5 + 0*z**u - z - z**4.
-z*(z - 1)**2*(z + 1)*(z + 2)
Suppose 2*h + 4 = -0*h. Let c be (-2)/4 - h/4. Factor 2/3*o**3 - 2/3*o**2 + 2/9*o + c - 2/9*o**4.
-2*o*(o - 1)**3/9
Let x(b) = -8*b**3 + 4 - 3*b**3 + 5*b**3 + b**2 + b. Suppose 0*m = 5*m + 25. Let d(o) = -5*o**3 + o**2 + o + 3. Let n(y) = m*d(y) + 4*x(y). Factor n(s).
(s - 1)**2*(s + 1)
Let o(v) be the second derivative of -1/10*v**5 + 5*v + 0*v**2 + 1/42*v**7 + 1/6*v**3 + 0*v**6 + 0*v**4 + 0. Factor o(a).
a*(a - 1)**2*(a + 1)**2
Suppose 0 = f + 3*y + 18, -4*f + 2*y + 3 = 5. Let u be f - (1 + 51/(-6)). Find o, given that -2*o**5 + 0 - 3*o**3 + u*o**4 + 0*o + 1/2*o**2 = 0.
0, 1/4, 1
Suppose -3*v - 32 = -5*p, -2*p + 3*v = -18 - 2. Suppose 2*n = -10, -n = -4*u - 2*n + 7. Factor -2/11*k**p + 0*k - 2/11*k**u + 0 + 0*k**2.
-2*k**3*(k + 1)/11
Let o be (5/(-6))/(15/(-12)). Factor o*d**3 - 4/9*d + 0 + 2/9*d**2.
2*d*(d + 1)*(3*d - 2)/9
Let n(x) = x**3 - x**2 - 5*x - 3. Let l be n(-3). Let u = -21 - l. Factor 4/3*s + 0 + 10/3*s**2 + 4/3*s**u.
2*s*(s + 2)*(2*s + 1)/3
Let w be (3 - 3)/(0 - -1). Factor q**5 + q + 1 - 2*q**2 - 2*q**3 - 3*q**4 + 3*q**4 + q**4 + w.
(q - 1)**2*(q + 1)**3
Let q be 2/(-5) - 492/(-30). Let h(i) = i**2 - 16*i + 3. Let x be h(q). Suppose 4/11*p - 10/11*p**2 + 8/11*p**x - 2/11*p**4 + 0 = 0. What is p?
0, 1, 2
Let o(y) be the first derivative of -y**8/6720 - y**3/3 - 2. Let f(w) be the third derivative of o(w). Find b such that f(b) = 0.
0
Let b(p) = p + 1. Let v be b(1). What is n in -4/9*n + 2/9 + 2/9*n**v = 0?
1
Suppose -56 = 2*z - 0*s - 2*s, 4*s + 112 = -3*z. Let w be 1/(-4)*z/6. Find h, given that -1/3 - h**2 + w*h = 0.
1/3, 1
Let z(y) be the first derivative of y**6/24 + y**5/20 - y**4/16 - y**3/12 - 5. Find l such that z(l) = 0.
-1, 0, 1
Let b be 11/(33/(-6)) - (-2 + 0). Factor 1/5*r**3 + b*r**2 + 0 - 1/5*r.
r*(r - 1)*(r + 1)/5
What is u in -6/7 + 12/7*u**2 - 4/7*u**3 + 2/7*u - 6/7*u**4 + 2/7*u**5 = 0?
-1, 1, 3
Suppose 7*i - 10*i = -9. Let l(m) be the first derivative of -1 + 0*m - 1/2*m**4 - 2/5*m**5 + 0*m**2 + 2/3*m**i + 1/3*m**6. What is y in l(y) = 0?
-1, 0, 1
Let n(y) = 84*y**5 - 100*y**4 + 32*y**3 - 8*y + 8. Let v(b) = 56*b**5 - 67*b**4 + 21*b**3 - 5*b + 5. Let j(x) = -5*n(x) + 8*v(x). Factor j(i).
4*i**3*(i - 1)*(7*i - 2)
Factor 392/11*n**2 - 56/11*n + 2/11.
2*(14*n - 1)**2/11
Factor 0*i + 0 - 1/2*i**2.
-i**2/2
Let v(u) = -u + 12. Let p be v(7). Let w = p - 3. Let 21/5*q**w + 3*q + 3/5 + 9/5*q**3 = 0. Calculate q.
-1, -1/3
Let t(u) be the second derivative of -u**8/2240 + u**4/12 - 6*u. Let y(r) be the third derivative of t(r). Determine f, given that y(f) = 0.
0
Let f = 8957/326 + 4/163. Let y = -27 + f. Factor 1/4*r**2 + y*r + 1/4.
(r + 1)**2/4
Let a be 7 + (1 - 3) - -3. Let k = 10 - a. Suppose -2/5*z**3 - 2/5*z - 4/5*z**k + 0 = 0. What is z?
-1, 0
Factor -2/7*m**2 + 2/7*m**4 - 2/7*m**5 + 0*m + 2/7*m**3 + 0.
-2*m**2*(m - 1)**2*(m + 1)/7
Let h(a) = a**3 - 4*a**2 + 2*a - 5. Let w be h(4). Let n = -3 + w. What is i in 6*i + n*i - 4*i - 2*i**3 = 0?
-1, 0, 1
Let u(x) be the second derivative of -x**8/16800 - x**4/6 + 5*x. Let v(y) be the third derivative of u(y). Factor v(r).
-2*r**3/5
Let v(z) be the first derivative of 13*z**4 + 22*z**3/3 - 26*z**2 - 10*z + 4. Let q(j) = -21*j**3 - 9*j**2 + 21*j + 4. Let c(o) = 12*q(o) + 5*v(o). Factor c(x).
2*(x - 1)*(x + 1)*(4*x + 1)
Let c(u) be the first derivative of u**4/4 + 4*u**3/3 + 5*u**2/2 + 2*u - 2. Factor c(b).
(b + 1)**2*(b + 2)
Let b = -6 + 8. Suppose -b = -2*l - 4*i, -1 - 1 = -2*l + 5*i. Let f(q) = -2*q**2 + q + 1. Let j(d) = -d**2 + d + 1. Let u(k) = l*j(k) - f(k). Factor u(v).
v**2
Let n(a) = -5*a**2 + 6*a - 4. Let z(c) = 5*c**2 - 5*c + 5. Let s(m) = -5*n(m) - 4*z(m). Factor s(x).
5*x*(x - 2)
Let m(n) be the second derivative of 2*n**6/15 + n**5/5 - n**4 - 10*n**3/3 - 4*n**2 - n. Factor m(k).
4*(k - 2)*(k + 1)**3
Let k(z) be the third derivative of 1/630*z**7 + 0*z**3 + 1/90*z**5 + 0*z**4 - 1/120*z**6 + 0*z + 0 - 3*z**2. Suppose k(w) = 0. Calculate w.
0, 1, 2
Determine n so that -3/4*n**5 + 1/4*n**2 + 7/4*n**4 + 0 - 5/4*n**3 + 0*n = 0.
0, 1/3, 1
Let g(p) be the first derivative of -126*p**5/25 - 9*p**4/2 + 8*p**3/15 + 4*p**2/5 - 4. Find w such that g(w) = 0.
-2/3, -1/3, 0, 2/7
Let q be 3 + 1*(-3 - -2). Find s, given that 3*s**3 + 6 + 0*s**3 + 15*s**q + 3 + 21*s = 0.
-3, -1
Let m(h) be the first derivative of -h**3/3 - 3*h**2 - 2*h + 1. Let n be m(-5). Factor -4/3*z**2 + 2/3 + 2/3*z**4 + 0*z + 0*z**n.
2*(z - 1)**2*(z + 1)**2/3
Let q(u) = u**5 - 7*u**4 - 11*u**3 + 9*u**2 + 3*u - 9. Let p(s) = s**5 - 6*s**4 - 10*s**3 + 8*s**2 + 3*s - 8. Let x(c) = -7*p(c) + 6*q(c). Factor x(z).
-(z - 1)**3*(z + 1)*(z + 2)
Factor -2 + 2 - 2*c + 2*c**3 - 171*c**2 + c**4 + 170*c**2.
c*(c - 1)*(c + 1)*(c + 2)
Suppose p = -3*p + 8. Factor 2 - 10*j - 2*j**3 + 2*j**2 + p + 6*j**2.
-2*(j - 2)*(j - 1)**2