*(g + 2)*(g + 6)
Let g(l) be the third derivative of l**6/360 + l**5/60 - l**3/6 + 2*l**2. Let j(y) be the first derivative of g(y). Let j(f) = 0. What is f?
-2, 0
Factor 0 - 2/3*k**4 + 0*k + 4/3*k**2 - 2/3*k**3.
-2*k**2*(k - 1)*(k + 2)/3
Let u(t) be the third derivative of -3*t**6/40 + t**5/5 - t**4/8 + 4*t**2. Factor u(a).
-3*a*(a - 1)*(3*a - 1)
Let w(i) be the first derivative of -4*i**3/3 - 4*i**2 + 12*i + 19. Factor w(k).
-4*(k - 1)*(k + 3)
Let x be ((-2)/(-8))/(1*2/40). Let p(c) be the second derivative of -1/20*c**x + 0 + 0*c**2 - 3*c + 1/3*c**4 - 2/3*c**3. Factor p(u).
-u*(u - 2)**2
Let c(f) be the third derivative of -f**5/100 + f**4/8 + 7*f**3/5 + 62*f**2. Factor c(r).
-3*(r - 7)*(r + 2)/5
Let x(d) = 8*d**5 + 3*d**4 - 13*d**3 - 47*d**2 - 33*d - 14. Let o(c) = 7*c**5 + 3*c**4 - 14*c**3 - 46*c**2 - 33*c - 13. Let z(l) = 5*o(l) - 4*x(l). Factor z(k).
3*(k - 3)*(k + 1)**4
Let s(t) be the second derivative of 1/18*t**4 + 0*t**3 - 1/3*t**2 + 0 - 7*t. Determine g, given that s(g) = 0.
-1, 1
Let u be -1 + -1 - 10/(-1). Let n(x) = x**3 - 8*x**2 + x - 6. Let o be n(u). Factor -1/5*p + 0 - 1/5*p**o.
-p*(p + 1)/5
Let a(n) be the first derivative of 1/16*n**5 + 0*n**3 - 1/48*n**4 - 1/30*n**6 + 1 + 0*n**2 + 2*n. Let l(t) be the first derivative of a(t). Factor l(m).
-m**2*(m - 1)*(4*m - 1)/4
Factor 0 - j - 1/4*j**2.
-j*(j + 4)/4
Suppose -2*n = -5*n + 96. Let j be (2/(-12))/((-8)/n). Factor -2/3 - 4/3*z**3 + j*z**4 + 4/3*z + 0*z**2.
2*(z - 1)**3*(z + 1)/3
Suppose -5*t + 2*u = -u + 5, -2*t - 2 = 5*u. Let h be (-3)/(-2)*t/(-6). Find m, given that 1/4*m**2 + 1/4*m - 1/4*m**4 + 0 - h*m**3 = 0.
-1, 0, 1
Let c(u) be the second derivative of -u**4/6 - 2*u**3/3 - u**2 - 2*u. Solve c(l) = 0.
-1
Let k(c) be the first derivative of 1 - 3/8*c**4 + 0*c**2 + 0*c - c**3. Let k(g) = 0. What is g?
-2, 0
Let l(f) = f**2 + 4*f. Let y be 13/4 + 19/(-76). Let h(v) = v**2 + 4*v. Let r(w) = y*l(w) - 4*h(w). Factor r(x).
-x*(x + 4)
Let h(g) be the second derivative of 2*g**7/147 - 2*g**6/21 + g**5/5 - g**4/7 + 48*g. Factor h(r).
4*r**2*(r - 3)*(r - 1)**2/7
Suppose o = 3*o - 16. Solve -5*c + 0*c + c + o*c**3 - 4*c**5 = 0.
-1, 0, 1
Let n(z) be the second derivative of -z**7/105 - 2*z**6/75 + 4*z**5/25 + 8*z**4/15 - 16*z**3/15 - 32*z**2/5 + 3*z. Factor n(v).
-2*(v - 2)**2*(v + 2)**3/5
Let v(p) be the second derivative of p**6/45 + p**5/10 + p**4/9 - 3*p. Solve v(l) = 0 for l.
-2, -1, 0
Let y = 51/4 + -25/2. Factor y*f**2 - 3/4*f + 1/2.
(f - 2)*(f - 1)/4
Let n(z) = -z**2 + 5*z + 7. Let b be n(6). Let l be ((-5)/60)/(b/(-4)). Factor -l + 2/3*o**2 - 1/3*o**4 - 1/3*o - 1/3*o**5 + 2/3*o**3.
-(o - 1)**2*(o + 1)**3/3
Let b(p) = -5*p**3 - 4*p**2 - 8*p. Let a(u) = -9*u**3 - 8*u**2 - 15*u. Let s = 5 - 12. Let f(r) = s*b(r) + 4*a(r). Factor f(g).
-g*(g + 2)**2
Let a(k) = k**2 + 7*k - 8. Let x(b) = 4*b - 4. Let v(l) = 3*a(l) - 5*x(l). Let p(z) = z**2 + z - 1. Let c(i) = 2*p(i) - v(i). Factor c(r).
-(r - 2)*(r + 1)
Let i(g) be the first derivative of -6*g - 9 + 8*g**3 + 15/4*g**4 + 3/2*g**2. Factor i(k).
3*(k + 1)**2*(5*k - 2)
Let d be 3/6*(-1 + -1 - -3). Find i, given that -3/2*i - i**4 + 1/2*i**2 + d + 3/2*i**3 = 0.
-1, 1/2, 1
Let z(p) be the first derivative of p**6/60 + p**5/40 - p**4/24 - p**3/12 + 3*p + 7. Let b(q) be the first derivative of z(q). Let b(t) = 0. Calculate t.
-1, 0, 1
Suppose 0*q**2 + 0 + 2/3*q**3 + 0*q = 0. What is q?
0
Let v(c) be the third derivative of c**7/630 - c**6/360 - c**5/180 + c**4/72 + 12*c**2. Suppose v(p) = 0. Calculate p.
-1, 0, 1
Let s(r) be the first derivative of 0*r + 3/10*r**5 + r**4 + 7/6*r**3 + 7 + 1/2*r**2. Let s(x) = 0. What is x?
-1, -2/3, 0
Let i be 2/(-9) + (-25)/9. Let d = 7 + i. Factor 12*w**3 + 2*w**5 + 2*w**2 - 2*w**4 + 10*w**d + 2*w + 6*w**2.
2*w*(w + 1)**4
Let u be -4 - -2 - (-4 + 2). Suppose c**3 + c**2 + 0*c**2 - 1 - c + u*c**3 = 0. What is c?
-1, 1
Suppose 0 = -9*c + 11*c - 12. Determine a so that 6/7*a - 4/7 + 40/7*a**2 - c*a**3 = 0.
-1/3, 2/7, 1
Let d(k) be the second derivative of k**4/42 - 20*k**3/21 + 100*k**2/7 - 11*k. Factor d(u).
2*(u - 10)**2/7
Factor -u - 2/5 + 4/5*u**3 + 1/5*u**5 + 4/5*u**4 - 2/5*u**2.
(u - 1)*(u + 1)**3*(u + 2)/5
Let a(p) be the first derivative of -25*p**6/2 + 12*p**5 + 63*p**4/4 - 20*p**3 + 6*p**2 + 3. Solve a(d) = 0.
-1, 0, 2/5, 1
Determine h so that -2/9*h**2 + 2/9 + 2/9*h**3 - 2/9*h = 0.
-1, 1
Let z(y) be the third derivative of -y**5/300 + y**4/120 - 11*y**2. Let z(f) = 0. What is f?
0, 1
Let c(j) be the third derivative of -3/2*j**3 + 1/2*j**4 + 0 + 7*j**2 + 0*j - 1/20*j**5. Suppose c(h) = 0. Calculate h.
1, 3
Let a = -81 - -245/3. Let 2*m**2 + 8/3*m + a = 0. Calculate m.
-1, -1/3
Let u = 28 - -26. Let y = -160/3 + u. Factor -q + 1/3*q**3 + 0*q**2 + y.
(q - 1)**2*(q + 2)/3
Let 9/2 + 3*u + 1/2*u**2 = 0. Calculate u.
-3
Let c = 921/5 - 184. Factor c*n**3 + 1/5*n**2 + 0 + 3/5*n**5 + 0*n - n**4.
n**2*(n - 1)**2*(3*n + 1)/5
Let y(u) be the first derivative of -4/3*u**3 - 7 + 3/2*u**2 + u. Factor y(d).
-(d - 1)*(4*d + 1)
Suppose 0 = -5*n - 0*n + 5*i - 10, 4*n = -4*i + 24. Let u(j) be the second derivative of 1/40*j**5 - 1/12*j**3 - 1/24*j**4 + 0 + 1/4*j**n - 2*j. Factor u(r).
(r - 1)**2*(r + 1)/2
Suppose 3*i + 2*i = 0. What is b in 7*b + i + 4*b**3 + 0*b - b + 9*b**2 + 1 = 0?
-1, -1/4
Find t, given that t**2 - 7*t**2 - 4*t + 10*t**2 = 0.
0, 1
Let s(g) be the second derivative of -g**6/135 - g**5/30 - g**4/18 - g**3/27 - 26*g. Suppose s(n) = 0. Calculate n.
-1, 0
Let k be (40/12 - 4) + 48/18. Solve -1/2*j + 0 - 2*j**3 + 2*j**k = 0 for j.
0, 1/2
Let d be 34524/8820 + 4/14 + 0. Factor d*n**2 + 12/5 - 48/5*n.
3*(n - 2)*(7*n - 2)/5
Let t be 2 + (-15)/10 - 3/(-18). Let l be (0 - 0)/(-1) + 4. Suppose 2/3*i + t*i**5 + 0 + 0*i**2 - 4/3*i**3 + 0*i**l = 0. Calculate i.
-1, 0, 1
Suppose -43*w = -46*w + 15. Factor -1/2*o**2 + 0 - 9/4*o**w - 5/4*o**3 + 0*o + 4*o**4.
-o**2*(o - 1)**2*(9*o + 2)/4
Let y be ((-10)/8)/((-1)/(-4)). Let g = -3 - y. Determine x, given that -25*x**3 + 9*x**3 + 7*x**5 + 38*x**4 - 21*x**5 - 8*x**g = 0.
-2/7, 0, 1, 2
Let t(j) = -4*j**2 - 3*j. Let v(b) = 4*b**2 + 2*b. Let z(i) = -2*t(i) - 3*v(i). Suppose z(g) = 0. Calculate g.
0
Let x = -65 - -44. Let t = x - -21. Factor -2/9*i**3 + 2/3*i - 4/9 + t*i**2.
-2*(i - 1)**2*(i + 2)/9
Let h(r) be the third derivative of r**7/1260 - r**5/60 - r**4/4 - 3*r**2. Let t(p) be the second derivative of h(p). Determine n, given that t(n) = 0.
-1, 1
Let z(g) be the third derivative of -g**6/360 - g**5/60 - g**4/24 - g**3/3 + g**2. Let a(j) be the first derivative of z(j). Factor a(i).
-(i + 1)**2
Let w(j) = j**2 + 8*j + 4. Let s be w(-8). Let u be s*3/(-6)*-1. Factor -3 + 0 + 3 - 3*h**u - 3*h.
-3*h*(h + 1)
Let p(d) be the second derivative of -d**4/28 + 3*d**3/14 - 10*d. Factor p(u).
-3*u*(u - 3)/7
Let s(t) = -t**3 + 5*t**2 - 2*t - 4. Let c be -3 - -5 - (0 - 2). Let r be s(c). Solve r*f**2 + 2*f**2 + 12*f - 2*f - 18*f**3 + 2 = 0.
-1/3, 1
Let m(x) = 2*x**4 - 5*x**3 - x**2 - 3*x. Let b(k) = k**4 - k**3 - k. Let i(j) = 6*b(j) - 2*m(j). Let i(t) = 0. What is t?
-1, 0
Let u(p) be the second derivative of 2/15*p**6 + 0 - 5/3*p**4 - 3/5*p**5 + 2/21*p**7 - 4/3*p**3 + 0*p**2 + 7*p. Factor u(d).
4*d*(d - 2)*(d + 1)**3
Let a(r) be the second derivative of 1/65*r**5 + 0*r**2 + 0 + 0*r**4 - 1/195*r**6 - 1/273*r**7 - 2*r + 0*r**3. Factor a(u).
-2*u**3*(u - 1)*(u + 2)/13
Determine c, given that 3/2*c**3 + 0 - 3/2*c**2 - 3*c = 0.
-1, 0, 2
Let x(m) be the first derivative of m**6/6 - 4*m**5/5 + m**4 + 2*m**3/3 - 5*m**2/2 + 2*m + 8. Factor x(y).
(y - 2)*(y - 1)**3*(y + 1)
Let y(g) = 4*g**3 + 4*g**2 + 3*g + 3. Let q(l) be the first derivative of -7*l**4/4 - 7*l**3/3 - 5*l**2/2 - 5*l - 2. Let z(s) = 6*q(s) + 10*y(s). Factor z(p).
-2*p**2*(p + 1)
Factor v**2 + 2*v - 2*v**2 + 9*v**2 + 6*v**3.
2*v*(v + 1)*(3*v + 1)
Let w = 23/6 + -5/2. Factor -4*r**2 - 11/3*r**3 + w*r + 25/3*r**5 + 0 + 10*r**4.
r*(r + 1)**2*(5*r - 2)**2/3
Let o(x) be the third derivative of -x**10/7560 + x**8/560 + x**7/315 + x**4/3 + 5*x**2. Let d(v) be the second derivative of o(v). Factor d(l).
-4*l**2*(l - 2)*(l + 1)**2
Let a(i) be the first derivative of -4*i**3/3 - 2*i**2 + 8*i + 3. Find v, given that a(v) = 0.
-2, 1
Factor 16/7*a**4 - 10/7*a**5 + 0*a + 0 - 2/7*a**3 - 4/7*a**2.
-2*a**2*(a - 1)**2*(5*a + 2)