 the second derivative of 1/40*s**6 + 1/48*s**4 + 0*s**3 + 0 - 4*s - 3/80*s**5 - 1/168*s**7 + 0*s**2. Factor j(n).
-n**2*(n - 1)**3/4
Let m(t) be the third derivative of t**5/48 - 7*t**4/24 - t**3/2 - 10*t**2. Find k such that m(k) = 0.
-2/5, 6
Let a(o) = -7*o**3 + 11*o**2 - 11*o - 3. Let z(n) = n**2 + 1. Let i(q) = a(q) + 5*z(q). Determine u, given that i(u) = 0.
2/7, 1
Factor 39*l**2 - 8*l + 6 - 15 - 42*l**2 + 20*l.
-3*(l - 3)*(l - 1)
Factor 1 + 153*y**2 - 152*y**2 - 2*y - 1.
y*(y - 2)
Let w(a) be the third derivative of -5*a**8/336 + a**6/12 - 5*a**4/24 + 15*a**2. Factor w(r).
-5*r*(r - 1)**2*(r + 1)**2
Let d(v) be the second derivative of -v**6/960 - v**5/480 + v**4/96 + v**2/2 + 2*v. Let w(y) be the first derivative of d(y). Determine x, given that w(x) = 0.
-2, 0, 1
Let r(x) be the second derivative of 7*x**6/40 - 3*x**5/16 - 9*x**4/16 + 5*x**3/8 + 3*x**2/4 + x. Suppose r(g) = 0. Calculate g.
-1, -2/7, 1
Let v(j) be the third derivative of j**6/120 - j**5/20 - 2*j**3/3 + 4*j**2. Let m(i) be the first derivative of v(i). Factor m(q).
3*q*(q - 2)
Let g be 34/51 - -1*(-2 - -2). Let -g*t + 1/3*t**2 + 1/3 = 0. Calculate t.
1
Suppose 2*q + 8 = -2*f - 0*f, -f - 4*q = 16. Let i(g) be the first derivative of f*g - 3 - 1/2*g**2 - 3/4*g**4 - 1/5*g**5 - g**3. Factor i(m).
-m*(m + 1)**3
Let x(l) = -l**2 + 5*l - 4. Let q be x(4). Let i be q + (33/9 - 3). What is f in 0 + 2/3*f + i*f**2 = 0?
-1, 0
Let r be 4*((-6)/(-4) + -1). Let p(x) = -3*x**3. Let k(j) = 3*j**3 + j**2 - j - 1. Let w(o) = r*p(o) + 3*k(o). Factor w(v).
3*(v - 1)*(v + 1)**2
Let d be (-8)/(-6)*12/8. Factor d*u + 2*u**5 - 2 - 4*u**3 + 1 + 1.
2*u*(u - 1)**2*(u + 1)**2
Let s(t) be the second derivative of -t**8/3360 - t**7/840 + t**5/120 + t**4/48 + t**3/3 - 4*t. Let v(m) be the second derivative of s(m). Solve v(d) = 0 for d.
-1, 1
Let p(v) = v**4 - v**3 - 2*v**2 + 2*v + 2. Suppose -3 = m + 3. Let a(c) = -8*c**4 + 8*c**3 + 17*c**2 - 17*c - 17. Let n(f) = m*a(f) - 51*p(f). Factor n(s).
-3*s**3*(s - 1)
Let r = 354/2189 + 4/199. Suppose -4/11*c**2 + 0*c**3 - r*c + 0 + 4/11*c**4 + 2/11*c**5 = 0. What is c?
-1, 0, 1
Let x(n) be the first derivative of 2*n**6/27 + 28*n**5/45 + 5*n**4/3 + 4*n**3/3 + 22. Factor x(g).
4*g**2*(g + 1)*(g + 3)**2/9
Let o(k) be the second derivative of k**7/840 + k**6/240 - k**5/240 - k**4/48 + k**2 + 5*k. Let v(b) be the first derivative of o(b). Factor v(d).
d*(d - 1)*(d + 1)*(d + 2)/4
Solve 7*w**4 + 196*w**2 + 4*w**5 - 212*w**2 + 5*w**4 = 0 for w.
-2, 0, 1
Let w(j) be the third derivative of -7*j**5/20 - j**4/2 - 28*j**2. Solve w(l) = 0.
-4/7, 0
Let u(m) = -m - 1. Let n be u(-1). Let f(c) be the third derivative of 1/8*c**4 + 0*c**5 + 3*c**2 + 0 + 1/3*c**3 + n*c - 1/120*c**6. Solve f(p) = 0 for p.
-1, 2
Suppose -20 = -s + 3*p, -p - 6 = -5*s + 24. Let z = 17/3 - s. What is d in -2/3*d**4 + z*d**5 + 2/3*d + 4/3*d**2 - 2/3 - 4/3*d**3 = 0?
-1, 1
Let o be 0 + (-14)/(-2) + -2. Let t(i) be the second derivative of 0*i**2 + 0*i**4 + 0 - 1/6*i**3 + 1/20*i**o + i. Factor t(a).
a*(a - 1)*(a + 1)
Let v(r) = r**3 + r**2 + 2. Let z = -6 - -6. Let a be v(z). Solve 0*t**5 + 2*t - 2*t**5 - a*t = 0.
0
Let y = 0 - -12. Solve 3*b - 3/2*b**2 - y*b**3 - 15/2*b**4 + 0 = 0 for b.
-1, 0, 2/5
Let a be (-99)/21 + (-4)/14. Let w be (a/(-20))/((-10)/(-32)). Suppose -6/5*g**3 - 14/5*g - 16/5*g**2 - w = 0. What is g?
-1, -2/3
Let o(y) be the first derivative of -4*y**3/3 - 13*y**2/2 - 3*y + 11. Suppose o(d) = 0. What is d?
-3, -1/4
Let t be 0/2 - (5 - 6). Factor 4*d**2 - 2*d - t - 2*d**3 + 1.
-2*d*(d - 1)**2
What is a in 4/11*a + 2/11 + 2/11*a**2 = 0?
-1
Factor -96/7*k**2 + 26/7*k + 72/7*k**3 - 2/7.
2*(k - 1)*(6*k - 1)**2/7
Let g(j) = 29*j**2 + 61*j + 21. Suppose -4*u + 2*r = -52, 4*r + 38 = 2*u - 0. Let b(h) = -6*h**2 - 12*h - 4. Let m(i) = u*b(i) + 2*g(i). Factor m(z).
-2*(z + 1)*(4*z + 1)
Let y be (9/6)/((-6)/(-8)). Solve 6*a**2 + 2 + 3*a - 2*a**y - 3*a**2 = 0.
-2, -1
Let g(f) be the first derivative of 2*f**5/55 - f**4/11 + 2*f**2/11 - 2*f/11 + 4. Factor g(a).
2*(a - 1)**3*(a + 1)/11
Let r(f) be the first derivative of -f**6/3 + 9*f**5/5 + 47*f**4/32 - 3*f**3/2 + 5*f**2/16 + 23. Find o such that r(o) = 0.
-1, 0, 1/4, 5
Let j(f) be the second derivative of f**9/1512 - f**7/210 + f**5/60 + 5*f**3/6 - 7*f. Let v(t) be the second derivative of j(t). Factor v(i).
2*i*(i - 1)**2*(i + 1)**2
Let a(r) be the first derivative of -8*r**4/5 - 16*r**3/5 - 9*r**2/5 - 2*r/5 + 7. Suppose a(i) = 0. Calculate i.
-1, -1/4
Factor 3*h**5 - h**5 - 3*h**5 + 3*h**5.
2*h**5
Let h(l) be the first derivative of 2*l**5/35 - 7. Let h(d) = 0. Calculate d.
0
Let z = -4 + 14. Let t = 13 - z. Factor -2*y + y**t + y**3 + 0*y**3 - 6*y**2 + 4 + 2*y**4.
2*(y - 1)**2*(y + 1)*(y + 2)
Let p(t) be the second derivative of 0*t**3 - 1/30*t**6 + 0*t**2 + 1/20*t**5 - 1/42*t**7 + 1/12*t**4 - 2*t + 0. Factor p(r).
-r**2*(r - 1)*(r + 1)**2
Let p(q) be the second derivative of q**4/4 - q**3 + 7*q. Factor p(y).
3*y*(y - 2)
Let r be (8 + -3)*6/(-5). Let h = -4 - r. Factor -z**3 + 0*z - 1/2*z**h + 0 - 1/2*z**4.
-z**2*(z + 1)**2/2
Let q(n) be the first derivative of -n - n**2 + 0*n**3 + 1/5*n**5 + 2 + 1/2*n**4. What is u in q(u) = 0?
-1, 1
Factor -8/7*l**2 + 0 - 2/7*l**3 + 2/7*l**4 + 8/7*l.
2*l*(l - 2)*(l - 1)*(l + 2)/7
Let k(z) be the third derivative of -z**7/210 + z**6/60 - z**4/12 + z**3/6 - 27*z**2. Factor k(p).
-(p - 1)**3*(p + 1)
Factor -4*o**2 - 3*o**3 - 1598 + 1622 + 12*o - 2*o**2.
-3*(o - 2)*(o + 2)**2
Let z be ((-7)/(-147))/((-3)/(-18)). Factor -4/7*i**2 - z*i**3 + 0 + 0*i + 2/7*i**4.
2*i**2*(i - 2)*(i + 1)/7
Let b(c) = c. Let y(u) be the second derivative of u**4/6 - 8*u**3/3 + u**2 + 3*u. Let o(k) = 12*b(k) + y(k). Factor o(j).
2*(j - 1)**2
Let a = 5 + -5. Suppose -3*m + 6 + 0 = a. Factor 2*y - y**m - 4*y - 9*y**2 - 8*y**3 + 0*y**2.
-2*y*(y + 1)*(4*y + 1)
Let b = -2 - -1. Let m(l) = -5 + 0*l + 4 + l. Let t(p) = 2*p**2 - 2*p + 8. Let f(n) = b*t(n) - 6*m(n). Let f(g) = 0. Calculate g.
-1
Let b(w) = -w**3 - 6*w**2 + 6*w - 5. Let j be b(-7). Let i = j + 0. Let i - 2 - z**3 = 0. Calculate z.
0
Determine f so that -2*f**2 - 6/5 - 2/5*f**3 - 14/5*f = 0.
-3, -1
Suppose 4 = 2*s - 4. Let -10*m**3 - 4*m**4 + 37*m**5 + 0*m**s - 27*m**5 + 4*m**2 = 0. Calculate m.
-1, 0, 2/5, 1
Let n be (-24)/(-27) - ((-160)/24)/(-10). Factor -4/9*x**3 + 0*x**4 + 0 + n*x + 2/9*x**5 + 0*x**2.
2*x*(x - 1)**2*(x + 1)**2/9
Factor 0*f + 0 + 0*f**3 - 1/6*f**4 + 0*f**2 + 1/6*f**5.
f**4*(f - 1)/6
Let u(c) be the third derivative of c**7/2520 + c**3/3 - c**2. Let s(q) be the first derivative of u(q). Factor s(j).
j**3/3
Let c be 31/11 - 4/(-22). Factor 2 + 2 - 3*k**2 + 8*k + k**3 + 5*k**2 + c*k**2.
(k + 1)*(k + 2)**2
Let w(c) be the third derivative of -c**8/1008 - c**7/210 - c**6/120 - c**5/180 + 5*c**2. Factor w(m).
-m**2*(m + 1)**3/3
Let w(a) = -49*a**5 - 324*a**4 - 762*a**3 - 752*a**2 - 272*a - 30. Let z(d) = -d**4 - d**3 + 1. Let h(s) = w(s) - 2*z(s). Let h(g) = 0. What is g?
-2, -2/7
Let o(q) be the third derivative of 1/3*q**3 + 1/10*q**5 + 0*q - 9*q**2 + 0 + 1/4*q**4 + 1/60*q**6. Suppose o(r) = 0. What is r?
-1
Let w(j) be the first derivative of 1/4*j + 1/4*j**3 + 1/2*j**2 + 2. Factor w(k).
(k + 1)*(3*k + 1)/4
Let t(s) = -54*s**5 - 10*s**4 - 4 + 4*s**4 - 3*s**3 + 0 + 51*s**5. Let f(p) = -5*p**5 - 11*p**4 - 5*p**3 - 7. Let v(n) = -4*f(n) + 7*t(n). Factor v(h).
-h**3*(h - 1)**2
Let r(k) = -4*k**2 - 8*k + 4. Let c(a) = -4*a**2 - 8*a + 3. Let h(d) = 4*c(d) - 3*r(d). Factor h(m).
-4*m*(m + 2)
Determine f so that 1/2*f**2 + 1/2*f - 1 = 0.
-2, 1
Suppose -16*h + 42 = -38. Suppose 4/3*t**2 - 4/3*t**3 + 2/3 + 2*t - 2/3*t**h - 2*t**4 = 0. Calculate t.
-1, 1
Let r(b) be the second derivative of -b**6/6 - b**5 + 46*b. Find m such that r(m) = 0.
-4, 0
Find q such that 5*q**2 - 10*q**2 + 17*q**2 - 10*q + 2*q - 4*q**4 = 0.
-2, 0, 1
Let o be (-8)/20*10/(-7). Factor -o*m + 4/7*m**3 - 2/7*m**4 + 0*m**2 + 2/7.
-2*(m - 1)**3*(m + 1)/7
Let t(h) = h - 4. Let f be t(6). Factor -f*j**5 + j**5 + 2*j**4 - 4*j**4.
-j**4*(j + 2)
Factor -3*z**5 - 199*z**3 + 2*z**2 - 2*z**4 + 193*z**3 + 5*z**5 + 4*z.
2*z*(z - 2)*(z - 1)*(z + 1)**2
Let u be 82/(-205) + (-23)/(-20). Factor -u*n**4 + 0*n**2 - 3/4*n**3 + 0 + 0*n.
-3*n**3*(n + 1)/4
Let o(l) = 1 - l**4 + 0 - l**2 - 1. Let i(n) = 8*n**4 - 2*n**