
-6, 2
Factor 1 + 11/6*h + 2/3*h**2 - 1/6*h**3.
-(h - 6)*(h + 1)**2/6
Let z(p) be the first derivative of 1/6*p**4 + 4/3*p + 2/15*p**5 - 14 - 2/3*p**3 - 1/3*p**2. Factor z(c).
2*(c - 1)**2*(c + 1)*(c + 2)/3
Let v = -11 + 19. Let q(f) = f**3 - 8*f**2 + 3*f. Let h be q(v). Factor h*b**2 + 3 + 3*b**5 + 15*b**4 + 6*b**3 + 0*b**5 + 15*b + 24*b**3 + 6*b**2.
3*(b + 1)**5
Let p(n) be the third derivative of -n**5/450 - 23*n**4/180 - 4*n**3/3 - 4*n**2 + 48*n. Factor p(x).
-2*(x + 3)*(x + 20)/15
Let n be 2 - (7 + -1) - -4. Let v(w) be the second derivative of n + 2/21*w**3 - 2*w + 0*w**2 + 3/14*w**4. Factor v(l).
2*l*(9*l + 2)/7
Let t(w) be the second derivative of -w**7/840 + w**6/120 - w**4/6 + w**3/6 - 3*w**2 - 24*w. Let m(x) be the second derivative of t(x). Factor m(z).
-(z - 2)**2*(z + 1)
Factor 0*r + 1/4*r**2 - 1/4.
(r - 1)*(r + 1)/4
Let t(v) be the second derivative of v**6/30 + v**5/4 + 7*v**4/12 + v**3/2 + 39*v. Suppose t(i) = 0. Calculate i.
-3, -1, 0
Let i(p) be the third derivative of p**7/21 + 19*p**6/15 + 59*p**5/150 - 59*p**4/15 + 4*p**3 - 27*p**2. Determine f so that i(f) = 0.
-15, -1, 2/5
Let z(k) be the third derivative of 0*k**3 + 1/105*k**5 + 12*k**2 + 0*k + 1/252*k**4 + 1/140*k**6 + 0. Suppose z(p) = 0. Calculate p.
-1/3, 0
Let a(y) be the second derivative of 0 + 1/39*y**3 - 1/78*y**4 - 1/130*y**5 + 1/13*y**2 - 14*y. Factor a(n).
-2*(n - 1)*(n + 1)**2/13
Let d(r) = -r**2 - r + 1. Let g(p) = -15*p**2 + 6. Let a(u) = 9*d(u) - g(u). Factor a(z).
3*(z - 1)*(2*z - 1)
Let y be 1 - 36/(-160)*-4. Let k(n) be the second derivative of 0*n**4 - n**3 + 3/2*n**2 + 0 + 3*n - y*n**6 + 3/10*n**5. Factor k(z).
-3*(z - 1)**3*(z + 1)
Factor -t**3 - t**3 + 71*t - 94 + 130 + t**3 + 34*t**2.
-(t - 36)*(t + 1)**2
Suppose 1472/5*d - 944/5*d**2 + 276/5*d**3 - 768/5 - 38/5*d**4 + 2/5*d**5 = 0. What is d?
1, 4, 6
Let l(n) be the first derivative of n**3/12 - 13*n**2/8 + 3*n + 34. Factor l(d).
(d - 12)*(d - 1)/4
Factor 4 + 2/3*m**2 - 10/3*m.
2*(m - 3)*(m - 2)/3
Let w(q) be the second derivative of -q**7/189 - q**6/27 - 7*q**5/90 - q**4/18 - 18*q. Factor w(i).
-2*i**2*(i + 1)**2*(i + 3)/9
Let l(m) be the first derivative of -10 - 8*m + 16*m**2 - 14/3*m**3. Factor l(v).
-2*(v - 2)*(7*v - 2)
Let g(s) be the third derivative of -s**5/60 + s**4/12 + s**3/2 - 204*s**2. Solve g(p) = 0.
-1, 3
Let a(f) be the second derivative of f**6/60 - f**5/5 - 21*f**4/4 - 36*f**3 - 459*f**2/4 + 2*f - 2. Find k, given that a(k) = 0.
-3, 17
Let k(b) = -16*b**3 - 11*b**2 - 9*b + 7. Let w(l) = -9*l**3 - 6*l**2 - 5*l + 4. Let d(n) = 4*k(n) - 7*w(n). Suppose d(q) = 0. Calculate q.
-1, 0
Let v = 40 - 38. Factor -725*s**v + 725*s**2 + 4*s**3 - 4*s.
4*s*(s - 1)*(s + 1)
Let t(l) be the second derivative of 0 + 0*l**4 + 0*l**3 - 7*l + 1/50*l**5 + 0*l**2 - 1/75*l**6. Factor t(b).
-2*b**3*(b - 1)/5
Let s(v) = 7*v**5 - 4*v**4 + 2*v**3 + 4*v**2 + 9*v + 6. Let j(i) = 15*i**5 - 9*i**4 + 5*i**3 + 9*i**2 + 19*i + 13. Let m(t) = 6*j(t) - 13*s(t). Factor m(u).
-u*(u - 1)**2*(u + 1)*(u + 3)
Let l = 358 - 365. Let z be (-4)/l + (-32)/(-42). Factor 0*c**2 + 0 - 16/3*c + z*c**3.
4*c*(c - 2)*(c + 2)/3
Let z be 4/(-12)*-1 - (-464)/(-6). Let f = z - -387/5. Suppose -2/5*c**3 - 2/5 + f*c + 2/5*c**2 = 0. Calculate c.
-1, 1
Let v(u) be the third derivative of u**8/21 - 10*u**7/21 + 19*u**6/15 + 16*u**5/15 - 7*u**4 + 6*u**3 + 267*u**2. What is q in v(q) = 0?
-1, 1/4, 1, 3
Let s(k) = 4*k**3 + 7*k**2 + 4*k - 31. Let q(j) = -j**3 - 2*j**2 - j + 10. Let u(b) = 7*q(b) + 2*s(b). Let t be u(0). Factor -4*x - 8 - 6*x**2 + t.
-2*x*(3*x + 2)
Let k(u) be the second derivative of -u**5/90 - 37*u**4/54 - 40*u**3/3 - 36*u**2 + 19*u. Factor k(x).
-2*(x + 1)*(x + 18)**2/9
Let r(n) = 6*n**2 - 2*n. Let m(y) = 110*y**2 + 540*y + 41472. Let i(w) = 2*m(w) - 36*r(w). Solve i(j) = 0 for j.
-144
Let i(v) be the third derivative of v**7/70 + 13*v**6/40 + 23*v**5/20 + 11*v**4/8 + 447*v**2. Solve i(m) = 0 for m.
-11, -1, 0
Let f(s) be the first derivative of s**6/420 - s**5/70 + 4*s**3/21 - s**2 + 12. Let q(l) be the second derivative of f(l). Let q(m) = 0. Calculate m.
-1, 2
Let m(g) = 5*g**2 + 1241*g + 32455. Let k(c) = 3*c**2 + 827*c + 21637. Let s(t) = 7*k(t) - 5*m(t). Factor s(l).
-4*(l + 52)**2
Suppose -c + 3*j + 26 = 0, 18 = -4*j + 6. Suppose -8*q = -c*q + 36. Find x such that x**q - x**2 + 0 + 2/5*x**3 - 2/5*x = 0.
-1, -2/5, 0, 1
Let f = 7 - 7. Let c = -9/40 + 29/40. Solve 0 + 0*z - 1/2*z**4 + f*z**3 + c*z**2 = 0 for z.
-1, 0, 1
Let x(j) be the first derivative of j**3 + 7 + 3 - 7. Factor x(v).
3*v**2
Let r(v) = 245*v**3 + 1680*v**2 + 1310*v + 265. Let q(m) = 245*m**3 + 1680*m**2 + 1309*m + 266. Let y(k) = -5*q(k) + 4*r(k). Suppose y(s) = 0. What is s?
-6, -3/7
Factor 5*h + 5/4*h**3 + 1/8*h**4 + 33/8*h**2 + 2.
(h + 1)**2*(h + 4)**2/8
Let q(z) = 3*z**2 + 5*z + 4. Let x be q(-1). Suppose 7*f - 4*f - 8 - 20*f**2 + f + 24*f**x = 0. Calculate f.
-2, 1
Let t be -10*(-141)/900 - 3/2. Let d(z) be the third derivative of -7*z**2 - 1/105*z**7 + 1/24*z**6 - t*z**5 + 0*z + 1/24*z**4 + 0 + 0*z**3. Factor d(n).
-n*(n - 1)**2*(2*n - 1)
Let u = -19 + 22. Let -2*y**2 + 2*y**3 - 10*y**u + 6*y**3 = 0. Calculate y.
-1, 0
Let c = -92 + -152. Let z = c + 247. Factor 1/2 - 1/2*m**4 - m + 0*m**2 + m**z.
-(m - 1)**3*(m + 1)/2
Factor 36 - 3/2*t**2 + 15/2*t.
-3*(t - 8)*(t + 3)/2
Let w = 1150 - 1148. Let h(o) be the first derivative of 8*o**w + 0*o + 4/3*o**3 + 10. Suppose h(d) = 0. What is d?
-4, 0
Let y be 12360/5148 - (3 - 606/198). Let -32/13*j**2 + 2/13 + 2/13*j - y*j**3 = 0. What is j?
-1, -1/4, 1/4
Let p = 11 + -4. Suppose -3 = -8*a + p*a. Factor -5 + 2 - 27*b**2 - 21*b**a + 0 - 6*b**4 - 15*b.
-3*(b + 1)**3*(2*b + 1)
Let o(b) be the second derivative of b**5/110 - 7*b**4/66 + b**3/3 - 5*b**2/11 + b - 13. Factor o(d).
2*(d - 5)*(d - 1)**2/11
Let c(n) = -2*n**2 - 368*n + 2. Let p(f) = 10*f**2 + 1842*f - 11. Let o(u) = -11*c(u) - 2*p(u). Suppose o(g) = 0. Calculate g.
-182, 0
Let x(h) be the second derivative of -h**7/10080 + h**6/720 - h**5/120 + 25*h**4/12 + 15*h. Let j(r) be the third derivative of x(r). Factor j(s).
-(s - 2)**2/4
Let i(p) be the second derivative of p**6/40 + 3*p**5/40 - 7*p**4/16 + p**3/2 + 121*p. Factor i(u).
3*u*(u - 1)**2*(u + 4)/4
Let k(m) be the third derivative of m**5/12 + 5*m**4/24 - 5*m**3/3 - 6*m**2 - 2*m. Factor k(b).
5*(b - 1)*(b + 2)
Suppose -5*p + 42 = 2*x - 6*x, 4*p = x + 16. Factor 1/9*i + 2/9 - 1/9*i**p.
-(i - 2)*(i + 1)/9
Let x(g) be the second derivative of -g**5/110 + g**4/22 - 4*g**2/11 + 363*g. Find w such that x(w) = 0.
-1, 2
Factor 3/5*z**3 - 1 - 11/5*z**2 - 19/5*z.
(z - 5)*(z + 1)*(3*z + 1)/5
Suppose -324 = -8*b + 12*b. Let r = b - -81. Factor 10/7*o**4 - 6/7*o**3 - 4/7*o**2 + 0 + r*o.
2*o**2*(o - 1)*(5*o + 2)/7
Let x(a) be the third derivative of -a**6/200 + a**4/40 + 26*a**2. Factor x(t).
-3*t*(t - 1)*(t + 1)/5
Factor -8/3*g + 2/9*g**2 + 40/9.
2*(g - 10)*(g - 2)/9
Factor 0 - 8*y + 8/3*y**2 - 1/6*y**3.
-y*(y - 12)*(y - 4)/6
Let h(u) be the second derivative of -49*u**6/2160 - 7*u**5/360 - u**4/144 - 2*u**3/3 - 2*u. Let l(g) be the second derivative of h(g). Factor l(z).
-(7*z + 1)**2/6
Let k = -793/9 - -794/9. Factor 1/3*n**4 + 0 + 1/9*n**3 - 1/3*n**2 - k*n.
n*(n - 1)*(n + 1)*(3*n + 1)/9
Suppose -682/5*z + 196/5 - 18/5*z**3 - 896/5*z**2 = 0. Calculate z.
-49, -1, 2/9
Let s = -2567 - -2570. Let d(p) be the third derivative of 5/3*p**4 + 0*p**3 - 1/3*p**5 - s*p**2 - 1/12*p**6 + 1/42*p**7 + 0*p + 0. Factor d(k).
5*k*(k - 2)**2*(k + 2)
Suppose -4*t - 25 + 5 = 0. Let h be -1 - (t - (-68)/20). Find z such that -h*z + 6/5 - 3/5*z**2 = 0.
-2, 1
Let c = 3/16816 - -16789/151344. Factor 8/9 - c*b**2 + 2/9*b.
-(b - 4)*(b + 2)/9
Factor -180*k**3 - 14*k**5 + 24*k**5 + 486 + 30*k**4 - 261*k - 12*k**5 - 549*k + 540*k**2.
-2*(k - 3)**5
Suppose 2*w + 3*w - 40 = 0. Factor -105*d - w*d**3 - 6 + 32*d + 13*d - 32*d**2 + 34*d.
-2*(d + 3)*(2*d + 1)**2
Let x(t) be the first derivative of 2*t**3/39 + 4*t**2/13 - 24*t/13 - 83. Let x(k) = 0. What is k?
-6, 2
Factor 7/4*q**4 - 2*q**3 - 4*q**2 - 1/4*q**5 + 0*q + 0.
-q**2*(q - 4)**2*(q + 1)/4
Let f(q) = -16*q - 478. Let j be f(-30). Factor 1/2 + 0*t - 1/8*t**j.
-(t - 2)*(t + 2)/8
Suppose -w + 2*n - 1 = 3, -2 = -4*w - n. Let j(k) be the first derivative of -2/21*k**3 + w*k**2 + 0*k