e the third derivative of n**6/60 - n**5/15 + 2*n**2. Factor t(k).
2*k**2*(k - 2)
Suppose 14*n + 21 - 49 = 0. Factor -4/3*t**3 + 0*t**n + 4/3*t + 0.
-4*t*(t - 1)*(t + 1)/3
Let p(r) be the first derivative of -r**6/30 - r**5/10 + r**3/3 + r**2/2 + 3*r - 2. Let v(o) be the first derivative of p(o). Factor v(y).
-(y - 1)*(y + 1)**3
Let 4*u**4 + 6*u**5 - 3*u**4 - 4*u**4 + 4*u**2 - u**2 - 6*u**3 = 0. Calculate u.
-1, 0, 1/2, 1
Let q be (-6)/2 + 728/240. Let x(b) be the third derivative of b**2 + 0*b**3 + 0*b + 0 - q*b**5 - 1/12*b**4. Solve x(r) = 0 for r.
-1, 0
Suppose 3*z - 2*a = 23, -z + 3*z - 4*a = 26. Determine v, given that -3*v**5 + 6*v**3 - z*v + 0*v**5 + 2*v = 0.
-1, 0, 1
Let o = 113 - 111. Find m such that -2/5 + 4/5*m - 2/5*m**o = 0.
1
Let s(w) be the second derivative of -2*w**7/105 - 4*w**6/25 - 14*w**5/25 - 16*w**4/15 - 6*w**3/5 - 4*w**2/5 + 9*w. Factor s(g).
-4*(g + 1)**4*(g + 2)/5
Suppose 3*b = 5*b - 3*b. Factor 0 + t**4 - t**2 + 1/2*t + b*t**3 - 1/2*t**5.
-t*(t - 1)**3*(t + 1)/2
Let y(c) be the first derivative of 42*c**5/65 - 4*c**4/13 - 22*c**3/39 - 2*c**2/13 + 54. Solve y(m) = 0.
-1/3, -2/7, 0, 1
Let a(w) = w + 5. Let t be a(0). Suppose 0*v - t = -v. Factor 0 - 2/3*o**2 - 8/3*o**4 + 7/3*o**3 + 0*o + o**v.
o**2*(o - 1)**2*(3*o - 2)/3
Let q(j) be the third derivative of -j**6/60 + 19*j**5/210 - 2*j**4/21 - 4*j**3/21 - 5*j**2. What is s in q(s) = 0?
-2/7, 1, 2
Let a(i) be the first derivative of 2*i**6/3 - 16*i**5/5 + 3*i**4 + 16*i**3/3 - 8*i**2 + 10. Suppose a(u) = 0. Calculate u.
-1, 0, 1, 2
Let w(h) be the first derivative of h**3/3 + h**2 - 3*h - 5. Solve w(f) = 0 for f.
-3, 1
Suppose 16 = -2*k + 3*k. Suppose 3*u = 6, -k = -0*r - 4*r - 2*u. Determine x so that x**2 - 2*x**r - x**3 - x**3 - 2*x**4 - 3*x**2 = 0.
-1, 0
Let f(g) be the second derivative of g**5/10 + g**4/3 - 4*g**3/3 - 8*g**2 + 6*g. Factor f(w).
2*(w - 2)*(w + 2)**2
Let x = 11163/20 - 558. Let m(u) be the second derivative of 0*u**2 + 0 + 1/6*u**4 + u - 1/84*u**7 + 1/15*u**6 - x*u**5 - 1/12*u**3. Factor m(d).
-d*(d - 1)**4/2
Let f(a) be the first derivative of 0*a - 1/3*a**6 + 1/2*a**4 + 2/5*a**5 - 2/3*a**3 + 0*a**2 - 4. Solve f(v) = 0.
-1, 0, 1
Factor -4/3 + 37/3*v**2 + 4*v - 15*v**3.
-(v - 1)*(5*v + 2)*(9*v - 2)/3
Let l = -4 + 6. Let v(p) = p**2 + p - 1. Let w(y) = 2 + 0 + 0 + 0 - y**2 - 3*y. Let s(u) = l*v(u) + w(u). Factor s(q).
q*(q - 1)
Find u, given that -2/5*u**3 - 32/5*u + 4*u**2 + 0 = 0.
0, 2, 8
Let j(y) be the third derivative of 1/48*y**5 + 0*y - 7/96*y**4 + 0 - 3*y**2 + 1/12*y**3. Determine o, given that j(o) = 0.
2/5, 1
Let f(g) be the third derivative of g**5/150 - g**4/60 - 2*g**3/15 - 3*g**2. Factor f(l).
2*(l - 2)*(l + 1)/5
Let n(f) = -f**3 + f**2 + 1. Let o(q) = -4*q**3 + 6*q**2 - 2*q + 5. Let z(r) = 5*n(r) - o(r). Find h, given that z(h) = 0.
-2, 0, 1
Suppose -3 = 4*u + 13. Let l(o) = 5*o**2 - o + 2. Let h(m) = -m**2 - 1. Let q(b) = b**2 - 15*b - 17. Let r be q(16). Let g(s) = r*l(s) + u*h(s). Factor g(z).
-(z - 2)*(z + 1)
Let j(i) be the third derivative of i**8/420 + 13*i**7/525 + 2*i**6/25 + 3*i**5/50 + 10*i**2. Find s, given that j(s) = 0.
-3, -1/2, 0
Let -2*q - 18*q**2 - 4*q**4 + 13*q**3 + 10 - 4 - 2*q**3 + 7*q**3 = 0. Calculate q.
-1/2, 1, 3
Let r(w) be the first derivative of w**5/5 + 3*w**4/2 + 13*w**3/3 + 6*w**2 + 4*w + 4. Determine x, given that r(x) = 0.
-2, -1
Let f(q) be the first derivative of -q**6/630 + q**5/105 - q**4/42 + q**3 - 1. Let s(u) be the third derivative of f(u). Suppose s(d) = 0. What is d?
1
Suppose -2 = -k - 5*g, 3*g = -0*g. Let b(i) be the second derivative of -5/2*i**4 + 3*i**3 + 2*i - 1/5*i**6 - 2*i**k + 11/10*i**5 + 0. Factor b(l).
-2*(l - 1)**3*(3*l - 2)
Factor -2/3*c**2 + 2/3*c + 4/3.
-2*(c - 2)*(c + 1)/3
Let z = 4 - 2. Let n(m) be the first derivative of -1/4*m**4 + z + 0*m - 2/3*m**3 - 1/2*m**2. Factor n(d).
-d*(d + 1)**2
Suppose -3*f + 3 = -p - 14, -4*f + p = -21. Suppose -4 = 2*h + 6, f*h + 23 = x. Factor 2/3*t + 4/3*t**4 + 0*t**2 - 2*t**x + 0.
2*t*(t - 1)**2*(2*t + 1)/3
Factor 3/4 + 3/8*l**2 - 9/8*l.
3*(l - 2)*(l - 1)/8
Let v(g) = 5*g**4 - 6*g**3 + g**2 + 2. Let y(u) = -21*u**4 + 23*u**3 - 3*u**2 + u - 9. Let d(k) = 18*v(k) + 4*y(k). Suppose d(x) = 0. What is x?
-1/3, 0, 1, 2
Suppose -m = -3*c - 3*m + 12, 4 = c - 5*m. Let y(v) = 2*v**3 + 1 - c*v**3 + 1. Let i(p) = -p**4 + 5*p**3 + p**2 - 5. Let d(k) = -2*i(k) - 5*y(k). Factor d(x).
2*x**2*(x - 1)*(x + 1)
Let m(j) = 2*j**4 + 9*j**3 - 6*j**2 - 7*j - 6. Let z(k) = 4*k**4 + 17*k**3 - 11*k**2 - 13*k - 11. Let p(g) = -11*m(g) + 6*z(g). Let p(r) = 0. Calculate r.
-1, 0, 1/2
Let j = 298 - 2082/7. Determine t so that 2/7*t**2 + j + 6/7*t = 0.
-2, -1
Let r(v) be the third derivative of -v**9/15120 - v**8/4200 - v**7/4200 - v**3/2 + 5*v**2. Let m(f) be the first derivative of r(f). Factor m(l).
-l**3*(l + 1)**2/5
Let u(y) = y**2 + 4. Let b(t) = -t. Let w(v) = -3*b(v) - u(v). Let z be w(3). Let g(d) = d. Let l(c) = c**2 + c. Let h(a) = z*g(a) + 2*l(a). Solve h(o) = 0.
0, 1
Let m(l) = -l**3 + 7*l**2 - 3*l - 9. Let u be m(5). Factor a**3 + a**3 - u*a + 26*a.
2*a**3
Let b(w) = w**3 - 4*w**2 + w - 1. Let r be b(4). Suppose -36 = 3*h - 5*h. Suppose -30*f**4 - f - 13*f + h*f**5 - 3*f**3 + 28*f**2 - f**r + 2 = 0. What is f?
-1, 1/3, 1
Let w(z) be the first derivative of z**6/30 - 6*z**5/25 + 3*z**4/5 - 2*z**3/3 + 3*z**2/10 + 25. Determine s so that w(s) = 0.
0, 1, 3
Let x(n) = n**3 + 6*n**2 + 5*n + 3. Let k be x(-5). What is z in 22*z**2 + z**2 - 12*z + 13*z**2 - 15*z**k = 0?
0, 2/5, 2
Let -2/9*c**2 + 2/9 - 2/9*c**3 + 2/9*c = 0. What is c?
-1, 1
Let k(p) be the first derivative of p**3/3 + 5*p**2/6 + 2*p/3 - 31. Let k(c) = 0. What is c?
-1, -2/3
Factor 4*y - 2 + 9*y - 72*y**2 - 2*y + 13*y.
-2*(6*y - 1)**2
Let m(y) = -7*y**4 + 13*y**3 + 3*y**2 - 17*y - 2. Let h(d) = -155*d**4 + 285*d**3 + 65*d**2 - 375*d - 45. Let p(g) = -2*h(g) + 45*m(g). Factor p(n).
-5*n*(n - 3)*(n - 1)*(n + 1)
Factor -5/3 - 5*t - 5/3*t**3 - 5*t**2.
-5*(t + 1)**3/3
Suppose 4*p + 3*w = 6, 5*w + 2 = -2*p + w. Determine d so that 2/5*d**p + 0*d + 0 - 2/5*d**2 = 0.
0, 1
Let f = 7 + -8. Let q be (f - -4) + (-1 - -1). Factor -1/3*y**q + 2/3 + y + 0*y**2.
-(y - 2)*(y + 1)**2/3
Let c(o) = -o**3 - 12*o**2 - 11*o + 3. Let n be c(-11). Find d, given that -d**2 - 1/4*d**5 - d**4 - 3/2*d**n - 1/4*d + 0 = 0.
-1, 0
Let p be 2/14*(-112)/(-48). Find i such that 0 - p*i**5 + 2/3*i**2 + 0*i**3 + 1/3*i - 2/3*i**4 = 0.
-1, 0, 1
Let j(x) be the second derivative of -2*x**7/105 + 16*x**6/75 - 24*x**5/25 + 32*x**4/15 - 32*x**3/15 - 35*x. Factor j(b).
-4*b*(b - 2)**4/5
Suppose -3*d - 18 = -2*t, -4*d = 2*t + 3*t + 1. Suppose 0 = 8*w + 1 - 17. Factor -4/5*a**w - a - 2/5 - 1/5*a**t.
-(a + 1)**2*(a + 2)/5
Let d(o) be the third derivative of -o**8/840 - o**7/210 + o**6/180 + o**5/30 - o**3/6 - 2*o**2. Let u(j) be the first derivative of d(j). Factor u(x).
-2*x*(x - 1)*(x + 1)*(x + 2)
Let y(a) be the third derivative of 49*a**5/270 - 7*a**4/54 + a**3/27 + 8*a**2. Suppose y(c) = 0. Calculate c.
1/7
Suppose -415 + 418 = d. Suppose 0 - 7/5*n**4 + 4/5*n + 12/5*n**2 - 9/5*n**d = 0. What is n?
-2, -2/7, 0, 1
Factor 1/3*g**3 - 1/3 + g - g**2.
(g - 1)**3/3
Let v(y) be the first derivative of y**8/560 + 3*y**7/280 + y**6/60 - 2*y**3/3 + 5. Let h(x) be the third derivative of v(x). Factor h(g).
3*g**2*(g + 1)*(g + 2)
Solve 4/9*a - 4/9*a**2 + 8/9 = 0.
-1, 2
Let o(d) be the first derivative of d**4/16 + d**3/6 + d**2/8 - 40. Determine f, given that o(f) = 0.
-1, 0
Let u = -17 - -20. Find q such that 3*q + 3*q**2 - 3*q**2 + 3 - 3*q**2 - u*q**3 = 0.
-1, 1
Factor -1/4*m**2 - 1 - m.
-(m + 2)**2/4
Let g = -1 - -1. Factor 4*i**5 - 2*i**5 + g*i**5 - 4*i**5.
-2*i**5
Let o(w) be the second derivative of -2*w**7/7 + w**6/10 + 3*w**5/5 - w**4/4 + 6*w. Solve o(i) = 0.
-1, 0, 1/4, 1
Factor -7*i**2 + 2*i**5 + 4*i**4 - 2*i**3 + 0*i**4 - i**2 + 4*i**2.
2*i**2*(i - 1)*(i + 1)*(i + 2)
Solve -3*m**4 + 3*m**4 + m**4 + 2*m**3 = 0.
-2, 0
Let p(t) = t**2 + 2*t. Let s = -7 - -4. Let h be p(s). Factor -3*a**2 + 2*a + 2*a**h + 6*a**2 + a**2.
2*a*(a + 1)**2
Let m(f) be the second derivative of -f**5/10 - 11*f**4/15 - 28*f**3/15 - 8*f**2/5 + f. Factor m(s).
-2*(s + 2)**2*(5*s + 2)/5
Let a(d) = d**3 - 10*d**2 - 5*d - 6. Let c(f) = -10*f**3 + 110*f**2 + 55*f + 65. Let b(x