ivative of -g**8/1680 + g**7/840 + 2*g**3/3 - g. Let f(r) be the second derivative of u(r). Factor f(c).
-c**3*(c - 1)
Let y = -11 + 12. Let z(o) be the first derivative of y - 2/27*o**3 - 2/9*o - 2/9*o**2. Factor z(a).
-2*(a + 1)**2/9
Let g(o) be the second derivative of -o**6/90 - o**5/10 - 13*o**4/36 - 2*o**3/3 - 2*o**2/3 + 10*o. Factor g(r).
-(r + 1)**2*(r + 2)**2/3
Let r(v) be the first derivative of v**3 + 9*v**2/2 + 45. What is a in r(a) = 0?
-3, 0
Let v(z) be the third derivative of z**7/210 - z**6/120 - z**5/60 + z**4/24 - 18*z**2. Factor v(c).
c*(c - 1)**2*(c + 1)
Determine k so that -5/2*k**2 + 10 - 15/2*k = 0.
-4, 1
Let q be (((-6)/(-33))/(-1))/((-19)/209). Factor 12/5*w**4 - 6/5 + 12/5*w**3 - 3*w + 3/5*w**5 - 6/5*w**q.
3*(w - 1)*(w + 1)**3*(w + 2)/5
Let t(f) = -3*f**2 - 3*f - 1. Let q be t(-2). Let o = 7 + q. Factor o + 0*v + 1/2*v**4 + 1/2*v**3 + 0*v**2.
v**3*(v + 1)/2
Suppose -66*g**2 + 49*g + 35*g + 16*g**3 - 18*g**2 - 16 + 0 = 0. Calculate g.
1/4, 1, 4
Let n(k) = -k**2 - k + 44. Let d be n(6). Solve 4/11 - 2/11*a**4 - 2/11*a**d - 6/11*a**3 + 6/11*a = 0 for a.
-2, -1, 1
Find s, given that 18/5*s**4 - 4/5*s**2 + 0 + 0*s + 14/5*s**3 = 0.
-1, 0, 2/9
Solve -12*n**3 + 8*n + 12*n + 18*n**2 - 6 + n - 3*n**2 = 0.
-1, 1/4, 2
Let y be -2 - (3 + -1 + -8). Suppose -5*m + 10 = -3*r, m + 4*r = 3*m - y. Factor -2 + 4 + 0*w**2 - 3 + w**m.
(w - 1)*(w + 1)
Let h = 22/79 - 40/711. Determine q, given that 0 + 2/9*q**3 - 2/9*q**5 - h*q**4 + 2/9*q**2 + 0*q = 0.
-1, 0, 1
Let y(n) be the first derivative of -n**2 + 0*n**4 - 1/180*n**5 + 0*n**3 + 0*n - 1. Let i(c) be the second derivative of y(c). What is p in i(p) = 0?
0
Let k(i) be the second derivative of -i**4/48 + i**3/12 - i**2/8 - 18*i. Factor k(a).
-(a - 1)**2/4
Let g be 2/(-9) + ((-219)/(-135) - 0). Determine r so that 3/5*r**4 - 8/5*r**3 + 0 - 2/5*r + g*r**2 = 0.
0, 2/3, 1
Let l = 89/135 + -7/27. Let v(q) be the second derivative of -l*q**2 + 1/30*q**4 + 1/15*q**3 - q + 0. Suppose v(t) = 0. What is t?
-2, 1
Let t = -74 + 34. Let d be 6/15 - (-6)/t. Find s, given that -1/4*s**2 + d*s + 0 = 0.
0, 1
Let d(b) = 2*b**5 - 10*b**4 + 2*b**3 - 6*b**2 - 4*b + 4. Let q(a) = a**4 + a**3 + a**2 + a - 1. Let f(x) = -d(x) - 4*q(x). Factor f(l).
-2*l**2*(l - 1)**3
Let m(g) be the third derivative of g**8/4200 - g**6/900 + 2*g**3/3 - g**2. Let i(k) be the first derivative of m(k). Solve i(l) = 0 for l.
-1, 0, 1
Suppose 2*z + 8*z**3 - 6*z**2 - z**2 - 3*z**2 + 0*z**2 = 0. Calculate z.
0, 1/4, 1
Let g(j) be the third derivative of -j**9/5040 - j**8/1680 + j**7/2520 + j**6/360 + j**4/8 + 3*j**2. Let u(f) be the second derivative of g(f). Factor u(n).
-n*(n + 1)**2*(3*n - 2)
Let k(w) be the second derivative of w**7/5460 - w**6/780 + w**5/260 - w**4/156 - w**3/3 - 3*w. Let x(q) be the second derivative of k(q). Factor x(z).
2*(z - 1)**3/13
Let i(k) = k**3 + k**2 + k. Suppose -u - 1 = -4. Let q(c) = 2*c**u + c**2 + c**2 - c**2. Let w(b) = i(b) - q(b). Let w(v) = 0. Calculate v.
-1, 0, 1
Let l = -17 + 24. Let m(n) be the third derivative of 11/12*n**4 - 1/21*n**l + 17/60*n**6 - 7/10*n**5 - 3*n**2 - 2/3*n**3 + 0*n + 0. Factor m(f).
-2*(f - 1)**3*(5*f - 2)
Let x(c) be the first derivative of c**7/105 - c**5/15 + c**3/3 + c**2/2 - 1. Let k(i) be the second derivative of x(i). Suppose k(r) = 0. What is r?
-1, 1
Let l be 2 + 0 + (-1)/(-1). Suppose -2*n + 3*n - 1 = 0. Factor 2*m - n - m**3 - m - 4*m - l*m**2.
-(m + 1)**3
Let p(x) be the third derivative of -2*x**2 + 1/24*x**3 + 1/80*x**5 + 0 + 0*x + 1/480*x**6 + 1/32*x**4. Factor p(t).
(t + 1)**3/4
Let d(t) be the first derivative of -7/9*t**3 - 1/2*t**2 + 1/4*t**4 + 1/3*t**5 - 2 + 2/3*t. Determine n, given that d(n) = 0.
-1, 2/5, 1
Let d(a) be the second derivative of -a**7/21 - 2*a**6/15 - a**5/10 - 6*a. Factor d(g).
-2*g**3*(g + 1)**2
Let q(u) be the third derivative of u**8/20160 - u**7/840 + u**6/80 + u**5/60 - 8*u**2. Let x(t) be the third derivative of q(t). Find n such that x(n) = 0.
3
Let 10*v**2 - 26/3*v - 4/3 = 0. What is v?
-2/15, 1
Let t(n) = -7*n**3 - 9*n**2 + 6*n - 4. Let z(x) = -6*x**3 - 8*x**2 + 5*x - 3. Let m(o) = 3*t(o) - 4*z(o). Factor m(l).
l*(l + 2)*(3*l - 1)
Let n(o) = -o**3 + 7*o**2 - 4*o - 7. Let u be n(6). Factor -u*r**3 + r**3 - 2*r**3 + 2*r - r**2 + 5*r**3.
-r*(r - 1)*(r + 2)
Let y(h) be the first derivative of -1 - 2/33*h**3 + 0*h**2 + 0*h. Solve y(q) = 0.
0
Let g = -669288/10745 + 4/1535. Let t = -62 - g. Let 10/7*a**2 - 16/7*a + 8/7 - t*a**3 = 0. Calculate a.
1, 2
Let h = 54 + -36. Let b be h/(-60)*(-2)/3. Determine f so that 1/5*f**2 + 0 + b*f = 0.
-1, 0
Find l such that 4*l - 52/3*l**2 + 0 + 16/3*l**5 - 20*l**4 + 28*l**3 = 0.
0, 3/4, 1
Suppose 0 = 2*k - 14. Let t be (6/(-21))/((-5)/k). Factor -t*g**2 + 2/5*g**4 + 0 + 2/5*g - 2/5*g**3.
2*g*(g - 1)**2*(g + 1)/5
Let x(j) be the first derivative of j**5/15 + j**4/6 + j**3/9 + 9. Let x(m) = 0. What is m?
-1, 0
Let j(d) be the second derivative of 1/3*d**3 - 1/10*d**5 - 1/30*d**6 + 0 + 1/2*d**2 + 0*d**4 + 2*d. Factor j(o).
-(o - 1)*(o + 1)**3
Let j(n) = 2*n**4 + 62*n**3 + 350*n**2 + 768*n + 574. Let k(w) = 9*w**4 + 309*w**3 + 1749*w**2 + 3840*w + 2869. Let t(c) = 11*j(c) - 2*k(c). Factor t(l).
4*(l + 2)**2*(l + 6)**2
Let u = -6 - -8. Suppose -3*v - 19 = 5*t, 4*t = v + u*t - 12. Factor -18*r**v - 8/5 - 10*r**3 - 48/5*r.
-2*(r + 1)*(5*r + 2)**2/5
Let a(z) be the second derivative of -z**4/42 - 2*z**3/21 - 3*z. Suppose a(m) = 0. What is m?
-2, 0
Let y(k) be the second derivative of -k**6/780 + k**5/390 + 5*k**2/2 - 6*k. Let q(b) be the first derivative of y(b). Solve q(w) = 0 for w.
0, 1
Let l be 1 + (-14)/12 + 270/1575. Let x(j) be the second derivative of -1/30*j**6 + 1/6*j**3 - 1/6*j**4 - 2*j + 1/10*j**5 - 1/10*j**2 + 0 + l*j**7. Factor x(s).
(s - 1)**5/5
Suppose 4*v + 9 + 7 = 0. Let l = -3 - v. Let g(t) = 2*t**3 + 4*t**2 + 7*t - 5. Let f(u) = u - 1. Let d(w) = l*g(w) - 5*f(w). Factor d(k).
2*k*(k + 1)**2
Let y(p) be the first derivative of 5 + 0*p**2 + 0*p + 4/5*p**5 - 2/3*p**3 - 1/2*p**4. Factor y(v).
2*v**2*(v - 1)*(2*v + 1)
Factor -4*l + 2*l**2 + 0*l - 2*l + 6*l**3 + 1 - 5 + 2*l**4.
2*(l - 1)*(l + 1)**2*(l + 2)
Find v, given that -91*v**2 + 86*v**2 - 80 - 18*v - 22*v = 0.
-4
Suppose -4*b + 15 + 3 = -n, -4*b + 2*n = -20. Solve -10*k + 2*k - 6*k**2 - 2*k**2 + b - 6*k = 0.
-2, 1/4
Let n be (6/5 + -2)/((-20)/150). Factor n*z - 6 - 3/2*z**2.
-3*(z - 2)**2/2
Suppose -14*x + 10*x = -28. Let -2*q**5 + 0*q**5 + 4*q**3 - 9*q + x*q = 0. What is q?
-1, 0, 1
Let -p**3 + 3*p**4 - 3*p**5 - p + 0*p**5 + 5*p**5 - 3*p**2 = 0. Calculate p.
-1, -1/2, 0, 1
Solve 2/5*q**2 + 32/5 + 16/5*q = 0.
-4
Solve -18*n - 3*n**3 - 9*n - 29*n**2 + 11*n**2 = 0.
-3, 0
Let x be 6/((-4)/(-2)) + -9. Let h be ((-14)/(-147))/((-2)/x). Solve 2/7*j**2 - h*j + 0 = 0.
0, 1
Let x(w) be the first derivative of -w**4/2 - 2*w**3/3 + 13. Factor x(f).
-2*f**2*(f + 1)
Let x(r) be the third derivative of 1/60*r**6 + r**2 + 0 - 1/12*r**4 + 1/30*r**5 - 1/3*r**3 + 0*r. Let x(p) = 0. What is p?
-1, 1
Let q(b) = -2*b**3 - b**2 + 1. Let x be q(-1). Let t(j) be the first derivative of x*j**4 - 2/5*j**5 - 2*j + 4*j**2 - 4*j**3 + 3. Solve t(z) = 0.
1
Let p be 15/(-27)*6/(-15). Let w(v) be the first derivative of -1 - 2/45*v**5 - 1/9*v**2 + 0*v - p*v**3 - 1/6*v**4. Solve w(i) = 0 for i.
-1, 0
Let a(h) be the second derivative of -4*h**4/3 - 4*h**3/3 - h**2/2 - 8*h. Solve a(t) = 0 for t.
-1/4
Let q = 66 + -66. Let 0 + q*s - 4/3*s**3 - 1/3*s**2 = 0. What is s?
-1/4, 0
Let b(v) be the second derivative of v**5/120 - v**4/36 - 13*v**3/36 - 5*v**2/6 + 34*v. Let b(m) = 0. Calculate m.
-2, -1, 5
Suppose 0 - 2/5*p**5 - 8/5*p**2 - 12/5*p**3 + 16/5*p + 2*p**4 = 0. What is p?
-1, 0, 2
Let f(l) be the second derivative of -l**2 - 1/180*l**5 - 1/18*l**3 + 0 - 3*l - 1/36*l**4. Let o(v) be the first derivative of f(v). Let o(p) = 0. Calculate p.
-1
Solve -1/2*j**2 + 3/10*j**3 - 2/5*j**5 + 1/10*j + 1/2*j**4 + 0 = 0 for j.
-1, 0, 1/4, 1
Let c = -1165 - -1169. Factor -28/3*j - 20/3*j**3 + 12*j**2 + 8/3 + 4/3*j**c.
4*(j - 2)*(j - 1)**3/3
Let q(w) be the third derivative of -1/240*w**6 - 1/840*w**7 + 1/48*w**4 + 0*w**5 - 2*w**2 + 0*w + 1/24*w**3 + 0. Factor q(n).
-(n - 1)*(n + 1)**3/4
Let d(y) be the first derivative of 2/15*y**3 + 3/5*y**2 + 4/5*y + 3. Find q such that