e second derivative of p**8/3360 + p**7/3780 - p**6/360 - p**5/180 + p**4/3 - 2*p. Let i(m) be the third derivative of h(m). Factor i(b).
2*(b - 1)*(b + 1)*(3*b + 1)/3
Let g(h) = h**2 - 8*h + 9. Let f be g(6). Let v = f - -6. Let -d - 5*d**3 - 2*d**v + 4*d**2 + d**2 + 3*d**4 = 0. What is d?
0, 1/3, 1
Let z(c) be the third derivative of 0*c + 1/180*c**5 - 1/18*c**3 + 2*c**2 - 1/72*c**4 + 1/360*c**6 + 0. Let z(d) = 0. What is d?
-1, 1
Let x(d) = d + 9. Let w be x(-9). Solve w*u**5 + 2*u**3 + 2*u**3 - 6*u**4 - 2*u**4 + 4*u**5 = 0 for u.
0, 1
Let m(v) = -v**3 + 4*v**2 - 3*v. Let f be m(2). Let t be f/5*(-12)/(-8). Factor -6/5 + 6/5*g**2 + 3/5*g - t*g**3.
-3*(g - 2)*(g - 1)*(g + 1)/5
Let j be (4/14)/((-1)/(-7)). Factor -5*o**j + 4*o**2 - 2 + 1 + 2*o.
-(o - 1)**2
Let h(i) be the first derivative of -i**5/10 + i**3 - 2*i**2 + 4*i + 2. Let u(g) be the first derivative of h(g). Factor u(m).
-2*(m - 1)**2*(m + 2)
Let c(r) be the second derivative of -r**4/36 + r**3/18 - 12*r. Factor c(y).
-y*(y - 1)/3
Let g be (-8)/(-4)*4/(24/15). Let n(u) be the second derivative of -1/8*u**4 - 1/16*u**g + u**2 - 1/120*u**6 + u + 1/6*u**3 + 0. Factor n(o).
-(o - 1)*(o + 2)**3/4
Let g be 2*2*(-9)/(-12). Suppose x = -g*x + 8. Solve -6*l**2 + 3*l**2 + l**3 + 2*l**x = 0 for l.
0, 1
Let y(t) be the first derivative of -2*t**6/3 + 4*t**5/5 + 2*t**4 - 8*t**3/3 - 2*t**2 + 4*t + 33. Suppose y(k) = 0. What is k?
-1, 1
Let l(f) be the second derivative of f**6/75 + 13*f**5/50 + 19*f**4/10 + 19*f**3/3 + 10*f**2 - 20*f - 1. Factor l(v).
2*(v + 1)*(v + 2)*(v + 5)**2/5
Let s(l) be the third derivative of l**9/151200 - l**8/25200 + l**7/12600 - l**5/10 - 3*l**2. Let n(w) be the third derivative of s(w). Factor n(r).
2*r*(r - 1)**2/5
Let c(d) be the second derivative of 0*d**3 + 0 + 2*d - 1/48*d**4 - 3/2*d**2 - 1/240*d**5. Let w(p) be the first derivative of c(p). Factor w(j).
-j*(j + 2)/4
Let m(s) be the second derivative of 2*s**7/3 - 8*s**6/5 - 4*s**5/5 + 14*s**4/3 - 2*s**3 - 4*s**2 - 10*s. Factor m(a).
4*(a - 1)**3*(a + 1)*(7*a + 2)
Let j(x) be the third derivative of -x**8/112 - x**7/35 + x**5/10 + x**4/8 - x**2. Determine q so that j(q) = 0.
-1, 0, 1
Let h = 257/400 + -9/16. Let s = h + 94/75. Factor 2/3*j**3 + 0 + 2/3*j - s*j**2.
2*j*(j - 1)**2/3
Factor 0 + 2/7*k**2 + 2/7*k.
2*k*(k + 1)/7
Suppose 2*m + 5 = h - 3*m, 5 = -5*m. Let r(c) be the first derivative of 0*c - 1/2*c**4 + c**2 + h*c**3 + 1. Factor r(w).
-2*w*(w - 1)*(w + 1)
Let f = 671/3 - 223. Let -4/3*j**2 + 0*j - f*j**5 + 0 - 10/3*j**3 - 8/3*j**4 = 0. What is j?
-2, -1, 0
Find d such that 5/2*d**4 - 5/4*d - 5*d**2 - 5/4*d**5 + 5/2*d**3 + 5/2 = 0.
-1, 1, 2
Let q(g) be the second derivative of -3*g**7/7 - 17*g**6/20 + 27*g**5/40 + 19*g**4/8 + 3*g**3/4 - 3*g**2/2 + 7*g. Find k, given that q(k) = 0.
-1, -2/3, 1/4, 1
Factor 10*z**5 + 9*z**5 - 27*z**5 - 2*z**4 + 9*z**5.
z**4*(z - 2)
Let z(p) = -p**3 + p**2 + p. Let i(s) = -3*s**3 + 3*s**2 + 4*s + 1. Let b(h) = -i(h) + 4*z(h). Let m(c) = -1. Let t(u) = -b(u) + m(u). Factor t(j).
j**2*(j - 1)
Let y be 6/9*9/2. Factor -1 - 4*l + 2 + 5 + 9*l**3 - 5*l - 3*l**4 - y*l**2.
-3*(l - 2)*(l - 1)**2*(l + 1)
Let w(o) be the first derivative of o**4/6 + o**3/3 + 2*o - 2. Let x(y) be the first derivative of w(y). Factor x(c).
2*c*(c + 1)
Let k be (2/(-4))/((-5)/30). Factor d**k - 1 - 2*d**2 - d**2 + 12*d - 9*d.
(d - 1)**3
Let n = 4 + 0. Solve -4*o**3 - 2 - n*o**2 - 1 - 2*o + 2 + 11*o**2 = 0 for o.
-1/4, 1
Factor 0*p - 16/3*p**3 + 0 - 50/9*p**5 + 10*p**4 + 8/9*p**2.
-2*p**2*(p - 1)*(5*p - 2)**2/9
Let t(q) be the third derivative of q**6/320 - q**5/160 - q**4/32 + 19*q**2. Factor t(c).
3*c*(c - 2)*(c + 1)/8
Let i(s) be the second derivative of s**8/448 + s**7/140 - s**5/40 - s**4/32 - s**2/2 - 4*s. Let r(n) be the first derivative of i(n). Factor r(a).
3*a*(a - 1)*(a + 1)**3/4
Suppose -2*o - 1 = -7. Factor 2*r**4 - 4/3*r**2 - 2*r - 2/3 + 4/3*r**o + 2/3*r**5.
2*(r - 1)*(r + 1)**4/3
Factor 2/11*k + 2/11*k**2 - 4/11.
2*(k - 1)*(k + 2)/11
Let j(l) be the third derivative of -l**6/360 + l**5/90 - l**4/72 - l**2. Let j(q) = 0. What is q?
0, 1
Let v(z) = 4*z**3 - 2*z**2 + 4*z. Let r(f) = 4*f - 9*f**2 - 2*f**3 + 13*f**3 + 10*f**3 + 17*f. Let j(x) = 4*r(x) - 22*v(x). Factor j(s).
-4*s*(s - 1)**2
Let o(s) be the second derivative of s**7/21 - s**6/5 + 2*s**4/3 - 28*s. Determine c so that o(c) = 0.
-1, 0, 2
Let l = 34 - 32. Solve -2/3*i + l*i**2 + 2/3*i**3 - 2/3*i**4 - 4/3 = 0 for i.
-1, 1, 2
Find l such that 2/5 + 4/15*l - 2/15*l**2 = 0.
-1, 3
Let y(g) be the first derivative of 2 - 1/30*g**4 + 0*g - 3/2*g**2 - 1/15*g**3 - 1/150*g**5. Let s(n) be the second derivative of y(n). Let s(r) = 0. What is r?
-1
Let i(l) be the second derivative of -5*l + 1/4*l**4 + 0 + 1/2*l**3 - 3*l**2. Factor i(o).
3*(o - 1)*(o + 2)
Solve 0 + 2/5*i - 6/5*i**2 = 0.
0, 1/3
Let p be 0 + (-4)/(-16)*2. Let s(v) be the first derivative of -1/3*v**3 + 0*v + 1 - p*v**2. Factor s(z).
-z*(z + 1)
Let m = 114 + -569/5. Factor -2/5*r**2 + m*r**3 + 1/5*r + 0.
r*(r - 1)**2/5
Factor 8/3 - 2*k - 2/3*k**2.
-2*(k - 1)*(k + 4)/3
Let x = 83/120 + -1/40. Let k(n) = n**3 - 2*n**2 - 2*n - 1. Let z be k(3). Find o such that -1/3 + x*o - 1/3*o**z = 0.
1
Let y(k) be the first derivative of k**5 - 15*k**4/2 + 65*k**3/3 - 30*k**2 + 20*k + 30. Solve y(j) = 0.
1, 2
Let v(j) be the second derivative of j**4/6 - j**3/3 - 2*j**2 + 9*j. Solve v(t) = 0.
-1, 2
Let d be 1/5 + 126/70. Suppose -5*g - 8 + 28 = 0. Factor 1 - o**g + d*o**2 + 0*o**3 - 2 - 2*o**3 + o**5 - 2*o + 3*o.
(o - 1)**3*(o + 1)**2
Let k = 4279 + -1797. Let j = k - 27282/11. Solve 10/11*i + 2/11 + 2/11*i**5 + 10/11*i**4 + 20/11*i**3 + j*i**2 = 0.
-1
Factor 1/6*u**4 + 0*u - 1/3*u**2 + 1/6*u**3 + 0.
u**2*(u - 1)*(u + 2)/6
Factor 0*h + 32/3*h**4 + 16/3*h**3 + 2/3*h**2 + 0.
2*h**2*(4*h + 1)**2/3
Solve -2 + 2 + 32*f + 4*f**2 - 36*f = 0 for f.
0, 1
Let q(b) = -b**2 - 1. Let j(u) = -2*u**4 + 2*u**3 + 16*u**2 - 10*u + 14. Let w(c) = -j(c) - 10*q(c). Factor w(p).
2*(p - 1)**3*(p + 2)
Let m(u) be the third derivative of u**7/630 - u**6/180 + u**5/180 - 20*u**2. Suppose m(i) = 0. What is i?
0, 1
Let s(f) be the second derivative of -f**5/5 + f**4/3 + 8*f**3/3 - 8*f**2 - 7*f. Suppose s(o) = 0. What is o?
-2, 1, 2
Let g(y) be the third derivative of y**6/60 - y**5/30 - y**4/12 + y**3/3 + 10*y**2. Let g(f) = 0. What is f?
-1, 1
Let r(c) be the second derivative of -1/40*c**5 - 1/24*c**4 + 0*c**2 + 5*c + 1/60*c**6 + 1/84*c**7 + 0*c**3 + 0. Factor r(p).
p**2*(p - 1)*(p + 1)**2/2
Let n(o) = 2*o**2 + 2*o - 1. Let b be n(-2). Factor 6 + 5 + b*t - 3*t**2 - 3 - 2.
-3*(t - 2)*(t + 1)
Let c be (-181)/(-60) - (-9 - -12). Let y(o) be the second derivative of -c*o**5 - 3*o - 1/18*o**3 + 0*o**2 - 1/18*o**4 + 0. Let y(a) = 0. Calculate a.
-1, 0
Solve -109*p - 81*p**3 + 115*p - 3 + 84*p**4 - 9*p**2 + 3 = 0 for p.
-2/7, 0, 1/4, 1
Let r(g) be the second derivative of g**5/20 + g**4/4 - 2*g**2 + 15*g. Suppose r(z) = 0. What is z?
-2, 1
Let r(n) be the third derivative of -2*n**5/105 + 5*n**4/84 - n**3/21 + 17*n**2. Suppose r(h) = 0. What is h?
1/4, 1
Let m(u) be the first derivative of u**4/14 + 2*u**3/3 + 15*u**2/7 + 18*u/7 + 8. Find r such that m(r) = 0.
-3, -1
Let g be (-3 - -3)/(2/2). Let d = 0 - -2. Suppose g + 2/5*j**d - 2/5*j = 0. Calculate j.
0, 1
Let j(v) = -112*v**2 - 244*v + 45. Let z(b) = 22*b**2 + 49*b - 9. Let w(n) = 2*j(n) + 11*z(n). Determine p so that w(p) = 0.
-3, 1/6
Let q(r) = -15*r**5 - 4*r**4 + 13*r**3 + 17*r**2 - 11*r + 13. Let m(d) = -7*d**5 - 2*d**4 + 6*d**3 + 8*d**2 - 5*d + 6. Let h(o) = 13*m(o) - 6*q(o). Factor h(p).
-p*(p - 1)*(p + 1)**3
Suppose 5*a - 5*y - 10 = 0, -2*a + 3*y + 10 = -2*y. Suppose -d + 2*u + 4 = -0, 4*u + 8 = 0. Factor a*g - 2*g + 2*g**3 + d*g.
2*g*(g - 1)*(g + 1)
Let x be 3 + 145/(-45) - 26/(-117). Suppose x + 0*t + 4/5*t**2 = 0. Calculate t.
0
Suppose 0*l - 3*l + 30 = 0. Find o such that -2*o**2 + l*o**3 - 6*o + 6*o**4 - 3*o - 4 - o = 0.
-1, -2/3, 1
Let r be (-328)/(-1230)*(1 + 2). Factor -2*i - r - 6/5*i**2.
-2*(i + 1)*(3*i + 2)/5
Let k be (-1 - -1) + 2 + -2. Suppose 6 = -k*q + 3*q. Solve -v - 6*v**3 + 5*v**3 - v**q + v**4 + 2*v**3 = 0.
-1, 0, 1
Let j(b) be the first derivative of b + 4*b**4 - 1 + 9/2*b**2 + 8*b**3. Find l such that j(l) = 0.
-1, -1/4
Let c(s) be the first deri