
Let x(l) be the third derivative of l**6/36 + l**5/135 - 5*l**4/36 - 2*l**3/27 - 18*l**2. Factor x(z).
2*(z - 1)*(z + 1)*(15*z + 2)/9
Let x(r) be the third derivative of r**8/336 - r**7/105 - r**6/40 + 2*r**5/15 - r**4/6 + 2*r**2. Factor x(l).
l*(l - 2)*(l - 1)**2*(l + 2)
Suppose -x = -i - 4*i, -24 = -4*x - 4*i. Solve -2 - 55/4*y**3 - 9/4*y**x + 1/2*y**2 + 21/2*y**4 + 7*y = 0.
-2/3, 1/3, 1, 2
Let u(w) be the first derivative of -w**8/840 + w**7/140 - w**6/180 - w**5/20 + w**4/6 + w**3 + 4. Let a(q) be the third derivative of u(q). Factor a(y).
-2*(y - 2)*(y - 1)**2*(y + 1)
Let u(o) be the second derivative of -o**5/30 + o**4/3 - o**3 + 3*o**2/2 - 4*o. Let h(l) be the first derivative of u(l). Factor h(c).
-2*(c - 3)*(c - 1)
Let c(h) = h**2 + h + 1. Let l(w) = -7*w**2 - 7*w - 10. Let t(q) = 40*c(q) + 5*l(q). Factor t(u).
5*(u - 1)*(u + 2)
Let x(w) be the first derivative of 0*w**3 - 5 + w**3 - 3*w**2 + 0*w**2. Find u, given that x(u) = 0.
0, 2
Let r be (14/(-60) - (-12)/30)*2. Let l be -1 + (-1)/(-3) + 1. Determine b, given that 1/3 - l*b + 1/3*b**3 - r*b**2 = 0.
-1, 1
Let q(m) be the third derivative of 0 - 1/168*m**8 + 0*m**4 + 3*m**2 + 0*m**6 + 0*m**3 + 0*m - 1/105*m**7 + 0*m**5. Factor q(f).
-2*f**4*(f + 1)
Let y be -4 + 1/(-3) + 4 - -1. Determine i so that -2/9*i**2 - y*i + 0 = 0.
-3, 0
Let s(p) = -p - 7. Let b be s(-7). Let m(y) = 3*y + 74. Let t be m(-24). Factor -4/5*j**t + b + 1/5*j.
-j*(4*j - 1)/5
Let s(f) = 3*f**3 + 3*f**2 + 3*f + 2. Let p be s(-2). Let j = -13 - p. Factor -1/2*v**2 + 0*v**j + 1/6*v**4 - 1/3*v + 0.
v*(v - 2)*(v + 1)**2/6
Suppose 7 + 8 = -5*c. Let r = 6 + c. Factor 2/3 + b**r - 2/3*b + 3/2*b**4 - 11/6*b**2.
(b + 1)**2*(3*b - 2)**2/6
Let j(g) be the third derivative of 1/3*g**5 + g**2 - 2/3*g**3 - 1/10*g**6 + 0 + 0*g - 1/6*g**4. What is k in j(k) = 0?
-1/3, 1
Let g(l) be the first derivative of -4*l**3/3 - 4*l**2 + 12*l - 11. Find t such that g(t) = 0.
-3, 1
Let c(b) be the third derivative of b**6/60 - b**5/180 - b**4/18 - b**3/18 - 3*b**2. Factor c(z).
(z - 1)*(2*z + 1)*(3*z + 1)/3
Suppose y + 5 - 4 = 0, -9 = -4*a - 3*y. Let m(o) be the first derivative of -3/2*o**2 + 4*o**a + 1 + 9/4*o**4 - 6*o. Solve m(b) = 0 for b.
-1, 2/3
Let d be (1/(-4) - 38/40)*-5. Let u(w) be the second derivative of 1/30*w**d + 3*w - 2/3*w**3 + 2*w**2 - 1/4*w**4 + 0 + 1/10*w**5. Determine o so that u(o) = 0.
-2, 1
Suppose -5*s - 3*q + 54 = 0, s = -6*q + q + 24. Let u be (-2)/s + 119/252. Factor 0 - 1/4*x**4 + u*x**3 - 1/4*x**5 + 0*x + 1/4*x**2.
-x**2*(x - 1)*(x + 1)**2/4
Let a(w) = -w**3 - 7*w**2 - 8*w - 7. Let r be a(-6). Let k(s) = 6*s. Let p(v) = v**2 - 12*v. Let y(z) = r*k(z) + 2*p(z). Let y(m) = 0. Calculate m.
-3, 0
Let t(h) be the second derivative of 1/30*h**5 - 5/9*h**3 + 0 + 2/3*h**2 + 10*h - 1/45*h**6 + 1/6*h**4. What is g in t(g) = 0?
-2, 1
Let t be (0 + 6)/(39/(-104)). Let c(p) = 4*p**3 - 4*p**2 + 12*p + 20. Let x(h) = -h - 1. Let u(r) = t*x(r) - c(r). Determine l so that u(l) = 0.
-1, 1
Let -2/7*g**2 + 0*g + 0 = 0. Calculate g.
0
Let v(n) be the second derivative of n**4/54 + 10*n**3/27 + 25*n**2/9 - 6*n + 1. Factor v(a).
2*(a + 5)**2/9
Let l(f) be the first derivative of -f**4/4 - f**3 - 17. Factor l(b).
-b**2*(b + 3)
Let d(t) be the first derivative of -1 - 1/6*t**2 - 1/6*t**4 + 0*t - 1/3*t**3. Solve d(z) = 0 for z.
-1, -1/2, 0
Let o(a) be the second derivative of a**7/147 - a**6/105 - a**5/70 + a**4/42 + 11*a. Factor o(f).
2*f**2*(f - 1)**2*(f + 1)/7
Let d = -4 - -6. Suppose 3*v = 3*u - 9, 2*u + 2*u = -d*v + 18. Suppose -2*x**2 + 5*x**4 + 2*x**2 - 2*x**u = 0. Calculate x.
0
Let c(z) be the third derivative of z**7/210 + 9*z**2. Factor c(q).
q**4
Factor 16/7*z**5 + 0*z**2 - 4/7*z**3 + 0*z + 0 - 12/7*z**4.
4*z**3*(z - 1)*(4*z + 1)/7
Let w(k) be the second derivative of k**4/20 - 6*k**2/5 + 2*k. Let w(j) = 0. Calculate j.
-2, 2
Factor 1/2*i**2 - 1 - 1/2*i.
(i - 2)*(i + 1)/2
Let x(b) be the second derivative of b**9/6048 - b**8/3360 - b**7/1680 + b**6/720 - b**3/6 + 3*b. Let k(w) be the second derivative of x(w). Factor k(y).
y**2*(y - 1)**2*(y + 1)/2
Let p = -191/2 - -96. Suppose -p*w + 1/4*w**2 + 0 = 0. Calculate w.
0, 2
Suppose -21 = 2*w + 5*n, 2*w - 4*w - 6 = 2*n. Let b(s) be the second derivative of -1/18*s**4 + 1/3*s**2 + 0 - 1/30*s**5 + w*s + 1/9*s**3. Factor b(f).
-2*(f - 1)*(f + 1)**2/3
Let j(i) be the second derivative of 5*i - 1/18*i**4 - 5/126*i**7 + 0*i**3 + 0 + 1/12*i**5 + 1/45*i**6 + 0*i**2. Solve j(o) = 0.
-1, 0, 2/5, 1
Let y(c) be the first derivative of c**5/300 - c**4/40 + c**3/15 - 3*c**2/2 + 3. Let z(g) be the second derivative of y(g). Factor z(v).
(v - 2)*(v - 1)/5
Suppose 0 = -y + y - 3*y. Let -2/5*a**2 + 2/5 + y*a = 0. What is a?
-1, 1
Let j = -48 - -50. Let i(v) be the first derivative of 0*v**j + 1/14*v**4 + 0*v + 0*v**3 - 2. Determine g so that i(g) = 0.
0
Let j = -1/73 - -85/876. Let n(z) be the first derivative of -j*z**3 - 1/4*z**2 - 1/4*z - 1. Let n(h) = 0. What is h?
-1
Let y be 8 - (3 + 0 + -1). Determine z, given that 14*z**2 - y + 4*z + 6 = 0.
-2/7, 0
Let i(h) be the third derivative of h**7/70 - h**6/20 + 5*h**2. Factor i(f).
3*f**3*(f - 2)
Let n = -284/3 - -96. Let k(y) be the first derivative of n*y - y**2 + 4 + 2/9*y**3. Factor k(p).
2*(p - 2)*(p - 1)/3
Let t(o) be the third derivative of 1/840*o**8 - 1/150*o**6 + 4/75*o**5 - o**2 - 7/60*o**4 - 2/525*o**7 + 0*o + 0 + 2/15*o**3. Suppose t(c) = 0. What is c?
-2, 1
Suppose -89 - 16*l + 31 + 32 + 4*l**2 + 38 = 0. What is l?
1, 3
Let l(u) be the second derivative of -3*u**5/40 - u**4/8 + u**3/2 - u. Factor l(i).
-3*i*(i - 1)*(i + 2)/2
Factor 0 + 1/3*m**3 + 0*m + 5/3*m**2.
m**2*(m + 5)/3
Suppose 0 = 5*f + 2*f. Let r(h) be the third derivative of -1/60*h**6 - 2*h**2 - 1/6*h**3 - 1/12*h**5 - 1/6*h**4 + 0 + f*h. Factor r(x).
-(x + 1)**2*(2*x + 1)
Let i(w) be the second derivative of 2*w**3/3 + 3*w. Let s be i(1). Find m such that -6*m + 4*m**2 + s*m + 2*m**3 - 2*m**2 - 2 = 0.
-1, 1
Let r(g) = -g**2 + 18*g + 22. Let s be r(19). Solve 0 - 1/5*k**s + 0*k - 1/5*k**2 = 0 for k.
-1, 0
Let q(k) = -2*k**3 - 5*k**2 - k + 5. Let n(b) = 3*b**3 + 9*b**2 + 2*b - 9. Let v(r) = 3*n(r) + 5*q(r). Find o such that v(o) = 0.
-1, 1, 2
Let h(d) = 2*d**2 + 1. Let x be h(1). Let 0*p - x*p**3 + 5*p**4 + 8*p**4 + 3*p - 9*p**2 - 4*p**4 = 0. Calculate p.
-1, 0, 1/3, 1
Let m(t) be the third derivative of t**8/6720 - t**7/1260 + t**6/720 + t**4/24 - t**2. Let q(v) be the second derivative of m(v). Let q(p) = 0. Calculate p.
0, 1
Let h(a) = 15*a. Let v(x) = x**2 - 29*x. Let m(w) = 5*h(w) + 3*v(w). Factor m(k).
3*k*(k - 4)
Let -2*w**4 + 6*w**2 - 4*w**2 - 2*w - 38*w**3 + 40*w**3 = 0. Calculate w.
-1, 0, 1
Let k(h) be the third derivative of h**5/100 - 3*h**4/10 + 18*h**3/5 + 18*h**2. Factor k(w).
3*(w - 6)**2/5
Let w(d) be the first derivative of 9*d**4/4 - d**3 - 9*d**2/2 + 3*d + 10. Factor w(p).
3*(p - 1)*(p + 1)*(3*p - 1)
Let y(c) be the second derivative of -c**6/1440 + c**4/96 - c**3/6 + 3*c. Let u(q) be the second derivative of y(q). Factor u(o).
-(o - 1)*(o + 1)/4
Suppose -2/3*c**2 + 4/9*c + 2/9*c**3 + 0 = 0. What is c?
0, 1, 2
Let 3/7 - 3/7*l**3 + 3/7*l - 3/7*l**2 = 0. What is l?
-1, 1
Let r(n) be the second derivative of n**5/40 - n**4/4 + n**3 - 2*n**2 - 2*n. Factor r(d).
(d - 2)**3/2
Let c(a) = -10*a**3 + 4*a**2. Let t(g) = -7*g**3 + 3*g**2. Let r be (-4)/10 + (-69)/15. Let d(w) = r*c(w) + 7*t(w). Factor d(p).
p**2*(p + 1)
Suppose d = 6*d. Suppose 3*v = 5*v - 4*u - 84, -4*v + 4*u + 152 = d. Let 9 + 42*t**3 - 9 + 4*t - v*t**4 + 10*t**5 - 22*t**2 = 0. Calculate t.
0, 2/5, 1
Let r(y) be the first derivative of 0*y - 1/2*y**4 + 3 + 0*y**2 + 1/3*y**3 - 3/5*y**5. Solve r(f) = 0 for f.
-1, 0, 1/3
Let b(g) be the first derivative of -g**3/12 - g**2/4 - g/4 - 1. Suppose b(o) = 0. Calculate o.
-1
Let h(c) be the third derivative of c**6/300 - c**5/25 + 32*c**3/15 - 28*c**2. Factor h(q).
2*(q - 4)**2*(q + 2)/5
Let k = -1124/15 - -75. Let w(d) be the third derivative of -k*d**6 + 0*d**5 - 2*d**2 - 1/168*d**8 + 4/105*d**7 + 0*d**3 + 0*d + 0*d**4 + 0. Factor w(z).
-2*z**3*(z - 2)**2
Let z = -9102/35 - -260. Let a = 41/105 + z. Find t such that 1/3*t**2 + 0*t - a = 0.
-1, 1
Factor 3*s**5 - 185*s**2 + 188*s**2 + 2*s**4 + 9*s**3 + 7*s**4.
3*s**2*(s + 1)**3
Suppose -2*j + 0*j = -1