l).
l**2*(l + 1)
Let n(c) be the third derivative of 1/21*c**4 + 0*c + 1/105*c**5 + c**2 + 0*c**3 + 0. Factor n(i).
4*i*(i + 2)/7
Let j(o) be the second derivative of o**6/90 - o**5/30 - o**4/36 + o**3/9 - 27*o. Factor j(n).
n*(n - 2)*(n - 1)*(n + 1)/3
Let y = 6 - 13. Let p = y - -9. Factor -x**2 + p*x**2 + 0*x**2.
x**2
Let p(l) be the third derivative of -l**7/105 + l**6/20 - l**5/15 + 3*l**2. Factor p(h).
-2*h**2*(h - 2)*(h - 1)
Let m(q) be the third derivative of q**5/390 + q**4/26 + 5*q**3/39 - 28*q**2. Factor m(j).
2*(j + 1)*(j + 5)/13
Find y, given that -8*y**2 - 5*y**2 + 11*y**2 + 38*y - 14*y = 0.
0, 12
Let h = -29 + 59/2. Let u(i) be the first derivative of -1/4*i**2 + h*i - 1/12*i**6 + 1/10*i**5 - 1/3*i**3 - 3 + 1/4*i**4. Solve u(r) = 0 for r.
-1, 1
Factor -78*u + 78*u + 2*u**4 + 10*u**3 + 6*u**2 - 2*u**5.
-2*u**2*(u - 3)*(u + 1)**2
Suppose 131*s - 111*s = 0. Factor -9/2*o + 3/2*o**2 + s.
3*o*(o - 3)/2
Let x(v) = 5*v**3 + 5*v**2 - 5*v - 5. Let b(l) = l**3 + l**2 - l - 1. Let d(g) = 9*b(g) - 2*x(g). Factor d(z).
-(z - 1)*(z + 1)**2
Let a be 6/9 + 8/6. Let y be (a + (1 - 3))/1. Factor 3*v**2 + y*v**2 + 2 - 3*v + 3*v**2 - 5*v**2.
(v - 2)*(v - 1)
Let k(t) = 10*t**3 - 13*t**2 + 7*t - 4. Let l(z) = 11*z**3 - 14*z**2 + 8*z - 5. Let n(y) = -5*k(y) + 4*l(y). Factor n(f).
-3*f*(f - 1)*(2*f - 1)
Determine d so that d**5 + 4*d**4 + 2*d + d**5 + 5*d**3 + 4 - 8*d**2 + 0*d**5 - 9*d**3 = 0.
-2, -1, 1
Factor 2*m**4 + 5*m**2 + 55*m**3 - m**4 - 2*m - 59*m**3 + 0*m.
m*(m - 2)*(m - 1)**2
Let b be (0 - (-4)/84) + 2/7. Factor b*a**3 - 2/3*a + 1/3*a**2 + 0.
a*(a - 1)*(a + 2)/3
Find x, given that 45 + 8*x + 15*x**2 - 18*x**2 + 8*x**2 - 38*x = 0.
3
Let j(o) be the second derivative of o**8/1440 + o**7/756 - o**6/540 + o**4/4 - 4*o. Let r(x) be the third derivative of j(x). Determine p so that r(p) = 0.
-1, 0, 2/7
Let j(v) be the second derivative of v**9/22680 - v**4/12 + 3*v. Let a(t) be the third derivative of j(t). What is s in a(s) = 0?
0
Let b(c) be the first derivative of -2*c**3/3 + 16*c**2 - 128*c + 3. Factor b(s).
-2*(s - 8)**2
Let f(u) be the second derivative of -u**10/90720 + u**9/22680 - u**8/20160 + u**4/4 + 3*u. Let v(b) be the third derivative of f(b). Find t such that v(t) = 0.
0, 1
Let t(o) be the first derivative of -o**5 + 15*o**4/4 - 5*o**3 + 5*o**2/2 + 30. Factor t(w).
-5*w*(w - 1)**3
Let z(n) be the first derivative of 3 + 1/15*n**3 + 0*n**2 - 3/20*n**4 + 0*n. What is o in z(o) = 0?
0, 1/3
Let b(u) be the first derivative of 5 + 0*u - 1/21*u**3 - 1/14*u**2. Solve b(t) = 0 for t.
-1, 0
Let i(q) be the third derivative of -5*q**9/3024 - q**8/240 - q**7/420 + q**3/3 - 3*q**2. Let s(w) be the first derivative of i(w). Factor s(l).
-l**3*(l + 1)*(5*l + 2)
Let y(m) = -m**3 + 8*m**2 - 8*m - 8. Let r(n) = 2*n**2 - 2*n - 2. Let g(l) = -18*r(l) + 4*y(l). Find q such that g(q) = 0.
-1, 1
Let w(q) be the first derivative of q**3/9 - q**2/6 - 9. Factor w(l).
l*(l - 1)/3
Suppose d = 6*d - 15. What is m in -3*m + m**4 - 4*m**2 + m**4 - 2*m**d + 3*m = 0?
-1, 0, 2
Let p(u) be the first derivative of 0*u**3 + 2 - 1/600*u**6 - 1/2*u**2 + 0*u - 1/120*u**4 - 1/150*u**5. Let q(z) be the second derivative of p(z). Factor q(m).
-m*(m + 1)**2/5
Factor -12/5*o**4 - 3/5*o**2 - 3*o**3 + 0*o + 0.
-3*o**2*(o + 1)*(4*o + 1)/5
Let o(q) be the third derivative of q**8/336 - q**7/210 + 7*q**2. Factor o(z).
z**4*(z - 1)
Solve 66/17*k**2 + 20/17*k**3 + 80/17*k + 32/17 + 2/17*k**4 = 0 for k.
-4, -1
Let t(n) be the third derivative of 0*n**3 + 1/30*n**4 - 1/150*n**5 + 0*n - 2*n**2 - 1/300*n**6 + 0. Factor t(w).
-2*w*(w - 1)*(w + 2)/5
Let c(i) = i + 1. Let k be c(3). Suppose 0 = 2*n - 2*t - 16, -k*n - 6*t - 3 = -3*t. Find m, given that -2/9*m**n + 4/9 + 2/9*m - 4/9*m**2 = 0.
-2, -1, 1
Let b(o) be the third derivative of o**7/840 + o**6/120 + o**5/40 + o**4/24 - o**3/3 - o**2. Let y(q) be the first derivative of b(q). Factor y(a).
(a + 1)**3
Factor -3*d**4 + 20*d**3 - 21*d + d - 15 - 2*d**4 + 10*d**2 + 10*d**4.
5*(d - 1)*(d + 1)**2*(d + 3)
Let z(u) be the second derivative of u**7/735 + u**6/420 + 3*u**2 + 2*u. Let g(o) be the first derivative of z(o). Factor g(c).
2*c**3*(c + 1)/7
Let o(g) be the first derivative of -g**4 + 2*g**2 - 3. Factor o(j).
-4*j*(j - 1)*(j + 1)
Let 0*t**3 - 5*t**2 + 3/2*t - 3/2*t**5 + 1 + 4*t**4 = 0. What is t?
-1, -1/3, 1, 2
Let w(i) be the second derivative of i**5/60 + i**4/6 + i**3/2 + 2*i**2/3 + 7*i. Factor w(t).
(t + 1)**2*(t + 4)/3
Let g(l) be the second derivative of -3*l - 2/3*l**3 + 0*l**2 + 0*l**4 - 1/180*l**6 - 1/60*l**5 + 0. Let s(u) be the second derivative of g(u). Factor s(z).
-2*z*(z + 1)
Suppose -39*r + 34*r + 15 = 0. Let a be 8/(-18)*(-315)/6. Solve -20/3*g**2 + 49/3*g**5 + 4/3*g + 0 - g**r + a*g**4 = 0 for g.
-1, 0, 2/7
Let s(f) = f**3 - 2*f + 9*f - 8*f**2 - 2 + f**2 - 4. Let b be s(6). Factor b - 1/5*j**2 + 0*j - 1/5*j**3.
-j**2*(j + 1)/5
Factor 1/2*r**4 - 1/4*r**5 - r - r**2 + 3/4*r**3 + 0.
-r*(r - 2)**2*(r + 1)**2/4
Let l = 126 + -3023/24. Let y(g) be the third derivative of 2*g**2 + 0 + 1/120*g**5 - l*g**4 + 0*g + 1/12*g**3. Factor y(h).
(h - 1)**2/2
Factor -u**5 - 3*u**5 - 8*u**2 + 8*u**4 - 19*u + 23*u.
-4*u*(u - 1)**3*(u + 1)
Let -3/7*l**2 + 0 + 3/7*l = 0. Calculate l.
0, 1
Let d(r) be the second derivative of 2*r**7/7 + 14*r**6/15 + r**5 + r**4/3 - 7*r. What is s in d(s) = 0?
-1, -1/3, 0
Let r(z) be the first derivative of -4*z**3/21 + 10*z**2/7 - 16*z/7 + 23. Determine t, given that r(t) = 0.
1, 4
Let i(c) be the third derivative of c**6/540 - c**5/270 + 7*c**2. Suppose i(q) = 0. Calculate q.
0, 1
Let i = -81/4 - -83/4. Factor 1/2*w - i*w**3 + 1/2 - 1/2*w**2.
-(w - 1)*(w + 1)**2/2
Let l(n) be the first derivative of -3*n**4/4 + 3*n**2/2 + 2. Factor l(q).
-3*q*(q - 1)*(q + 1)
Suppose -3*z + 16 = 5*z. Let q(u) be the first derivative of -2/21*u**3 + 0*u**z + 1 + 0*u + 3/14*u**4 + 1/21*u**6 - 6/35*u**5. Let q(l) = 0. What is l?
0, 1
Let o(j) = -4*j**3 - j**5 - 4*j**2 + 5*j + 4*j**2. Let l(w) = w**5 - w**2 - w + 1. Let s(n) = 4*l(n) + 2*o(n). Factor s(d).
2*(d - 2)*(d - 1)*(d + 1)**3
Let 1/2*w**5 - 1/2*w**3 - 7/2*w**2 + 2 + 0*w + 3/2*w**4 = 0. What is w?
-2, -1, 1
Suppose 12 = -r - 3*n - n, -5*r = -3*n - 9. Let u(b) be the third derivative of 0 + 0*b**5 + 0*b + 1/60*b**6 + 0*b**3 + b**2 + r*b**4. Factor u(w).
2*w**3
Let i(q) = 3*q**4 - 6*q**3 - 11*q**2 - 7*q + 5. Let d(g) = 4*g**4 - 6*g**3 - 12*g**2 - 8*g + 6. Let v(y) = -5*d(y) + 6*i(y). Suppose v(t) = 0. What is t?
-1, 0
Let j(g) be the second derivative of g**5/20 - 5*g**4/4 - g**3/6 + 15*g**2/2 - 25*g. Let j(m) = 0. What is m?
-1, 1, 15
Let u = -2/821 - -1013/78816. Let c(m) be the third derivative of 0 + 0*m**3 - u*m**4 + 0*m + 2*m**2 + 1/240*m**5. Factor c(q).
q*(q - 1)/4
Let p = 6386/7 + -912. Find w such that -12/7*w**3 - 8/7*w**2 + 0 - 2/7*w - 8/7*w**4 - p*w**5 = 0.
-1, 0
Let s(a) be the third derivative of -a**5/75 + a**4/15 - 2*a**3/15 - 9*a**2. Solve s(g) = 0 for g.
1
Suppose -5*a = 2*z - 15, 0*z + 3*z - 34 = 4*a. Suppose -5*r = -5*x + z, -3*r - 5*x = 2 - 28. Factor -6 + r*d**4 - 6*d**2 - 3*d**3 + 5*d**3 - 10*d + 2.
2*(d - 2)*(d + 1)**3
Let w(m) be the second derivative of -m**4/4 - m**3/2 - 2*m. Solve w(h) = 0 for h.
-1, 0
Let l(i) = -i**3 + 7*i**2 - 6*i + 5. Let j be l(6). Suppose -j*w = -6*w + 3. Determine x so that 7*x**3 + 1 - 5*x**5 - 2*x**5 - w*x + 3*x**5 - x**2 = 0.
-1, 1/2, 1
Let k(a) be the third derivative of -a**6/150 - a**5/150 + a**4/12 - 2*a**3/15 - 8*a**2. Factor k(m).
-2*(m - 1)*(m + 2)*(2*m - 1)/5
Let k(i) be the third derivative of -1/6*i**3 + 1/1440*i**6 + i**2 + 0 + 0*i + 1/240*i**5 + 0*i**4. Let g(f) be the first derivative of k(f). Factor g(m).
m*(m + 2)/4
Let z be (-2)/(-8) + 94/8. Suppose 3*l + 5*p + 20 = 0, -p = -2*l + 2*p + z. Factor 1/2*c**5 + l*c**3 + 0 - c**4 + c**2 - 1/2*c.
c*(c - 1)**3*(c + 1)/2
Let k = 1 + 2. Let 2*w**2 + 5*w**4 - 3*w**2 + w**k - 4 + 4 + 3*w**5 = 0. Calculate w.
-1, 0, 1/3
Let l = 116 - 112. Find v, given that -14/13*v**l + 14/13*v**2 + 4/13*v + 8/13*v**3 - 12/13*v**5 + 0 = 0.
-1, -2/3, -1/2, 0, 1
Let y = -265 + 118. Let t = -585/4 - y. What is v in 1 + t*v**3 + 1/4*v**2 - 2*v = 0?
-2, 2/3, 1
Let s(w) be the first derivative of w**6/36 - w**4/6 - w**3/9 + w**2/4 + w/3 - 19. Solve s(p) = 0.
-1, 1, 2
Let o(g) be t