**4 - 3*r + j. Factor d(w).
2*w*(w + 1)/7
Factor 4/5*t - 2/5 - 2/5*t**2.
-2*(t - 1)**2/5
Factor 0*p**2 + 0*p**3 - 5/3*p**5 + 0*p + 0 - 10/3*p**4.
-5*p**4*(p + 2)/3
Let j(y) be the third derivative of y**5/12 + 5*y**4/8 - 2*y**2. Factor j(v).
5*v*(v + 3)
Suppose 7*v = 8*v + 5*l - 7, v - l = 1. Factor 1/3*r - 1/3*r**v + 0.
-r*(r - 1)/3
Let z(n) be the first derivative of n**3/5 - 9*n**2/5 + 27*n/5 - 10. Factor z(u).
3*(u - 3)**2/5
Let u(j) be the second derivative of j**4/12 - j**3/2 - 2*j**2 - 8*j. Solve u(f) = 0 for f.
-1, 4
Let i be 2*-1*(-2)/16. Let m(y) be the third derivative of -2/3*y**3 - 1/30*y**5 - i*y**4 + y**2 + 0 + 0*y. Factor m(z).
-2*(z + 1)*(z + 2)
Let h(k) be the second derivative of k + 3/20*k**5 + 0*k**2 + 0 - 2/3*k**3 + 1/15*k**6 - 1/3*k**4 - 1/42*k**7. Factor h(s).
-s*(s - 2)**2*(s + 1)**2
Let g(o) be the second derivative of 2/27*o**3 - 3*o + 0 + 0*o**2 - 5/54*o**4. Factor g(f).
-2*f*(5*f - 2)/9
Let f(i) be the first derivative of -5/8*i**2 + 7/12*i**3 - 1/2*i + 2. Factor f(b).
(b - 1)*(7*b + 2)/4
Suppose -f + 2 + 3 = 0. Factor -2*x**f - 2*x**5 + 0*x**5 + 3*x**3 + x**3.
-4*x**3*(x - 1)*(x + 1)
Let y(z) be the third derivative of -z**8/448 + z**7/40 - z**6/10 + z**5/10 - z**4/12 - 4*z**2. Let s(d) be the second derivative of y(d). Factor s(o).
-3*(o - 2)**2*(5*o - 1)
Let y(f) be the third derivative of -2*f**7/105 - 2*f**6/15 - 2*f**5/5 - 2*f**4/3 - 2*f**3/3 - 2*f**2. Let y(m) = 0. What is m?
-1
Let x(s) be the third derivative of s**8/784 - 2*s**7/245 + s**6/56 - s**5/70 - 7*s**2. Let x(r) = 0. Calculate r.
0, 1, 2
Let w = -9/89 - 28613/445. Let j = -64 - w. Determine i, given that -8/5 - j*i**2 + 8/5*i = 0.
2
Suppose 2 = -5*h + 12. Factor 28 - 28 - g**h - 2*g.
-g*(g + 2)
Let b(c) be the second derivative of 2*c - 1/30*c**6 + 0*c**3 + 0*c**5 + 0 + 0*c**2 + 1/12*c**4. Factor b(t).
-t**2*(t - 1)*(t + 1)
Let s = -6 - -10. Factor o**3 - o**3 - 5*o**3 + 4*o**3 - 2*o**2 + o**s.
o**2*(o - 2)*(o + 1)
Let j(i) be the third derivative of 0*i**3 - 1/105*i**7 + 0*i - 1/15*i**5 + 0 - 1/24*i**6 - 1/24*i**4 + 5*i**2. Factor j(h).
-h*(h + 1)**2*(2*h + 1)
Let t(p) be the second derivative of p**7/210 - p**5/60 + 2*p**2 - 5*p. Let y(w) be the first derivative of t(w). Factor y(q).
q**2*(q - 1)*(q + 1)
Let k(i) be the first derivative of 1/9*i**2 + 2/27*i**3 + 1 + 0*i - 1/18*i**4 - 2/45*i**5. Solve k(p) = 0.
-1, 0, 1
Let g(d) be the third derivative of d**7/70 + d**6/20 - 3*d**5/20 - d**4/2 + 2*d**3 - 17*d**2. Factor g(s).
3*(s - 1)**2*(s + 2)**2
Let m be ((-12)/10)/((-3)/50). Suppose 5*o = m + 20. Solve o*j**4 - 2*j - 3*j**5 - 12*j**3 + 6*j**2 + j + 2*j**4 = 0 for j.
0, 1/3, 1
Let l(i) be the second derivative of i**10/151200 - i**8/16800 + i**6/3600 - i**4/6 + 4*i. Let r(y) be the third derivative of l(y). Factor r(z).
z*(z - 1)**2*(z + 1)**2/5
Let w be (24/(-36))/((-2)/15). Let z(x) be the third derivative of 1/420*x**6 + 0*x**4 - 1/105*x**w + 0*x + 3*x**2 + 1/735*x**7 + 0 + 0*x**3. Factor z(r).
2*r**2*(r - 1)*(r + 2)/7
Suppose 8 = 2*h - 0*h. Let b = h - 5. Let l(i) = -5*i**3 + 3*i**2 + 2*i + 6. Let x(q) = -q**3 + 1. Let y(r) = b*l(r) + 6*x(r). Factor y(v).
-v*(v + 1)*(v + 2)
Let u(h) be the second derivative of -h**4/72 - h**3/12 - h**2/6 - 15*h. Find r such that u(r) = 0.
-2, -1
Factor 512/5 - 64/5*c + 2/5*c**2.
2*(c - 16)**2/5
Let x(v) be the second derivative of v**5/150 - v**3/45 - 16*v. Factor x(p).
2*p*(p - 1)*(p + 1)/15
Let d(f) be the first derivative of f**6/14 + 3*f**5/35 - 3*f**4/14 - 2*f**3/7 + 3*f**2/14 + 3*f/7 - 9. Factor d(v).
3*(v - 1)**2*(v + 1)**3/7
Suppose 5*o = 5*f + 10, -2*o + 2 = -0*f - 3*f. Factor b - o + 7*b - b + 3*b**2 - 2.
(b + 3)*(3*b - 2)
Factor -3/7*l**2 - 12/7*l - 12/7.
-3*(l + 2)**2/7
Let n be (-2)/(-1) - 0/((-1)/1). Solve 0*g**3 + 0 + 0*g**n + 0*g + 3/4*g**4 = 0 for g.
0
Let w(j) = 13*j + 143. Let b be w(-11). What is v in 1/6*v - 1/6*v**2 + b = 0?
0, 1
Let d(g) be the first derivative of g**4/2 - 2*g**3 + 2*g**2 + 2. Factor d(c).
2*c*(c - 2)*(c - 1)
Solve 6 - 3*m**2 - 61*m + 12*m**2 + 76*m = 0 for m.
-1, -2/3
Let o(m) = m**2 + 2*m - 1. Let v be o(1). Suppose 0 + 4/3*a - 2/3*a**v = 0. Calculate a.
0, 2
Let c(l) be the second derivative of 0*l**2 + 0 + 1/180*l**6 - 1/72*l**4 + 0*l**5 + 0*l**3 + 3*l. Suppose c(a) = 0. What is a?
-1, 0, 1
Let y = -243/4 + 61. Let -1/4*u**5 + y*u**3 + 0*u + 0*u**4 + 0*u**2 + 0 = 0. Calculate u.
-1, 0, 1
Suppose 0 = -2*q + 2*n + 10, 0 = -5*q - 2*n - 3 + 14. Factor 8/3*z**q + 0*z - 2/3*z**2 + 0.
2*z**2*(4*z - 1)/3
Let a = -34 - -38. Determine f, given that -2/3*f**a + 2/3 - 4/3*f**3 + 0*f**2 + 4/3*f = 0.
-1, 1
Suppose -2*h + 3*h + 6 = 2*l, 3*l = h + 9. Let i = -13 + 19. Let 26/7*m**2 - i*m**3 + h - 4/7*m = 0. What is m?
0, 2/7, 1/3
Suppose -3*n + 5*n = 0. Suppose n = -3*b + 4 + 2. Factor -9/2*x**2 - b + 7*x - 27/4*x**3 + 27/4*x**4.
(x + 1)*(3*x - 2)**3/4
Let c(v) be the first derivative of -2/5*v**5 - 2/3*v**3 + 0*v**2 + 1 - v**4 + 0*v. Factor c(m).
-2*m**2*(m + 1)**2
Let m(j) = -j**2 + 11*j + 5. Let g(r) = -5*r**2 + 45*r + 19. Let w(d) = 6*g(d) - 26*m(d). Factor w(y).
-4*(y + 2)**2
Let 0*c + 0*c**2 + 4*c**4 + 8/3*c**3 + 4/3*c**5 + 0 = 0. Calculate c.
-2, -1, 0
Let z(w) be the first derivative of 2*w**5/45 - 7*w**4/18 + 35. Factor z(c).
2*c**3*(c - 7)/9
Let h(u) be the third derivative of -u**5/12 - 5*u**4/3 - 17*u**2. Suppose h(l) = 0. Calculate l.
-8, 0
Let x(g) = g - 5. Let i be x(5). Let q(k) be the third derivative of -1/270*k**5 + i + 0*k**4 - 2*k**2 + 0*k**3 + 0*k. Factor q(h).
-2*h**2/9
Let b be 10/(-6)*(238/35 + -8). Factor 2 + 16/3*i + 10/3*i**b.
2*(i + 1)*(5*i + 3)/3
Let a(t) be the first derivative of 2*t**6/3 - 4*t**5/5 + t**4/4 - 17. Suppose a(f) = 0. What is f?
0, 1/2
Find x, given that -64 + 5632*x**3 + 25*x + 319*x**2 - 426*x**2 + 1764*x**5 + 679*x - 2805*x**2 - 5124*x**4 = 0.
2/7, 2/3, 1
Suppose 0 = -2*a - 5*h + 43, 4*h = 3*a - 0*h - 7. Let m = 12 - a. Solve -2/3*g**5 - 1/3 + 2/3*g**2 - 8/3*g**m + 2/3*g + 7/3*g**4 = 0 for g.
-1/2, 1
Suppose 0 = 3*l + 4*k - 55, -7*k = -2*k - 20. Determine r, given that -5*r**3 + 2*r**4 - 8*r**5 - 2*r**2 + l*r**3 + 0*r**3 = 0.
-1, 0, 1/4, 1
Let w = 5 + -2. Suppose -7 = -5*d + u - 1, -w*d - 2*u + 14 = 0. Find h, given that -7*h + 7*h - d*h**3 + 2*h**5 = 0.
-1, 0, 1
Let i(o) be the third derivative of 1/240*o**5 + 0*o**3 + 2*o**2 + 0 + 0*o**4 + 0*o. Factor i(x).
x**2/4
Let i(p) be the second derivative of 0*p**2 - 2/3*p**3 + 5*p + 1/5*p**5 + 0 + 0*p**4. Suppose i(g) = 0. What is g?
-1, 0, 1
Let k(s) = -s**2 - 13*s + 9. Suppose -x - 3 = 2. Let j(n) = n**2 + 19*n - 13. Let d(p) = x*j(p) - 7*k(p). Let d(w) = 0. What is w?
1
Let x = 12 + -10. Solve -11*z**2 + 12*z - z**2 - 4 - x + 3 = 0 for z.
1/2
Let b(v) = v**4 + v**3 + v**2. Let f(j) = -j**5 - 4*j**4 - 10*j**3 - 6*j**2. Let x(q) = 14*b(q) + 2*f(q). Factor x(z).
-2*z**2*(z - 1)**3
Suppose 2*i = -3*q - 4, 5*i + 3 + 12 = -5*q. Let g be 1*(2 + (-5)/3). What is u in 0 + g*u - 1/3*u**3 + 0*u**q = 0?
-1, 0, 1
Let i(r) be the third derivative of -1/12*r**3 + 1/16*r**4 - 1/40*r**5 + 0 + 0*r + 9*r**2 + 1/240*r**6. Factor i(u).
(u - 1)**3/2
Let d(c) = 7*c**5 - 7*c**4 - 2*c**3 - 3*c**2 - 5*c - 5. Let r(p) = 20*p**5 - 20*p**4 - 6*p**3 - 8*p**2 - 14*p - 14. Let w(b) = -14*d(b) + 5*r(b). Factor w(n).
2*n**2*(n - 1)**2*(n + 1)
Let j(x) = x**2 + x + 1. Let b be (3 - 2 - 0)/1. Let g(r) = -r**3 + 5*r**2 + 5*r + 3. Let n(q) = b*g(q) - 4*j(q). Solve n(s) = 0.
-1, 1
Suppose -5/4*l**5 + 1/2*l + 13/4*l**4 - 1/4*l**2 + 0 - 9/4*l**3 = 0. Calculate l.
-2/5, 0, 1
Let h(c) be the second derivative of 3*c**7/77 - 3*c**6/55 - 7*c**5/110 + 3*c**4/22 - 2*c**3/33 - 9*c. Determine a, given that h(a) = 0.
-1, 0, 1/3, 2/3, 1
Let r = 6 + -3. Let z be (-1)/10 + (-3)/(-6). Factor -z*k**2 - 2/5*k**r + 2/5*k**4 + 2/5*k + 0.
2*k*(k - 1)**2*(k + 1)/5
Let g(b) = b**2 + b + 1. Let f(h) = 4*h**2 + 4*h + 5. Let m(a) = 3*f(a) - 15*g(a). Determine y, given that m(y) = 0.
-1, 0
Let y(v) be the first derivative of -v**3/6 + 11*v**2/2 - 121*v/2 - 59. Suppose y(j) = 0. Calculate j.
11
Let j(m) be the second derivative of m**5/100 + m**4/60 + 18*m. Solve j(x) = 0.
-1, 0
Let q = -111 - -114. Let z(u) be the first derivative of 0*u**2 + 4 + 0*u - 4/21*u**q - 1/14*u**4. Solve z(v) = 0.
-2, 0
Let c be (-76)/4*(-3 - -2). Suppose 6*p - c