derivative of 0 - 1/225*s**6 - s**2 + 0*s - 3/100*s**5 + 1/3*s**3 - 1/30*s**4. Let g(x) be the first derivative of a(x). Factor g(m).
-2*(m + 2)*(4*m + 1)/5
Let h(d) = -d**3 + 3*d**2 - 2. Let a be (-1 - -6) + (1 - 3). Let l(f) = -f**3 + 4*f**2 - 3. Let j(r) = a*h(r) - 2*l(r). Factor j(s).
-s**2*(s - 1)
Let j(y) = y**2 + y. Let t = 21 + -11. Suppose -t = -4*h - 26, g = 4*h + 15. Let w(n) = n**3 - 3*n**2 - 4*n. Let l(r) = g*w(r) - 3*j(r). Solve l(k) = 0.
-1, 0, 1
Let j(v) be the second derivative of v**5/90 + v**4/18 + v**3/9 + 3*v**2/2 + v. Let n(m) be the first derivative of j(m). Factor n(p).
2*(p + 1)**2/3
Let b(n) be the third derivative of 0 + 1/360*n**6 + 1/36*n**3 - 1/72*n**4 + 0*n + 0*n**5 - 2*n**2 - 1/1260*n**7. Solve b(x) = 0 for x.
-1, 1
Let h(n) be the first derivative of -2*n**5/5 + 5*n**4 - 16*n**3 - 10*n**2 + 50*n + 23. Factor h(v).
-2*(v - 5)**2*(v - 1)*(v + 1)
Let q(j) = -j**3 + 7*j**2 + 9*j - 5. Let h be q(8). Let f(r) be the second derivative of 0*r**h - 1/18*r**4 - r + 0 + 0*r**2 - 1/60*r**5. Factor f(x).
-x**2*(x + 2)/3
Let n be 35/30 + 5/(-10). Let p(q) be the second derivative of 0 + 0*q**4 - q**2 + n*q**3 - 1/5*q**5 + q + 1/15*q**6. Factor p(j).
2*(j - 1)**3*(j + 1)
Factor 3/2*t**3 + 6*t + 6*t**2 + 0.
3*t*(t + 2)**2/2
Suppose -2*h + 0 = -10. Let v = h + -3. Solve 5/4*a - 1/4*a**4 + 3/4*a**v + 1/2 - 1/4*a**3 = 0 for a.
-1, 2
Let x = -9 - -85/9. Find r such that r**4 - 4*r**3 - 8/3*r + x + 47/9*r**2 = 0.
1/3, 2/3, 1, 2
Suppose 19 = 2*x - b + 8, -5*b = 25. Let r(d) be the third derivative of 0 - 1/30*d**5 + d**2 + 0*d**x + 1/12*d**4 + 0*d. Factor r(a).
-2*a*(a - 1)
Let c(a) be the third derivative of a**6/360 - a**5/45 + a**4/18 - 6*a**2. Factor c(y).
y*(y - 2)**2/3
Let n(s) = 6*s**4 - 6*s**2 + 4*s - 4. Let m(k) = 13*k**4 - k**3 - 12*k**2 + 9*k - 9. Let b(j) = -4*m(j) + 9*n(j). Factor b(y).
2*y**2*(y - 1)*(y + 3)
Determine b so that 0*b - 2/7*b**4 + 4/7*b**2 - 2/7 + 0*b**3 = 0.
-1, 1
Let z = 17/48 - 7/24. Let x(o) be the first derivative of 0*o - 1 - z*o**4 + 0*o**3 + 0*o**2. Solve x(u) = 0 for u.
0
Let a(q) be the first derivative of 2*q**3/3 - 2*q - 28. Find o such that a(o) = 0.
-1, 1
Let v(q) = 2*q + 8. Let z be v(-3). Let n(o) be the second derivative of -1/10*o**5 + 0 + 1/6*o**4 + o + 2/3*o**3 + 0*o**z. Determine p, given that n(p) = 0.
-1, 0, 2
Suppose 22*o - 25*o = 0. Factor -1/2*f**5 - 1/2*f + 0*f**4 + f**3 + o*f**2 + 0.
-f*(f - 1)**2*(f + 1)**2/2
Let j(x) be the first derivative of 2*x**3/21 + 4*x**2/7 + 8*x/7 - 13. Let j(q) = 0. Calculate q.
-2
Let i(u) = 10*u**2 - 17*u - 8. Let l(s) = s**2 + s + 1. Let g(q) = i(q) + 5*l(q). Determine m so that g(m) = 0.
-1/5, 1
Factor -9*w**2 - 8*w**2 + 28*w + 13*w**2.
-4*w*(w - 7)
Let h(x) = -6*x**5 + 3*x**4 + 9*x**3 - 2*x**2 - 3*x + 6. Let u(w) = -5*w**5 + 3*w**4 + 8*w**3 - 2*w**2 - 3*w + 5. Let t(l) = -6*h(l) + 7*u(l). Factor t(m).
(m - 1)*(m + 1)**4
Let y(t) = 3*t**2 + 3*t. Let u(v) = v**2 + 12 + v - 12. Let o(k) = 8*u(k) - 3*y(k). Factor o(a).
-a*(a + 1)
Let l(z) be the third derivative of z**8/30240 - z**7/1890 + z**6/270 - 2*z**5/15 + 3*z**2. Let i(x) be the third derivative of l(x). Factor i(h).
2*(h - 2)**2/3
Let l = 808 + -808. Factor -1/9*d**2 + l*d + 0.
-d**2/9
Let n(v) = -8*v**4 + 27*v**3 - 19*v**2. Let j(o) = -4*o**4 + 14*o**3 - 10*o**2. Let f(r) = 11*j(r) - 6*n(r). Solve f(q) = 0 for q.
0, 1
Let p = -4 - -3. Let w be 378/245*(6 - p). Factor -18/5*l**2 - 54/5 + w*l + 2/5*l**3.
2*(l - 3)**3/5
Let p(y) be the third derivative of y**7/350 - y**6/40 + y**5/25 + 32*y**2. Find k, given that p(k) = 0.
0, 1, 4
Suppose 6 = 2*n + 2. Suppose 0 + 1/2*t - 1/4*t**n = 0. Calculate t.
0, 2
Let h(j) be the first derivative of -2*j**6/3 + 4*j**5 - 10*j**4 + 40*j**3/3 - 10*j**2 + 4*j + 40. Solve h(u) = 0 for u.
1
Suppose -13*k - 95/4*k**3 - 57/2*k**2 - 2 - 25/4*k**4 = 0. What is k?
-2, -1, -2/5
Factor 2*m**3 + 5/2*m**2 + 0 + m + 1/2*m**4.
m*(m + 1)**2*(m + 2)/2
Let m be ((-3)/4)/(-12 - -5 - -4). Let x(f) be the first derivative of -m*f**2 - 3 + 1/6*f**3 + 0*f. Suppose x(r) = 0. Calculate r.
0, 1
Let u(z) be the third derivative of -z**6/60 - z**5/6 - 7*z**4/12 - z**3 - 7*z**2. Factor u(o).
-2*(o + 1)**2*(o + 3)
Let t(d) = -9*d**3 + 19*d**2 + 11. Let y(u) = -u**3 + u**2 + 1. Let i(w) = 2*t(w) - 22*y(w). Factor i(v).
4*v**2*(v + 4)
Let c(q) be the third derivative of -7/48*q**8 + 0*q**3 + 0*q + 4*q**2 + 3/8*q**6 + 0 + 1/6*q**4 + 7/15*q**5 - 2/15*q**7. Determine m so that c(m) = 0.
-1, -2/7, 0, 1
Factor 12/5*h**3 + 0*h - 2/5*h**4 - 18/5*h**2 + 0.
-2*h**2*(h - 3)**2/5
Suppose 6 = 4*u - 2. Suppose -u*o = -0*o. Factor 2/3*i**3 + o*i + 4/3*i**2 + 0.
2*i**2*(i + 2)/3
Let k(s) be the third derivative of s**7/210 + s**6/120 - s**5/60 - s**4/24 + 6*s**2. What is r in k(r) = 0?
-1, 0, 1
Let j(o) = 6*o**3 + o**2 - 7*o - 5. Let g(i) = -i**3 + i + 1. Let b(n) = 5*g(n) + j(n). Factor b(t).
t*(t - 1)*(t + 2)
Suppose -w - 4 = -3. Let i = w + 4. Determine x so that 6*x**2 + x**5 - 3*x**4 - 3*x**2 + 3*x**i - 4*x**2 = 0.
0, 1
Factor 3*r**2 + 4*r + 11*r - 10 + 22.
3*(r + 1)*(r + 4)
Let f(c) be the third derivative of -1/300*c**6 + 0*c - 1/12*c**4 + 2/15*c**3 + 0 - 5*c**2 + 2/75*c**5. Suppose f(d) = 0. Calculate d.
1, 2
Let p = -3 + 0. Let l be (-6)/p - (0 + 0). Determine t, given that -20*t**3 + l*t + 4*t**2 + 11*t**4 + 35*t**5 - 2*t = 0.
-1, 0, 2/7, 2/5
Suppose -5*w + 17 = 3*h, 4*h - 2*w - 14 = -0*w. Let o(x) be the first derivative of 0*x**2 + 2/3*x**3 + 0*x + 1 + 1/2*x**h. Let o(n) = 0. Calculate n.
-1, 0
Let r(t) = -6*t**2 + 54*t + 74. Let l(z) = z**2 - 11*z - 15. Let n(j) = -14*l(j) - 3*r(j). Factor n(m).
4*(m - 3)*(m + 1)
Suppose -f = -3*f + 8. Let g(w) be the first derivative of -1/3*w**3 + 3/4*w**f + 0*w + 0*w**2 - 1. Factor g(k).
k**2*(3*k - 1)
Let k(r) be the first derivative of r + 1/12*r**3 + 1/2*r**2 - 3. Let k(n) = 0. What is n?
-2
Solve 0 + 0*b**4 - 1/6*b - 1/6*b**5 + 1/3*b**3 + 0*b**2 = 0 for b.
-1, 0, 1
Let s(q) be the first derivative of 4*q**5/15 - q**4/3 - 4*q**3/9 + 2*q**2/3 + 2. Factor s(c).
4*c*(c - 1)**2*(c + 1)/3
Let -11*p**4 + 40*p**4 - 2*p**2 - 23*p**4 - p**3 + 5*p**3 = 0. What is p?
-1, 0, 1/3
Let j(m) = 519*m**2 - 377*m + 65. Let s(f) = 259*f**2 - 189*f + 33. Let o(z) = -3*j(z) + 7*s(z). Solve o(a) = 0 for a.
3/8
Let m = 502/903 - -2/129. Let s be (-2)/(-3)*18/4. Determine l so that -30/7*l + 32/7*l**s + m + 48/7*l**2 = 0.
-2, 1/4
Let n(m) be the second derivative of -m**6/180 + m**5/30 - 2*m**3/3 + 2*m. Let s(c) be the second derivative of n(c). Solve s(j) = 0.
0, 2
Suppose 6 - 9*z + 21 - 7 - 5*z**2 + 40*z**3 - 31*z - 15*z**4 = 0. What is z?
-1, 2/3, 1, 2
Let n = -2 + 2. Let 0*i**2 + n*i - 3/4*i**3 + 0 = 0. What is i?
0
Let v(u) be the first derivative of 5*u**6/6 - u**5 - 5*u**4/4 + 5*u**3/3 + 2. Suppose v(a) = 0. Calculate a.
-1, 0, 1
Let d(j) be the third derivative of 1/108*j**4 + 4*j**2 - 1/270*j**5 + 0 - 1/540*j**6 + 1/945*j**7 + 0*j**3 + 0*j. Factor d(g).
2*g*(g - 1)**2*(g + 1)/9
Let o(g) = -22*g**3 + 56*g**2 + 16*g - 8. Let i(z) = -7*z**3 + 19*z**2 + 5*z - 3. Let a(m) = -8*i(m) + 3*o(m). Find k such that a(k) = 0.
-2/5, 0, 2
Let q(n) be the third derivative of 6*n**2 - 1/56*n**4 + 1/280*n**6 + 0*n + 0 + 0*n**3 + 0*n**5. Factor q(z).
3*z*(z - 1)*(z + 1)/7
Factor -2*c**4 + 4*c**2 + 22*c - 22*c - 2.
-2*(c - 1)**2*(c + 1)**2
Suppose -3*n + 155 + 19 = 0. Let z = n - 231/4. Suppose -3/2*p**3 - 1/4*p**5 + p**4 + p**2 - z*p + 0 = 0. Calculate p.
0, 1
Suppose 4*p + 18 = 7*p. Suppose -p*t + t + 10 = 0. Solve 2/3*q**t - 4/3*q + 2/3 = 0 for q.
1
Factor 0 + 1/4*l**3 + 1/4*l - 1/2*l**2.
l*(l - 1)**2/4
Let w(o) = -o**2 - o + 2. Let f be w(0). Solve 15*x - 36*x**f + 25*x - x**4 - x**4 - 16 + 14*x**3 = 0 for x.
1, 2
Let c(m) = -m + 4. Let x be c(0). Suppose -3*i = 2*g - x, -5*i - 4*g + 11 - 5 = 0. Factor 2*d + 2*d**i + 0 + 2 + 2*d.
2*(d + 1)**2
Suppose 3*c - 2*g - 14 = 0, -4 = 8*g - 4*g. Factor 1/2 - 7*k**3 - 3*k**2 + 1/2*k - 3/2*k**5 - 11/2*k**c.
-(k + 1)**4*(3*k - 1)/2
Factor -1/2 + 1/6*w**2 - 1/3*w.
(w - 3)*(w + 1)/6
Let g(p) = -3*p**2 + 9*p - 9. Suppose 4*a + 2 = 5*u - 1, 5 = -5*u. Let i(k) = -k**2 + k - 1. Let c(r) = a*i(r) + 2*g(r). Factor c(h).
-4*(h - 2)**2
Let j(t) = -t**3 - 3*t**2 + 2*t - 8. Let k be j(-4). Let q(g) be the third derivative of 0*g + k + 0*g**5 - g**2 - 1