he third derivative of -s**5/180 - 5*s**4/72 - s**3/3 + 21*s**2. Factor m(p).
-(p + 2)*(p + 3)/3
Suppose z - 4*z = -z. Factor 4/3*u + 2/3*u**2 + z.
2*u*(u + 2)/3
Let v = 11 - 7. Let p = -2 + v. Solve -4*t**3 - t**5 + 8*t**4 - t**2 - 9*t**p + 6*t**5 - t + 2 = 0.
-1, 2/5, 1
Suppose -3*a = -2*a + 2*s + 3, -16 = 4*s. Let f(x) be the third derivative of 0 + 0*x - 1/240*x**a + 1/96*x**4 - x**2 + 0*x**3. Factor f(u).
-u*(u - 1)/4
Suppose z = -4*z - 25, -x = -5*z - 25. Let f(q) be the second derivative of 1/10*q**5 + 3*q + 0 + 0*q**3 + 0*q**4 + x*q**2. Suppose f(r) = 0. What is r?
0
Let w(f) = -f - 15. Let h be w(-18). Let p(u) be the first derivative of -1/5*u**5 + 1 + 0*u**4 + 0*u**2 + 1/3*u**h + 0*u. Factor p(l).
-l**2*(l - 1)*(l + 1)
Let p(q) be the third derivative of 0*q - 1/21*q**3 + 0 - 1/42*q**4 - 1/210*q**5 - q**2. Suppose p(m) = 0. What is m?
-1
Let x be (2/(-6))/(-5 + (-26)/(-6)). Factor -x*y**2 + 0 + 3/2*y**4 + 2*y**3 - y.
y*(y + 1)**2*(3*y - 2)/2
Let c(q) be the third derivative of q**5/90 + q**4/18 + q**3/9 - 6*q**2. Factor c(b).
2*(b + 1)**2/3
Let m(a) = a**4 - 2*a**3 + 5*a**2 - 4. Let z(l) = l**4 - 2*l**3 + 6*l**2 - 5. Let h(f) = 5*m(f) - 4*z(f). Factor h(q).
q**2*(q - 1)**2
Let o = -212 - -1910/9. Let k(h) be the first derivative of o*h**3 - 3 + 0*h - 2/3*h**2 + 1/6*h**4. Determine c, given that k(c) = 0.
-2, 0, 1
Let c = 12 + -15. Let j be 1/((-4)/(-12)) + c. Find i, given that 8*i**2 + j - 8/7*i - 14*i**3 = 0.
0, 2/7
Let s(j) = -2*j**2 - 34*j + 36. Let v be s(-18). Solve 0 - 1/6*o**2 + v*o = 0 for o.
0
Let o(g) be the third derivative of g**6/45 - g**5/20 - g**4/12 + g**3/2 - g**2. Let f(s) be the first derivative of o(s). Let f(i) = 0. Calculate i.
-1/4, 1
Let r be (-8)/(-28) + (-3 - 80/(-14)). Let b(s) be the first derivative of 1/4*s**2 - r - 1/10*s**5 + 1/6*s**3 - 1/8*s**4 + 0*s. Find l such that b(l) = 0.
-1, 0, 1
Let n(h) = 0 + 3*h - 1 - 2*h. Let m(l) = -l**2 + 5*l - 4. Suppose a - 5*a = 20. Let d(y) = a*n(y) + m(y). Let d(u) = 0. What is u?
-1, 1
Let a(g) be the third derivative of -g**6/24 + 5*g**4/8 - 5*g**3/3 - 2*g**2. What is z in a(z) = 0?
-2, 1
Let p = -41 - -46. Let h(y) be the first derivative of -3/8*y**2 + 1/24*y**6 - 3/20*y**p + 2 + 1/6*y**3 + 1/8*y**4 + 1/4*y. Factor h(i).
(i - 1)**4*(i + 1)/4
Let z(w) be the second derivative of 3/10*w**5 + 2*w + 0*w**3 + 0 - 1/4*w**4 + 0*w**2 - 1/10*w**6. Factor z(q).
-3*q**2*(q - 1)**2
Let o(g) be the first derivative of -g**6/15 + 4*g**5/25 + 3*g**4/40 - g**3/6 - g**2/10 - 29. Suppose o(c) = 0. Calculate c.
-1/2, 0, 1, 2
Suppose -4*s + 27 = 19. Factor -2/3 + 2*j + 8/3*j**s.
2*(j + 1)*(4*j - 1)/3
Let p(r) = 9*r**3 + 18*r**2 + 6*r. Let v(k) = 2*k**3 - k**3 + 0*k**2 - k - k**2 + 0*k**2. Let w(i) = -p(i) - 3*v(i). What is n in w(n) = 0?
-1, -1/4, 0
Factor -f**2 + f**4 + 0 + 1/3*f**3 + 1/3*f**5 - 2/3*f.
f*(f - 1)*(f + 1)**2*(f + 2)/3
Let f(k) be the second derivative of 3*k - k**2 + 0 + 2/3*k**3 - 1/6*k**4. Factor f(i).
-2*(i - 1)**2
Let p = -1/31 + 33/62. Let m(h) be the first derivative of -2 + 0*h + 0*h**3 - p*h**4 + 2/5*h**5 + 0*h**2. Suppose m(q) = 0. Calculate q.
0, 1
Factor -4/11*s**2 + 2/11*s - 2/11*s**3 + 4/11.
-2*(s - 1)*(s + 1)*(s + 2)/11
Let y = 438 - 1751/4. Determine t so that 0 + y*t**2 + 0*t = 0.
0
Let m(x) be the third derivative of -10*x**2 + 1/504*x**8 - 5/36*x**4 + 4/315*x**7 - 2/9*x**3 - 1/45*x**5 + 0*x + 1/45*x**6 + 0. Factor m(q).
2*(q - 1)*(q + 1)**3*(q + 2)/3
Let q(f) be the third derivative of -1/360*f**6 + 1/180*f**5 + 0 + 0*f**3 - f**2 - 1/630*f**7 + 0*f + 0*f**4 + 1/1008*f**8. Let q(v) = 0. Calculate v.
-1, 0, 1
Find f such that 0*f + 0 + 1/2*f**2 + 1/2*f**4 - f**3 = 0.
0, 1
Let f(k) be the third derivative of 49*k**5/300 + 7*k**4/30 + 2*k**3/15 + 2*k**2. Suppose f(i) = 0. What is i?
-2/7
Let x(f) = -3*f**2 - 9*f - 9. Let y(c) = -3*c**2 - 8*c - 8. Let u(i) = -4*x(i) + 3*y(i). Factor u(v).
3*(v + 2)**2
Let l(w) be the first derivative of 3*w**4/16 + 5*w**3/12 - w**2/2 - w - 15. Determine g so that l(g) = 0.
-2, -2/3, 1
Let s(g) be the second derivative of -g**5/15 - 11*g**4/9 - 80*g**3/9 - 32*g**2 - 63*g. Solve s(o) = 0.
-4, -3
Let c(i) be the second derivative of 0 + 1/4*i**2 - 1/12*i**3 - 4*i - 1/24*i**4 + 1/40*i**5. Suppose c(w) = 0. Calculate w.
-1, 1
Determine c so that 1/4*c**4 + 1/4 + c + c**3 + 3/2*c**2 = 0.
-1
Let j(r) be the first derivative of 1/27*r**6 + 0*r**5 + 1/9*r**2 - 3 + 0*r**3 - 1/9*r**4 + 0*r. Factor j(f).
2*f*(f - 1)**2*(f + 1)**2/9
Suppose 4*u = 2*k, -5*u + 0*u + 5*k - 10 = 0. Suppose 2*o - 2 = u. What is n in n**3 + 0*n**2 + 5*n**2 - n**2 - 3*n**o = 0?
-1, 0
Factor 3*s**2 - 5 - 7 - 8 + 6*s + 11.
3*(s - 1)*(s + 3)
Let j = -22 - -22. Let c(f) be the second derivative of -1/6*f**2 + 0*f**3 - f + j + 1/36*f**4. Factor c(i).
(i - 1)*(i + 1)/3
Let f(r) be the third derivative of 0 - 1/2*r**3 + 0*r + 7*r**2 - 1/60*r**5 + 1/6*r**4. What is k in f(k) = 0?
1, 3
Let n(c) be the third derivative of -c**5/330 + c**4/66 - 4*c**2. Factor n(d).
-2*d*(d - 2)/11
Let d(w) = w**2 - 6*w + 4. Let c be d(6). Suppose -n - 6 = -z, -c*z + 5*n + 24 = -2*z. Let q**3 - 8*q - 2*q**z + 2 + 0*q**3 + 7*q = 0. What is q?
-1, 1, 2
Let h(s) be the second derivative of 1/5*s**2 - 1/30*s**4 + 0 + 0*s**3 + 2*s. Factor h(k).
-2*(k - 1)*(k + 1)/5
Let n(r) be the third derivative of -9*r**6/200 + 21*r**5/100 - 2*r**4/5 + 2*r**3/5 - 3*r**2. Determine y so that n(y) = 0.
2/3, 1
Let l(h) = 3*h**3 - 2*h**2. Let c(t) = -t**3. Let n(k) = 10*c(k) + 2*l(k). Factor n(v).
-4*v**2*(v + 1)
Let r(y) be the third derivative of 6*y**2 + 1/15*y**5 - 5/8*y**4 + 0 - 2/3*y**3 + 0*y. Find x, given that r(x) = 0.
-1/4, 4
Let w(m) = -8*m**2 + 14*m - 16. Let s(h) = -3*h**2 + 5*h - 5. Let t(l) = 10*s(l) - 3*w(l). Let t(c) = 0. Calculate c.
1/3, 1
Let j(a) be the first derivative of 2*a**6/21 - 12*a**5/35 + 3*a**4/7 - 4*a**3/21 + 1. Suppose j(f) = 0. What is f?
0, 1
Let f(s) be the third derivative of -3*s**7/175 - s**6/50 + 2*s**5/15 - 2*s**4/15 + s**2. Factor f(u).
-2*u*(u + 2)*(3*u - 2)**2/5
Let t be (-96)/(-90) + (-14)/21. Find y, given that -2/5*y - t*y**2 + 4/5 = 0.
-2, 1
Let p(o) = 25*o + 1. Let q be p(1). Let s(g) = -2*g**3 - 5*g**2 + 8*g - 4. Let i(w) = -9*w**3 - 20*w**2 + 32*w - 16. Let m(z) = q*s(z) - 6*i(z). Factor m(x).
2*(x - 2)**2*(x - 1)
Let n(f) be the third derivative of -f**7/10080 + f**6/1440 + f**4/12 + 3*f**2. Let y(x) be the second derivative of n(x). Factor y(m).
-m*(m - 2)/4
Let x(i) = -3*i - 4. Let v(j) = -2*j - 5. Let w(n) = 4*v(n) - 3*x(n). Let t be w(8). Determine r so that 0 - 4/3*r**4 + t*r + r**3 + 1/3*r**2 = 0.
-1/4, 0, 1
Let x = -15012 + 555499/37. Let h = x + 1/74. Suppose 0*l**2 + h*l**3 + 0*l + 0 + 3/2*l**4 = 0. What is l?
-1, 0
Let -4*y**4 + 2*y + 0*y - 14*y**5 + 4*y**2 + 12*y**5 = 0. What is y?
-1, 0, 1
Let w(v) be the first derivative of 5*v**4/4 - 5*v**2/2 - 15. Factor w(g).
5*g*(g - 1)*(g + 1)
Factor -3/7*o + 1/7*o**2 + 0.
o*(o - 3)/7
Let o(i) be the third derivative of -2*i**7/35 - 2*i**6/15 + i**5/15 + i**4/3 + i**2. Factor o(x).
-4*x*(x + 1)**2*(3*x - 2)
Let y(q) = -q + 2. Let m be y(-10). Factor -m*c**2 - 3*c**3 + 20*c - 12*c + 9*c**3 - c**4.
-c*(c - 2)**3
Let v(l) be the second derivative of 7*l**4/3 + 2*l**3 - 6*l + 3. Factor v(j).
4*j*(7*j + 3)
Let m be 3 - (-2 - (-86)/18). Factor m + 0*o - 2/9*o**2.
-2*(o - 1)*(o + 1)/9
Let t be (185/(-165) + 1)*21/(-14). Factor t*k**2 + 4/11 + 6/11*k.
2*(k + 1)*(k + 2)/11
Suppose 120 = 2*m - 7*m. Let d be 8/(-32) - 22/m. Find q, given that -2/3*q**4 - d*q**2 + 0 + 4/3*q**3 + 0*q = 0.
0, 1
Let j(v) be the second derivative of v**8/20160 - v**7/7560 + v**4/4 - v. Let u(r) be the third derivative of j(r). Solve u(p) = 0 for p.
0, 1
Suppose -4*u + 19 - 3 = 0. Determine c so that 2*c**3 + u*c**3 - 5*c**2 + 2*c - 2*c**4 - c**2 = 0.
0, 1
Factor 0 - 4/21*k**3 + 2/21*k**4 - 2/21*k**2 + 4/21*k.
2*k*(k - 2)*(k - 1)*(k + 1)/21
Let m(h) be the first derivative of h**5/15 - h**4/12 - h**3/9 + h**2/6 + 15. Let m(q) = 0. Calculate q.
-1, 0, 1
Let d be (-11)/(-5) - 5/25. Factor 2*o**4 + 2*o**5 + d*o**5 - 2*o**5.
2*o**4*(o + 1)
Let i(o) be the first derivative of 0*o + 3/4*o**2 - 5 + 1/4*o**3. Factor i(k).
3*k*(k + 2)/4
Let p(u) = 51*u**3 + 300*u**2 - 454*u + 160. Let x(q) = -q**3 - q. Let a(b) = -p(b) - 6*x(b). Factor a(i).