 1/10. Let d(h) be the first derivative of -j*h**3 + 2/5*h**5 + h**2 + 0*h + 2 - 1/2*h**4. Factor d(n).
2*n*(n - 1)**2*(n + 1)
Let i = 17 - 151/9. Factor i*h**2 + 2/9*h - 4/9.
2*(h - 1)*(h + 2)/9
Let p = 7 + -3. Let d(m) = 9*m**4 + 28*m**3 + 5*m**2 - 6*m. Let b(k) = -k**3 + k**2. Let c(h) = p*b(h) + d(h). Factor c(s).
3*s*(s + 1)*(s + 2)*(3*s - 1)
Suppose 17 - 47 = 3*w. Let p = w - -31/3. Determine y so that -1/6*y - 1/2*y**2 + p = 0.
-1, 2/3
Let g(a) be the third derivative of 5*a**8/192 + 3*a**7/56 + a**6/48 + 3*a**2. Factor g(o).
5*o**3*(o + 1)*(7*o + 2)/4
Let q be (8/18)/(4/3). Determine v so that -q*v**2 + 1/3*v + 0 = 0.
0, 1
Let u(m) be the first derivative of m**5/40 + m**4/48 - m**3/12 - m**2/8 + m + 1. Let w(s) be the first derivative of u(s). Suppose w(g) = 0. Calculate g.
-1, -1/2, 1
Let m = -209/42 - -5. Let y(f) be the third derivative of 0*f**3 - 1/60*f**6 + 2*f**2 + 0 + 1/12*f**4 - 1/12*f**5 + 0*f + m*f**7. Determine d so that y(d) = 0.
-1, 0, 2/5, 1
Let j(m) = m**4 + 3*m**3 - 7*m**2 - 3. Let s(o) = 2*o**4 + 5*o**3 - 13*o**2 - 5. Let u(n) = 5*j(n) - 3*s(n). Find z, given that u(z) = 0.
-2, 0, 2
Let r(a) be the second derivative of -4*a**7/105 - 7*a**6/60 + a**5/15 - 3*a**2/2 - a. Let y(l) be the first derivative of r(l). Factor y(i).
-2*i**2*(i + 2)*(4*i - 1)
Let h(q) = -2*q**3 + 2*q**2 - 2*q - 6. Let x(i) = i**3 - i**2 - i + 1. Let u(y) = h(y) + 6*x(y). Factor u(p).
4*p*(p - 2)*(p + 1)
Let f(g) be the second derivative of g**4/16 + 5*g**3/4 + 75*g**2/8 - 8*g. Factor f(l).
3*(l + 5)**2/4
Factor -2*i - 6*i**4 + 2*i**5 - 27*i**3 - 2*i + 29*i**3 + 6*i**2.
2*i*(i - 2)*(i - 1)**2*(i + 1)
Let t(n) be the second derivative of -n**4/24 + n**3/12 + n**2/2 - 28*n. Factor t(l).
-(l - 2)*(l + 1)/2
Let 2/5*q**3 - 2/5*q**4 + 2*q**2 + 6/5*q + 0 = 0. What is q?
-1, 0, 3
Let g(v) = v**3 - 2*v + 1. Let c be g(1). Let h(b) be the third derivative of 0*b**4 + 2*b**2 + c*b + 1/300*b**6 + 0 + 0*b**5 + 0*b**3. Factor h(k).
2*k**3/5
Let n = -57 - -229/4. Factor -3/4*y - 1/4*y**3 - 3/4*y**2 - n.
-(y + 1)**3/4
Let k(n) be the second derivative of -n**4/4 + 2*n**3 - 9*n**2/2 - n. Determine w, given that k(w) = 0.
1, 3
Determine f so that 5/2*f + 1/2*f**3 + 1 + 2*f**2 = 0.
-2, -1
Factor -2*u**4 - 15 + 15 + 3*u**2 + 3*u**3 - 2*u.
-u*(u - 2)*(u + 1)*(2*u - 1)
Suppose -3*x + 5*w = -20, 5*x + 5*w - 107 + 7 = 0. Factor -x*q**4 + 2*q**3 + 4*q**3 - q**5 + 7*q**5.
3*q**3*(q - 2)*(2*q - 1)
Let s(z) be the third derivative of z**9/3024 - z**8/840 + z**7/840 - 2*z**3/3 - 4*z**2. Let p(n) be the first derivative of s(n). Let p(y) = 0. What is y?
0, 1
Let m(k) = 32*k**2 + 142*k + 122. Let a(y) = 3*y**2 + 13*y + 11. Let o(z) = -68*a(z) + 6*m(z). Factor o(g).
-4*(g + 2)*(3*g + 2)
Factor 2/7*s**4 + 48/7*s + 32/7 + 2/7*s**2 - 12/7*s**3.
2*(s - 4)**2*(s + 1)**2/7
Let r(c) be the third derivative of -2*c**6/15 - 2*c**5/5 - c**4/2 - c**3/3 - c**2 - 18. Factor r(l).
-2*(2*l + 1)**3
Factor -2/5 - 1/5*r**2 - 3/5*r.
-(r + 1)*(r + 2)/5
Let l(g) = -5*g + 27. Let c be l(6). Let y be ((24 + -4)/(-5))/c. Solve 0*r**3 - y*r**2 + 2/3 + 2/3*r**4 + 0*r = 0.
-1, 1
Let r(q) = -6*q**3 + 5*q. Let p(o) = 5*o**3 + 1 + 0 - 1 - 4*o. Let k be 5 + -3 + 0 + 2. Let z(b) = k*r(b) + 5*p(b). Factor z(d).
d**3
Let n(m) be the third derivative of m**7/1365 - m**6/390 - m**5/390 + m**4/78 + 6*m**2. Find y, given that n(y) = 0.
-1, 0, 1, 2
Let b(j) = 3*j**3 - 7*j**2 + 7*j**3 + 0*j**2 + 5*j - 3*j**3. Let v(w) = -6*w**3 + 6*w**2 - 4*w. Let m(k) = -4*b(k) - 5*v(k). Factor m(o).
2*o**2*(o - 1)
Let g be (-36)/(-81)*(-321)/2. Let n = -70 - g. Let -10*r**2 - 14/3*r**4 + 38/3*r**3 + 2/3*r + n = 0. Calculate r.
-2/7, 1
Let t(j) be the second derivative of 9*j**5/10 - 11*j**4/6 + 2*j**3/3 - 6*j. Suppose t(f) = 0. Calculate f.
0, 2/9, 1
Let f(v) be the second derivative of 0 + 0*v**2 - 6*v - 1/10*v**6 - 1/4*v**4 + 0*v**3 + 3/10*v**5. Factor f(o).
-3*o**2*(o - 1)**2
Let t be (12/9)/(2/6). What is r in -3*r - 3 - 18*r**5 + r**4 - t*r**4 + 6*r**2 + 15*r**5 + 6*r**3 = 0?
-1, 1
Let o be 54/30 + (-2)/(-10). Factor -3/2 - o*q - 1/2*q**2.
-(q + 1)*(q + 3)/2
Factor -4/3*w**3 + 2/3 + 2/3*w + 2/3*w**4 - 4/3*w**2 + 2/3*w**5.
2*(w - 1)**2*(w + 1)**3/3
Let p be 8/(-36)*18/(-8). Let y = 1 + 2. Determine n, given that -p*n**y + 0*n**2 + 0 + 1/2*n = 0.
-1, 0, 1
Let t(u) = 0*u - 2*u + u. Let g(y) = -y**3 - 19*y**2 - 2*y + 19*y**2. Let c(i) = g(i) - 2*t(i). Solve c(n) = 0 for n.
0
Let v be 1/(-4) - 399/(-76). Factor 32/9*c**2 - 28/9*c**3 - 2*c - 2/9*c**v + 4/3*c**4 + 4/9.
-2*(c - 2)*(c - 1)**4/9
Let h(v) be the third derivative of -v**7/525 + v**6/60 - 7*v**5/150 + v**4/20 - 15*v**2. Let h(g) = 0. Calculate g.
0, 1, 3
Solve 0*j**2 + 0 - 2/3*j + 2/3*j**3 = 0 for j.
-1, 0, 1
Let l(k) be the third derivative of 4/3*k**3 + 0 + 1/105*k**7 + 2*k**2 - 1/10*k**5 + 0*k - 1/30*k**6 + 1/3*k**4. Factor l(c).
2*(c - 2)**2*(c + 1)**2
Factor -5*i**2 + 4*i**2 + 4*i**2 - 3*i.
3*i*(i - 1)
Let r(j) be the third derivative of j**5/20 + j**4/4 + j**3/2 + 5*j**2. Determine m so that r(m) = 0.
-1
Let b(r) be the first derivative of 3*r**4/2 + 21*r**3 - 33*r**2/2 - 45. Factor b(y).
3*y*(y + 11)*(2*y - 1)
Let d be (-1)/10*8/(-42). Let k(y) be the third derivative of 3*y**2 + 0*y**3 - 1/15*y**5 + d*y**7 + 0 - 1/60*y**6 + 1/168*y**8 + 0*y + 0*y**4. Factor k(g).
2*g**2*(g - 1)*(g + 1)*(g + 2)
Let u = 18 - 9. Let h = u - 6. Let r + r**h - 2*r**3 + 2*r - 2*r = 0. Calculate r.
-1, 0, 1
Let u(j) be the third derivative of 0*j + 2/105*j**6 - 2/105*j**5 + 1/588*j**8 - 4/21*j**3 + 0 - 5/42*j**4 - 9*j**2 + 8/735*j**7. Suppose u(s) = 0. What is s?
-2, -1, 1
Factor -1/4*p**3 + 3 + 2*p - 1/4*p**2.
-(p - 3)*(p + 2)**2/4
Let z(v) be the third derivative of v**6/420 - v**5/210 - v**4/21 + 4*v**3/21 + 8*v**2. Suppose z(m) = 0. Calculate m.
-2, 1, 2
Let o(x) = x**3 - 8*x**2 + 6*x + 10. Let t be o(7). Factor 4*p + 10*p**4 - 6*p**t - 4*p + 2*p**2 - 6*p**2.
2*p**2*(p - 1)*(5*p + 2)
Let j(l) be the first derivative of 1/9*l**3 - 2/3*l - 1/6*l**2 + 4. Suppose j(v) = 0. What is v?
-1, 2
Let g(r) be the third derivative of -2*r**6/105 - r**5/35 + r**4/42 + 5*r**2. Find k, given that g(k) = 0.
-1, 0, 1/4
Let v(g) = g**2 - 5*g + 2. Let c be v(5). Factor 9*p - 9*p**c + 0 - 2 + 2*p.
-(p - 1)*(9*p - 2)
Let a(y) = 5*y**2 - y - 2. Let c(z) = 11*z**2 - z - 5. Let m(p) = 5*a(p) - 2*c(p). Solve m(w) = 0 for w.
0, 1
Let -1545*d**4 + 4*d + 3*d**2 - 15*d**3 + 2*d + 9*d**5 + 1542*d**4 = 0. Calculate d.
-1, -2/3, 0, 1
Let q(f) be the second derivative of f**6/6 - f**5/4 - 10*f**4/3 + 10*f**3 + 2*f + 43. Factor q(i).
5*i*(i - 2)**2*(i + 3)
Let y(z) be the third derivative of z**8/1680 + z**7/315 + z**6/180 + z**4/12 - 3*z**2. Let x(u) be the second derivative of y(u). Suppose x(d) = 0. What is d?
-1, 0
Factor -27*l**3 - 5*l**4 + 0*l**4 - 72*l**2 - 8*l**4 + 10*l**4 - 48*l.
-3*l*(l + 1)*(l + 4)**2
Let k(u) be the third derivative of -u**7/525 + u**6/300 + u**5/150 - u**4/60 - 16*u**2. Find v such that k(v) = 0.
-1, 0, 1
Suppose 0*t - t + 16 = 0. Suppose 3*x + 0*h - h = -4, -4*h = 2*x - t. Factor x*b**2 - 3*b**3 + b**2 + 4*b**3.
b**2*(b + 1)
Suppose 2*w - 71 = -3*s - 5, -4*s + 74 = -2*w. Let a be 47/s + 6/(-8). Let 4/5 - x**2 - a*x = 0. What is x?
-2, 2/5
Let k = -4 - -2. Let j be (0/(-3 + 0))/k. What is p in 1/4*p**4 + j*p**2 + 0 + 0*p + 0*p**3 = 0?
0
Let -4/3 - 9*k**4 - 8*k - 5/3*k**5 - 53/3*k**2 - 55/3*k**3 = 0. Calculate k.
-2, -1, -2/5
Suppose -2/5*m + 1/5*m**2 + 1/5 = 0. What is m?
1
Let o(i) be the first derivative of -i**9/7560 + i**8/2100 - i**7/2100 + 4*i**3/3 - 4. Let k(w) be the third derivative of o(w). Let k(r) = 0. What is r?
0, 1
Suppose 0 = -2*p + 12*p - 20. Let a(v) be the third derivative of 0 - 1/60*v**6 + 1/12*v**4 - 1/105*v**7 + 0*v**3 + 1/30*v**5 - 3*v**p + 0*v. Factor a(k).
-2*k*(k - 1)*(k + 1)**2
Suppose -g + 1 = 2. Let d be 15/(-6) - -2 - g. Factor d*q**3 + 0*q**2 + 0 - 1/2*q.
q*(q - 1)*(q + 1)/2
Factor 2*a**2 + 6*a**2 - 1 - 7*a**2.
(a - 1)*(a + 1)
Let h = -12 - -13. Let q be ((-20)/8 + h)*-2. Factor -m**2 + 1/3*m**4 + 2/3 - 1/3*m**q + 1/3*m.
(m - 2)*(m - 1)*(m + 1)**2/3
Suppose 0 = w - 2*u - 7, -4*u = -3*w + 2 + 15. Solve 2*h - 2*h + 2*h**4 + 0*h - 4*h**w = 0.
0, 2
Let b(j) be the third derivative of -j**9/45360 + j**8/10080 - j**7/7560 - j**4/8 + j**2. Let z(h) be the seco