4 + 2*y**2 - 1/18*y**3 + 0*y + 0 - w*y**5. Factor d(p).
-(p + 1)**2/3
Let u(f) be the second derivative of -f**7/6300 - f**6/300 - 3*f**5/100 + 7*f**4/12 - 2*f. Let t(p) be the third derivative of u(p). Let t(o) = 0. Calculate o.
-3
Let v(y) be the first derivative of -5*y**3/3 + 20*y + 1. Factor v(a).
-5*(a - 2)*(a + 2)
Let q be (-5)/(10/(-8)) - (9 - 7). Factor 1/4*n + 0 - 1/2*n**q + 1/4*n**3.
n*(n - 1)**2/4
Let p(u) be the first derivative of -2*u**3/3 - 12. Determine d so that p(d) = 0.
0
Suppose 0 = c - 3 + 1. Suppose c*m + 4 = 5*x, -2*x = -3*m + 2*x + 1. Factor 0 + 2/9*n + 0*n**4 + 2/9*n**5 - 4/9*n**m + 0*n**2.
2*n*(n - 1)**2*(n + 1)**2/9
Let l(r) be the first derivative of r**3/18 - r**2/6 + r/6 - 10. Factor l(q).
(q - 1)**2/6
Let x(j) be the first derivative of 1/10*j**5 - 1/3*j**3 + 3 + 0*j**2 + 1/30*j**6 + j - 1/12*j**4. Let z(r) be the first derivative of x(r). Factor z(s).
s*(s - 1)*(s + 1)*(s + 2)
Suppose 4*z - 4 = -2*r + 4, 3*r - 12 = 4*z. Let d(q) be the first derivative of z*q + 2/3*q**3 + 3 + q**2. Find b, given that d(b) = 0.
-1, 0
Let d(m) be the first derivative of -m**3/21 - m**2/14 + 2*m/7 + 35. Suppose d(n) = 0. What is n?
-2, 1
Let p be 245/(-147) + 29/12. Solve 1/4*a**3 + 0*a + 1 - p*a**2 = 0.
-1, 2
Let v(a) be the first derivative of a**5/25 + a**4/5 - 8*a**2/5 - 16*a/5 + 48. Suppose v(r) = 0. What is r?
-2, 2
Suppose 2*v - 11 = 5. Suppose 2*q - v = -2*q. Factor 0 - 1/2*g**q - 1/2*g.
-g*(g + 1)/2
Let u(k) be the third derivative of k**6/12 - 17*k**5/30 + 4*k**4/3 - 4*k**3/3 - 20*k**2. Factor u(s).
2*(s - 2)*(s - 1)*(5*s - 2)
Let p(k) = 44*k**2 - 4*k - 16. Let h(l) = -9*l**2 + l + 3. Let x be (-19 + 21)/(2/5). Let i(t) = x*p(t) + 24*h(t). Let i(c) = 0. What is c?
-2, 1
Factor 12/5*j**4 - 3/5*j - 3/5*j**5 + 0 - 18/5*j**3 + 12/5*j**2.
-3*j*(j - 1)**4/5
Let f(w) be the third derivative of w**7/490 - w**6/70 + 3*w**5/70 - w**4/14 + w**3/14 - 2*w**2. Factor f(b).
3*(b - 1)**4/7
Let y(o) be the first derivative of -o**4/4 + o**3/3 + o**2 + 6. Factor y(v).
-v*(v - 2)*(v + 1)
Let m = 1 + -1. Find u, given that -2/7*u**4 + 0 + m*u + 2/7*u**5 + 0*u**3 + 0*u**2 = 0.
0, 1
Let a(y) be the second derivative of -2*y**2 + 0 + 5/3*y**3 + y + 1/10*y**5 - 2/3*y**4. Solve a(b) = 0.
1, 2
Suppose z**3 - 1/3*z**4 - 5*z - 6 + 7/3*z**2 = 0. What is z?
-2, -1, 3
Let a be 72/105 + 48/(-120). Find p, given that -a*p**3 + 0*p + 4/7*p**4 + 0*p**2 + 0 - 2/7*p**5 = 0.
0, 1
Factor -6*p - p**4 - 60*p**2 + 3*p**5 - 9*p**3 + 45*p**2 + 4*p**4.
3*p*(p - 2)*(p + 1)**3
Let q(h) be the first derivative of -h**3/6 - 9*h**2/4 + 28. Factor q(x).
-x*(x + 9)/2
Let g = -11/8 - -37/24. Let p(h) be the second derivative of 0 - 1/36*h**4 + g*h**2 + 0*h**3 - 3*h. Factor p(n).
-(n - 1)*(n + 1)/3
Let -16/3*k + 2 + 32/9*k**2 = 0. Calculate k.
3/4
Let h = -4 - -7. Let f(p) = 4*p**5 + p**3 - 3*p**2 + p. Let s(n) = n**5 + n**3 - n**2. Let w(u) = h*s(u) - f(u). Solve w(d) = 0 for d.
-1, 0, 1
Let q(y) = -y**3 - 2*y**2 + 2*y. Let f be q(-3). Let u(g) = g**2 - 3*g. Let z be u(f). Determine h, given that 0*h**2 + z*h + 2/5*h**3 + 2/5*h**4 + 0 = 0.
-1, 0
Let o be 6*(78/12)/13. Factor 0 - 2/7*n**o - 4/7*n - 6/7*n**2.
-2*n*(n + 1)*(n + 2)/7
Factor -3/10*x**2 - 1/10*x**4 + 0*x + 0 - 2/5*x**3.
-x**2*(x + 1)*(x + 3)/10
Let p(r) be the second derivative of r**6/5 + r**5/2 + r**4/3 - 5*r. Solve p(w) = 0 for w.
-1, -2/3, 0
Find g, given that -15 - 16*g - 2*g - 4*g**2 - 14*g - 49 = 0.
-4
Let n = -1/77 + 157/231. Factor -2/3*c**3 + 0 - n*c + 4/3*c**2.
-2*c*(c - 1)**2/3
Factor 31 - 120*w - w**5 + 145*w**2 - 21*w**3 + 5 + 15*w**4 - 51*w**3 - 3*w**3.
-(w - 6)**2*(w - 1)**3
Let -2/3*s**3 - 2/3*s + 0 + 4/3*s**2 = 0. Calculate s.
0, 1
Suppose 2*n - 15 = -3*n. Let m(z) be the second derivative of 2/5*z**2 + 0 + 2*z + 3/10*z**4 + 1/75*z**6 + 1/10*z**5 + 7/15*z**n. Factor m(t).
2*(t + 1)**3*(t + 2)/5
Let t = 1026/7 - 146. Solve 0 + 10/7*f**3 - t*f + 6/7*f**2 = 0 for f.
-1, 0, 2/5
Let w(p) be the first derivative of -p**6/6 + 3*p**4/4 - 2*p**3/3 + 3. Factor w(s).
-s**2*(s - 1)**2*(s + 2)
Let s(y) be the third derivative of 1/120*y**5 - 1/12*y**3 + 0*y + 0 + 0*y**4 - y**2. Suppose s(p) = 0. What is p?
-1, 1
Let v(n) = n**3 - n**2 + n. Let q(l) = -9*l**3 + 9*l**2 - 3*l - 3. Let d(r) = q(r) + 6*v(r). Factor d(u).
-3*(u - 1)**2*(u + 1)
Suppose -13*h + 15*h = 0. Find n, given that h*n + 0 + 1/3*n**3 + 0*n**2 = 0.
0
Let n(j) be the second derivative of -j**5/20 - j**4/4 + j**2 - j. Let y(x) be the first derivative of n(x). Factor y(o).
-3*o*(o + 2)
Let g(u) be the third derivative of -u**8/896 + u**7/56 - 3*u**6/32 + u**5/4 - 25*u**4/64 + 3*u**3/8 + 5*u**2 - u. Factor g(x).
-3*(x - 6)*(x - 1)**4/8
Let r be (-24)/(-84) + (-52)/(-14). Suppose 0 = y + 3*y - 16. Factor 2*j**3 + 4 + 2*j - r*j**2 - y.
2*j*(j - 1)**2
Let n(j) be the second derivative of j**6/6 - 7*j**5 + 225*j**4/2 - 810*j**3 + 3645*j**2/2 + 10*j. Factor n(g).
5*(g - 9)**3*(g - 1)
Let c(k) = -k**3 - k**2 - k + 3. Let m(v) = -7*v**3 + 3 + 8*v**3 + 0 - 4. Let b(f) = -c(f) - 2*m(f). Suppose b(n) = 0. What is n?
-1, 1
Let c = -13 + 19. Suppose 0 = o - 3*o + c. Factor 10/3*p**4 + 2/3*p**5 + 4/3*p + 6*p**o + 0 + 14/3*p**2.
2*p*(p + 1)**3*(p + 2)/3
Let u be 5/(-10)*-2*2. Let 3*o**2 - 4*o - o**2 - u - 4*o**2 + 0*o**2 = 0. Calculate o.
-1
Suppose -3*v - 6*h = -3*h - 12, 5*v - 2*h = 6. Suppose -2 = -v*u + 2. Factor 3/4*r + 3/4*r**u + 1/4 + 1/4*r**3.
(r + 1)**3/4
Let n(y) be the second derivative of 2*y**7/21 + 4*y**6/15 + y**5/5 - 19*y. Factor n(r).
4*r**3*(r + 1)**2
Let y(m) be the third derivative of 3*m**2 + 0 + 1/120*m**5 - 1/24*m**4 + 0*m + 1/12*m**3. Factor y(l).
(l - 1)**2/2
Let z(d) be the second derivative of d**6/160 - d**5/80 - d**4/16 - 2*d**2 + 6*d. Let r(m) be the first derivative of z(m). Factor r(g).
3*g*(g - 2)*(g + 1)/4
Let h(v) = -6*v**4 - 5*v**3 + 7*v**2 - 3*v - 5. Let c(i) = 17*i**4 + 14*i**3 - 20*i**2 + 8*i + 14. Let u(f) = -4*c(f) - 11*h(f). Factor u(x).
-(x - 1)*(x + 1)**2*(2*x - 1)
Find x such that 0 + 1/2*x**4 - 4*x - 1/2*x**5 - 2*x**2 + 3*x**3 = 0.
-2, -1, 0, 2
Let b(x) be the first derivative of -1/2*x**4 - x + 1/3*x**3 + 0*x**2 - 1/15*x**6 + 2 + 3/10*x**5. Let o(c) be the first derivative of b(c). Factor o(d).
-2*d*(d - 1)**3
Let b be (-9)/12 + (-38)/(-8). Let u(k) be the second derivative of -1/3*k**b + 2*k**2 + 1/10*k**5 - 1/3*k**3 + 0 - k. Determine a so that u(a) = 0.
-1, 1, 2
Let s(t) be the first derivative of -t**5/15 - 5*t**4/12 - t**3 - 7*t**2/6 - 2*t/3 - 2. Factor s(b).
-(b + 1)**3*(b + 2)/3
Let s(j) = 10*j**2 + 2*j - 12. Let r(n) = -n**2 + n. Let h(o) = -18*r(o) - 2*s(o). Let h(i) = 0. What is i?
-12, 1
Let x(b) be the first derivative of b**6/2 - 3*b**4/4 - 6. Factor x(g).
3*g**3*(g - 1)*(g + 1)
Factor -3 - 4*o**2 + 10 - 3.
-4*(o - 1)*(o + 1)
Let f = 621 - 21733/35. Let p(i) be the first derivative of 0*i**2 + 1/7*i**6 - 2 - 1/7*i**4 + 0*i**3 - f*i**5 + 0*i. Factor p(y).
2*y**3*(y - 1)*(3*y + 2)/7
Let x(g) be the first derivative of g**3/12 - g**2/8 + 10. Suppose x(l) = 0. What is l?
0, 1
Find z such that 22/13*z**3 - 30/13*z**2 - 6/13*z**4 - 4/13 + 18/13*z = 0.
2/3, 1
Let d(b) = 3*b + 4. Let m(s) = 1. Let z(o) = -d(o) + 4*m(o). Let u be z(-1). Factor u*t**3 + 2*t**3 - 4*t**3 - t.
t*(t - 1)*(t + 1)
Let l(j) = j**3 + j**2 - j - 1. Let w(c) = 6*c**3 + 9*c**2 - 6*c - 9. Let i be (-2)/(-5) - (-7)/(-5). Let o(d) = i*w(d) + 9*l(d). Factor o(q).
3*q*(q - 1)*(q + 1)
Let d(z) be the third derivative of z**8/504 - z**7/315 - z**6/90 - 4*z**2. Factor d(p).
2*p**3*(p - 2)*(p + 1)/3
Let x(z) = 5*z**2 - z - 4. Let f(c) be the second derivative of c**4/2 - c**3/6 - 5*c**2/2 - c. Let a(m) = 4*f(m) - 5*x(m). Let a(t) = 0. What is t?
0, 1
Let k = -253/3 + 85. Let t be (48/60)/((-1)/(10/(-12))). Factor 0 - k*l**2 - 2/3*l**5 + t*l**3 + 2/3*l**4 + 0*l.
-2*l**2*(l - 1)**2*(l + 1)/3
Factor -2/19*k**3 + 4/19 + 0*k**2 + 6/19*k.
-2*(k - 2)*(k + 1)**2/19
Let d(k) be the first derivative of -1/2*k**4 + 2/3*k**3 + 1/6*k**6 + 1/2*k**2 - k - 1 - 1/5*k**5. Factor d(x).
(x - 1)**3*(x + 1)**2
Let g(p) be the first derivative of p**4/2 + 8*p**3/3 + 4*p**2 - 6*p - 2. Let u(w) be the first derivative of g(w). Factor u(t).
2*(t + 2)*(3*t + 2)
Find y, given that -2 - 9*y + 1 - 3*y**2 + 3 + 9*y**3 + 1 = 0.
-1, 1/3, 1
Let f be ((-4)/(-21))/(2/9). Let 4