0*u**3. Factor h(w).
w*(w + 1)**4/4
Let l(m) be the second derivative of 2/9*m**4 + 7/9*m**3 + m - 2/3*m**2 + 0. Determine c, given that l(c) = 0.
-2, 1/4
Let t(m) be the first derivative of 1/4*m**2 + 1 + 2/5*m**5 + 0*m + 1/12*m**6 + 3/4*m**4 + 2/3*m**3. Factor t(k).
k*(k + 1)**4/2
Let n(h) be the second derivative of 0*h**2 + 2*h + 0 - 1/12*h**3 - 1/48*h**4. Factor n(m).
-m*(m + 2)/4
Let w = -6/13 - -44/39. Let w*i + 1/3*i**2 + 1/3 = 0. Calculate i.
-1
Let d = -122/9 - -14. Solve -2/9*f**4 + 0*f**2 + d*f - 4/9*f**3 + 2/9 = 0 for f.
-1, 1
Let k(j) = -4*j - 86. Let t be k(-22). Suppose -2/9*c**t - 2/9*c + 0 = 0. Calculate c.
-1, 0
Let q(r) be the first derivative of -r**3/6 - 3*r**2/4 + 2*r + 28. Determine d so that q(d) = 0.
-4, 1
Let j(x) be the third derivative of 0 + 0*x - 1/96*x**4 - 1/120*x**5 + 1/420*x**7 + 1/120*x**6 + 3*x**2 - 1/448*x**8 + 0*x**3. Solve j(t) = 0.
-1, -1/3, 0, 1
Let s be (-7)/(-20)*7/49. Let p(c) be the second derivative of s*c**4 + 0 + 1/5*c**2 + 3*c + 1/6*c**3. Solve p(u) = 0 for u.
-1, -2/3
Factor 1/2*z**5 + 3/2*z**4 + 0*z**2 + 0*z + 0 + z**3.
z**3*(z + 1)*(z + 2)/2
Let c(g) be the third derivative of -3*g**7/70 + g**6/40 + 3*g**5/20 - g**4/8 + 2*g**2. Solve c(o) = 0 for o.
-1, 0, 1/3, 1
Let z be (-1 + -68)*(-8)/(-24). Let m = 26 + z. Let -88/9*l + 140/9*l**2 - 50/9*l**m + 16/9 = 0. Calculate l.
2/5, 2
Factor -3*t**2 - t**2 - 22*t - 400 - 59*t + t.
-4*(t + 10)**2
Find d, given that 2/3*d + 2/9*d**5 + 4/9*d**2 + 0*d**4 - 8/9*d**3 - 4/9 = 0.
-2, -1, 1
Let f(d) be the third derivative of d**6/240 + d**5/20 + d**4/4 + 2*d**3/3 + 3*d**2. Factor f(m).
(m + 2)**3/2
Let i(x) = 7*x**3 - 3*x**2 + 5*x. Let s be 6/(-4)*12/9. Let l(f) = 3*f**3 - f**2 + 2*f. Let c(m) = s*i(m) + 5*l(m). What is a in c(a) = 0?
-1, 0
Suppose -2*l = -b - 3, -3*b + 1 - 2 = -2*l. Let h**3 - 3*h**3 + 4*h**l + h + 3*h**3 + 2*h**3 = 0. What is h?
-1, -1/3, 0
Let s(z) be the third derivative of -z**8/840 - z**7/300 - z**6/450 + z**3/3 + 3*z**2. Let w(p) be the first derivative of s(p). Factor w(n).
-2*n**2*(n + 1)*(5*n + 2)/5
Suppose b + 5 = -4*x - 14, -7 = 2*x + 3*b. Let g = x + 5. Solve g + 0*p**2 - 1/3*p + 1/3*p**3 = 0.
-1, 0, 1
Let i(c) be the second derivative of -c**7/14 - c**6/5 + 9*c**5/80 + 9*c**4/16 - 2*c. Determine x, given that i(x) = 0.
-3/2, 0, 1
Let r(i) = 3*i**3 + 7*i**2 - i - 1. Let m be r(-2). Let x be 16/9 - (-4)/6. Find h such that 8/9*h + 8/9*h**2 + 2*h**m - 4/3*h**4 + 0 - x*h**3 = 0.
-2/3, 0, 1
Factor 12/5*c**2 + 63/5*c + 3.
3*(c + 5)*(4*c + 1)/5
Let h(p) = -65*p**4 + 155*p**3 + 660*p**2 - 395*p - 880. Let k(l) = -3*l**4 + 7*l**3 + 30*l**2 - 18*l - 40. Let w(u) = 2*h(u) - 45*k(u). Factor w(c).
5*(c - 2)**2*(c + 1)*(c + 2)
Let k(d) be the second derivative of -d**8/10080 - d**7/3780 + d**4/2 - 5*d. Let r(x) be the third derivative of k(x). Factor r(c).
-2*c**2*(c + 1)/3
Let s(f) be the second derivative of 2*f**7/21 - 4*f**6/15 + f**5/5 + 4*f. Solve s(p) = 0.
0, 1
Factor 8 + 18*g + 0*g**2 - 6*g + 5*g**2 - g**2.
4*(g + 1)*(g + 2)
Let c be 7/1 + 20/(-3). Solve -2/3 + 1/3*b + c*b**2 = 0.
-2, 1
Let n(j) = j - 4. Suppose s + 5*a = -21, 5*s - 3*a - 23 = 3*s. Let y be n(s). Determine h, given that 1 + 6*h + 4 + y + 3*h**2 - 2 = 0.
-1
Factor 15*c - 82*c**3 + 15*c**2 + 87*c**3 + 1 + 4.
5*(c + 1)**3
Let f(t) be the second derivative of 1/2*t**2 + 0 + 1/6*t**3 - 1/12*t**4 + t - 1/20*t**5. Find p such that f(p) = 0.
-1, 1
Let x(r) be the second derivative of -r**5/5 + 2*r**3/3 - 47*r. Factor x(u).
-4*u*(u - 1)*(u + 1)
Let f(t) = -5*t**2 + 5*t + 5. Let x(r) = 5*r**2 - 5*r - 4. Let j(n) = -6*f(n) - 5*x(n). Factor j(c).
5*(c - 2)*(c + 1)
Suppose -2*j - 2*j - 22 = -2*h, -3*h - 11 = 5*j. Let a(n) be the third derivative of 1/3*n**h + 1/6*n**4 + 2*n**2 + 1/30*n**5 + 0 + 0*n. Factor a(v).
2*(v + 1)**2
Factor -4/11 - 8/11*m**2 + 2/11*m**3 + 10/11*m.
2*(m - 2)*(m - 1)**2/11
Let f(v) be the first derivative of 2/3*v**2 + 1/3*v + 1/3*v**4 + 2/3*v**3 + 1/15*v**5 + 2. Factor f(l).
(l + 1)**4/3
Let k(m) be the second derivative of -14*m**6/45 - 26*m**5/15 + 29*m**4/9 + 80*m**3/3 - 24*m**2 + 6*m. What is u in k(u) = 0?
-3, 2/7, 2
Let k(a) be the second derivative of 0 + 1/10*a**5 - 1/3*a**4 + 2*a + 1/3*a**3 + 0*a**2. Factor k(m).
2*m*(m - 1)**2
Let i(h) be the first derivative of 2*h**2 - 1/24*h**3 + 4 + 0*h + 0*h**4 + 1/240*h**5. Let y(p) be the second derivative of i(p). Factor y(x).
(x - 1)*(x + 1)/4
Suppose -2*o + 0*a + 54 = -2*a, 3*a = -2*o + 39. Let f be 9/10*o/18. Factor 2/5*c**2 + f*c**3 - 4/5*c + 0.
2*c*(c + 1)*(3*c - 2)/5
Let n(v) be the third derivative of -v**6/600 + v**5/75 + v**4/24 + 15*v**2. Solve n(f) = 0 for f.
-1, 0, 5
Let z(o) be the first derivative of -o**5/35 + o**4/14 - o**3/21 - 4. Let z(h) = 0. Calculate h.
0, 1
Let g(a) = 3*a**3 - 15*a**2 - 6*a. Suppose -4*j - 12 = -2*s + 6*s, -j - 5 = -s. Let m(d) = -d**3 + d**2. Let i(t) = s*g(t) + 6*m(t). Solve i(h) = 0.
-2, -1, 0
Suppose -3*q = -2*p, -3*p + q = p. Suppose p*c = -c. Determine n so that c + 2/3*n**2 - 2/9*n - 2/3*n**3 + 2/9*n**4 = 0.
0, 1
Let l(p) be the first derivative of -p**5/20 - p**4/8 - 23. Factor l(b).
-b**3*(b + 2)/4
Suppose -2*g - z + 3 = 0, -g = 4*z - z - 4. Let d be (5/15)/g - 0. Factor d*c + 2/3 - 1/3*c**2.
-(c - 2)*(c + 1)/3
Suppose 5*t + 5*m = 55, -t + 1 - 2 = -5*m. Suppose -4*l - 3*u + 8 + t = 0, 2*l - 1 = u. Find y such that 6*y - 4*y - 2 + 2 - 2*y**l = 0.
0, 1
Factor -4*c**4 + 2*c**5 + 2*c**4 - 2*c**3 + 0*c**5 + 2*c**2.
2*c**2*(c - 1)**2*(c + 1)
Let j(f) be the first derivative of 0*f + 0*f**2 + 2*f**3 - 1 - 27/5*f**5 + 21/4*f**4. What is h in j(h) = 0?
-2/9, 0, 1
Let s = 18 - 19. Let g(t) = 3*t**2 + t. Let j be g(s). Factor 2*w**3 + j*w + 3*w**2 + 1/2 + 1/2*w**4.
(w + 1)**4/2
Let d(v) be the first derivative of -v**6/18 + v**5/10 - v**3/18 + 7. Factor d(b).
-b**2*(b - 1)**2*(2*b + 1)/6
Let z(m) = -2*m**2 - 5*m - 3. Let f be z(-3). Let x = f - -8. Factor -3/4*k - 3*k**x + 1/2 - 7/4*k**3.
-(k + 1)**2*(7*k - 2)/4
Let i(d) = d**2 - 3*d - 2. Let f be i(4). What is w in f*w - 5*w + w + 2*w**2 = 0?
0, 1
Let l be 2*(-2 - -1)/(-1). Solve 3 + 3*w**3 - 3*w**l - 1 - 3*w + 1 = 0.
-1, 1
Let k(h) be the second derivative of h**5/210 - 4*h**3/63 + 19*h. Find c, given that k(c) = 0.
-2, 0, 2
Let f(t) = -3*t - 30. Let q be f(-12). Suppose r = 4*r - q. Factor 0*c + 0 - 1/3*c**3 + 0*c**r.
-c**3/3
Let a(t) = -2*t**5 + 3*t**4 + 14*t**3 + 13*t**2 + 6*t + 2. Let r(h) = 3*h**5 - 2*h**4 - 14*h**3 - 12*h**2 - 5*h - 2. Let z(g) = 4*a(g) + 3*r(g). Factor z(f).
(f + 1)**4*(f + 2)
Let u(w) = w**3 - w**2 - w. Suppose 8 + 2 = -5*x. Let g(p) = 2*p**3 + 2*p**2 - 3*p**3 - 4*p + 6*p. Let q(h) = x*u(h) - g(h). Factor q(s).
-s**3
Let g(y) = -2*y**4 + 17*y**3 - 11*y**2 - 41*y + 27. Let f(x) = -x**4 + 16*x**3 - 10*x**2 - 40*x + 27. Let t(o) = -5*f(o) + 4*g(o). What is r in t(r) = 0?
-3, 1
Let k(x) be the first derivative of -3 + 7/6*x**3 + 1/2*x**2 + 0*x + 1/12*x**6 + 9/8*x**4 + 1/2*x**5. Factor k(j).
j*(j + 1)**3*(j + 2)/2
Let a(x) = 3*x**2 + 4*x + 2. Let r be a(-2). Suppose -t = -3*t + r. Factor -23*q**2 - 77*q**2 + 19 - t - 8*q + 50*q**3.
2*(q - 2)*(5*q - 2)*(5*q + 2)
Let i be 4/(-6)*18/(-4). Suppose -i*f - 5*r = -29, 0*r + r - 19 = -5*f. Factor 0*h**2 + 2/3*h**4 + 4/3*h**f - 2*h**5 + 0*h + 0.
-2*h**3*(h - 1)*(3*h + 2)/3
Let y be 8/6 - (-11 + 7). Let r(g) be the first derivative of -20/3*g**2 + 2/15*g**5 - 4 + 4*g**3 + y*g - 7/6*g**4. Suppose r(n) = 0. What is n?
1, 2
Solve -2/19*t**2 + 4/19 + 2/19*t = 0.
-1, 2
Let i(t) be the second derivative of -t**7/420 - t**6/540 + t**3/6 + 3*t. Let u(w) be the second derivative of i(w). Determine o, given that u(o) = 0.
-1/3, 0
Let h(b) = 6*b**3 - 77*b**2 + 150*b - 17. Let g(o) = -2*o**3 + 26*o**2 - 50*o + 6. Let m(a) = -17*g(a) - 6*h(a). Factor m(d).
-2*d*(d - 5)**2
Suppose 0*o + 60 = 2*o. Let y be ((-9)/(-15))/(27/o). Solve -y*r**2 - 2/3 + 4/3*r = 0.
1
Factor 5/4*p + 0 + 0*p**2 - 5/4*p**3.
-5*p*(p - 1)*(p + 1)/4
Factor 0 + 2*m - m**2 + 2 + 2*m**2 - 3*m**2 - 2*m**3.
-2*(m - 1)*(m + 1)**2
Let b(w) = 2*w + 5. Let a be b(0). Let r(l) be the second derivative of -2*l - 3/80*l**a + 0 + 1/8*l**3 + 3/4*l**2 - 1/8*l**4. Factor r(v).
-3*(v - 1)*(v + 1)*(v + 2)/4
Let p(c) = c + 13. Let w(j) = -1. Let l(f) = p(f) + w(f). Let y be l(-9). What is n in -5*n**y - 2*n**5 +