u - 1/15*z**3 - 2*z - 1/50*z**5 + 0*z**2 + 1/15*z**4. Factor q(p).
-2*p*(p - 1)**2/5
Let w be (-39)/(-56) - (8/(-14))/(-1). Let q(a) be the first derivative of -3 + w*a**4 - 1/4*a**2 - 1/6*a**3 + 1/2*a. Factor q(r).
(r - 1)**2*(r + 1)/2
Let y(q) be the third derivative of -q**7/210 + q**6/15 - 2*q**5/5 + 4*q**4/3 - 8*q**3/3 - 25*q**2. Factor y(z).
-(z - 2)**4
Let c(l) be the first derivative of -l**8/1008 + l**7/630 + l**6/360 - l**5/180 - l**2/2 + 2. Let g(x) be the second derivative of c(x). What is t in g(t) = 0?
-1, 0, 1
Suppose -m = -0*a - a + 20, -a = m - 18. Let w = a - 17. Factor -2/7*h**w + 4/7 + 2/7*h.
-2*(h - 2)*(h + 1)/7
Let j = -5 + 6. Factor -3*x**4 + 3*x + 3 + 9*x**2 - j - 8 - 3*x**3.
-3*(x - 1)**2*(x + 1)*(x + 2)
Let d(j) be the second derivative of -j**9/7560 + j**7/420 + j**6/180 - j**4/4 + j. Let c(h) be the third derivative of d(h). Factor c(w).
-2*w*(w - 2)*(w + 1)**2
Let x(w) be the third derivative of -w**5/150 + w**4/10 - 3*w**3/5 + 5*w**2. Determine c, given that x(c) = 0.
3
Let f(z) be the third derivative of 0 + 1/40*z**6 + 7/40*z**4 - 1/5*z**3 - 1/350*z**7 + 0*z - 9/100*z**5 - 4*z**2. Factor f(m).
-3*(m - 2)*(m - 1)**3/5
Suppose -34 = 5*t - 4*r, 4*t + t - 2*r + 32 = 0. Let c be (2/(-4))/(2/t). Factor -3/2*g - c*g**2 - 1/2*g**3 - 1/2.
-(g + 1)**3/2
Let l(j) be the first derivative of -9/16*j**4 + 0*j**2 + 0*j + 1/4*j**3 - 4. Factor l(k).
-3*k**2*(3*k - 1)/4
Let u(b) be the third derivative of 0*b**5 + 0*b**4 + 0*b - b**2 + 0*b**3 + 1/105*b**7 + 0 + 1/60*b**6. Factor u(c).
2*c**3*(c + 1)
Let i be 1/((1/(-3))/(-1)). Suppose 6 - 8 = -q. Factor r**3 - i*r**4 + r**q + r - 2*r**4 - 2*r**3 + 4*r**4.
-r*(r - 1)*(r + 1)**2
Let d(q) = 7*q**4 - 3*q**3 - 3*q**2 - q. Let z = 1 + 3. Let u(t) = t**4 - t. Let f(y) = z*u(y) - d(y). Factor f(r).
-3*r*(r - 1)**2*(r + 1)
Suppose 7*p + 3*q - 8 = 0, -1 = -5*p + 5*q + 19. Solve 0 + 1/3*l**p + 1/3*l = 0.
-1, 0
Suppose 3*v = 3*z + 15, 11 = 4*v - 2*v - 3*z. Let l be (213/v)/(2/8). Factor 58*h**5 + 16*h**2 + l*h**4 - 208*h**5 + 7*h**4 - 104*h**3.
-2*h**2*(3*h - 2)*(5*h - 2)**2
Let y(p) be the second derivative of -p**6/60 + 9*p**5/160 - p**4/16 + p**3/48 + 9*p. Factor y(q).
-q*(q - 1)**2*(4*q - 1)/8
Let d(b) be the first derivative of 3*b + 3*b**3 + 3 - 9/2*b**2 - 3/4*b**4. Determine a so that d(a) = 0.
1
Let d(z) = -4 + 3*z - 6*z + z + 0*z. Let h be d(-3). Suppose 3*v**2 - 2*v**2 + 4*v**2 - 2*v**h = 0. What is v?
0
Suppose -3 - 41 = -11*y. Let j(o) be the second derivative of 0*o**3 + 0 + 1/6*o**y + 0*o**2 - 4*o - 3/20*o**5 + 1/30*o**6. Factor j(z).
z**2*(z - 2)*(z - 1)
Let p(r) be the first derivative of 2/15*r**5 - 7/12*r**4 + 0*r**2 + 0*r + 2 + 7/18*r**6 - 2/9*r**3. Determine b, given that p(b) = 0.
-1, -2/7, 0, 1
Let i(d) = -5*d**4 + 5*d**2 - 3*d + 3. Let u(q) = -q**3 + 16. Let k be u(0). Let y(z) = 26*z**4 - 26*z**2 + 16*z - 16. Let p(c) = k*i(c) + 3*y(c). Factor p(o).
-2*o**2*(o - 1)*(o + 1)
Let y(w) be the second derivative of -5*w**7/42 + 4*w**6/3 - 9*w**5/2 + 45*w**3/2 - 10*w. Factor y(b).
-5*b*(b - 3)**3*(b + 1)
Suppose 2*k - 5*k = -6. Let 2 - 5*w**2 + w + 4*w**3 + 0 - k = 0. Calculate w.
0, 1/4, 1
Let n(i) be the first derivative of -i**4/4 + 4*i**3/3 - 3*i**2/2 + i + 1. Let s be n(2). Factor -2/5 + 2/5*h**2 + 2/5*h**s - 2/5*h.
2*(h - 1)*(h + 1)**2/5
Let c(h) be the third derivative of -2*h**2 + 0*h + 5/42*h**5 - 5/14*h**4 + 3/7*h**3 + 0. Factor c(u).
2*(5*u - 3)**2/7
Factor 0 + 12/7*m**2 - 12/7*m - 3/7*m**3.
-3*m*(m - 2)**2/7
Suppose 3*g - 16 = g. Suppose -d = 3*d - g. Factor -b**3 - 3*b**3 + 2*b**3 + 2*b**d.
-2*b**2*(b - 1)
Let a(g) be the second derivative of -1/14*g**3 + 0*g**2 + 5*g + 1/28*g**4 + 0. Determine d so that a(d) = 0.
0, 1
Let l(n) be the third derivative of n**5/60 + 2*n**4/3 + 32*n**3/3 - 6*n**2. Let l(d) = 0. What is d?
-8
Let y(n) = -3*n**3 + 9*n**2 + 52*n + 36. Let b(s) = 2*s**3 - 10*s**2 - 51*s - 36. Let a(u) = 4*b(u) + 3*y(u). Let a(v) = 0. What is v?
-6, -1
Let y(o) be the first derivative of 5*o**6/21 - 16*o**5/35 - 9*o**4/14 + 16*o**3/21 + 4*o**2/7 - 15. Suppose y(v) = 0. What is v?
-1, -2/5, 0, 1, 2
Let v be 12 + 0 - (-1 - 2). Let y = -15 + v. Factor -1/4*z**2 + y + 1/4*z.
-z*(z - 1)/4
Let d(g) = g**2 - g - 1. Let t(y) = -2*y**2 - 2*y + 8. Let i(m) = 4*d(m) + t(m). Let i(w) = 0. What is w?
1, 2
Let f(g) = -8*g**2 - 40*g - 100. Let h(b) = -b**2. Let c(v) = f(v) - 4*h(v). Let c(p) = 0. Calculate p.
-5
Suppose 2*w + 2*t - 23 = -3, 4*w - 4*t = 40. Let a be 8/(-30)*(-45)/w. Suppose 9/5*c - a - 3/5*c**2 = 0. Calculate c.
1, 2
Let z = 8 + -5. Suppose a + z*a - 12 = 0. Factor -2*u**3 - 2*u**a + 2*u**2 + u**4 - 3*u**4 + 2*u + 2*u**3.
-2*u*(u - 1)*(u + 1)**2
Let b(v) be the first derivative of -2*v**5/35 - v**4/14 - 11. Solve b(k) = 0 for k.
-1, 0
Let u(w) be the first derivative of -3/2*w - 9/4*w**2 - 3/8*w**4 - 3/2*w**3 - 2. Suppose u(o) = 0. What is o?
-1
Let k(w) be the third derivative of w**8/840 - w**7/210 + w**5/30 - w**4/12 + w**3/2 + w**2. Let m(h) be the first derivative of k(h). Factor m(l).
2*(l - 1)**3*(l + 1)
Find d, given that 3/2*d**5 + 0*d + 0*d**2 - 1/2*d**3 + 0 - d**4 = 0.
-1/3, 0, 1
Factor -31*v**2 + 51 - v**2 - 75*v - 49*v**2 - 45.
-3*(v + 1)*(27*v - 2)
Let i(g) be the first derivative of -g**8/1120 + g**7/280 - g**6/240 + 2*g**3/3 - 1. Let b(l) be the third derivative of i(l). Solve b(n) = 0.
0, 1
Let v(n) be the first derivative of -3/20*n**4 + 2/5*n**3 - 3/10*n**2 + 0*n + 3. Solve v(a) = 0 for a.
0, 1
Let d(w) be the first derivative of -w**4 - 8*w**3/3 - 2*w**2 + 10. Determine s, given that d(s) = 0.
-1, 0
Let r(m) = m**3 + 15*m**2. Let i be r(-15). Let c(j) be the second derivative of -1/36*j**4 + 2*j + i + 0*j**2 + 0*j**3. Factor c(k).
-k**2/3
Let c(d) be the first derivative of d**6/21 + 12*d**5/35 + 6*d**4/7 + 20*d**3/21 + 3*d**2/7 - 24. Let c(i) = 0. What is i?
-3, -1, 0
Let d(v) = v**3 + 5*v**2. Let q be d(-5). Let b be (-7)/3 - (-3 - q). Solve 32/9*w**3 - b*w**2 - 4/9*w - 28/9*w**5 + 0 + 2/3*w**4 = 0.
-1, -2/7, 0, 1/2, 1
Let w = 2/107 - -87/1070. Let u(i) be the first derivative of 0*i**2 + 0*i**3 + 2 - w*i**5 + 0*i - 1/8*i**4. Find b such that u(b) = 0.
-1, 0
Suppose 4 = -l - g, l + 2*g + 8 = -3*l. Let p(o) be the second derivative of -o + 1/27*o**3 - 1/90*o**5 + 0*o**4 + l*o**2 + 0. Factor p(x).
-2*x*(x - 1)*(x + 1)/9
Let g(j) be the second derivative of -3*j - 1/8*j**4 + 1/4*j**3 + 0 - 1/4*j**2 + 1/40*j**5. Let g(d) = 0. What is d?
1
Let s(n) = -2*n**3 - 2*n**2 + 2*n + 1. Let g be s(-2). Let w = 8/5 + -6/5. Solve 0*p + w*p**g + 4/5*p**4 + 0*p**2 + 2/5*p**3 + 0 = 0.
-1, 0
Suppose 0 = -q - 5*s, 4*q = -s - 0*s. Factor 1/4*h**2 + 1/4*h**4 + q + 1/2*h**3 + 0*h.
h**2*(h + 1)**2/4
Let p = 5716/7659 + -41/333. Let o = p - -1/23. What is g in 0 + 0*g + o*g**3 - 4/3*g**4 + 0*g**2 = 0?
0, 1/2
Let t(c) = -8*c + 12. Let o(q) = -q**2 + q - 1. Let g(u) = 4*o(u) + t(u). Suppose g(k) = 0. Calculate k.
-2, 1
Suppose 90 = -5*q - 5*j, 5*j = -0*q - 2*q - 33. Let p = q - -59/3. Factor -2/3 - 4/3*h - p*h**2.
-2*(h + 1)**2/3
Let v(j) be the first derivative of -j**6/720 + j**5/60 - j**4/12 + 4*j**3/3 + 2. Let u(h) be the third derivative of v(h). Let u(q) = 0. Calculate q.
2
Suppose v - 20 = 7. Suppose 8 = 3*a + 2*y, -2*a + v = -0*a - 3*y. Solve a - 2*s**4 - 6 = 0 for s.
0
Let g(j) be the second derivative of j**5/30 - j**4/6 + j**3/3 - j**2 - j. Let z(b) be the first derivative of g(b). Factor z(y).
2*(y - 1)**2
Let a(t) be the second derivative of -5*t**7/42 + 2*t**6/5 + 11*t**5/20 - 13*t**4/6 - 2*t**3 + 4*t**2 + 27*t. Solve a(p) = 0 for p.
-1, 2/5, 2
Let v be (-2)/(-2)*-2 + 4. Let f(j) be the first derivative of v + 0*j**3 + 1/16*j**4 + 0*j**2 + 0*j. Factor f(r).
r**3/4
Let w = -653 - -1307/2. Factor -w*h**2 + 0 - 1/4*h**3 - 1/4*h.
-h*(h + 1)**2/4
Let h(q) be the second derivative of 2*q + 0*q**3 + 1/42*q**4 - 1/70*q**5 + 0 + 0*q**2. Determine a, given that h(a) = 0.
0, 1
Let v(a) be the second derivative of 2/3*a**3 + 0*a**4 - a + 0 - 1/5*a**5 + 1/15*a**6 - a**2. Factor v(p).
2*(p - 1)**3*(p + 1)
Factor 2/3 - 1/3*y**2 - 1/3*y.
-(y - 1)*(y + 2)/3
Let j(b) be the first derivative of -2*b**3/27 + b**2 - 16*b/9 + 22. Find v, given that j(v) = 0.
1, 8
Let z(m) be the first derivative of -4*m**5/5 - 2*m**4 + 4*m**3/3 + 4*m**2 + 12. Factor z(k).
-4*k*