 the first derivative of z(v). Factor m(b).
b**2*(b - 1)*(b + 1)/3
Let r(t) = -2*t**2 - 14*t + 14. Let j(u) = 2*u**2 - u. Let g(d) = -4*j(d) - 2*r(d). Determine f, given that g(f) = 0.
1, 7
Factor 2/17*d + 0 + 2/17*d**2 - 2/17*d**3 - 2/17*d**4.
-2*d*(d - 1)*(d + 1)**2/17
Let p(m) be the first derivative of -m**4/4 - m**3/3 + m**2/2 + m + 1. Find i, given that p(i) = 0.
-1, 1
Suppose 5*o + 4*o - 27 = 0. Let w(u) be the second derivative of 0 + 0*u**2 + 0*u**o - 1/50*u**5 + 0*u**4 + 1/75*u**6 - u. What is c in w(c) = 0?
0, 1
Let t(q) be the second derivative of -q**7/126 - q**6/30 + q**4/9 + 7*q. What is n in t(n) = 0?
-2, 0, 1
Let f = 0 - -8. Solve -2*p**4 - 2*p**3 + 0*p**3 - 2 + p**3 - f*p - 12*p**2 - 7*p**3 = 0 for p.
-1
Let -m**5 - 4894*m**3 + 8*m**2 + 2*m**5 + 4888*m**3 - 3*m = 0. What is m?
-3, 0, 1
Let y(q) be the second derivative of -q + 0 + 1/30*q**5 - 1/9*q**3 - 1/6*q**2 + 1/90*q**6 + 0*q**4. Solve y(s) = 0.
-1, 1
Let f be (-2)/15 - 4/(-30). Let h(m) be the second derivative of 0*m**5 + f + 0*m**3 + 1/45*m**6 + 1/3*m**2 + m - 1/9*m**4. Solve h(q) = 0.
-1, 1
Suppose 0 = -2*j + 5*j. Let h(n) be the second derivative of -3/40*n**6 - n + 5/48*n**4 + 1/12*n**3 + j*n**2 + 0 - 3/40*n**5. Find o such that h(o) = 0.
-1, -1/3, 0, 2/3
Let x(q) = -q**2 + 13*q - 36. Let b be x(9). Factor -2/5*v**3 - 2/5*v**4 + 2/5*v**2 + 2/5*v + b.
-2*v*(v - 1)*(v + 1)**2/5
Let j(n) be the third derivative of -1/6*n**4 + 0 + 0*n**3 + 0*n - 3*n**2 - 1/60*n**6 + 1/10*n**5. Factor j(t).
-2*t*(t - 2)*(t - 1)
Let t(f) be the first derivative of f**8/84 + f**7/70 - 7*f**6/90 - f**5/10 + f**4/3 + 7*f**3/3 - 2. Let p(x) be the third derivative of t(x). Factor p(z).
4*(z - 1)*(z + 1)**2*(5*z - 2)
Let n(p) be the first derivative of -p**6/2 - 12*p**5/5 - 15*p**4/4 - 2*p**3 - 18. Determine a so that n(a) = 0.
-2, -1, 0
Factor -3*r**5 + 0 + 6/5*r + 3/5*r**2 - 27/5*r**3 - 39/5*r**4.
-3*r*(r + 1)**3*(5*r - 2)/5
Suppose -5*l + 11 + 14 = 0, 0 = 3*h - 3*l + 15. Suppose -1/4*z**5 + h - 3/4*z**3 + 0*z - 3/4*z**4 - 1/4*z**2 = 0. Calculate z.
-1, 0
Let p(a) be the second derivative of a**7/21 - 2*a**6/15 - a**5/10 + a**4/3 + 23*a. Factor p(h).
2*h**2*(h - 2)*(h - 1)*(h + 1)
Let l be 3*40/45 + -2. What is a in -2/3*a**3 - 2/3*a**4 + l*a + 2*a**2 - 4/3 = 0?
-2, -1, 1
Suppose 21*i**4 - 10*i**2 - 5*i + 10*i**3 - 6*i**4 - 10*i + 5*i**5 - 5 = 0. What is i?
-1, 1
Let j(u) = u + 8. Let y be j(0). Factor -y*m**2 + 0*m**3 - 4*m + 3*m**3 - 4*m**3 - 3*m**3.
-4*m*(m + 1)**2
Let f(x) be the first derivative of x**8/504 + x**7/315 - x**6/180 - x**5/90 - x**2/2 - 2. Let o(s) be the second derivative of f(s). Let o(q) = 0. Calculate q.
-1, 0, 1
Let l(u) = -u - 8. Let z be l(-10). Factor 4*a**2 + 2*a**z + 2*a**2 - 5*a**2 - 6*a.
3*a*(a - 2)
Let b(v) = 3*v**2 - 2 + 2 + 2*v**3 - 1 - v**3. Let z be b(-2). Find t, given that 8/5*t + 12/5*t**2 + 8/5*t**z + 2/5 + 2/5*t**4 = 0.
-1
Let g = 33/7 - 158/35. Let f = 91/110 + -5/22. Factor 4/5*m**3 - g*m + 0 + f*m**2.
m*(m + 1)*(4*m - 1)/5
Factor -3/2*x**3 - 324 - 27*x**2 - 162*x.
-3*(x + 6)**3/2
Suppose -2*q - 3*x = -q + 7, -q - 1 = x. Solve 6*m**2 + q*m**3 - 2*m**3 - 8 + 2 + 9*m - 9*m**3 = 0.
-1, 2/3, 1
Let c = 109/10 + -21/2. Let x = 3 - 0. Factor c*p + 0 - 2/5*p**x + 2/5*p**4 - 2/5*p**2.
2*p*(p - 1)**2*(p + 1)/5
Let k(m) be the second derivative of m**7/168 - m**6/24 + m**5/10 - m**4/12 + 8*m. Factor k(c).
c**2*(c - 2)**2*(c - 1)/4
Let 1 - 1/3*h**2 + 2/3*h = 0. Calculate h.
-1, 3
Let h(y) be the second derivative of -y**5/60 - y**4/12 - y**3/9 + 44*y. Factor h(g).
-g*(g + 1)*(g + 2)/3
Let q be 2*(-1 - 92/24). Let l = -9 - q. Find g such that 3*g**3 + 0 + l*g - 11/3*g**2 = 0.
0, 2/9, 1
Let o(d) be the second derivative of -d**6/30 - d**5/20 + d**4/4 + d**3/6 - d**2 + 19*d. Factor o(l).
-(l - 1)**2*(l + 1)*(l + 2)
Let v(t) be the third derivative of -t**6/420 - t**5/210 + 7*t**2. Suppose v(q) = 0. Calculate q.
-1, 0
Let i(q) be the third derivative of q**7/105 - q**6/10 + 2*q**5/5 - 5*q**4/6 + q**3 - 7*q**2. Factor i(t).
2*(t - 3)*(t - 1)**3
Let i = -133 + 933/7. Factor -2/7*j**3 + 0 + i*j**5 + 2/7*j**2 + 0*j - 2/7*j**4.
2*j**2*(j - 1)**2*(j + 1)/7
Let p be (-2)/(-1) - (-3 + 0 - -1). Suppose -2*d = -5*d - 5*k - 11, 2*d + 5*k + 14 = 0. Let 3*r**3 - 7*r**p + 32*r**5 - 9*r**4 - r**d = 0. Calculate r.
0, 1/4
Let s be (-2 - -6)*(-1 - -2). Suppose 5 + 3 = -4*k + 5*v, 0 = 4*k - 3*v. Factor 0*j + 0*j**2 - 1/4*j**k + 1/4*j**s + 0.
j**3*(j - 1)/4
Let b(w) = -5*w**2 - 19*w - 5. Let g(h) = h**2 - h - 1. Let t(o) = 2*b(o) - 18*g(o). Factor t(c).
-4*(c + 1)*(7*c - 2)
Let v(o) be the third derivative of -3*o**8/2240 + o**7/420 + o**6/80 - o**5/20 + o**4/8 - 6*o**2. Let w(g) be the second derivative of v(g). Solve w(b) = 0.
-1, 2/3, 1
Factor 5*x**3 - 4 - x**3 - 19*x**2 + 7*x**2 + 12*x.
4*(x - 1)**3
Factor 6/7*d**5 + 0 + 0*d + 0*d**3 + 0*d**2 + 4/7*d**4.
2*d**4*(3*d + 2)/7
Let u be (1 + 3/(-2))*0. Suppose -5*b - 13 = -u*f + f, 3*b = -4*f - 1. Find c, given that 0*c + 0*c**f - 2/3*c**4 + 0 + 0*c**3 = 0.
0
Let g(m) be the first derivative of -m**4/4 + 3*m**3/2 - 3*m**2 - 2*m + 4. Let v(h) be the first derivative of g(h). Factor v(o).
-3*(o - 2)*(o - 1)
Factor -8*o**3 + 6*o**2 + 4*o - 6 - o**3 + 6*o - o.
-3*(o - 1)*(o + 1)*(3*o - 2)
Suppose 5*c + 12 = 27, 3*c = z + 5. Suppose -6*k + k = -d - 12, -z*k = -4*d. Determine x so that 0*x**k - 1/5*x**4 + 0*x + 0 + 1/5*x**5 + 0*x**2 = 0.
0, 1
Factor -16*d**3 + 5*d**5 + 19*d**3 + 5*d - 13*d**3.
5*d*(d - 1)**2*(d + 1)**2
Let q(p) be the first derivative of 8 + 3/20*p**4 - 12/5*p + 12/5*p**2 - p**3. Factor q(g).
3*(g - 2)**2*(g - 1)/5
Let j(t) = -3*t**2 - t + 1. Let b be j(1). Let l = b - -5. Factor 4*p**2 - 3*p**l + 2*p**2.
3*p**2
Let h(n) = 28*n**3 + 12*n**2 - 24. Let d(l) = -l**3 - l**2 + 1. Let j(x) = -24*d(x) - h(x). Factor j(b).
-4*b**2*(b - 3)
Suppose 0 = -j - 4*j + 230. Let r = -137/3 + j. What is i in -r*i**2 + 1/3 + 0*i = 0?
-1, 1
Let u(b) be the first derivative of 2 - 4/3*b**3 + 4*b**2 - 16/3*b + 1/6*b**4. Factor u(g).
2*(g - 2)**3/3
Suppose -14 + 54 = 5*f. Factor -6*u**3 - u**5 + f*u**3 - u + u**4 - u**4.
-u*(u - 1)**2*(u + 1)**2
Let f(w) be the third derivative of w**6/160 + w**5/20 + 5*w**4/32 + w**3/4 + 2*w**2. Factor f(k).
3*(k + 1)**2*(k + 2)/4
Let b(x) = -x - 1. Let v(q) = q**2 - 4*q + 1. Let t be v(2). Let s be b(t). What is j in 0*j**4 + 2*j**4 - 4*j**3 - 2*j**s + 4*j**2 = 0?
0, 1
Let o = 4 - 2. Factor -3*h - 4*h**o - 1 + 3 + h + 2*h**4 - 2*h**5 + 4*h**3.
-2*(h - 1)**3*(h + 1)**2
Let z be 20/(-15)*(-2)/5. Let h(t) be the first derivative of 1 - t**4 - 8/9*t**3 - 1/3*t**2 + 0*t - 1/9*t**6 - z*t**5. Factor h(k).
-2*k*(k + 1)**4/3
Factor -3/2*v - 3/2*v**2 + 3.
-3*(v - 1)*(v + 2)/2
Let d(h) be the first derivative of -h**6/3 + h**4 - h**2 - 7. Solve d(y) = 0 for y.
-1, 0, 1
Find d such that 25 - 5*d**4 - 25 - 10*d**3 - 5*d**2 = 0.
-1, 0
Let d(s) be the second derivative of s**7/357 + 2*s**6/255 - s**5/85 - 4*s**4/51 - 7*s**3/51 - 2*s**2/17 - 18*s. Factor d(c).
2*(c - 2)*(c + 1)**4/17
Let r(s) be the third derivative of s**7/1470 + 16*s**2. Factor r(m).
m**4/7
Let p = -3 + 10. Let t(z) be the third derivative of 0*z - 1/36*z**4 - 2*z**2 + 1/9*z**3 + 1/36*z**6 + 0 - 2/315*z**p - 1/30*z**5. Factor t(u).
-2*(u - 1)**3*(2*u + 1)/3
Suppose -5*p - l + 12 = 0, -3*l - 3 = 3*p - 15. Find v, given that -1/4*v**p - 3/2*v - 9/4 = 0.
-3
Let b be ((-16)/6)/((-2)/3). Factor -q**2 + 0*q**4 + 3*q**5 + b*q**4 - q**3 - 3*q**4 - 2*q**5.
q**2*(q - 1)*(q + 1)**2
Let z(x) be the first derivative of -1 + 1/2*x**4 - 2*x**3 + 3*x**2 - 2*x. Factor z(n).
2*(n - 1)**3
Let m(c) be the first derivative of c**4/18 - 10*c**3/9 + 25*c**2/3 - 250*c/9 + 26. Factor m(p).
2*(p - 5)**3/9
Let h(g) = g. Let u be h(0). Let r(w) be the second derivative of 1/12*w**4 + 0 + 1/10*w**6 + 2*w + u*w**2 - 1/42*w**7 + 0*w**3 - 3/20*w**5. Factor r(m).
-m**2*(m - 1)**3
Suppose 0 = 5*f - 4 - 6. Let g be (18/18)/(1/f). Solve l**g + 2/3*l**3 - 4/3 - 1/3*l**4 - 4/3*l = 0.
-1, 2
Let m(v) be the first derivative of -v**5/30 + v**3/3 - v**2 + 1. Let p(o) be the second derivative of m(o). What is h in p(h) = 0?
-1, 1
Let t(v) be the second derivative of -v**8/2240 - v**7/840 + v**6/240 + v**5/40 - v**4/12 - 6*v. Let a(q) be the third derivative of t(q). Factor a(c).
-3*(c - 1)*(c + 1