et g(d) be the second derivative of d**9/15120 + d**8/3360 + d**7/2520 + d**4/12 - 2*d. Let f(v) be the third derivative of g(v). Factor f(b).
b**2*(b + 1)**2
Factor 0*b + 1/3*b**3 + 0 + 0*b**2 + 1/3*b**4.
b**3*(b + 1)/3
Let u(w) = -40*w**5 - 12*w**4 + 16*w**3 + 20*w**2 - 16*w - 8. Let s(p) = p**5 - p**4 + p**2 + p. Let j(y) = -20*s(y) - u(y). Factor j(t).
4*(t - 1)*(t + 1)**3*(5*t - 2)
Factor -18*p**2 + 140*p - 120 - 25*p**2 + 5*p**3 - 7*p**2.
5*(p - 6)*(p - 2)**2
Let w(p) be the third derivative of 1/210*p**5 - 1/420*p**6 + 0*p**4 + 3*p**2 + 0 + 0*p + 0*p**3. What is u in w(u) = 0?
0, 1
Let u(t) be the third derivative of t**8/7 - 12*t**7/35 - 23*t**6/40 + 3*t**5/4 - t**4/4 - 19*t**2. What is k in u(k) = 0?
-1, 0, 1/4, 2
Let x(a) be the second derivative of a**4/6 - 2*a**3/3 - 20*a. Solve x(n) = 0 for n.
0, 2
Let o be 4/(-10) - 26/(-40). Let x = 2 - 7/4. Factor -o + 1/2*k**3 - 1/4*k + 1/2*k**2 - x*k**4 - 1/4*k**5.
-(k - 1)**2*(k + 1)**3/4
Factor 0 + 3/8*f - 3/8*f**3 - 3/8*f**4 + 3/8*f**2.
-3*f*(f - 1)*(f + 1)**2/8
Let a(x) be the second derivative of 2*x**7/35 + 3*x**6/40 - x**5/20 + 2*x**2 - 2*x. Let f(c) be the first derivative of a(c). Solve f(k) = 0.
-1, 0, 1/4
Let b(p) be the third derivative of -p**8/1512 + 4*p**7/945 + p**6/270 - 2*p**5/45 - p**4/12 + 3*p**2. What is k in b(k) = 0?
-1, 0, 3
Factor 4*u**2 - 2*u**4 - 2*u**3 - 4*u**2.
-2*u**3*(u + 1)
Let h(m) be the first derivative of m**6/9 + m**5/2 + 2*m**4/3 + m**3/6 - m**2/6 - 8. Solve h(c) = 0.
-2, -1, 0, 1/4
Let u(r) be the second derivative of -r**4/6 - 5*r**3/3 - 4*r**2 - 3*r. Solve u(s) = 0.
-4, -1
Let t = -374/5 + 75. Let q(j) be the first derivative of -t*j**2 + 0*j + 2/15*j**3 - 2. Factor q(s).
2*s*(s - 1)/5
Let a = -4783397/28060 - -10476/61. Let j = a + -2/115. Determine k so that 1/2*k**2 - j*k**3 + 0*k + 0 + 3/4*k**4 = 0.
0, 2/3, 1
Let v(f) = 4*f**3 + 2*f**2 + 5*f + 5. Let n(z) = z**3 + z + 1. Let u(o) = -15*n(o) + 3*v(o). Factor u(i).
-3*i**2*(i - 2)
Let l(m) be the second derivative of m**6/105 - m**5/70 - m**4/14 + 5*m**3/21 - 2*m**2/7 - 3*m - 5. Determine j, given that l(j) = 0.
-2, 1
Let p = -83 + 47. Let i be 4*(100/p + 3). Factor i + 8/3*l - 14/9*l**2.
-2*(l - 2)*(7*l + 2)/9
Let d be 15/20*9*1. Let v be (-2)/18 - (-2)/18. Factor -63/4*t**3 - 12*t**2 + v - 3*t - d*t**4.
-3*t*(t + 1)*(3*t + 2)**2/4
Suppose 14 = 2*k + 4*f, 2*k - 5 - 8 = -3*f. Let j(z) be the third derivative of -2*z**2 + 1/30*z**k + 0*z + 1/3*z**3 + 0 - 1/6*z**4. Factor j(u).
2*(u - 1)**2
Let m(s) be the first derivative of 2*s**3 - 2*s**2 + 6*s - 1. Let a(i) = -4*i**2 + 3*i - 4. Let w(q) = -8*a(q) - 5*m(q). Suppose w(o) = 0. Calculate o.
1
Factor -3/5*y - 1/5 - 3/5*y**2 - 1/5*y**3.
-(y + 1)**3/5
Let l = 3 + -4. Let c be 2 - (0 - 3 - l). Factor 2*u**2 - 4*u**2 + 0*u**4 + 2*u**5 + c*u**4 - 6*u**3 + 4*u - 2*u**4.
2*u*(u - 1)**2*(u + 1)*(u + 2)
Let r = -18 - -23. Let u(x) be the second derivative of 0*x**3 + x - 1/30*x**4 + 1/75*x**6 + 0*x**2 + 0 + 2/105*x**7 - 1/25*x**r. Let u(d) = 0. Calculate d.
-1, -1/2, 0, 1
Let r(i) be the second derivative of 1/54*i**4 + 1/27*i**3 + 0*i**2 + i + 0. Factor r(w).
2*w*(w + 1)/9
Let n(d) be the first derivative of 2/25*d**5 - 2/5*d**4 + 0*d + 2/3*d**3 + 2 - 2/5*d**2. Find g, given that n(g) = 0.
0, 1, 2
Suppose 0 = -j - 2. Let q = -2 - j. Factor q*k - 10/9*k**4 + 4/9*k**2 + 2/3*k**3 + 0.
-2*k**2*(k - 1)*(5*k + 2)/9
Let s(p) be the first derivative of 4*p**5/5 - 3*p**4 + 4*p**3 - 2*p**2 - 15. Let s(y) = 0. Calculate y.
0, 1
Let a(k) be the first derivative of 1/15*k**5 - 9 - 1/9*k**3 - 1/6*k**2 + 1/12*k**4 + 0*k. Suppose a(t) = 0. What is t?
-1, 0, 1
Suppose -17*t + 16*t = 0. Suppose t - 2/5*c**2 + 2/5*c**3 + 2/5*c**4 + 0*c - 2/5*c**5 = 0. Calculate c.
-1, 0, 1
Let a(z) be the third derivative of -z**11/110880 + z**9/10080 - z**7/1680 + z**5/20 + 6*z**2. Let n(b) be the third derivative of a(b). Factor n(y).
-3*y*(y - 1)**2*(y + 1)**2
Suppose 8*d = -0*d + 16. Solve 1 - i + 1/4*i**d = 0 for i.
2
Let f(o) be the second derivative of -o**7/5040 + o**6/480 - o**5/120 + o**4/6 + 2*o. Let q(p) be the third derivative of f(p). Factor q(t).
-(t - 2)*(t - 1)/2
Suppose -2*h - 11 = -15, -5*o = -h + 2. Solve 1/3*n**2 + 1/3*n + o = 0.
-1, 0
What is y in -4/9*y - 2/9*y**4 + 2/9 + 0*y**2 + 4/9*y**3 = 0?
-1, 1
Let a(q) = -3*q**3 + 6*q**2 + 3*q. Let l(y) = y**3 - y**2 - y. Let j(c) = a(c) + 6*l(c). What is o in j(o) = 0?
-1, 0, 1
Factor -2*y**4 + 2*y**5 - 2*y**3 - y**5 + y**5 + 2*y**2.
2*y**2*(y - 1)**2*(y + 1)
Suppose 1 = -3*t - 29. Let d be t/(-84) + (-8)/(-48). Find v, given that -d*v**2 - 2/7*v + 0 = 0.
-1, 0
Let f(t) be the second derivative of -t + 1/220*t**6 + 0*t**3 + 0*t**4 + 0 + 1/165*t**5 - 2*t**2. Let z(p) be the first derivative of f(p). Factor z(s).
2*s**2*(3*s + 2)/11
Suppose h = -2*f + 2*h + 4, 0 = 3*h + 12. Suppose f = -c + 2 + 3. Factor x + 4*x**4 + x - 4*x**2 + 3*x**5 - c*x**5.
-2*x*(x - 1)**3*(x + 1)
Let g(u) be the first derivative of -2*u**5/15 - 2*u**4/3 - 2*u**3/3 + 4*u**2/3 + 8*u/3 + 1. Solve g(h) = 0 for h.
-2, -1, 1
Let v(k) = k**3 - 2*k**2 + 2. Let f be v(2). Factor 2*b**2 - b**2 + f*b - b.
b*(b + 1)
Suppose 0 = -x + j - 3 + 5, -2*x + 6 = -j. Let 2/3*d - d**2 + d**5 - 3*d**3 + 0 - 1/3*d**x = 0. What is d?
-1, 0, 1/3, 2
Let o(k) = -9*k**2 - 13*k - 15. Let q(b) = -b**2 - b - 1. Let g(x) = 2*o(x) - 22*q(x). Factor g(c).
4*(c - 2)*(c + 1)
Let v(r) be the first derivative of -r**6/720 - r**5/60 - r**4/12 - r**3 - 2. Let o(f) be the third derivative of v(f). Factor o(k).
-(k + 2)**2/2
Let q be (-6)/((-6)/(-5)) - (-5 + 0). Factor 9/5*m**2 + 6/5*m + q*m**3 - 3/5*m**4 + 0.
-3*m*(m - 2)*(m + 1)**2/5
Let f = 338/7 - 48. Solve 2/7*q**3 - f*q**2 + 0*q + 0 = 0 for q.
0, 1
Let u(r) be the first derivative of -r**5/30 + r**4/6 - r**3/9 - r**2/3 + r/2 - 8. Find s, given that u(s) = 0.
-1, 1, 3
Let n(j) = j + 17. Let c be n(-13). Suppose 0*o = c*o. Let o + 2/5*v**2 + 2/5*v = 0. What is v?
-1, 0
Let l be ((-1)/6)/((-10)/(-110)). Let y = 5/2 + l. Factor y*k**3 + 2/3*k**2 - 2/3*k - 2/3.
2*(k - 1)*(k + 1)**2/3
Let i(g) = -3*g**4 - 27*g**3 - 51*g**2 - 33*g - 6. Let d(m) = -9*m**4 - 80*m**3 - 152*m**2 - 98*m - 17. Let s(n) = -6*d(n) + 17*i(n). Factor s(k).
3*k*(k + 1)*(k + 3)**2
Let i(a) be the second derivative of 0 + 3*a**2 + 5/4*a**4 - 7/2*a**3 - 2*a. Suppose i(t) = 0. Calculate t.
2/5, 1
Let n(y) be the second derivative of y**9/5040 + y**8/560 + y**7/168 + y**6/120 - y**4/12 + 3*y. Let q(b) be the third derivative of n(b). Factor q(j).
3*j*(j + 1)**2*(j + 2)
Let q(g) be the second derivative of g**6/10 - 7*g. Find z such that q(z) = 0.
0
Let t(u) = -u**3 + 6*u**2 + 2*u - 9. Let q be t(6). Find w, given that 4*w**2 - w**4 - 8*w**q - 7*w**4 + 12*w**4 = 0.
0, 1
Let m(s) be the second derivative of s**5/50 + s**4/30 - s**3/3 + 3*s**2/5 + 7*s. Factor m(p).
2*(p - 1)**2*(p + 3)/5
Suppose -16 + 13 = -s. Let n(z) be the first derivative of 0*z - 2/3*z**3 - z**2 - s. Suppose n(j) = 0. Calculate j.
-1, 0
Let a(y) = y - 14. Let p be a(14). Suppose p*q = q. Find l such that 1/4*l**3 - 3/4*l**2 + 1/2*l + q = 0.
0, 1, 2
Let z(u) be the second derivative of -u**6/15 + 13*u**5/10 - 21*u**4/2 + 45*u**3 - 108*u**2 - 23*u. Factor z(x).
-2*(x - 4)*(x - 3)**3
Let i = -1 + 4. Let r(c) be the first derivative of c - 4 + 3*c**2 + 6 + i*c**3 + 0*c. Solve r(d) = 0.
-1/3
Let f = 6 + -10. Let o = f - -6. Factor 2*u**2 + 3*u**4 - o*u**4 + 1 - 4*u**2.
(u - 1)**2*(u + 1)**2
Let u(d) be the first derivative of 12*d**5/5 - 21*d**4/4 + 2*d**3 + 3*d**2/2 + 11. Determine o so that u(o) = 0.
-1/4, 0, 1
Let x(b) be the first derivative of 2*b**3/15 + 4*b**2/5 + 6*b/5 - 12. Factor x(c).
2*(c + 1)*(c + 3)/5
Let o(q) be the third derivative of -q**8/168 - q**7/105 + q**6/60 + q**5/30 + 8*q**2. Suppose o(m) = 0. What is m?
-1, 0, 1
Let -2*b**2 - b**2 - 4*b - 4 + 2*b**2 = 0. Calculate b.
-2
Let a(d) be the first derivative of -3*d**4/28 + 3*d**3/7 - 12*d/7 + 1. Factor a(j).
-3*(j - 2)**2*(j + 1)/7
Let r(s) = 4*s**2. Let f be r(1). Suppose 4*b = 5*b. Find m such that 2/11*m**3 - 2/11*m**5 - 2/11*m**f + 0 + b*m + 2/11*m**2 = 0.
-1, 0, 1
Suppose -2/19*t**4 + 8/19*t**3 + 0*t + 0 - 8/19*t**2 = 0. Calculate t.
0, 2
Let s(h) be the first derivative of h**3/33 - h/11 - 5. Factor s(n).
(n - 1)*(n + 1)/11
Let n(l) = l**3 -