econd derivative of o**6/15 + o**5/5 + o**4/6 - 8*o. Factor h(q).
2*q**2*(q + 1)**2
Let n(b) be the second derivative of -2*b**6/5 + 2*b**5 - 3*b**4 + 4*b**3/3 - 3*b. Determine t so that n(t) = 0.
0, 1/3, 1, 2
Suppose 4*b - 73 = -65. Factor -2*c - 2/3*c**3 + 8/3*c**b + 0.
-2*c*(c - 3)*(c - 1)/3
Suppose 0 = 15*o - 12*o - 39. Suppose 67/2*y**3 - 7/2*y + 1 - o*y**2 + 42*y**4 = 0. What is y?
-1, -1/3, 1/4, 2/7
Factor 15*k + 1 - 3*k**3 + 6*k**2 - 1 - 18*k.
-3*k*(k - 1)**2
Let o(k) be the second derivative of -k**5/50 + k**4/6 + k**3/15 - k**2 + 12*k. What is p in o(p) = 0?
-1, 1, 5
Let i(o) be the first derivative of o**4/24 + o**3/6 + 4*o + 3. Let l(f) be the first derivative of i(f). Factor l(p).
p*(p + 2)/2
Let y = -605/102 - -9/34. Let c = y + 6. Factor -1/3*d**5 + 0 + c*d + 2/3*d**4 + 0*d**3 - 2/3*d**2.
-d*(d - 1)**3*(d + 1)/3
Let t = -3 - -3. Suppose -2 = -u - t*u. Factor -2 + 0*w**u + 0*w**2 + 2*w**2.
2*(w - 1)*(w + 1)
Suppose 5*l = -z + 5, -z - 5 = -l - 4*l. Let v be 0/(l*(2 + -3)). Suppose 2/3*c**2 - 1/3*c**3 + v - 1/3*c = 0. What is c?
0, 1
Let y = 4427/417 + 7/139. Let m = y + -10. What is i in -4/3*i - 2/3*i**2 - m = 0?
-1
Let o(z) be the third derivative of z**5/20 - 3*z**4/8 - 5*z**3 + 8*z**2. Factor o(c).
3*(c - 5)*(c + 2)
Let x(k) be the third derivative of -k**9/100800 + k**7/2800 - k**6/600 - k**5/20 + 2*k**2. Let w(o) be the third derivative of x(o). Factor w(s).
-3*(s - 1)**2*(s + 2)/5
Suppose 2*i + 0 - 2/3*i**2 = 0. What is i?
0, 3
Let j = 1/17 + 31/51. Let 0 + 0*k + j*k**3 + 8*k**4 - 2/3*k**2 = 0. What is k?
-1/3, 0, 1/4
Let j(o) be the third derivative of -o**6/60 + o**4/12 + 8*o**2. Factor j(v).
-2*v*(v - 1)*(v + 1)
Let r(m) = -2*m**5 + 13*m**4 + 13*m**3 - 13*m - 13. Let k(l) = -l**5 + 6*l**4 + 6*l**3 - 6*l - 6. Let j(t) = -13*k(t) + 6*r(t). Factor j(z).
z**5
Let c(d) be the second derivative of -d**6/30 + 3*d**5/20 - d**4/4 + d**3/6 + 9*d. Factor c(y).
-y*(y - 1)**3
Let a = -8/41 + 281/1230. Let k(r) be the third derivative of -a*r**5 + 0 - 2*r**2 + 0*r**3 + 1/105*r**7 + 1/60*r**6 + 0*r - 1/12*r**4. Factor k(q).
2*q*(q - 1)*(q + 1)**2
Let b(a) be the third derivative of -a**7/1120 + a**5/160 - a**3/2 - 4*a**2. Let h(k) be the first derivative of b(k). Determine f so that h(f) = 0.
-1, 0, 1
Let s(x) be the second derivative of 3*x**5/20 - 2*x**3 + 4*x. Factor s(l).
3*l*(l - 2)*(l + 2)
Let x(n) be the third derivative of n**5/20 + n**4/4 + 13*n**2. Suppose x(y) = 0. Calculate y.
-2, 0
Let s(h) = -15*h**4 + 33*h**3 - 30*h**2 + 12*h. Let l(v) = v**5 - v**3 + v - 1. Let y be 1/2 + (-1)/(-2). Let i(r) = y*s(r) + 3*l(r). Factor i(m).
3*(m - 1)**5
Factor -15/2*y - 1/2*y**3 + 9/2 + 7/2*y**2.
-(y - 3)**2*(y - 1)/2
Let b(d) = d**3 + 7*d**2 + 7*d. Let x(i) = -i**2 - i. Let w(u) = 2*b(u) + 6*x(u). Suppose w(h) = 0. Calculate h.
-2, 0
Factor 3*v**4 + 4*v**3 - 3*v**2 + 3*v**2 - 13*v**4.
-2*v**3*(5*v - 2)
Let s(v) = 4*v - 15. Let j be s(5). Let i(q) be the second derivative of 7/3*q**7 + 42/5*q**6 + 0 + 109/10*q**j + 6*q**4 - q + 4/3*q**3 + 0*q**2. Factor i(k).
2*k*(k + 1)**2*(7*k + 2)**2
Let w be 6/24*((-10)/(-3) - -2). Determine m, given that 2/3*m**2 + 2/3 - w*m = 0.
1
Let b(d) be the second derivative of -d**8/6720 - d**7/1120 - d**6/720 - d**3/6 + 5*d. Let r(x) be the second derivative of b(x). Solve r(y) = 0.
-2, -1, 0
Let u(k) be the second derivative of -k**5 - 17*k**4/3 - 32*k**3/3 - 8*k**2 - 14*k. Factor u(n).
-4*(n + 1)*(n + 2)*(5*n + 2)
Let o(f) be the third derivative of f**6/30 + f**5/15 - f**4/3 - f**2. Factor o(q).
4*q*(q - 1)*(q + 2)
Let x be 88/22 - 1938/484. Let j = 45/242 + x. Solve 4/11*n - j*n**3 + 2/11*n**2 + 0 = 0.
-1, 0, 2
Suppose 5*q + 39 = 49. Factor -1/4*l - 1/4*l**4 + 1/4*l**3 + 1/4*l**q + 0.
-l*(l - 1)**2*(l + 1)/4
Suppose -137 = 3*m + 5*i, -4*i - 130 = 3*m - 6*i. Let g be (m/21)/(6/(-9)). Let 4/7*v**2 + 0 + 0*v + 38/7*v**4 + 20/7*v**5 + g*v**3 = 0. What is v?
-1, -1/2, -2/5, 0
Let l(y) = -y**2 + 25*y - 43. Let t be l(2). Factor -2/9*m**t + 2/9*m**2 - 2/9 + 2/9*m.
-2*(m - 1)**2*(m + 1)/9
Let w(g) = -11*g**5 - 5*g**4 + 7*g**3 - 5*g**2 - 11*g + 5. Let a(x) = -5*x**5 - 2*x**4 + 4*x**3 - 2*x**2 - 5*x + 2. Let l(j) = 5*a(j) - 2*w(j). Solve l(n) = 0.
-1, 0, 1
Let u(w) = -20*w**2 + 17*w - 8. Let k(q) = 14 - 5*q**2 - 11 + 4*q - 5. Let r(i) = -22*k(i) + 6*u(i). Determine c, given that r(c) = 0.
2/5, 1
Let t(f) be the first derivative of 0*f**2 + 1/18*f**4 + 0*f - 4/27*f**3 + 3. Determine n, given that t(n) = 0.
0, 2
Suppose 2/19*t**2 - 2/19 - 6/19*t + 6/19*t**3 = 0. Calculate t.
-1, -1/3, 1
Let m(f) be the first derivative of -f**5/25 - f**4/20 + f**3/15 + f**2/10 - 16. Factor m(s).
-s*(s - 1)*(s + 1)**2/5
Suppose 0 = 2*i + 4 - 4. What is l in -1/2*l**2 + 5/4*l**4 + 0 + l**5 + i*l - 7/4*l**3 = 0?
-2, -1/4, 0, 1
Let q be 14*-1 - 15/(-10). Let j = -12 - q. Suppose j - 1/2*a**2 + 0*a = 0. What is a?
-1, 1
Suppose 4*y + 0*y = -3*v - 14, 4*v - 3 = -y. Let r be (v/(-4) - -1)*6. Factor 4*u**2 - 2*u - 2*u**2 + u**2 - u**2 + 2*u**r - 2*u**4.
-2*u*(u - 1)**2*(u + 1)
Let b(g) = g**3 - 1. Let t(y) = -5*y**3 - 9*y**2 - 7*y + 8. Let i(s) = -4*b(s) - t(s). Let j be i(-8). Factor -2*x**2 + 0*x + 6*x**2 - j + 10*x**3 - 10*x.
2*(x - 1)*(x + 1)*(5*x + 2)
Suppose f = 5*i + 15, -2*i - 1 - 18 = -3*f. Let a be (i + 5)*(-4)/(-3). Factor -2/11*x + 0*x**3 + 4/11*x**2 + 2/11*x**5 + 0 - 4/11*x**a.
2*x*(x - 1)**3*(x + 1)/11
Suppose u + 4 - 7 = 0, 0 = 2*i + 2*u - 96. Let b be (-4)/18 - (-19)/i. Factor -3/5*f - b + 3/5*f**3 + 1/5*f**2.
(f - 1)*(f + 1)*(3*f + 1)/5
Let d(a) = 2 + 2 - 3. Let h(n) = -3*n**2 + 6*n - 9. Let w(v) = -6*d(v) - h(v). Let w(u) = 0. What is u?
1
Let d be (-584)/(-72) + 8/36. Factor 0 + 20/3*o**2 - d*o**3 - 4/3*o.
-o*(5*o - 2)**2/3
Factor 0 + 18/7*d**2 - 3/7*d**3 - 27/7*d.
-3*d*(d - 3)**2/7
Let o be 0 - 0*(-3)/(-12). Let b(t) be the second derivative of -t + 0*t**4 - 1/60*t**5 + 1/6*t**3 - 1/3*t**2 + o. Factor b(k).
-(k - 1)**2*(k + 2)/3
Let z(l) be the first derivative of l**3/3 - 9*l**2/2 + 60. Factor z(u).
u*(u - 9)
Let h(n) be the first derivative of -4*n**3/15 - 8*n**2/5 - 16*n/5 - 2. Factor h(z).
-4*(z + 2)**2/5
Let d(t) = t + 9. Let q be d(-9). Solve 5*w + q*w**2 - 14*w**2 - 4*w**3 - 13*w + 2*w**4 = 0.
-1, 0, 4
Let z = -5 + 17. Suppose z*j = 13*j - 3. Factor -2/5*i**j + 2/5*i**2 + 2/5*i - 2/5.
-2*(i - 1)**2*(i + 1)/5
Suppose -5*w = 4*r + 25, -2*r - 11*w + 15 = -14*w. Solve r - 32/9*u**4 + 0*u - 16/9*u**3 - 2/9*u**2 = 0.
-1/4, 0
Let 0*u - 9/4*u**4 + 9/4*u**3 - 3/4*u**2 + 0 + 3/4*u**5 = 0. Calculate u.
0, 1
Let j = -1419/7 - -203. Suppose -4/7 - j*u**3 - 10/7*u - 8/7*u**2 = 0. Calculate u.
-2, -1
Let z = 9 - 6. Suppose 0*d = z*d - 18. Solve d - 3*h**3 + 10*h**3 - 15*h + 8*h**3 - 6*h**2 = 0 for h.
-1, 2/5, 1
Let h(f) be the second derivative of f**5/100 - f**4/60 - f**3/30 + f**2/10 + 26*f. Factor h(w).
(w - 1)**2*(w + 1)/5
Let w(f) be the second derivative of f**5/15 + f**4/6 + f**3/9 + 5*f. Factor w(a).
2*a*(a + 1)*(2*a + 1)/3
Let s(r) be the second derivative of -1/60*r**6 - 1/6*r**3 + 1/8*r**4 + 0*r**2 + 0 + 0*r**5 - 3*r. Factor s(a).
-a*(a - 1)**2*(a + 2)/2
Suppose -d + 3 = 1. Let i(c) = 3*c**2 - 17*c - 1. Let z be i(6). What is f in 13/3*f**4 + 16/3*f**3 + 0 + 4/3*f**d + 0*f + f**z = 0?
-2, -1/3, 0
Let j(n) be the first derivative of 1/3*n**6 - 1 + 0*n**3 - 2/5*n**5 + 0*n**2 + 0*n + 0*n**4. Factor j(w).
2*w**4*(w - 1)
Let l(z) be the first derivative of -z**7/630 - z**6/180 - z**5/180 - z**2 - 4. Let q(a) be the second derivative of l(a). Solve q(v) = 0.
-1, 0
Let x = 10 + -7. What is l in 0*l**5 + l**x + 0*l**5 - l**5 = 0?
-1, 0, 1
Let g(i) be the third derivative of i**8/40320 - i**7/10080 - i**5/20 + 3*i**2. Let t(f) be the third derivative of g(f). Factor t(x).
x*(x - 1)/2
Let z = -1527/7 - -219. Suppose 4/7*n**3 + 2/7*n**5 - 4/7*n**2 - z*n + 6/7*n**4 - 2/7 = 0. What is n?
-1, 1
Let u be 0 + 23/7 - 256/896. What is a in 0 - 10/7*a**4 - 8/7*a**2 + 16/7*a**u + 2/7*a**5 + 0*a = 0?
0, 1, 2
Let w = 639/13 + -344/39. Let n = w + -40. Factor 0 + 4/3*t + 5/3*t**3 + 8/3*t**2 + n*t**4.
t*(t + 1)*(t + 2)**2/3
Let j(z) be the first derivative of -z**5 - 5*z**4/4 + 5*z**3/3 + 5*z**2/2 - 22. Factor j(n).
-5*n*(n - 1)*(n + 1)**2
Let c be (-4)/(-6) + 385/36. Let n = c - 10/9. Determine r so that 11/4*r - 7*r**4 + 0*r**2 - n*r