 Let o(r) be the second derivative of 0*r**2 - 1/105*r**6 + r - 1/70*r**5 + c + 0*r**4 + 0*r**3. Factor o(z).
-2*z**3*(z + 1)/7
Let a(b) = -b**3 + 21*b**2 + 21*b + 23. Let t be a(22). Let z be 6/36 + t/2. Solve -2/3*p**5 + 0 - 2/3*p**2 + 2/3*p**4 + 0*p + z*p**3 = 0 for p.
-1, 0, 1
Let v be (0 + -4 - 10) + 784/40. Factor 2/5*u**2 + 98/5 - v*u.
2*(u - 7)**2/5
Let x(z) be the third derivative of -z**8/5040 - z**7/1260 - z**6/1080 + 5*z**3/6 - 8*z**2. Let u(w) be the first derivative of x(w). Let u(m) = 0. What is m?
-1, 0
Let a(y) be the third derivative of -y**7/1260 - y**6/240 + 327*y**2. Find s such that a(s) = 0.
-3, 0
Let t = 61/100 - -41/25. Determine q so that -t + 3*q - 3/4*q**2 = 0.
1, 3
Let n(f) be the first derivative of -8/3*f**3 - f**4 + 0*f - 2 - 2*f**2. Factor n(x).
-4*x*(x + 1)**2
Let s = 373/530 + -11/106. Factor 0 + s*d**2 - 6/5*d.
3*d*(d - 2)/5
Let -112/13*i - 1568/13 - 2/13*i**2 = 0. Calculate i.
-28
Let k(q) be the first derivative of -2/15*q**3 - 2/5*q**2 + 6/5*q + 25. Solve k(m) = 0 for m.
-3, 1
Let r(k) be the third derivative of -44*k**2 - 5/42*k**3 + 0*k + 0 - 1/42*k**4 + 1/420*k**5. Determine h so that r(h) = 0.
-1, 5
Let r(h) = -5*h**3 + 6*h**2 - 3*h. Let x(c) = 11*c**3 - 13*c**2 + 7*c. Let b = -1 - -3. Let d(s) = b*x(s) + 5*r(s). Factor d(f).
-f*(f - 1)*(3*f - 1)
Find k such that -15/4*k**2 - 10 + 27/2*k + 1/4*k**3 = 0.
1, 4, 10
Factor -248/3*u - 150*u**3 + 340*u**2 + 16/3.
-2*(u - 2)*(15*u - 2)**2/3
Let j(l) = 11*l**2 + 11*l + 12. Let n(h) = -12*h**2 - 12*h - 14. Let g(w) = 7*j(w) + 6*n(w). Let g(r) = 0. Calculate r.
-1, 0
Let i(x) be the first derivative of 12 + 2/3*x**3 + 1/2*x**4 - x**2 - 2*x. Factor i(g).
2*(g - 1)*(g + 1)**2
Let v(d) be the first derivative of 2*d**7/21 - 2*d**5/5 + 2*d**3/3 + 9*d + 12. Let r(w) be the first derivative of v(w). Factor r(z).
4*z*(z - 1)**2*(z + 1)**2
Let g(k) be the second derivative of 25 + 0*k**4 - 2/15*k**6 + 6/5*k**5 + 0*k**3 + 0*k**2 + 2*k. Solve g(r) = 0.
0, 6
Factor -31 + 22*n**2 + 3 - 18*n**2 + 24*n.
4*(n - 1)*(n + 7)
Let c(n) be the second derivative of 0 + 0*n**4 - 3*n + 0*n**3 + 1/180*n**6 + 1/45*n**5 - 5/2*n**2. Let z(i) be the first derivative of c(i). Factor z(l).
2*l**2*(l + 2)/3
Let m = 5522 + -5522. Factor 2/7*x + m - 2/7*x**3 + 0*x**2.
-2*x*(x - 1)*(x + 1)/7
Let m(z) be the first derivative of -z**5 - 75*z**4/2 - 1385*z**3/3 - 1950*z**2 - 3380*z + 69. Find l such that m(l) = 0.
-13, -2
Let n(v) be the first derivative of -3*v**4/20 + 4*v**3/5 - 3*v**2/2 + 6*v/5 - 195. Determine l, given that n(l) = 0.
1, 2
Suppose -6 = -4*w - 2*r, 24 = w - 3*r + 5. Let h(q) be the second derivative of 0 + 0*q**2 + 1/54*q**w - 1/27*q**3 + q. Factor h(y).
2*y*(y - 1)/9
Suppose -7*p + 92 = -6. Let a be (-9)/(-42)*4 - 8/p. Factor 0*u + a*u**3 - 6/7*u**2 + 8/7.
2*(u - 2)**2*(u + 1)/7
Let t(z) be the third derivative of -z**8/168 - z**7/20 + 7*z**6/96 - z**5/40 - 5*z**2 + 3. What is b in t(b) = 0?
-6, 0, 1/4, 1/2
Let f(j) be the first derivative of -j**5/60 + j**4/6 - 2*j**3/3 - 6*j**2 + 7. Let n(k) be the second derivative of f(k). Determine x, given that n(x) = 0.
2
Let y(m) be the second derivative of 1/32*m**4 - 1/4*m**3 + 0 + 1/80*m**5 - 1/2*m**2 - m. Let z(i) be the first derivative of y(i). Find n, given that z(n) = 0.
-2, 1
Let -317 + 28 + 5*k**2 - 191 - 635*k - 92 - 68 = 0. What is k?
-1, 128
Let x(b) be the first derivative of -1/6*b**3 + 24 + 1/2*b**2 + 0*b. What is k in x(k) = 0?
0, 2
Let f(c) = -5 + 1 - 5 + 1 + 2*c. Let n be f(5). Factor 2/5*z + 0 + 2/5*z**3 - 4/5*z**n.
2*z*(z - 1)**2/5
Let z(u) = u**2 - 16*u + 28. Let q be z(15). Suppose -3*y = -q + 7. Factor -2/7*k - 2/7*k**y + 0.
-2*k*(k + 1)/7
Suppose 10*d = 5*d - 10, 5*i - 40 = 5*d. Let l(c) be the first derivative of 0*c**4 - 6 + c**2 + 0*c + 4/5*c**5 - 1/3*c**i - 4/3*c**3. Factor l(t).
-2*t*(t - 1)**3*(t + 1)
Let m(z) be the second derivative of -z**6/360 - z**5/60 + z**4/24 + z**3/18 - 5*z**2/24 - 2*z - 14. Find y, given that m(y) = 0.
-5, -1, 1
Let j be (-2)/(-7) + -6*(-78)/126. Let 3*i + 3*i**3 + i**j + i - 5*i**2 - 2*i - i**5 = 0. Calculate i.
-2, 0, 1
Let o(y) = -y**2 - 14*y - 28. Let k be o(-11). Let m(c) be the second derivative of 0 - 2/3*c**4 + 5*c + 0*c**2 - 1/45*c**6 + 8/9*c**3 + 1/5*c**k. Factor m(s).
-2*s*(s - 2)**3/3
Let a(w) be the first derivative of -6/7*w + 2/7*w**3 + 3/14*w**2 - 3/28*w**4 - 1. Determine l, given that a(l) = 0.
-1, 1, 2
Let v = 7281 + -7278. Factor -4/3*h**4 - 8/3*h + 0 + 4*h**2 + 0*h**v.
-4*h*(h - 1)**2*(h + 2)/3
Let l(r) be the third derivative of -r**8/84 + 4*r**7/35 + 2*r**6/3 - 8*r**5/5 - 32*r**4/3 + 115*r**2. What is c in l(c) = 0?
-2, 0, 2, 8
Let l(g) be the first derivative of g**4/30 + 2*g**3/15 - g**2/15 - 2*g/5 - 714. Factor l(y).
2*(y - 1)*(y + 1)*(y + 3)/15
Let a(z) be the third derivative of 3/10*z**5 - 5/3*z**3 - 3 + 0*z + 1/30*z**6 + 7*z**2 - 1/2*z**4. Determine j, given that a(j) = 0.
-5, -1/2, 1
Let x(k) be the third derivative of k**9/181440 - k**8/60480 - k**7/7560 + 2*k**5/15 + 15*k**2. Let y(z) be the third derivative of x(z). Factor y(s).
s*(s - 2)*(s + 1)/3
Let u(r) be the third derivative of -r**8/4032 - r**7/168 - r**6/16 + 7*r**5/30 + 3*r**2. Let z(n) be the third derivative of u(n). Let z(g) = 0. Calculate g.
-3
Let m = 6 - -6. Suppose 2*i - 12 - 3 = 3*z, -i - 5*z = m. Factor -7*h**3 - 4*h**3 - 18*h**2 - 4*h - i*h**3.
-2*h*(h + 1)*(7*h + 2)
Let h(r) = r**2 + r + 5. Let w(s) = 140*s**2 - 5*s - 30. Let u(m) = 6*h(m) + w(m). Factor u(k).
k*(146*k + 1)
Let c = 73 - 71. Factor 2*d**2 + 5*d**2 - 25*d**c - 5*d**3 - 2*d**2.
-5*d**2*(d + 4)
Let o(s) be the third derivative of s**8/840 + 17*s**7/1050 + s**6/20 - 29*s**5/300 - s**4/6 + 209*s**2. Find c such that o(c) = 0.
-5, -4, -1/2, 0, 1
Let b be (0 + 55)/(-10 - -11). Factor 4*t + 2*t + b*t**2 - 58*t**2 - 3.
-3*(t - 1)**2
Let s = 2 - 1. Let a(b) = 3*b**3 + 3*b**2 + 9*b - 3. Let z(n) = -n**3 - n. Suppose -147*u + 144*u + 18 = 0. Let k(f) = s*a(f) + u*z(f). Solve k(l) = 0 for l.
-1, 1
Let y(w) = 5*w**2 + 43*w - 52. Let r(t) = 20*t**2 + 171*t - 209. Let j(u) = -2*r(u) + 9*y(u). Factor j(d).
5*(d - 1)*(d + 10)
Suppose 5*q - 2*q = 6. Let d = q + 2. Determine o so that 42*o**2 + 3*o**3 - 40*o**2 - 2*o**4 + 3*o**d = 0.
-2, -1, 0
Factor -1/2*p + 0*p**2 - 1/4 + 1/2*p**3 + 1/4*p**4.
(p - 1)*(p + 1)**3/4
Determine d so that -24/7*d**2 + 18/7 - 3*d + 15/7*d**3 = 0.
-1, 3/5, 2
Suppose 499*p = 472*p. Factor 3/4 + p*v - 3/2*v**2 + 3/4*v**4 + 0*v**3.
3*(v - 1)**2*(v + 1)**2/4
Suppose 4*o - 7 = 3*o. Let z(s) be the second derivative of 0 + 4/9*s**2 + 4/27*s**3 - o*s + 1/54*s**4. Factor z(a).
2*(a + 2)**2/9
Suppose -4*f - 22 = 10. Let x be (f/18)/(8/(-12)). Find y, given that -1/3*y**5 - x + 4/3*y**2 + 2/3*y**3 - 1/3*y - 2/3*y**4 = 0.
-2, -1, 1
Let c be 11/(-55)*(35/2)/(10/(-10)). Factor 5/2*x**4 - c*x - 3/2*x**2 + 7/2*x**3 - 1.
(x - 1)*(x + 1)**2*(5*x + 2)/2
Let z(s) be the second derivative of s**5/70 + s**4/42 - 8*s**3/3 + 144*s**2/7 - 216*s. Factor z(c).
2*(c - 4)**2*(c + 9)/7
Let s(g) = g**2 - 9*g - 6. Let i be s(11). Factor 2*h - 2*h**3 - 4 + 13*h**3 + 14*h**4 + 30*h**2 + i*h**3 + 11*h**3.
2*(h + 1)**3*(7*h - 2)
Let p = -33408 + 100240/3. Factor 0*a + p*a**2 - 32*a**3 + 0 + 36*a**4.
4*a**2*(3*a - 2)*(9*a - 2)/3
Let j(u) be the third derivative of -u**8/6720 - u**7/420 - u**6/60 + 3*u**5/20 + 8*u**2. Let k(f) be the third derivative of j(f). Factor k(c).
-3*(c + 2)**2
Let w(u) be the first derivative of -1/2*u**4 + 2/3*u**3 + 0*u - 2/5*u**5 - 5 + u**2. Factor w(d).
-2*d*(d - 1)*(d + 1)**2
Factor -848/3*z - 44944/3 - 4/3*z**2.
-4*(z + 106)**2/3
Suppose 3*w = -2*a, -3*w = 7*a - 3*a + 12. Let x be 2 - (a/(-2) - 1). Factor 21*h - 8 - 19*h - 18*h**4 + 38*h + 60*h**3 + x - 74*h**2.
-2*(h - 1)**2*(3*h - 2)**2
Let c be 3/7 + (-11196)/(-3276) - 2/(-13). Factor 0*v**2 + 0*v + 0 + 4/3*v**3 - 1/3*v**c.
-v**3*(v - 4)/3
Suppose -4*r = -10*r + 24. Suppose -r*d**2 + 9*d**2 - d**5 + 3*d**3 - 7*d**2 = 0. What is d?
-2, 0, 1
Let z be (-1 - -6) + ((-16)/(-4) - 4). Determine k, given that -4 + 0*k**z + 2*k**5 + 8*k**2 - 60*k - 4*k**4 + 62*k - 4*k**3 = 0.
-1, 1, 2
Factor 9*u - 21*u**2 - 2*u**2 - 3*u**3 - u + 2*u - 2*u.
-u*(u + 8)*(3*u - 1)
Let t(z) = -2*z**2 - 110*z + 3031. Let c(f) = -f**2 - 110*f + 3029. Let b(s) = -3*c(s) + 2*t(s). Deter