tive of i(a). Factor o(h).
-2*h*(h - 1)**2*(h + 1)/5
Let u = -17 + 21. Suppose 0*z**u - z**4 - 2*z**2 - 3 + 2*z**4 + 4 = 0. What is z?
-1, 1
Let d(x) be the second derivative of x**6/135 - x**5/30 - x**4/54 + x**3/9 + 143*x. Factor d(l).
2*l*(l - 3)*(l - 1)*(l + 1)/9
Let b = -43814 + 481960/11. Suppose -8/11 + 2/11*j**2 + b*j = 0. Calculate j.
-4, 1
Let t(w) be the second derivative of -w**6/10 + 18*w**5/5 - 54*w**4 + 432*w**3 - 1944*w**2 + 115*w. Factor t(n).
-3*(n - 6)**4
Let r(z) be the second derivative of z**7/21 - 7*z**6/15 - 11*z**5/10 + 19*z**4/6 + 38*z**3/3 + 16*z**2 - 36*z. Factor r(d).
2*(d - 8)*(d - 2)*(d + 1)**3
Let y = -5/108 + 143/2700. Let b(a) be the third derivative of 1/30*a**3 - 1/120*a**4 + 0*a + 10*a**2 - y*a**5 + 0. Factor b(p).
-(p + 1)*(2*p - 1)/5
Suppose 0 = -10*k - 27 + 27. Factor -1/9*z + k + 1/9*z**2.
z*(z - 1)/9
Let r(x) = -2*x - 8. Let l be r(-8). Let z be ((-4)/l)/(1/(-4)). Factor -s - 1 - s**2 - z*s - 1.
-(s + 1)*(s + 2)
Let v = 15 - 21. Let n be 2 + 8/v + 2/(-3). Factor n + 1/4*g**2 + 0*g - 1/2*g**3.
-g**2*(2*g - 1)/4
Let m be 2/9 + 160/90. Factor 3*t - 13*t - 25*t**m + 20*t**2.
-5*t*(t + 2)
Let c(o) be the second derivative of 43/66*o**4 + 0 - 43*o - 36/77*o**7 + 1/11*o**2 + 21/110*o**5 - 48/55*o**6 - 13/33*o**3. Suppose c(q) = 0. What is q?
-1, 1/6, 1/3
Find y such that -20/7*y**3 + 180/7*y - 216/7 + 4/7*y**4 - 12/7*y**2 = 0.
-3, 2, 3
Let t(c) = -c**2 + 4*c + 6. Let z(v) = -1. Suppose 0*k + 5*k + 30 = 0. Let f(h) = k*z(h) - t(h). Suppose f(u) = 0. What is u?
0, 4
Let c(q) = -q**3 - q**2. Let l(k) = 2*k**3 + 44*k**2 + 483*k + 441. Let x(u) = -2*c(u) - 2*l(u). Factor x(t).
-2*(t + 1)*(t + 21)**2
Suppose 30*h - 35*h = 0, 0 = -5*a - h + 20. Let f(w) be the first derivative of 1/3*w**3 + 0*w - a + 0*w**2. Factor f(l).
l**2
Suppose 584 = 4*a + 8*q, -56*q + 626 = 4*a - 54*q. Determine i, given that -40*i**2 - a*i - 5/2*i**3 + 0 = 0.
-8, 0
Let u(o) = 65*o**3 - 30*o**2 - 120*o + 85. Let n(t) = -11*t**3 + 5*t**2 + 20*t - 14. Let z(s) = 35*n(s) + 6*u(s). Solve z(a) = 0 for a.
-2, 1, 2
Let s(o) be the first derivative of 5*o**4/4 + 425*o**3/3 + 8815*o**2/2 - 9245*o - 494. Factor s(a).
5*(a - 1)*(a + 43)**2
Let t be (-17 + 22)*4/10. Factor -5*r - 4*r**t + 2*r + 3*r + 4*r**4.
4*r**2*(r - 1)*(r + 1)
Let c(o) = 10*o**2 - 130*o + 270. Let t(i) = 5*i**2 - 66*i + 135. Let u(w) = 3*c(w) - 5*t(w). Factor u(j).
5*(j - 9)*(j - 3)
Let y(q) = 35*q - 2. Let z be y(1). Let n = 33 - z. Suppose n + 1/6*k**3 + 1/6*k + 1/3*k**2 = 0. What is k?
-1, 0
Let x(g) = -g**2 + 10*g - 5. Let o be x(9). Factor -2 + 34 - 4*s**o - 3*s**2 + 11*s**2 + 0*s**2 + 12*s**3 - 48*s.
-4*(s - 2)**2*(s - 1)*(s + 2)
Let p(g) be the second derivative of 2*g**6/15 - 18*g**5 + 88*g**4/3 + 60*g**3 - 178*g**2 - 694*g. Factor p(s).
4*(s - 89)*(s - 1)**2*(s + 1)
Factor -12 - 14*o - 3*o**5 - 32*o - 25*o**4 + 9*o**4 + o**5 - 48*o**3 - 68*o**2.
-2*(o + 1)**3*(o + 2)*(o + 3)
Suppose -267*o - 4 = -271*o + 12. Let 4/3*t + 0 + 14/3*t**2 - 14/3*t**o - 4/3*t**3 = 0. What is t?
-1, -2/7, 0, 1
Suppose 5 + 10 = 5*y. Solve 8 - 15*a + 7*a**2 - a**3 - a**2 + y*a + 0*a**3 = 0.
2
Let r(w) = -w**3 + w**2 + w - 1. Let d = 49 + -52. Let m(k) = 2*k**3 - 3*k**2 - 2*k + 3. Let o(a) = d*m(a) - 3*r(a). Factor o(f).
-3*(f - 2)*(f - 1)*(f + 1)
Let n(l) = -5*l**4 + 79*l**2 - l - 1. Let y(w) = w**2 + w + 1. Let r(x) = n(x) + y(x). Factor r(s).
-5*s**2*(s - 4)*(s + 4)
Let w(f) be the third derivative of f**6/300 - f**5/25 - f**4/60 + 2*f**3/5 + 283*f**2. Factor w(j).
2*(j - 6)*(j - 1)*(j + 1)/5
Let n(a) be the first derivative of 3/11*a**2 - 2/33*a**3 + 0*a - 28 - 3/22*a**4 + 2/55*a**5. Solve n(q) = 0 for q.
-1, 0, 1, 3
Let t(o) be the third derivative of -o**7/1960 + 3*o**5/280 - o**4/28 - 2*o**3 - 6*o**2. Let v(l) be the first derivative of t(l). Factor v(k).
-3*(k - 1)**2*(k + 2)/7
Let g = -32 - -36. Let -2*q + q**3 + 167*q**2 + 0*q + q**g - 170*q**2 + q + 2 = 0. What is q?
-2, -1, 1
Let i(r) be the third derivative of -r**6/420 + 128*r**5/105 - 4096*r**4/21 + 91*r**2 - 2*r. Factor i(g).
-2*g*(g - 128)**2/7
Factor -2/3*s**5 - 2/3 - 4/3*s**2 + 2*s**4 + 2*s - 4/3*s**3.
-2*(s - 1)**4*(s + 1)/3
Let d = -378364/13 + 29106. Factor -d - 16/13*m - 2/13*m**2.
-2*(m + 1)*(m + 7)/13
Let w(d) be the first derivative of 0*d - 19 + 1/9*d**3 + 1/3*d**2. Find y such that w(y) = 0.
-2, 0
Let w(r) be the first derivative of -1/54*r**4 + 1/9*r**2 - 1 - 1/27*r**3 - 2*r + 1/90*r**5. Let k(y) be the first derivative of w(y). Factor k(p).
2*(p - 1)**2*(p + 1)/9
Let l(g) be the third derivative of 0*g**6 - 1/525*g**7 + 0 - 1/1680*g**8 - 5*g**2 + 0*g + 0*g**3 + 1/120*g**4 + 1/150*g**5. Factor l(h).
-h*(h - 1)*(h + 1)**3/5
Let s(z) be the third derivative of -z**5/12 - 505*z**4/12 - 51005*z**3/6 + 9*z**2 - 26*z. Factor s(i).
-5*(i + 101)**2
Let j(m) = m**2 - 1. Let b be j(-1). Suppose -5*l - 7*c + 3*c + 39 = b, 3*l = 4*c + 17. Suppose i**3 + 0*i**3 - l*i**2 + 11*i**2 + 3*i = 0. What is i?
-3, -1, 0
Find q such that -19872/7*q**2 - 46656/7 - 7776*q - 116/7*q**4 - 2384/7*q**3 - 2/7*q**5 = 0.
-18, -2
Factor 64*l + 42*l - 2*l**3 + 204*l**2 + 42 - 96 + 23*l + 23*l**3.
3*(l + 1)*(l + 9)*(7*l - 2)
Let d(t) be the third derivative of -t**9/181440 - t**8/30240 - t**7/15120 - t**5/60 - 12*t**2. Let j(w) be the third derivative of d(w). Factor j(v).
-v*(v + 1)**2/3
Let i(p) = 12*p**2 - 32*p - 64. Let l(k) = -k**2. Let t be (8/(-6) + 2)/((-8)/12). Let m(n) = t*i(n) - 16*l(n). Factor m(g).
4*(g + 4)**2
Let z = -13502/5 - -2701. Factor 24/5*o - z*o**2 - 48/5.
-3*(o - 4)**2/5
Let q(z) be the second derivative of 8*z**2 - 4/3*z**3 + 1/12*z**4 + 0 + 6*z. Factor q(t).
(t - 4)**2
Determine k, given that 16/5*k**3 - 4*k**2 + 8/5*k + 0 - 4/5*k**4 = 0.
0, 1, 2
Let r(c) = -4*c**2 - 18*c - 14. Let h(n) = 8*n**2 + 37*n + 27. Suppose 3*q = -5*q - 16. Let b(w) = q*h(w) - 5*r(w). Factor b(a).
4*(a + 2)**2
Let n be (28/(-63))/((-6)/63). Let q(w) be the second derivative of 0 - w - 4*w**2 + 2/3*w**6 - w**4 + n*w**3 - 7/5*w**5. Suppose q(h) = 0. Calculate h.
-1, 2/5, 1
Let j(o) = o**2 - 11 - 2*o**2 - 12*o + 0*o**2 - 3*o. Let r be j(-14). Factor k**4 + r*k**5 + k**4 - 2*k**2 - 2*k**3 + 0*k**4 - k**5.
2*k**2*(k - 1)*(k + 1)**2
Suppose 3*h + 2*n = 23, -3*h + h = 5*n - 30. Suppose 0 = -4*u + h*g - 5, u + 0*g - 3*g + 10 = 0. Factor 0*y**2 + 3/4*y**3 + 0*y + 3/8*y**4 + 0 - 9/4*y**u.
-3*y**3*(2*y + 1)*(3*y - 2)/8
Let y = 3 + 0. Suppose -y - 9 = -2*s. What is b in -6*b + 2*b**2 + s*b - 4*b - b**3 + 3*b**3 = 0?
-2, 0, 1
Let u = -78 + 73. Let q(x) = -3*x**2 - 21*x - 8. Let j(o) = 4*o**2 + 32*o + 12. Let b(p) = u*j(p) - 8*q(p). Determine i, given that b(i) = 0.
-1
Suppose -d - 1 = c, -7*d + 5*c = -2*d - 15. Suppose -8 = -3*g + d. Factor -3/2*a**5 + 3/2 - 3/2*a - g*a**2 + 3/2*a**4 + 3*a**3.
-3*(a - 1)**3*(a + 1)**2/2
Let z(f) be the third derivative of f**7/1050 + f**6/600 - f**5/60 + f**4/40 - 70*f**2. Factor z(r).
r*(r - 1)**2*(r + 3)/5
Solve -2/17*h**4 + 12/17*h**2 + 0*h**3 + 16/17*h + 6/17 = 0.
-1, 3
Let d(f) be the third derivative of f**5/240 - 5*f**4/16 + 76*f**2. Factor d(g).
g*(g - 30)/4
Let l(h) be the third derivative of 0 - 30*h**2 - 1/3*h**5 + 0*h**3 + 0*h + 0*h**4 + 1/30*h**6. Factor l(f).
4*f**2*(f - 5)
Let x be (((-3160)/(-705))/4)/((-14)/(-9)). Let z = x + -7/47. Factor -2/7*h**5 + 0 + 0*h + 0*h**2 - 2/7*h**3 + z*h**4.
-2*h**3*(h - 1)**2/7
Let f(b) be the first derivative of -3*b**4/32 + 51*b**3/4 - 2601*b**2/4 + 14739*b + 180. Factor f(h).
-3*(h - 34)**3/8
Let m(d) be the first derivative of 3/20*d**4 + 0*d**2 + 3/5*d**3 - 8 + 0*d. Find s, given that m(s) = 0.
-3, 0
Factor -2*r**2 - 2 - 9 + 20*r - 16 - 5.
-2*(r - 8)*(r - 2)
Let o = 4 + -5. Let q(h) = -h + 3. Let y(p) = 1. Let l(b) = o*q(b) + 2*y(b). Let j(r) = -r**2 - 7*r + 6. Let f(x) = -j(x) - 6*l(x). Factor f(u).
u*(u + 1)
Let y(q) be the second derivative of 0*q**2 + 0*q**3 - 12*q + 0 + 1/105*q**6 + 3/70*q**5 + 1/21*q**4. Solve y(s) = 0 for s.
-2, -1, 0
Let j(f) = 26*f**2 - 27*f + 1. Let l(a) = a**2 - a. Let u(o) = j(o) + 2*l(o). Let t(b) = -28*b**2 + 28*b. Let w(c) = 3*t(c) + 4*u(c). Factor w(p).
4*(p - 1)*(7*p - 1)
Let q(h) = -h**2 - h + 45. Suppose -25 = -8*d + 23. Let v be q(d). Determine c, given that 0*c - 3/7*c**4 + 6/7*c**2 + 3/7*c**v + 0 = 0.
-1, 0, 2
Suppose -1/5*p**3 - p**2 - 4