701. Factor i*b**3 + 2/11*b + 16/11*b**2 + 0.
2*b*(4*b + 1)**2/11
Let m(x) be the first derivative of x**4/108 - x**3/54 - x**2/9 - 6*x + 11. Let f(z) be the first derivative of m(z). Suppose f(k) = 0. What is k?
-1, 2
Let m(a) = a**2 - 14*a + 2. Let y be m(14). Let 2*t**4 - 4 + 150*t**2 - 6*t**4 + y*t**5 + 2*t - 4*t**3 - 142*t**2 = 0. What is t?
-1, 1, 2
Solve 32/5 - 16/5*j + 14/5*j**3 - 46/5*j**2 + 2/5*j**5 + 14/5*j**4 = 0.
-4, -1, 1
Let d be -2 + -5 + (-21)/(-3). Factor 4/7*f**2 + d + 6/7*f**3 + 0*f + 2/7*f**4.
2*f**2*(f + 1)*(f + 2)/7
Let f be ((-12)/(-2))/(50*96/320). Let d be 8/(-5) - 10/(-5). What is u in 0 + f*u**3 - 4/5*u**2 + 4/5*u**4 - d*u = 0?
-1, -1/2, 0, 1
Let i(n) = -n**2 - 3*n - 6. Let k be i(-3). Let v be (-8)/k + 20/30. Factor -4*j - 1 - 2*j**v + j**2 - 1 - j**2.
-2*(j + 1)**2
Let c = 20 - 11. Let g be (c + -39)/((-3)/2). Factor 30*r**2 - 46*r**2 + 22*r**2 - g*r + 6.
2*(r - 3)*(3*r - 1)
Let w(n) be the third derivative of n**2 + 1/17*n**3 + 1/51*n**4 + 0*n + 1/510*n**5 + 15. Factor w(a).
2*(a + 1)*(a + 3)/17
Let k(d) = -d + 11. Let z be k(7). Solve 2*a**z - 4 + 2*a**3 - a**4 + 3 - 2*a = 0 for a.
-1, 1
Find q, given that 4/7 + 625/7*q**2 - 100/7*q = 0.
2/25
Suppose -w = 14*b - 9*b - 9, -11 = -4*b + 3*w. Factor 14*z**2 - 14*z**2 + 8*z**b + 2*z**4 + 8*z**3.
2*z**2*(z + 2)**2
Determine a so that -1/9*a + 2/3 - 1/9*a**2 = 0.
-3, 2
Let l = 184/3 + -1282/21. Factor 0 + 2/7*q**2 - l*q.
2*q*(q - 1)/7
Let f(t) be the third derivative of -t**8/1344 + t**6/160 + t**5/120 + 249*t**2 - 2*t. Factor f(x).
-x**2*(x - 2)*(x + 1)**2/4
Suppose 20*f + 0*f = -1860. Let a = f - -98. Factor -4/7 + 8/7*c**2 - 4/7*c**a - 4/7*c**4 + 8/7*c**3 - 4/7*c.
-4*(c - 1)**2*(c + 1)**3/7
Let h = -38 + 42. Factor -118*t**4 + 4*t**3 + 2 - 4*t + 56*t**h + 60*t**4.
-2*(t - 1)**3*(t + 1)
Let h(g) = 29*g + 261. Let s be h(-9). Let n(b) be the third derivative of -1/180*b**5 + 3*b**2 + 1/72*b**4 - 1/360*b**6 + 1/18*b**3 + 0 + s*b. Factor n(d).
-(d - 1)*(d + 1)**2/3
Let x = 1/44 + 5/22. Suppose 13*t + 160 + 119 = 318. Solve -1/4*s**2 + x*s**4 + 0 + 0*s + 1/4*s**5 - 1/4*s**t = 0.
-1, 0, 1
Let w = -6692 + 73626/11. Suppose 6/11*o**4 + 0*o - w*o**2 - 2/11*o**5 + 2/11*o**3 + 8/11 = 0. What is o?
-1, 1, 2
Let s(y) = 5*y**2. Let v(a) = 6*a**2 + 3*a - 130. Let o(p) = s(p) - v(p). Factor o(r).
-(r - 10)*(r + 13)
Suppose 2*t + 2*t - x - 12 = 0, -5*t - 3*x = -32. Suppose c - u - t = 0, c - u - 20 = 4*u. Factor c*k**2 + 3 - 3 - k**2.
-k**2
Let w = 43417/54 - 804. Let a(i) be the second derivative of w*i**4 + 4/9*i**2 + 4/27*i**3 + 0 - 5*i. Let a(d) = 0. What is d?
-2
Factor 0 + 100/13*s**3 + 206/13*s**2 - 2/13*s**4 + 8*s.
-2*s*(s - 52)*(s + 1)**2/13
Suppose 242 = -27*r + 296. Let s(d) be the third derivative of 1/60*d**6 + 0*d**4 + 0*d**3 + 14*d**r + 1/63*d**7 - 1/45*d**5 + 0 + 0*d. Factor s(u).
2*u**2*(u + 1)*(5*u - 2)/3
Determine u so that -3*u**3 - 12 + 14*u**2 + 9*u**3 - 2*u**3 - 2*u**4 - 2*u**3 - 2*u = 0.
-2, -1, 1, 3
Let l(u) = 2*u**2 - 5*u - 3. Let i(y) = 4*y**2 + 6*y - 2*y + 11*y + 10 - 9*y**2. Let r(b) = 3*i(b) + 10*l(b). Suppose r(d) = 0. Calculate d.
0, 1
Suppose -104272*f + 5*f**5 + 104407*f - 60*f**3 + 81 + 9 - 10*f**2 = 0. Calculate f.
-3, -1, 2, 3
Let o = 87/37 - 311/148. Find w such that 1/4*w**2 + 1/2*w + o = 0.
-1
Let s(p) = 102*p + 5814. Let x be s(-57). Factor 2*v**3 + x + 7/2*v**2 - v.
v*(v + 2)*(4*v - 1)/2
Find p such that -2/9*p**5 - 4/3*p**3 - 2/3 + 14/9*p + 10/9*p**4 - 4/9*p**2 = 0.
-1, 1, 3
Let n = -136/5 + 137/5. Solve n*j**3 + 8/5*j**2 + 21/5*j + 18/5 = 0 for j.
-3, -2
Let h(t) be the first derivative of 3 + 0*t + 0*t**2 + 3/2*t**4 - 2/3*t**3 + 8/5*t**5. Find l such that h(l) = 0.
-1, 0, 1/4
Let m(l) = -l**3 - 2*l + 2. Let k(h) = -6*h**2 + 5*h**2 + 0*h**2 - 1 + h. Let s = -12 - -11. Let x(q) = s*m(q) - 2*k(q). Factor x(j).
j**2*(j + 2)
Let -2/3*x**2 - 34/9*x**4 - 4/3*x**5 + 2/9*x + 0 - 10/3*x**3 = 0. What is x?
-1, 0, 1/6
Let f(g) = 3*g - 5. Let b(q) = -q. Let z(k) = 2*b(k) + f(k). Let s be z(7). Factor -2*x**3 + 0*x**3 - 16*x**s - 2*x**2 - 10*x**3 - 3 - 12*x - 3*x**4.
-3*(x + 1)**4
Suppose -6*a + 13*a = 21. Let x(o) be the first derivative of -7/4*o**a + 0*o + 3/8*o**2 - 27/20*o**5 + 45/16*o**4 + 4. Factor x(u).
-3*u*(u - 1)*(3*u - 1)**2/4
Let t = 35 - 25. Let o be -4*1/t + 12/30. Solve 0*g**2 - 6*g**4 + 14/3*g**5 + o*g + 4/3*g**3 + 0 = 0 for g.
0, 2/7, 1
Let m be (9/(-36))/(3/24)*(-2)/13. Suppose 0 + m*i - 16/13*i**4 + 6/13*i**3 + 14/13*i**2 - 8/13*i**5 = 0. What is i?
-2, -1/2, 0, 1
Factor l**4 - 4*l**3 - l**4 + 3*l**4 + 4*l + 0*l - 5*l**4 + 2*l**2.
-2*l*(l - 1)*(l + 1)*(l + 2)
Suppose -3*c - 10 = -5*a - 5*c, a - 2*c = 14. What is u in -3*u**4 - 14*u**3 - 4*u**4 + 6*u**a - 125 - 50*u + 60*u**2 + 2*u**4 = 0?
-1, 5
Let t(m) be the second derivative of 11*m**4/16 - 3*m**3 + 3*m**2/2 + 31*m. Factor t(s).
3*(s - 2)*(11*s - 2)/4
Let c = 35676 + -35672. Find n, given that -4/3*n**2 + 4/3*n**4 + 4*n**3 + 0 - c*n = 0.
-3, -1, 0, 1
Let l = 10414 - 31631/3. Let o = l - -131. Factor -2/3*n**3 - 8/3*n**2 - 10/3*n - o.
-2*(n + 1)**2*(n + 2)/3
Let u = -7 + 9. Suppose -3*p = u*a - 0*a - 21, a + 12 = 3*p. Factor -2*z**3 - 10*z**a + 12*z**4 + 4*z**5 + 2*z**2 + 2*z**2 - 8*z**5.
-4*z**2*(z - 1)**3
Suppose -14*r - 131*r = -435. Factor 0*c**2 + 0*c + 6/5*c**4 + 0 + 0*c**r - 6/5*c**5.
-6*c**4*(c - 1)/5
Suppose 20 = 5*m + 5*a, -2*m - 4*a + 13 = 3. Factor 0 - 40/3*w**m + 50/3*w**4 + 8/3*w**2 + 0*w.
2*w**2*(5*w - 2)**2/3
Let w(r) be the second derivative of 0 - 1/14*r**4 + 0*r**2 - 1/105*r**6 - 14*r + 3/70*r**5 + 1/21*r**3. Factor w(x).
-2*x*(x - 1)**3/7
Let q be 5 - (((-170)/11)/(-2) - 4). Let l = -1014 - -11162/11. Suppose 0*y + q*y**4 + 0 - 2/11*y**2 - l*y**5 - 4/11*y**3 = 0. Calculate y.
-1/4, 0, 1
Let n(d) be the second derivative of 3*d**4/2 - 92*d**3/3 + 20*d**2 - 109*d. Determine j so that n(j) = 0.
2/9, 10
Suppose 3*s - 4 - 5 = 0. Solve -41*y - 2*y**3 - 2*y**5 + 31*y + 20*y**2 + 2 + 10*y**4 - 18*y**s = 0 for y.
1
Factor 12063 + 11726 - 122*h - 208*h + 3436 + h**2.
(h - 165)**2
Let v(s) be the third derivative of s**5/15 - 14*s**4/3 + 392*s**3/3 + 17*s**2 - 2*s. What is y in v(y) = 0?
14
Let f(c) = 33*c**4 + 69*c**3 - 93*c**2 - 432*c - 345. Let r(d) = 8*d**4 + 17*d**3 - 23*d**2 - 108*d - 86. Let p(i) = -5*f(i) + 21*r(i). Factor p(h).
3*(h - 3)*(h + 1)*(h + 3)**2
Suppose 3*j - 2*q - 1 - 1 = 0, -4*j + 3*q = -2. Suppose -2*s + 8 = -4*c, -2*c - 6 = -2*s - 0*c. Factor j*g**s - 3*g**2 - 9 - 3*g + 0*g**2 + 9*g.
-(g - 3)**2
Suppose 7*k - 16 = -k. Factor -3 + 3 + 20*r + 14*r**2 + 6*r**k - 15*r**3.
-5*r*(r - 2)*(3*r + 2)
Let v(b) be the third derivative of b**5/510 + 77*b**4/204 + 282*b**2. Factor v(w).
2*w*(w + 77)/17
Let x(q) be the third derivative of -q**8/14 - 17*q**7/35 - 27*q**6/40 + 13*q**5/20 + 11*q**4/8 - 3*q**3/2 - 13*q**2 - 6*q. Find k such that x(k) = 0.
-3, -1, 1/4, 1/2
Let q(c) = -21*c**3 - 23*c**2 - 48*c - 40. Let g(u) = -58*u**3 - 67*u**2 - 144*u - 121. Let t(v) = 4*g(v) - 11*q(v). Factor t(j).
-(j + 2)**2*(j + 11)
Let f(z) be the first derivative of -2/3*z - 2/3*z**2 + 1/3*z**4 + 0*z**3 - 43 + 2/15*z**5. Factor f(j).
2*(j - 1)*(j + 1)**3/3
Let t(a) be the second derivative of -a**5/20 + a**3/6 - 2*a**2 + 13*a. Let j(d) = 3*d**3 + d**2 - 3*d + 9. Let z(g) = -2*j(g) - 5*t(g). Factor z(y).
-(y - 1)*(y + 1)*(y + 2)
Let k(z) = z**3 - 11*z**2 - 8*z - 20. Let a be k(12). Find p such that -27*p**3 - 6*p + 21*p**2 + 89*p**5 - 35*p**5 + 15*p**4 - 29*p**5 - a*p**5 = 0.
0, 1, 2
Let i(f) be the third derivative of -f**6/80 - 3*f**5/10 + 19*f**4/16 + 39*f**3/2 - 253*f**2. Solve i(x) = 0 for x.
-13, -2, 3
Let x(i) = 2*i**5 + 4*i**4 - 16*i**3 + 10*i + 10. Let k(n) = n**5 + 2*n**4 - 8*n**3 + 4*n + 4. Let c(h) = 15*k(h) - 6*x(h). Let c(f) = 0. What is f?
-4, 0, 2
Let h(l) be the third derivative of -2*l**7/105 + l**6/6 - 4*l**5/15 + 169*l**2. Suppose h(o) = 0. What is o?
0, 1, 4
Suppose -5*o - 9*c + 65 = -4*c, 5*o - c = 41. Suppose 4*b - o = b. Factor 3/2*s**2 + 0 - 3/2*s**b - 3/2*s**4 + 3/2*s.
-3*s*(s - 1)*(s + 1)**2/2
Solve -5*n**2 + 61*n + 42*n + 76*n + 84*n + 220 - 363*n = 0 for n.
-22, 2
Let b(g) be the first derivative of g**3/3 - g**2/2 - 6*g + 290. Factor b(u).
(u - 3)*(u + 2)
Let b be 8/6 - (-32)/12. Let l(q) be the first derivative of q**4 - 16*q - q**b + 3*q**3 +