827. Find h, given that a(h) = 0.
1
Factor -1 - 7/2*z - 9/2*z**2 - 5/2*z**3 - 1/2*z**4.
-(z + 1)**3*(z + 2)/2
Let m(s) be the first derivative of -7*s**6/11 - 166*s**5/55 + 31*s**4/11 + 184*s**3/11 + 184*s**2/11 + 64*s/11 - 207. Suppose m(g) = 0. What is g?
-4, -1, -2/3, -2/7, 2
Factor -42 + 282 + 15*p**2 - 2184*p + 1814*p.
5*(p - 24)*(3*p - 2)
Let y(s) = 4*s**3 + 25*s**2 + 32*s - 13. Let r be y(-4). Factor 9/2*h**3 - 33/2*h**2 + 11/2*h + r + 7/2*h**4.
(h - 1)**2*(h + 3)*(7*h + 2)/2
Let m(v) be the second derivative of -v**7/14 - 13*v**6/10 - 93*v**5/20 + 101*v**4/4 + 70*v**3 - 294*v**2 + 468*v + 1. Determine x, given that m(x) = 0.
-7, -2, 1, 2
Suppose 3*s - 120 = u, -7*u + 3*u - 90 = -2*s. Let h(a) = 19*a**2 + 6*a. Let q(k) = -3*k**2 - k. Let f(d) = s*q(d) + 6*h(d). Factor f(w).
-3*w*(w + 1)
Let o(j) be the first derivative of -3*j**4/4 - 10*j**3/3 - 9*j**2/2 + j + 22. Let h(c) = c - 1. Let n(g) = 3*h(g) + 3*o(g). Determine k, given that n(k) = 0.
-2, -4/3, 0
Let k = 1253/471 + 1/157. Determine o so that 0 - 14/9*o**4 + 8/9*o**2 + k*o**3 + 0*o = 0.
-2/7, 0, 2
Let a be (-13)/1 - (-5)/5. Let s(y) = y**3 + 12*y**2 + y + 14. Let o be s(a). Factor -4*l**o - 6*l + l + 14 - 6 + l.
-4*(l - 1)*(l + 2)
Factor -5/3*h**4 - 95/3*h - 10 - 15*h**3 - 35*h**2.
-5*(h + 1)**3*(h + 6)/3
Solve 30 + 3*m**5 - 40*m**2 + 9*m + 7*m + m + 2*m**5 - 30*m**3 + 10*m**4 + 8*m = 0 for m.
-3, -1, 1, 2
Let q = -5473 + 5476. Solve 0*u - 3/7*u**2 + 3/7*u**q + 0 = 0 for u.
0, 1
Let w(s) be the first derivative of -s**6/21 + 22*s**5/35 - 23*s**4/7 + 60*s**3/7 - 81*s**2/7 + 54*s/7 + 98. Factor w(h).
-2*(h - 3)**3*(h - 1)**2/7
Let o(h) be the first derivative of -5*h**3/3 + 105*h**2/2 - 450*h - 173. Factor o(n).
-5*(n - 15)*(n - 6)
Let d(w) = w**2 + 51*w - 402. Let o be d(-58). Find x, given that -6/7*x**2 + 6/7*x**o + 0*x + 0 + 2/7*x**5 - 2/7*x**3 = 0.
-3, -1, 0, 1
Let j(m) be the first derivative of m**4/10 + 48*m**3/5 + 1296*m**2/5 - 205. Factor j(u).
2*u*(u + 36)**2/5
Suppose -4 = -3*s + 20. Let p be 0/s - (-2)/(-4)*0. Factor 0*c**3 + 0*c - 2/5*c**2 + p + 2/5*c**4.
2*c**2*(c - 1)*(c + 1)/5
Let q = -26094/17 + 1536. Determine i so that -12/17*i**3 + 0*i - q*i**4 - 2/17*i**2 + 0 = 0.
-1/3, 0
Let i(w) be the third derivative of w**6/1620 + w**5/540 - w**3/3 - 11*w**2. Let b(a) be the first derivative of i(a). Determine z so that b(z) = 0.
-1, 0
Let m(j) be the second derivative of 0*j**3 + 0*j**5 + 1/32*j**4 - 7/2*j**2 + 0 - 1/160*j**6 + 7*j. Let i(t) be the first derivative of m(t). Factor i(u).
-3*u*(u - 1)*(u + 1)/4
Let r(u) = -u**2 - 8*u + 3. Suppose -7*v + 3*p - 47 = -3*v, 0 = 3*v + p + 19. Let t be r(v). Factor -4/3 + 4/3*f - 1/3*f**t + 1/3*f**2.
-(f - 2)*(f - 1)*(f + 2)/3
Let i(q) be the first derivative of 34*q**5/75 + 26*q**4/5 + 108*q**3/5 + 36*q**2 + 54*q/5 + 188. Let i(g) = 0. Calculate g.
-3, -3/17
Let o(j) be the second derivative of j**8/12320 - j**7/770 + j**6/110 - 2*j**5/55 - 4*j**4/3 - 4*j. Let m(s) be the third derivative of o(s). Factor m(n).
6*(n - 2)**3/11
Find v such that -3/7*v**2 + 3/7*v**4 + 6*v - 6*v**3 + 0 = 0.
-1, 0, 1, 14
Solve 2/23*b**2 + 40/23 + 42/23*b = 0 for b.
-20, -1
Let u(w) be the second derivative of -w**5/70 + 5*w**4/42 - w**3/3 + 3*w**2/7 - w + 10. Factor u(p).
-2*(p - 3)*(p - 1)**2/7
Let w(b) = b**2 - 2*b + 1. Let l(o) = o - 1. Let y(z) = 5*l(z) - w(z). Let j be y(5). Determine u, given that 40*u + j*u**2 - 40*u - 4*u**3 = 0.
0, 1
Let i be 12/(-15) + 726/770. Suppose -5/7*v**2 + 3/7*v**5 + 5/7*v**4 + 0 - i*v**3 - 2/7*v = 0. Calculate v.
-1, -2/3, 0, 1
Let s(r) = -6*r + 3. Let a(w) be the first derivative of -w**3/3 - 5*w**2/2 + 2*w - 10. Let n(d) = 3*a(d) - 2*s(d). Factor n(i).
-3*i*(i + 1)
Suppose 0 = -12*p + 17*p - 50. Let t be 60/(-6)*(-4)/p. Factor 4*x**4 - 2*x**3 + 0*x**t - 5*x**4 + 2*x**2 - x**4 + 2*x**5.
2*x**2*(x - 1)**2*(x + 1)
Let y(d) be the second derivative of 1/22*d**4 + 0*d**2 + 0 - 2/33*d**3 + 0*d**5 - 1/165*d**6 - 12*d. Factor y(h).
-2*h*(h - 1)**2*(h + 2)/11
Let g(q) = -q**3 - 2*q**2 - 2*q + 2. Let w(d) = -d**3 - 4*d + 4*d + d - 1. Suppose -22 = 2*b - 20. Let a(z) = b*g(z) - 2*w(z). What is t in a(t) = 0?
-2/3, 0
Let c(u) be the first derivative of 121*u**4/4 + 33*u**3 - 324*u**2 + 432*u - 432. Factor c(a).
(a + 3)*(11*a - 12)**2
Let d(r) = -2*r**2 - 10*r + 2. Let h be d(-5). Let p be 6 - (-48)/(-9) - h/3. Factor p + 1/4*v**4 + 1/4*v**3 + 0*v + 0*v**2.
v**3*(v + 1)/4
What is o in 10/3*o**3 + 0 + 6*o**2 - 4/3*o = 0?
-2, 0, 1/5
Let o be (-19)/(11913/(-143260)) + (-2)/(-11). Factor o*n**5 + 128/3*n + 616*n**3 + 800/3*n**2 + 1862/3*n**4 + 0.
2*n*(n + 1)*(7*n + 4)**3/3
Suppose -4*o = -3*v - 33 + 6, 0 = -o - 3*v - 12. Factor 8*h**o - 4*h + h**3 + 3*h**2 + 4*h.
3*h**2*(3*h + 1)
Let k = 5/3567 + 791/1189. Find n, given that 32/3 + 8*n + 0*n**2 - k*n**3 = 0.
-2, 4
Suppose 530*l = 1079*l - 536*l - 39. Let k = -8 + 14. Factor -39*z**l + 0 + k*z**2 + 147/4*z**5 + 0*z + 105/2*z**4.
3*z**2*(z + 2)*(7*z - 2)**2/4
Let f = 97 + -96. Let y(b) = b**4 - b**3 + b**2 - b. Let p(t) = 12*t**4 - 99*t**3 + 144*t**2 - 69*t + 12. Let g(q) = f*p(q) + 15*y(q). Factor g(d).
3*(d - 2)*(d - 1)**2*(9*d - 2)
Let q(a) = -a**3 + 4*a**2 - 6. Let p be (12/(-10))/(40/(-100)). Let i be q(p). Determine c, given that -5/2*c**2 - c - 2*c**i - 1/2*c**4 + 0 = 0.
-2, -1, 0
Let s(r) be the first derivative of 7*r**5/4 + 5*r**4 + 5*r**3/2 - 5*r**2 + 5*r - 50. Let t(v) be the first derivative of s(v). Factor t(y).
5*(y + 1)**2*(7*y - 2)
Let x(z) be the first derivative of -8*z**3/3 + 277*z**2 - 138*z + 451. Find f such that x(f) = 0.
1/4, 69
Let w(q) be the first derivative of -q**6/300 - q**5/150 + q**4/60 + q**3/15 - 2*q**2 + 9. Let l(u) be the second derivative of w(u). Factor l(a).
-2*(a - 1)*(a + 1)**2/5
Let z = 34 + -21. Suppose 25*w + 3 + 2*w**2 - 28*w**3 + 3*w**3 - z + 8*w**2 = 0. Calculate w.
-1, 2/5, 1
Let -2*o**2 - 13456 - 3*o**2 + 4*o**2 + 464*o - 7*o**2 + 4*o**2 = 0. What is o?
58
Let g(c) = -c**2 + 2*c + 3. Let d be g(-3). Let m = 15 + d. Solve -2*p**m + p**2 + 2*p**2 - 3*p**2 + 2*p**2 = 0 for p.
0, 1
Let p(q) be the third derivative of -7*q**2 + 0*q - 1/6*q**3 + 1/180*q**5 - 1/36*q**4 + 0. What is w in p(w) = 0?
-1, 3
Suppose 2*c + c = -5*v + 8, 0 = v + 5. Suppose 16 = c*n - 17. Find l such that 0 + 2/3*l**2 - 1/3*l + 1/3*l**5 - 2/3*l**4 + 0*l**n = 0.
-1, 0, 1
Let b(y) = 37*y**2 - 149*y - 43. Let c(l) = 38*l**2 - 150*l - 44. Let z(q) = 6*b(q) - 5*c(q). Find f such that z(f) = 0.
-1/4, 19/4
Let x(k) be the first derivative of -75/4*k**2 - 28*k**3 + 23 - 9/2*k - 6*k**4. Factor x(a).
-3*(a + 3)*(4*a + 1)**2/2
Let s be (55/(-33))/(69/(-18) - -3). Solve 2*l + 0 - 2/3*l**s = 0 for l.
0, 3
Let o(m) be the first derivative of 29 - 13/20*m**5 + 1/12*m**6 + 5/2*m**2 + 2*m**4 - 37/12*m**3 - m. Find x, given that o(x) = 0.
1/2, 1, 2
Let o(p) be the third derivative of -12*p**2 + 0 + 2/7*p**3 + 1/105*p**6 + 2/735*p**7 - 4/105*p**5 - 1/21*p**4 + 0*p. Solve o(u) = 0.
-3, -1, 1
Let l(w) be the third derivative of 7*w**2 + 2*w**3 + 1/15*w**5 + 0 + 0*w - 2/3*w**4. Factor l(y).
4*(y - 3)*(y - 1)
Let p(f) be the first derivative of 0*f - f**4 - 4/5*f**5 + 0*f**2 - 17 + 0*f**3. Let p(q) = 0. What is q?
-1, 0
Let d(n) be the second derivative of 3/8*n**2 + 3/16*n**4 + 3/80*n**5 + 0 + 22*n + 3/8*n**3. Find f, given that d(f) = 0.
-1
Suppose 0*l - 3*l + 15 = 0. Let u(r) = -2 - 2 + l + 2*r**4 - 2*r**2. Let g(o) = -o**4 + o**2 + 1. Let q(y) = g(y) - u(y). Factor q(b).
-3*b**2*(b - 1)*(b + 1)
Solve 62/5*i**4 + 0 - 4/5*i + 2*i**2 + 22/5*i**5 + 54/5*i**3 = 0 for i.
-1, 0, 2/11
Let y(m) be the second derivative of m**4/6 - 58*m**3/3 + 841*m**2 - m - 48. Let y(k) = 0. What is k?
29
Let k(o) = -2*o**2 + 8*o + 28. Let v be k(6). Let f(a) be the second derivative of 0 - 5/2*a**3 + a**v + 3/2*a**2 + 5*a. Suppose f(s) = 0. What is s?
1/4, 1
Let 116/5*b - 1682/5 - 2/5*b**2 = 0. What is b?
29
Let g(q) be the first derivative of 3*q**4/16 - 17*q**3/4 + 21*q**2/4 + 24*q + 256. Factor g(v).
3*(v - 16)*(v - 2)*(v + 1)/4
Let u(p) be the third derivative of p**6/80 + 27*p**5/40 - 15*p**4/8 - 14*p**3 + 318*p**2. Suppose u(f) = 0. Calculate f.
-28, -1, 2
Determine y so that 0*y + 0 - 18*y**2 - 3/2*y**4 + 39/2*y**3 = 0.
0, 1, 12
Let b(p) = -30*p - 19. Let q be b(4). Let o = -687/5 - q. Factor -o