36. Let a = v - 130. Find b such that 0*b**3 - 4/3*b + 0 - 2*b**2 + 2/3*b**a = 0.
-1, 0, 2
Let h(o) be the first derivative of 0*o**3 + 0*o + 0*o**2 + 1/10*o**5 - 1/12*o**6 + 10 + 0*o**4. Solve h(x) = 0 for x.
0, 1
Let m be ((2 - 8) + 9)*(1 - 0). Solve z**4 - 17*z**3 + 11*z**3 + 7*z**m = 0 for z.
-1, 0
Factor -6052*l**2 - 2*l + 6062*l**2 - 10 + 4*l**3 - 2*l.
2*(l - 1)*(l + 1)*(2*l + 5)
Let -8/11*a**2 + 0*a + 6/11*a**4 + 0*a**3 + 0 - 2/11*a**5 = 0. What is a?
-1, 0, 2
Let q(m) be the first derivative of -2*m**3/21 - 138*m**2/7 - 9522*m/7 + 52. Suppose q(f) = 0. What is f?
-69
Let 8/9*i - 2/9*i**3 - 20/9*i**2 + 80/9 = 0. What is i?
-10, -2, 2
Let k(i) = -4*i**3 + 18*i**2 + 13*i - 12. Let l be k(5). Find a, given that -4/15*a**4 + 8/3*a + 16/15 + 4/5*a**2 - 2/3*a**l = 0.
-2, -1/2, 2
Let v(c) = -4*c**3 + 152*c**2 + 564*c - 336. Let a(o) = -26 - 23 + o**3 + o - o**2 + 50. Let p(w) = 12*a(w) + v(w). Factor p(u).
4*(u + 9)**2*(2*u - 1)
Let u(z) = -z**2 - z - 1. Let g(y) = 2*y**2 - 9*y - 17. Let x(o) = -g(o) - 3*u(o). Let x(r) = 0. Calculate r.
-10, -2
Let b(j) be the first derivative of -1/7*j**3 + 30/7*j**2 - 300/7*j + 14. Factor b(w).
-3*(w - 10)**2/7
Let a be 35/273*180/150. Let -6/13*b**3 + 6/13*b - a*b**2 + 0 + 2/13*b**4 = 0. Calculate b.
-1, 0, 1, 3
Factor -2/7*h**3 + 404/7*h**2 - 20402/7*h + 0.
-2*h*(h - 101)**2/7
Let n(b) = -b**2 - 8*b - 3. Let f be n(-5). Factor 5 - 3*r**2 - 6*r**3 + f - 3*r**4 - 17.
-3*r**2*(r + 1)**2
Let y = -3029/2 - -1519. Suppose 0 - 3/4*m - 27/4*m**3 + y*m**2 = 0. What is m?
0, 1/3
Suppose -10*v = -11*v + 2. Solve 7 + 17 + 0*d - 8 + 8*d**v - 36*d = 0 for d.
1/2, 4
Solve 1294*j + 17*j**2 - 1244*j + 26 - 10*j**2 + 15*j**2 - 2*j**3 = 0 for j.
-1, 13
Let l(f) be the second derivative of 5/6*f**3 - 4*f - 5/18*f**4 - 1/6*f**5 - 5/6*f**2 + 0 - 5/126*f**7 + 1/6*f**6. Factor l(k).
-5*(k - 1)**4*(k + 1)/3
Let c = 1674/2905 - 2/415. Let n(d) be the first derivative of -1/7*d**2 - 1 + c*d**3 - 1/14*d**4 - 4/35*d**5 - 4/7*d. Solve n(w) = 0 for w.
-2, -1/2, 1
Let j(a) = -8*a**2 + 53*a + 147. Let z(f) = 3*f**2 - 18*f - 49. Let y(v) = -4*j(v) - 11*z(v). Factor y(m).
-(m + 7)**2
Let l = 21 + -18. Factor 0*d**4 - 7*d**3 - d**3 + 6*d**l - 2*d**4.
-2*d**3*(d + 1)
Suppose 13 - 10 = -g. Let o be (-8)/28 + (g - 239/(-28)). Find t, given that o*t**2 - 9/2 - 57/4*t = 0.
-2/7, 3
Let r(b) be the first derivative of -1/40*b**4 + 3 + 27/10*b - 27/20*b**2 + 3/10*b**3. What is j in r(j) = 0?
3
Let i be (8/(-28))/((-7)/98). Let s(f) be the first derivative of i - f - 1/12*f**3 + 1/2*f**2. What is g in s(g) = 0?
2
Let m(l) be the second derivative of l**4/3 + 38*l**3/3 - 40*l**2 - 4*l - 10. Find u such that m(u) = 0.
-20, 1
Let n(f) be the second derivative of f**7/42 + 5*f**6/24 + f**5/4 - 15*f**4/8 - 4*f**2 + 21*f. Let k(m) be the first derivative of n(m). Factor k(o).
5*o*(o - 1)*(o + 3)**2
Let a be 2/(-1)*-6*2/8. Factor -h**3 - 7*h**3 + 7*h**a.
-h**3
Let j be (-58)/5 - (9/(-15) - -1). Let h be (-4)/j - 5/(-12). Find q, given that 3/4*q**4 + 0 - h*q**3 + 0*q - 1/4*q**5 + 1/4*q**2 = 0.
0, 1
Let f be (11 + 1 + -11)*0. Find d, given that f*d + 0 - 2/7*d**3 - 2/7*d**2 = 0.
-1, 0
Suppose 13 = -4*g + 25. What is i in -6 - 4*i**2 + 3*i**3 - 2 - 2*i**g + 17*i - 6*i**2 = 0?
1, 8
Let x(y) be the first derivative of -120*y**2 + 320*y + 42 - 5/4*y**4 - 25*y**3. Determine m, given that x(m) = 0.
-8, 1
Factor 13*n**5 - 15*n**5 - 5 + 6*n**4 - 18*n + 4*n**2 - 5 + 20*n**3.
-2*(n - 5)*(n - 1)*(n + 1)**3
Let p(i) = 4*i**2 + 3*i - 4. Let w be p(1). Let h(s) = 3*s**2 + 2*s + 1. Let q be h(-2). Suppose -q*v - 2 + w + 7*v**2 + 1 = 0. Calculate v.
2/7, 1
Let n(g) = -3*g**4 - 30*g**3 + 120*g**2 - 162*g + 87. Let z(q) = -5*q**4 - 60*q**3 + 238*q**2 - 324*q + 173. Let r(a) = -11*n(a) + 6*z(a). Factor r(u).
3*(u - 3)**3*(u - 1)
Let f be -3*(-141)/63 - 14/(-49). Let l be 2/(-4)*(-1 - 3). Solve -2*v**2 + 6*v**l + v**3 + f*v**5 + 23*v**3 + v**5 - 28*v**4 - 8*v = 0.
-1/2, 0, 1, 2
Suppose -54*z + 3*z**2 - 89 + 332 + 0*z**2 = 0. Calculate z.
9
Find o, given that 40/13*o**4 - 6/13*o**5 - 88/13*o**3 - 2/13*o + 68/13*o**2 - 12/13 = 0.
-1/3, 1, 2, 3
Let y = -119/6 - -20. Suppose -5*f = -5*m + 52 - 47, 5*f - 17*m + 17 = 0. Factor 1/3*d + f + y*d**2.
d*(d + 2)/6
Suppose 5*y - 60 = -0*y. Let u = -6 + y. Suppose -j + u*j**2 + 3*j**5 - 6*j**4 + 2*j - 4*j = 0. Calculate j.
-1, 0, 1
Let w(l) be the second derivative of l**5/30 + l**4/6 + l**3/3 + l**2/3 + 4*l - 24. Let w(u) = 0. Calculate u.
-1
Let t(y) be the second derivative of y**6/45 + 8*y**5/15 + 5*y**4/6 - 694*y. Determine k so that t(k) = 0.
-15, -1, 0
Let v = 9 + -2. Determine c so that v*c**3 + 68*c**4 - 1 - 70*c**4 + 4*c - 9*c**2 + c = 0.
1/2, 1
Let m(c) be the third derivative of 2/27*c**3 + 9*c**2 - 7/108*c**4 + 0 + 1/135*c**6 - 1/54*c**5 + 0*c. Factor m(j).
2*(j - 2)*(j + 1)*(4*j - 1)/9
Suppose -4*d - 31 + 11 = 4*c, -2*c + 4*d + 20 = 0. Suppose -30*a - 2*a = -c*a. Determine n, given that 1/2*n**3 + 0 + 0*n**4 + a*n**2 + 0*n - 1/2*n**5 = 0.
-1, 0, 1
Let a = -106 - -104. Let d be ((2 + a)/1)/1. Let 0 + 1/2*z**4 + 1/2*z**3 + d*z + 0*z**2 = 0. Calculate z.
-1, 0
Find o, given that -728/9*o**2 - 440/9*o + 98/9*o**3 - 64/9 = 0.
-2/7, 8
Let r(k) be the second derivative of -k**7/28 + 9*k**6/40 - 13*k**4/8 - 3*k**3/4 + 27*k**2/8 + 2*k - 102. Let r(x) = 0. What is x?
-1, 1/2, 3
Suppose g = h + 3*h + 23, -4*g + 114 = -5*h. Suppose -91 = -v - g. Suppose 8*x + 3*x - 44*x**2 + 29*x**3 - 3*x - v*x**5 + 44*x**4 + 23*x**3 = 0. What is x?
-1, 0, 1/3, 2/5, 1
Let x(q) be the third derivative of 2*q**7/105 + 7*q**6/120 + q**5/20 + 60*q**2. Factor x(o).
o**2*(o + 1)*(4*o + 3)
Let y(u) be the second derivative of 1/3*u**2 + 0 + 0*u**3 + 0*u**5 + 1/45*u**6 - 1/9*u**4 - 11*u. Factor y(d).
2*(d - 1)**2*(d + 1)**2/3
Let q(h) = 117*h + 7020. Let c be q(-60). What is t in 2/21*t**2 - 2/21*t**3 + 0 + c*t = 0?
0, 1
Let t(l) = 5*l + 8. Let o(s) = -4*s - 9. Let w(n) = 4*o(n) + 3*t(n). Let j be w(-12). Solve 5*x**2 - 5*x**2 - 2*x - 1 - x**2 + j = 0.
-1
Let o = -2373 - -7127/3. Suppose -4*j + o + 4/3*j**2 = 0. Calculate j.
1, 2
Let w(l) be the second derivative of -l**4/4 - l**3/2 + 2*l - 496. Factor w(p).
-3*p*(p + 1)
Let i = -1434 - -1440. Let g(y) be the first derivative of -9/10*y**2 + 3/5*y + 3/5*y**3 + i - 3/20*y**4. Factor g(k).
-3*(k - 1)**3/5
Let t(v) = -3*v - 5 - 2 + 8. Let r be t(-3). Factor 26*n - n**2 + 3 + 9 + r*n - 45*n**3 - 2*n**2.
-3*(n - 1)*(3*n + 2)*(5*n + 2)
Let r = -136 + 140. Suppose -5*d + 2*d = k - 2, -2*k + r = 0. Factor -2/9*b**3 + d*b + 0*b**2 + 0.
-2*b**3/9
Let g(b) be the second derivative of b**6/2520 - b**4/168 - 23*b**3/6 + 27*b. Let t(x) be the second derivative of g(x). Factor t(m).
(m - 1)*(m + 1)/7
Let v(b) be the second derivative of -b**6/70 + 3*b**5/28 - 9*b**4/28 + b**3/2 - 3*b**2/7 - 139*b - 2. Let v(k) = 0. What is k?
1, 2
Factor 22/13*j**2 + 210/13*j + 108/13.
2*(j + 9)*(11*j + 6)/13
Factor 1/3*v**2 + 0 - 4/3*v.
v*(v - 4)/3
Let r(v) be the first derivative of -5*v**4 + 4*v**3 + 4*v**2 + 82. Factor r(y).
-4*y*(y - 1)*(5*y + 2)
Factor 8/3*b - 2/3*b**3 + 2/3*b**2 - 8/3.
-2*(b - 2)*(b - 1)*(b + 2)/3
What is k in -12 + 122*k + 70 - 30 - 18*k**2 = 0?
-2/9, 7
Let h(t) be the first derivative of 4 + 2*t**2 - t**3 + 1/6*t**4 - t. Let w(b) be the first derivative of h(b). What is u in w(u) = 0?
1, 2
Solve 63/5*q + 3/5*q**2 - 3*q**3 + 3/5*q**4 - 54/5 = 0 for q.
-2, 1, 3
Factor -16/9*k + 4/3*k**3 + 4/9*k**4 + 0*k**2 + 0.
4*k*(k - 1)*(k + 2)**2/9
Let h(n) = n**2 + 81*n + 392. Let t be h(-76). Solve 12*k**3 - 21/4*k**4 - 12*k - 6*k**2 + t + 3/4*k**5 = 0 for k.
-1, 2
Let w(v) be the first derivative of -v**6/3 + 14*v**5/5 + 9*v**4 + 4*v**3/3 - 17*v**2 - 18*v - 51. Determine u so that w(u) = 0.
-1, 1, 9
Let q(r) be the third derivative of 0 + 0*r + 0*r**4 + 0*r**3 - 1/60*r**6 - 1/420*r**7 - 22*r**2 - 1/30*r**5. Solve q(h) = 0.
-2, 0
Let z be ((-4)/32)/(165/(-8)). Let b(x) be the second derivative of -8*x - 2/11*x**2 + 5/33*x**3 + 0 + z*x**6 - 1/110*x**5 - 1/22*x**4. Factor b(g).
2*(g - 1)**3*(g + 2)/11
Let y(x) be the first derivative of -x**4/18 + 4*x**2/3 - 32*x/9 + 153. Solve y(g) = 0 for g.
-4, 2
Let z = 40 - 35. Suppose -5*l - 18 = -6*l. Factor -l*t - 28*t**3 + 32*t**2 - 2*t**z - t**3 + 12*t**4 + 7*t**3 + 4 - 6*t**3.
-2*(t - 