(3). Let u = n - 50. Factor -j - 20 + 26 - 33*j + 40*j**u.
2*(4*j - 1)*(5*j - 3)
Suppose -18 = 13*d - 22*d. Let f be 37/7 + 2/1 + -7. Factor -4*i - 14 - f*i**d.
-2*(i + 7)**2/7
Let i(s) be the second derivative of s**5/170 + 5*s**4/34 - 6*s**3/17 - 32*s**2/17 + 4*s - 10. Solve i(r) = 0.
-16, -1, 2
Let t(c) be the first derivative of 16*c**2 - 137 + 256*c + 1/3*c**3. Solve t(q) = 0 for q.
-16
Let h = -175072 - -175075. Factor 2/3*z**4 - 4/3*z**2 + 0*z - 2/3*z**h + 0.
2*z**2*(z - 2)*(z + 1)/3
Let g(x) be the first derivative of x**6/18 - 31*x**5/15 + 37*x**4/2 + 320*x**3/9 - 256*x**2/3 - 2402. Find u such that g(u) = 0.
-2, 0, 1, 16
Suppose 3*l = -4*v + 14, 8 = -3406*l + 3409*l + v. Let 2 + l*g + 1/2*g**2 = 0. Calculate g.
-2
Let t(p) be the third derivative of -p + 0 + 1/660*p**5 - 5/22*p**4 + p**2 + 150/11*p**3. What is d in t(d) = 0?
30
Let i(f) be the second derivative of -f**6/21 - 11*f**5/10 - 15*f**4/7 + 116*f**3/21 + 8*f**2 - 1432*f. Suppose i(r) = 0. What is r?
-14, -2, -2/5, 1
Factor 920/19*u - 144/19*u**2 - 2/19*u**3 - 1248/19.
-2*(u - 4)*(u - 2)*(u + 78)/19
Suppose 0 = 9*r - 2271 + 129. Let s be (-82)/(-30) + r/(-170). Factor 4*n - s*n**2 + 0.
-4*n*(n - 3)/3
Solve -2/3*c**4 + 0 - 24*c + 8*c**3 - 46/3*c**2 = 0.
-1, 0, 4, 9
Let q(y) be the second derivative of -y**5/360 - y**4/24 - y**3/4 - 3*y**2 - 7*y. Let w(x) be the first derivative of q(x). Determine k, given that w(k) = 0.
-3
Suppose -4*m - 5*w + 22 = 0, 0 = -2*m + 6*m + 2*w - 16. Factor k**2 - 1652*k + k**m - 1 + 0 + 1651*k.
(k - 1)*(k + 1)**2
Let k = 638201/9 + -70911. Determine h, given that k*h**5 + 14/9*h**4 - 64/9*h - 8/3 + 2/3*h**3 - 46/9*h**2 = 0.
-6, -1, 2
Let s(t) be the first derivative of 4/5*t**5 - 3*t**4 + 6*t**2 - 8*t + 4/3*t**3 - 58. Solve s(i) = 0 for i.
-1, 1, 2
Let y = 1661 - 79727/48. Let x(s) be the second derivative of -1/24*s**3 - 1/4*s**2 + 0 + 12*s + y*s**4. Solve x(b) = 0.
-1, 2
Factor 0 - 2/7*i**3 + 606/7*i + 28*i**2.
-2*i*(i - 101)*(i + 3)/7
Let j be 2/(-12)*2*(-144)/32. Let u(c) be the first derivative of -32 + 3/2*c**3 - j*c**2 - 3/8*c**4 + 0*c. Factor u(z).
-3*z*(z - 2)*(z - 1)/2
Let t(p) be the second derivative of -2/7*p**2 + 1/147*p**7 - 12 + 3/7*p**3 + 2*p + 1/5*p**5 - 8/21*p**4 - 2/35*p**6. Solve t(r) = 0 for r.
1, 2
Factor -2/7*r**2 - 176/7 - 38/7*r.
-2*(r + 8)*(r + 11)/7
Let p be (181 - 196)*-2*(-3)/(-60). Let q(t) be the first derivative of -9 + p*t**3 - 3*t**2 + 2*t. Factor q(r).
(3*r - 2)**2/2
Let m(l) be the third derivative of l**7/490 + l**6/280 - 11*l**5/140 - 9*l**4/56 + 9*l**3/7 - 2280*l**2. Let m(c) = 0. What is c?
-3, -2, 1, 3
Let x(k) be the second derivative of 3*k**5/20 - 473*k**4/4 - 8*k + 48. Factor x(z).
3*z**2*(z - 473)
Suppose -18*r + 83*r = 23*r + 126. Determine n, given that -15/2*n**r + 15/4*n**5 + 0 - 3*n**2 + 19/4*n**4 + 2*n = 0.
-2, -2/3, 0, 2/5, 1
Let n be 21 - 49 - -17 - -13. Factor -325*j - 573/4*j**n - 169 - 1/4*j**4 + 25/2*j**3.
-(j - 26)**2*(j + 1)**2/4
Let x = 3248807/67965 - 16/13593. Suppose -11/5*h - 6/5 + x*h**4 + 84/5*h**5 + 67/5*h**2 + 227/5*h**3 = 0. Calculate h.
-1, -2/3, -3/7, 1/4
Let s(y) = 19*y**4 + 61*y**3 - 9*y**2 - 712*y - 672. Let g(c) = 9*c**4 + 31*c**3 - 3*c**2 - 356*c - 336. Let z(x) = 11*g(x) - 5*s(x). Let z(w) = 0. Calculate w.
-7, -4, -1, 3
Let 760*n - 774*n + 12 + 88*n**2 - 86*n**2 = 0. What is n?
1, 6
Let w(r) be the third derivative of r**7/42 - 9*r**6/8 - 223*r**5/12 - 835*r**4/8 - 255*r**3 - 130*r**2 + 2*r + 5. Find u such that w(u) = 0.
-3, -1, 34
Solve 196/15 - 2/15*q**3 - 196/15*q**2 + 2/15*q = 0.
-98, -1, 1
Let b(p) = p**4 - p**3 - p**2 + p + 1. Let z(l) = -9*l**4 + 317*l**3 + 9*l**2 - 317*l - 8. Let u(g) = -40*b(g) - 5*z(g). Factor u(s).
5*s*(s - 309)*(s - 1)*(s + 1)
Let u(b) be the first derivative of 3/2*b**2 - 1/4*b**4 + 0*b**3 + 2*b + 23. Find m, given that u(m) = 0.
-1, 2
Let q = -1093 + 580. Let z be -6 - 2*-1 - 2508/q. Let 4/9*w**3 - z + 14/9*w**2 + 8/9*w = 0. Calculate w.
-2, 1/2
Let u = 5566/54225 + 51/6025. Factor 19/9 + u*o**3 + 13/3*o + 7/3*o**2.
(o + 1)**2*(o + 19)/9
Let s be -4 + (1 - (-40)/5). Suppose -s*d + 80 = 4*n - d, -46 = -2*n - 5*d. Factor 30*q**3 + 5*q**5 + 20*q**2 + 23*q + 20*q**4 - n*q + 0*q**3.
5*q*(q + 1)**4
Let c(y) = 18*y - 62. Let r be c(17). Let i = r + -1217/5. What is o in -9/5*o + i*o**2 + 6/5 = 0?
1, 2
Suppose 10*b - 124 = -54. Suppose 0 = 6*v - b*v + 3. Determine r so that 3/4*r**5 - 3/2*r**4 + 0 - 21/4*r**3 - v*r**2 + 0*r = 0.
-1, 0, 4
Let l(k) be the first derivative of k**7/3360 + k**6/480 - k**5/120 - 40*k**3/3 + 163. Let w(x) be the third derivative of l(x). Factor w(c).
c*(c - 1)*(c + 4)/4
Determine u so that 630*u - u**2 + 909*u - 438*u - 1745 + 639*u + 6*u**2 = 0.
-349, 1
Let h = 834125 + -834125. Factor 4/3*d**2 + 0 + 0*d - 1/3*d**4 + h*d**3.
-d**2*(d - 2)*(d + 2)/3
Suppose 0 = -r - 4*w + 2, -4*r - 2*w = -3*r - 2. Suppose 2*k + 2 = -r*u, 3*u + 32 = 3*k - u. Find l, given that -l**3 + 2 - k*l - 5*l + 3*l + l + 4*l**2 = 0.
1, 2
Let h(y) be the first derivative of -y**6/40 + 13*y**5/20 - 6*y**4 + 18*y**3 + 6*y**2 + y - 34. Let w(o) be the second derivative of h(o). Factor w(s).
-3*(s - 6)**2*(s - 1)
Let p(x) be the second derivative of 3*x**5/20 - 11*x**4 - 139*x**3/2 - 141*x**2 + x + 79. Find v such that p(v) = 0.
-2, -1, 47
Let w(v) be the second derivative of 3*v**4 + 0*v**2 - 3*v + 6/5*v**5 + 2/9*v**6 + 7 + 1/63*v**7 + 3*v**3. Find x, given that w(x) = 0.
-3, -1, 0
Let p = -947/35 - -1213/35. Let -12/5 - 16/5*o**2 - p*o = 0. What is o?
-2, -3/8
Let s(t) be the first derivative of 2*t**5/15 - 4*t**3/3 - 8*t**2/3 - 2*t - 6613. Suppose s(h) = 0. What is h?
-1, 3
Factor 26*j**3 - 632/3*j**2 - 1/3*j**5 + 763/3*j + 68/3*j**4 - 92.
-(j - 69)*(j - 1)**3*(j + 4)/3
Let t = 56177/21 + -2675. Let n(s) be the first derivative of -6 - 2/7*s**2 - 2/35*s**5 + 0*s + t*s**3 + 1/7*s**4. Factor n(w).
-2*w*(w - 2)*(w - 1)*(w + 1)/7
Let c = -701417/4 - -175355. Factor c*v**2 + 75/4 + 15/2*v.
3*(v + 5)**2/4
Let q(o) be the first derivative of 3*o**5/5 - 21*o**4/4 + 4*o**3 + 18*o**2 + 1606. Factor q(b).
3*b*(b - 6)*(b - 2)*(b + 1)
Let s(r) = r**2 + 14*r - 6. Let b be s(-15). Let k be (2 - 4)/(((-24)/b)/4). Factor y**4 - 3 + 12*y**3 + 0 + 5 - 3*y**2 - 11*y**k - y.
(y - 1)**2*(y + 1)*(y + 2)
Suppose -438 + 437*r - 16637*r**2 + 33270*r**2 - 16632*r**2 = 0. What is r?
-438, 1
Let v(g) = g**2 - 599*g + 84449. Let f be v(227). Let 3/5*l**f - 7*l**3 + 4*l + 8/5*l**4 + 0 + 4/5*l**2 = 0. Calculate l.
-5, -2/3, 0, 1, 2
Let o(p) be the first derivative of -169*p**5/5 - 13*p**4 + 55*p**3 + 26*p**2 + 4*p + 1059. Factor o(s).
-(s - 1)*(s + 1)*(13*s + 2)**2
Let y(v) be the first derivative of -1/2*v**4 - 2/15*v**5 + 29 + 0*v - 2/3*v**2 + 1/9*v**6 + 10/9*v**3. What is g in y(g) = 0?
-2, 0, 1
Let g = -475891192 + 1283478562816/2697. Let k = g + -4/899. Solve 2/3*c**2 - k - 2*c = 0 for c.
-2, 5
Let k = 617510/3 + -205832. Suppose -12*o**3 - 2/3*o**5 - 26/3*o + 2 + k*o**4 + 44/3*o**2 = 0. What is o?
1, 3
Let r(x) be the third derivative of 1/56*x**4 - 1/280*x**6 + 2*x - 20*x**2 + 0 + 1/20*x**5 - 3/7*x**3 - 1/490*x**7. Find m, given that r(m) = 0.
-3, -1, 1, 2
Let a(c) be the second derivative of 0 + 0*c**3 + 1/170*c**5 + 9/34*c**4 + 130*c + 0*c**2. Suppose a(h) = 0. Calculate h.
-27, 0
Let z = -2362 + 2377. Let j(k) be the second derivative of 0*k**2 + 1/3*k**4 - 1/5*k**5 + z*k + 0 + 0*k**3 - 1/10*k**6. Find c such that j(c) = 0.
-2, 0, 2/3
Let g = -27628 + 27630. Suppose 1/7*s**g - 6/7*s + 0 = 0. Calculate s.
0, 6
Let b be -18*20/12*4/(-20). Let h be (b/8)/(567/108). Factor 0 + 1/7*f**3 + 0*f**2 - h*f.
f*(f - 1)*(f + 1)/7
Let q = 87/110 - -1/110. Factor 18/5*f**2 - 1/5*f**4 - 4*f - q*f**3 + 7/5.
-(f - 1)**3*(f + 7)/5
Let r(v) be the third derivative of -v**8/1344 - v**7/210 + v**6/96 + 4875*v**2. Find k, given that r(k) = 0.
-5, 0, 1
Let f be 0*(9 - 56/6). Let x(a) = -a**3 + 6*a**2 - 5*a + 3. Let v be x(5). Factor -9/4*k + f - 3/4*k**v + 3*k**2.
-3*k*(k - 3)*(k - 1)/4
Let w(m) = 13*m**3 - 109*m**2 + 46*m + 7. Let s(n) = 19*n**3 - 162*n**2 + 68*n + 11. Let a(j) = -7*s(j) + 11*w(j). Factor a(z).
5*z*(z - 6)*(2*z - 1)
Let 65 - 2445 - 5704*v**2 - 198*v + 5702*v**2 = 0. Calculate v.
-85, -14
Determine k so that 422851*k**3 - 2392*k + 13520 - 211427*k**3 + 124*k**2 - 211426*k**