19. Determine d so that 25*d**c - 21*d**5 + 5*d**4 - 4*d**3 + d**4 = 0.
-2, 0, 1/2
Factor 26/7*n**3 + 0 - 30/7*n**2 + 4/7*n.
2*n*(n - 1)*(13*n - 2)/7
Factor -2/9*n**2 + 2/9 + 2/9*n - 2/9*n**3.
-2*(n - 1)*(n + 1)**2/9
Let l be 3/6*(8 - 4). Let h be 0/(9/(-3)) - -3. Factor 3*q**4 + l*q**h + q**5 - 2 + 0*q**4 + 2.
q**3*(q + 1)*(q + 2)
Let v = 4561/50413 + 2/4583. Find g such that -v*g**2 + 0 + 0*g + 1/11*g**3 + 1/11*g**4 - 1/11*g**5 = 0.
-1, 0, 1
Let u be 0*(-19)/247 + 10/13. Solve -14/13*m - u*m**3 - 2/13*m**4 - 4/13 - 18/13*m**2 = 0.
-2, -1
Let i(h) be the second derivative of h**5/10 - h**4/3 - 3*h**3 + 18*h**2 + 11*h + 30. What is o in i(o) = 0?
-3, 2, 3
Let o(b) be the third derivative of 4/5*b**6 + 0*b**3 + 13/15*b**5 + 14*b**2 + 0*b + 34/105*b**7 + 1/21*b**8 + 1/3*b**4 + 0. Solve o(u) = 0.
-2, -1, -1/4, 0
Find n such that 4*n**3 - 1150 + 139*n**2 + 41*n**2 + 1932*n - 966 = 0.
-23, 1
Let d be ((-2)/(-3))/((-24)/(-54)). Let t = 152 - 605/4. Factor -t - 3/4*z**2 + d*z.
-3*(z - 1)**2/4
Let g = -9 - 21. Let s be (8/g)/(6/(-15)). Solve 0*m**2 - 1/3 + 2/3*m + 1/3*m**4 - s*m**3 = 0 for m.
-1, 1
Suppose -185*c - 242 = -612. Factor -108 - 3/4*f**c - 18*f.
-3*(f + 12)**2/4
Let t be (24/10)/(-3*3/360). Let x be 2/(-15) - t/45. Determine n, given that -2/9*n**4 - 8/9*n + 0*n**x + 2/3*n**3 + 0 = 0.
-1, 0, 2
Let c(u) be the first derivative of -1/36*u**6 + 5/12*u**2 - 1/6*u**4 + 2/15*u**5 - 9 - 1/3*u - 1/9*u**3. Let c(q) = 0. What is q?
-1, 1, 2
Suppose 2 = -i + 32. Factor 8 + i*u + 20*u**3 + 36*u**2 - 2*u - 28*u**4 + 32*u**4.
4*(u + 1)**3*(u + 2)
Let i(z) = -6*z**3 + 46*z**2 - 124*z + 116. Let c(o) = -o**3 + o**2 + 2*o + 2. Let t(f) = -2*c(f) + i(f). Find k such that t(k) = 0.
2, 7
Suppose -4*l = 32 + 36. Let j = l + 17. Factor j*q**2 - 26 - 4*q + 26 - 2*q**2.
-2*q*(q + 2)
Let a(i) = 12*i**2 + 21*i - 42. Let v(l) = -11*l**2 - 21*l + 44. Let q(t) = 4*a(t) + 3*v(t). Factor q(p).
3*(p - 1)*(5*p + 12)
Let w be -2 - ((-3)/9 + (-34)/6). Suppose 0*b - w*b + 410 = -5*d, -108 = -b + 4*d. Factor -60*c - 4/5*c**3 + b + 12*c**2.
-4*(c - 5)**3/5
Suppose 8*v - 5*v = -2*i + 22, 10 = 2*i. Determine d, given that 2*d**2 + 2*d - 2*d**4 + 6*d**3 - v*d - 4*d**3 + 0*d**2 = 0.
-1, 0, 1
Suppose 5*j - 5*b = 0, 18 = 4*j + 3*b + 2*b. Suppose 2*q - q = j. Solve 2*t**3 + 2 - 14*t**2 + 8*t**2 - 4*t**3 + 12*t**q - 6*t = 0 for t.
1
Let y(o) = o**2 + 1. Let z be y(1). Suppose z*j + 9 = 5*j. What is p in -3*p**j + 4*p**2 - p**3 - 8*p**2 = 0?
-1, 0
Find k, given that 27*k**2 + 1 - 405*k + 226*k**3 - 221*k**3 - 147*k**2 - 1 = 0.
-3, 0, 27
Let r be (-61)/5*((-835)/105 + 8). Let q = -8/21 - r. Let 2/5 - 3/5*w + 0*w**2 + q*w**3 = 0. What is w?
-2, 1
Let b(s) be the second derivative of s**4/12 - 5*s**3/6 + 3*s**2 - 108*s. Let b(y) = 0. What is y?
2, 3
Factor -4 - 1433*s + 718*s + 741*s + 14*s**2.
2*(s + 2)*(7*s - 1)
Let l = 41 + -39. Suppose -d - 7 = -2*w, 4*d = -w + 4*w - 3. Determine z, given that -5*z**3 - 6*z**2 + l*z**d - 3*z**2 + 12 = 0.
-2, 1
Let q(v) be the first derivative of -32*v**4/5 + 32*v**3/5 - 9*v**2/5 - 160. What is s in q(s) = 0?
0, 3/8
Let w = 286/51 - -805/102. Find s, given that 111/2*s - 6*s**2 - w = 0.
1/4, 9
Let a = 17 - 13. Let w be (-3)/(-3) - (a + -6). Factor -6*k**w - 2 - 8*k - 3*k**4 - 12*k**2 - 2*k**3 + k**4.
-2*(k + 1)**4
Let y(c) be the third derivative of 4*c**7/21 - 509*c**6/60 + 353*c**5/15 - 241*c**4/12 + 8*c**3 + 631*c**2. Let y(t) = 0. What is t?
1/5, 1/4, 1, 24
Let c = 14593/3 - 4864. Factor 2*q + c*q**3 + 5/3*q**2 + 0.
q*(q + 2)*(q + 3)/3
Let v(l) = -25*l**3 + 65*l**2 + 262*l + 180. Let n(h) = 2*h. Let k(f) = -n(f) - v(f). Solve k(c) = 0.
-6/5, 5
Let r = -138 + 178. Let a be ((-16)/r)/(8/(-30)). Let 0 - 2*q**4 + 0*q + 1/2*q**2 - a*q**3 = 0. Calculate q.
-1, 0, 1/4
Let d(p) be the second derivative of -37*p + 0 - 1/8*p**2 - 1/48*p**4 + 1/12*p**3. Solve d(m) = 0.
1
Let z(i) be the second derivative of 0*i**2 + 1/28*i**4 + 13/14*i**3 - 4*i + 7. Determine b so that z(b) = 0.
-13, 0
Let z(h) = -23*h**2 - 770*h - 29645. Let y(j) = -135*j**2 - 4620*j - 177870. Let w(d) = 6*y(d) - 35*z(d). Let w(c) = 0. What is c?
-77
Let z(p) be the third derivative of p**7/210 + p**6/120 - p**5/6 - p**4/6 + 4*p**3 + 81*p**2. What is c in z(c) = 0?
-3, -2, 2
Let f(t) be the first derivative of 13 - 3/10*t**4 - 1/12*t**6 + 0*t**2 + 0*t + 4/15*t**3 - 9/25*t**5. Factor f(s).
-s**2*(s + 2)**2*(5*s - 2)/10
Let m(r) be the second derivative of -r**7/21 + r**6/5 - r**5/5 - 5*r - 11. Factor m(k).
-2*k**3*(k - 2)*(k - 1)
Factor -4205 + 1505 - 4*r**2 + 164*r + 5*r**2 + 9424.
(r + 82)**2
Find o such that -62*o**5 + 133*o**5 - 436*o**2 + 432*o**3 - 73*o**5 - 140*o**4 + 146*o = 0.
-73, 0, 1
Let k(x) be the second derivative of -1/3*x**4 + 0 - 1/5*x**5 + 7*x + 2/3*x**3 + 2*x**2. Factor k(b).
-4*(b - 1)*(b + 1)**2
Suppose 2*q = 2*b - 4*b - 6, 0 = -2*b + 2*q + 14. Let 4*a**2 - 3*a**2 + 6 + 0*a**b + 2*a**2 + 9*a = 0. Calculate a.
-2, -1
Suppose -7 = -3*y + 2*h, 4*y = -0*y + 4*h + 8. Factor 3*m**4 - 6*m**3 - 3*m**3 + 4*m**y - 3*m**2 + 2*m**3 + 3*m**5.
3*m**2*(m - 1)*(m + 1)**2
Let t = 2539/76 - 630/19. Factor -2*h - t*h**2 - 4.
-(h + 4)**2/4
Let j(a) = -a**3 - 36*a**2 - 30*a - 1060. Let y be j(-36). Factor 0*k - 12*k**5 + y*k**4 - 28/3*k**3 + 0 + 4/3*k**2.
-4*k**2*(k - 1)*(3*k - 1)**2/3
Let z(h) be the third derivative of 3*h**8/224 - h**7/28 - h**6/16 + h**5/8 + h**4/8 + 17*h**2. What is q in z(q) = 0?
-1, -1/3, 0, 1, 2
Factor -2/5*s**2 + 8/5*s - 2/5*s**3 + 8/5.
-2*(s - 2)*(s + 1)*(s + 2)/5
Factor -116*c + 23*c - 55 - 12*c - 2*c**2 + 12*c**2.
5*(c - 11)*(2*c + 1)
Let k = -11 - -33. Suppose -4*c - 2*l + 2 = 0, -22*c + 4*l + k = -17*c. Factor 4/9*g + 4/9*g**4 + 4/9*g**5 - 8/9*g**3 - 8/9*g**c + 4/9.
4*(g - 1)**2*(g + 1)**3/9
Let q = 17 + -20. Let f be (3/q*-1)/(3 - 0). Find g, given that 0*g + f*g**2 + 1/3*g**3 + 0 = 0.
-1, 0
Let w(r) = r**4 - 2. Let l(h) = 4*h**4 - 4*h**3 + 38*h**2 - 56*h + 12. Let g(d) = l(d) - 6*w(d). Let g(v) = 0. Calculate v.
-6, 1, 2
Let o be 12*5/60*0/(-1). Let g(u) be the third derivative of u**2 - 1/3*u**4 - 1/15*u**5 + o*u**3 + 0*u + 0. Find v such that g(v) = 0.
-2, 0
Let o(t) = 18*t**3 - 3091*t**2 + 131071*t + 88759. Let p(a) = -9*a**3 + 1546*a**2 - 65536*a - 44380. Let k(v) = -4*o(v) - 7*p(v). Factor k(h).
-3*(h - 86)**2*(3*h + 2)
Let b(f) = 24*f**2 + 42*f + 6. Suppose a + 3*a - 8 = 0. Let p(c) = a*c - 5*c**2 + 7*c**2 - c - c**2. Let j(x) = b(x) - 9*p(x). Determine z so that j(z) = 0.
-2, -1/5
Factor 0 + 18*x - 1/2*x**4 + 71/2*x**2 + 17*x**3.
-x*(x - 36)*(x + 1)**2/2
Let l(u) be the first derivative of 3/4*u**4 + 3*u - 10 + 3*u**3 + 9/2*u**2. What is f in l(f) = 0?
-1
Factor 76/5*k - 16 + 4/5*k**2.
4*(k - 1)*(k + 20)/5
Let u(a) be the third derivative of 5/18*a**4 + 0*a**3 + 7/30*a**5 - 28*a**2 + 1/15*a**6 + 1/315*a**7 + 0 + 0*a. Determine r so that u(r) = 0.
-10, -1, 0
Let t(y) = -y**3 - y**2 + 1. Let l(f) = -8*f**3 + 72*f**2 + 52*f + 2. Let x(j) = -l(j) + 2*t(j). Solve x(w) = 0.
-2/3, 0, 13
Let h be (-8)/(56/(-21)) - (-1 - 1). Suppose -3*w = -4*b - 9 + h, 4*b + 2*w = 16. Factor 0 + 1/2*v**b + 0*v.
v**2/2
Let q be ((-6)/4)/((-90)/(-8388)). Let d = q - -140. Factor 3/5*l**2 + d*l**3 + 2/5*l + 0.
l*(l + 1)*(l + 2)/5
Let b = 4/313 - -305/626. Let j(i) be the first derivative of 3/4*i**2 - b*i**3 + 1/8*i**4 - 1/2*i - 1. Factor j(o).
(o - 1)**3/2
Find j such that -5*j - j**3 + 2*j - 5*j**2 + 0*j - 3*j = 0.
-3, -2, 0
Find l, given that 1/5*l**3 + 4/5*l**2 + 2/5 + l = 0.
-2, -1
Let i(o) = -o**3 + 1. Let s(q) = 6*q**3 + 5*q**2 - 8*q - 3. Let y be (-3)/8 + 5540/(-160). Let a(c) = y*i(c) - 5*s(c). Determine r so that a(r) = 0.
1, 2
Let b be (2/69)/(579/4439). Factor -b*r**2 - 32/9 - 16/9*r.
-2*(r + 4)**2/9
Let c(s) = s**2 + 4*s - 2*s + 3 - s + s. Let f be c(-1). Factor -10/9*u + 2/3*u**f + 2/9*u**3 - 2/9*u**4 + 4/9.
-2*(u - 1)**3*(u + 2)/9
Suppose 40*l + 54 - 134 = 0. Factor 2/5*o + 0 - o**l.
-o*(5*o - 2)/5
Let s(r) be the third derivative of -r**10/30240 + r**9/4032 - r**5/12 - 8*r**2. Let m(p) be the third derivative of s(p). Suppose m(c) = 0. Calculate c.
0, 3
Let i(w) = 27*w**2 + 6*w - 1. Let r be i(4). Let p = r - 251. Determine b so that -p*b + 206*b - 3*b**3 + b**3 = 0.
-1, 0, 1
Let f = -17 - -16. Let v be 0 - (-2 + 0/f). Factor p**4 + 2*p**3 - 2 - 6*p**5 + v + 