.
-1/4, 1
Factor 50*b**2 + 162*b - 29*b**2 - 7*b**2 - 4*b**2 + 159 - 7*b**2.
3*(b + 1)*(b + 53)
Let v(o) = o**2 + 5*o + 22. Let w be v(-4). Suppose 14*x + 0 + 2*x**2 + 2 - w = 0. Calculate x.
-8, 1
Let i be -3 + 11 + 2/8 + (-24073)/3620. Solve 4/5*u**4 + 6/5*u**3 - 8/5*u**2 - i*u - 2/5*u**5 + 0 = 0 for u.
-1, 0, 2
Let v be 9 + (-39)/3 - 9*-1. Let f(c) be the second derivative of 20*c + 1/20*c**v + 0*c**3 + 0 + 0*c**2 + 0*c**4. Factor f(p).
p**3
Suppose 13*c + 4*u - 15 = 12*c, -5*c - 5*u + 30 = 0. Suppose 2*x = -4*j + 2, 4*x - 4*j - 13 = 3. Find r, given that 3*r**x + 6*r**2 + 43 - 43 + c*r = 0.
-1, 0
Let t(o) = -28*o**3 - 35*o**2 + 214*o - 64. Let p(u) = -14*u**3 - 18*u**2 + 1307 - 665 + 108*u - 674. Let g(r) = 13*p(r) - 6*t(r). Factor g(k).
-2*(k - 2)*(k + 4)*(7*k - 2)
Let s = 1174 - 1164. Let f be (-5 - -2) + -49*s/(-140). Let -2*x**2 + 0 + 0*x + f*x**3 = 0. What is x?
0, 4
Let i be 1 + 0 + (0 - -3). Suppose 96*d**3 - 6*d - 69*d**3 + 24*d**2 + 2*d - 15*d**5 - 24*d**i - 8*d = 0. What is d?
-2, -1, 0, 2/5, 1
Let d be (910/1001)/(15/22). Factor 1/3*s**3 - 1/3*s**2 - 4/3*s + d.
(s - 2)*(s - 1)*(s + 2)/3
Let g(m) be the second derivative of 55*m - 9*m**2 + 7/2*m**3 - 1/4*m**4 + 0. Determine f, given that g(f) = 0.
1, 6
Suppose -2*d = -4*j + 38, -84*d + 86*d - 32 = -3*j. Let g(x) be the first derivative of -17 - 24*x + 4/3*x**3 - j*x**2. Let g(i) = 0. Calculate i.
-1, 6
Let q(d) be the second derivative of 2*d**7/21 + 14*d**6/3 + 288*d**5/5 - 108*d**4 - 1842*d. Factor q(k).
4*k**2*(k - 1)*(k + 18)**2
Factor 0 + 2/21*b**4 - 4/21*b**3 + 4/7*b - 10/21*b**2.
2*b*(b - 3)*(b - 1)*(b + 2)/21
Let k(j) = -12*j - 1 + 5*j + j - 2*j**2 + 3*j + 2*j. Let q(p) = 5*p**2 - 50*p + 61. Let z(n) = 4*k(n) + q(n). Suppose z(l) = 0. What is l?
-19, 1
Let a(l) = 14*l**2 + 80*l. Let c(t) = 4*t**2 + 26*t. Suppose 9*y - 170 = 26*y. Let p(b) = y*c(b) + 3*a(b). Factor p(s).
2*s*(s - 10)
Let h be 88/11 + (-15489)/(-15). Let l = h - 1039. Let 8/5*c**3 - 4/5*c**2 - l - 4*c = 0. Calculate c.
-1, -1/2, 2
Let s(h) be the third derivative of 19*h**7/350 + 17*h**6/200 - h**5/50 + 710*h**2. Factor s(a).
3*a**2*(a + 1)*(19*a - 2)/5
Suppose u - 49 = -5*n - 26, -2*u = -2*n + 2. Let i(b) be the first derivative of 4/5*b**3 + 1/10*b**n + 11/5*b**2 - 39 + 12/5*b. Factor i(v).
2*(v + 1)*(v + 2)*(v + 3)/5
Factor 0 + 468/7*z + 1/7*z**4 - 303/7*z**2 + 46/7*z**3.
z*(z - 3)**2*(z + 52)/7
Factor -28*h + 39 + 34 - 18 + 2*h**2 - 7.
2*(h - 12)*(h - 2)
Let f(j) be the first derivative of j**6/24 - 33*j**5/20 + 93*j**4/16 - 91*j**3/12 + 15*j**2/4 - 587. Factor f(u).
u*(u - 30)*(u - 1)**3/4
Let f(u) = -5*u + 24. Let x be f(4). Suppose 10 = -x*d + 9*d. What is v in 5*v - 2*v**5 - 3*v**d + 86*v**4 - 7*v**2 - 76*v**4 - 3*v**5 = 0?
-1, 0, 1
Let v be (0 - -3)*(-12)/(-9). Suppose -10 = -v*t - 2. Factor -18*l**4 - t*l**3 - 7*l**3 - 9*l**2 + 15*l**4 - 3*l.
-3*l*(l + 1)**3
Find i, given that -3*i**2 - 685*i + 4*i**2 - 99*i - 3*i**2 = 0.
-392, 0
Let j(p) be the first derivative of -p**3 + 69*p**2/2 - 306*p - 2579. Factor j(r).
-3*(r - 17)*(r - 6)
Solve 35*k**5 + 4*k + 48788*k**4 - 4*k + 40*k**2 - 48693*k**4 - 145*k**3 - 25*k**3 = 0.
-4, 0, 2/7, 1
Let h(l) be the second derivative of l**6/60 + 3*l**5/10 - 59*l**4/24 + 13*l**3/2 - 8*l**2 - 3*l + 49. Let h(z) = 0. Calculate z.
-16, 1, 2
Suppose -4*j = 4, 4*b - 2*j = 879 - 189. Let d = -170 + b. Factor -9 + 15/2*g - 3/2*g**d.
-3*(g - 3)*(g - 2)/2
Suppose -102 = 5*b - 39*b. Suppose t + 0 - 2 = 2*w, 0 = b*w. Determine z so that 50/13 + 2/13*z**t + 20/13*z = 0.
-5
Let l(p) be the third derivative of -p**6/480 + 43*p**5/240 - 97*p**4/48 + 19*p**3/3 - 79*p**2 - 6*p. Factor l(u).
-(u - 38)*(u - 4)*(u - 1)/4
Suppose -3*n + 1 = -2*w + 86, 32 = w - 5*n. Suppose -185 = 10*c - w*c. Factor 1/5*h**3 - 7/5*h**c + 0*h**2 + 6/5*h**4 + 0 + 0*h.
-h**3*(h - 1)*(7*h + 1)/5
Let g(n) be the second derivative of 4/39*n**4 + n + 1/195*n**6 + 0*n**2 + 7 + 3/65*n**5 + 0*n**3. Find k such that g(k) = 0.
-4, -2, 0
Let a be (50274/3591)/(21/10 - 0). Factor -a - 1/3*s**2 - 7*s.
-(s + 1)*(s + 20)/3
Solve -2*o**3 + 0 + 8/3*o + 0*o**2 - 2/3*o**4 = 0 for o.
-2, 0, 1
Let z(w) be the first derivative of -2*w**4/11 - 450*w**3/11 - 503*w**2/11 + 336*w/11 + 14495. What is c in z(c) = 0?
-168, -1, 1/4
Suppose 0*f + 128 = 2*p + 3*f, 0 = p - f - 64. Let y = p + -56. Solve -53*s**4 - 37*s**4 - y - 18*s**2 + 8 + 87*s**3 + 21*s**5 = 0.
0, 2/7, 1, 3
Let u(z) = -148*z**3 + 72*z**2 - 200*z. Let o(g) = -4*g**3 + g**2 - 4*g. Let d(h) = 36*o(h) - u(h). Suppose d(j) = 0. What is j?
0, 2, 7
Let s(q) be the first derivative of -2*q**2 + 38 - 8/3*q**3 + 4*q. Suppose s(g) = 0. Calculate g.
-1, 1/2
Factor -858*n**2 - 6*n + 860*n**2 - 30*n**3 + 36*n - 2*n**4.
-2*n*(n - 1)*(n + 1)*(n + 15)
Let 0 - 9/4*g**4 + 9/2*g**3 + 1/4*g**5 + 0*g**2 + 0*g = 0. What is g?
0, 3, 6
Let g(b) be the third derivative of 0*b**3 - 1/30*b**6 + 0*b - 5*b**4 + 0 + 31/15*b**5 - 135*b**2. Solve g(n) = 0 for n.
0, 1, 30
Let h(o) be the third derivative of -4*o**7/105 - 43*o**6/150 - 52*o**5/75 - 2*o**4/5 - 1205*o**2 + 3. Factor h(g).
-4*g*(g + 2)**2*(10*g + 3)/5
Let u(a) = 5*a - 9*a**3 + 48 - 85 + 38. Let n be u(-2). Suppose -26*j**4 + 9*j - 12*j**5 + n*j**3 + 19*j**4 + 16*j**4 + 51*j**2 = 0. Calculate j.
-1, -1/4, 0, 3
Let f = 35 - 31. Suppose f = -2*a + 8. Factor 6*z + a*z - 22*z**2 + 18*z**2.
-4*z*(z - 2)
Let k(f) = f**2 + 13*f + 43. Let p be k(-5). Suppose -3*i + 54 = p*r, 0 = -6*r + 2*r - i + 66. Factor -r*h + 5*h**2 - h**2 + 8*h**2 + 16*h**3 - 16 + 4*h**4.
4*(h - 1)*(h + 1)*(h + 2)**2
Let u(v) = -2*v**3 - v. Let f(i) = -5*i**3 + 93*i**2 - 937*i + 3024. Let k(t) = -f(t) + u(t). Solve k(z) = 0.
7, 12
Let n(p) be the third derivative of p**5/20 - 58*p**4 - 465*p**3/2 + 8*p**2 - 166. Factor n(u).
3*(u - 465)*(u + 1)
Factor 198/5*j**2 - 387/5*j + 192/5 - 3/5*j**3.
-3*(j - 64)*(j - 1)**2/5
Let z(r) be the second derivative of 191*r + 1/16*r**4 + 9*r**2 - 5/4*r**3 + 0. Suppose z(c) = 0. What is c?
4, 6
Let s be 36/(3024/20)*(-80)/(-50). Factor 2/7 - s*o + 2/21*o**2.
2*(o - 3)*(o - 1)/21
Let t(i) = 3*i**3 + 6*i**2. Suppose -3*d + 5 = -7. Let s(l) = -5*l**2 - d*l**3 - 3*l**2 + 3*l**2. Let u(z) = 2*s(z) + 3*t(z). Let u(r) = 0. Calculate r.
-8, 0
Let w(u) = -6*u**2 - u. Let c(j) = 4*j**3 - 62*j**2 + 415*j - 624. Let o(g) = -c(g) - 3*w(g). Factor o(y).
-4*(y - 13)*(y - 4)*(y - 3)
Let f(g) be the third derivative of 5/3*g**3 - 3/4*g**4 + 0*g - 75 + 1/10*g**5 + 1/60*g**6 - 2*g**2. Factor f(u).
2*(u - 1)**2*(u + 5)
Let y(r) be the first derivative of r**6/18 - 2*r**4 + 62*r**3/9 - 19*r**2/2 + 6*r + 4136. Factor y(k).
(k - 3)*(k - 1)**3*(k + 6)/3
Let i = 17498113/259 - 67560. Let j = 1/259 + i. Factor -j*m**4 + 8/7*m + 0 - 6/7*m**3 + 0*m**2.
-2*m*(m - 1)*(m + 2)**2/7
Solve 8*x**3 + 8*x**2 - 1/2*x**5 + 0*x + 0 - 1/2*x**4 = 0.
-4, -1, 0, 4
Let m = 158 + -195. Let l be -11 + 5 + (m - 3)/(-5). Factor -2/5*w**5 + 0 + 2/5*w**4 + 4/5*w - 2*w**l + 6/5*w**3.
-2*w*(w - 1)**3*(w + 2)/5
Factor 702*c**2 + 0 - 338*c + c**4 - 105/2*c**3.
c*(c - 26)**2*(2*c - 1)/2
Let p(u) be the first derivative of -27*u**5/10 + 407*u**4/8 - 68*u**3 + 7*u**2 + 4959. Find s such that p(s) = 0.
0, 2/27, 1, 14
Let f(d) = -5*d**2 - 22*d - 122. Let v be (-1 - -5) + 0/3 + -5. Let j(t) = -4*t**2 - 1. Let z(k) = v*f(k) + j(k). Factor z(m).
(m + 11)**2
Let -9123*s + 7571*s - 33*s**2 + 34*s**2 + 602176 = 0. Calculate s.
776
Let s be (-38)/361 - (-1416)/456. Let u(r) be the first derivative of 74/9*r**s + 38 + 20*r**2 + 24*r + 5/3*r**4 + 2/15*r**5. Determine b, given that u(b) = 0.
-3, -2
Factor 0 - 13*p**2 + 82/3*p - 1/3*p**3.
-p*(p - 2)*(p + 41)/3
Suppose -10*b + 52*b - 14*b + 84*b = 0. Let 0*w + 0*w**2 + b + 0*w**3 + 1/6*w**4 = 0. What is w?
0
Let w = -28 + 30. Factor -49*u**2 - 30*u**w + 2*u + 15*u**2 + 46*u - 20*u**4 - 132*u**3.
-4*u*(u + 1)*(u + 6)*(5*u - 2)
Let w(d) be the first derivative of -d**5/5 - 5*d**4/4 - 5*d**3/3 + 5*d**2/2 + 6*d - 1566. Solve w(x) = 0.
-3, -2, -1, 1
Let n = -610 + 3068/5. Let z = 4779 + -4777. Factor 2/5*b**z + n - 12/5*b.
2*(b - 3)**2/5
Let b = 16769/768 - 811/256. Factor -2/9*n**2 + b*n - 392.
-2*(n - 42)**2/9
Let x(s) = s**3 - 24*s**2 - 51*s - 26. Let y be x(26). Let l be 2/(1 - (2 - 9)). Solve l + y*o - 1/4*o**2 = 0.
-1, 1
Determine d so that -132*d + 422*d - 2