Let i = 128 - 50. Suppose -3*n - 63 = -i. Find y, given that 1/3 + 1/3*y - 2/3*y**2 + 1/3*y**n - 2/3*y**3 + 1/3*y**4 = 0.
-1, 1
Let h = 6 + -4. Let s(q) = 2 - 58*q**h + 62*q**2 - 4. Let z(o) = o**2. Let p(j) = -s(j) + 2*z(j). Factor p(g).
-2*(g - 1)*(g + 1)
Let z(a) = -7*a**2 + 52*a - 24. Let n(b) = 29*b**2 - 208*b + 98. Let p(f) = -4*n(f) - 18*z(f). Let p(d) = 0. What is d?
2/5, 10
Let u = -13577 - -13579. Solve -7/4*m**u - 1/4*m**4 + 3/4*m + 0 + 5/4*m**3 = 0.
0, 1, 3
Let x(u) = -10*u**2 + 22*u + 21. Let l(s) = 34*s**2 - 68*s - 62. Let m(g) = -6*l(g) - 20*x(g). Determine k, given that m(k) = 0.
-6, -2
What is c in 44*c**5 - 3*c**2 + 0*c - 11*c**3 - c - 36*c**5 + 3*c + c**3 + 12*c**4 = 0?
-2, -1/2, 0, 1/2
Let m(g) = -g**2 - 28*g - 52. Let u be m(-2). Factor -2/7*b**2 + u*b + 2/7.
-2*(b - 1)*(b + 1)/7
Suppose -105 = -11*h + 10*h. Let d be (-4)/(-30) + 16/h. What is p in 2/7*p**2 - 4/7 + d*p = 0?
-2, 1
Let w(y) = 2*y - 14. Let l be w(10). Suppose -l*m + 8 = -4. Determine b, given that 5*b - m*b - 3*b**4 - 9*b**3 + 3*b + 3*b**5 + 3*b**2 = 0.
-1, 0, 1, 2
Let r(m) be the first derivative of -m**4/30 - m**3/5 + 4*m**2/5 + 16*m - 10. Let k(y) be the first derivative of r(y). Factor k(o).
-2*(o - 1)*(o + 4)/5
What is y in 8649 + 7447*y + y**3 - 185*y**2 - 5835*y + 6851*y = 0?
-1, 93
Let x(q) = 17*q**3 + 566*q**2 + 412*q - 143. Let c(z) = 18*z**3 + 569*z**2 + 413*z - 142. Let u(h) = -3*c(h) + 2*x(h). Solve u(b) = 0.
-28, -1, 1/4
Factor 20*r**2 + 26*r + 26*r + 0*r**2 - 4*r**3 + 9 + 19.
-4*(r - 7)*(r + 1)**2
Let k(h) = -4*h**3 + h**2 + 7*h - 6. Let v(l) = -3*l**3 + 6*l - 6. Let d(p) = -4*k(p) + 5*v(p). Let t be d(4). Factor 2 - 4/3*b + 2/9*b**t.
2*(b - 3)**2/9
Let q(h) = h + 5. Let t be q(-5). Let o = t - -4. Factor 2*n**3 - 6*n**4 - n**3 - 19*n**o - 11*n**3.
-5*n**3*(5*n + 2)
Let j = -313 + 581. Let s = j - 1874/7. Factor -50/7 - 20/7*y - s*y**2.
-2*(y + 5)**2/7
Suppose 3*h + 2*w = 5 - 27, -5*w = -5. Let x(v) = v + 11. Let f be x(h). Factor -f*s**2 + 3*s - 75 + 75.
-3*s*(s - 1)
Suppose -15 + 15 = 12*s. Let b(o) be the second derivative of 0 - 8*o - 1/90*o**6 + 0*o**3 + 1/36*o**4 + s*o**5 + 0*o**2. Find t, given that b(t) = 0.
-1, 0, 1
Let n(b) be the third derivative of -b**7/525 + b**6/30 - 37*b**5/150 + b**4 - 12*b**3/5 + 196*b**2. Solve n(d) = 0 for d.
2, 3
Let c(s) be the second derivative of -s**9/756 + s**8/140 - s**7/70 + s**6/90 - 4*s**3/3 + 5*s. Let j(v) be the second derivative of c(v). Solve j(l) = 0.
0, 1
Let j(d) = 7*d**3 + 9*d**2 - 4*d + 2. Let h(z) = z**4 - 27*z**3 - 37*z**2 + 15*z - 9. Let s(q) = 4*h(q) + 18*j(q). Factor s(i).
2*i*(i + 2)*(i + 3)*(2*i - 1)
Let f = 286 + -286. Factor -2/11*z + f - 2/11*z**2.
-2*z*(z + 1)/11
Let r be (3/18)/(14/1008*18). Factor 22/3*x - r*x**2 + 0.
-2*x*(x - 11)/3
Let l(r) be the second derivative of r**4/12 - 8*r**3/3 - 18*r**2 + 8*r - 5. Let l(p) = 0. Calculate p.
-2, 18
Suppose -4*w - 4*w + 24 = 0. Factor -2*i**3 - 6*i**w + i**3 + 5*i**3 - 3*i**4.
-i**3*(3*i + 2)
Let -6/7*q**4 + 684/7*q + 116/7*q**3 - 162/7 - 632/7*q**2 = 0. What is q?
1/3, 1, 9
Let c(n) be the second derivative of 0*n**2 + 4*n + 1/24*n**4 - 3/40*n**5 - 1/60*n**6 + 0 + 1/6*n**3 + 1/84*n**7. Factor c(w).
w*(w - 2)*(w - 1)*(w + 1)**2/2
Factor 0 + 29/2*a + 1/2*a**2.
a*(a + 29)/2
Let j(t) be the second derivative of -t**7/70 + 13*t**6/150 - 7*t**5/50 - t**4/15 + 4*t**3/15 - 4*t + 1. Find m, given that j(m) = 0.
-2/3, 0, 1, 2
Determine a so that 6/5 + 19/5*a**2 - 41/5*a = 0.
3/19, 2
Determine q, given that 0 + 6/5*q + 19/5*q**2 + 1/5*q**5 + 21/5*q**3 + 9/5*q**4 = 0.
-6, -1, 0
Suppose 4/3*h**4 + 0 - 6*h**3 + 2/3*h**5 + 16/3*h - 4/3*h**2 = 0. What is h?
-4, -1, 0, 1, 2
Let g(j) = -j**5 + 6*j**4 - 12*j**3 + 32*j**2 - 3*j - 11. Let b(a) = -2*a**2 + 1. Let f(l) = -33*b(l) - 3*g(l). Suppose f(k) = 0. What is k?
0, 1, 3
Suppose 141*t = 239*t. Determine x, given that t*x + 0 + 0*x**3 + 0*x**2 - 2/5*x**5 + 0*x**4 = 0.
0
Let c(m) = 3*m + 20. Let y(p) = 13*p + 81. Let l(t) = 9*c(t) - 2*y(t). Let u be l(-14). Factor 0*f**3 - 4*f**4 + f**5 - f**3 + f + 7*f**3 - u*f**2.
f*(f - 1)**4
Let y be 2 + 0*(-6)/30. Suppose 9*j**2 - 4*j**y + 2*j**4 + 9*j**2 + 4*j**2 - 12*j**3 = 0. Calculate j.
0, 3
Suppose 5*b - 2*t = 27, -7 = -b + t - 1. Suppose b*q - 15 = 5*d, 10 = -4*d + 5*q - 5. Factor 8*n**4 + n**3 + 3*n**5 + d*n**3 + 3*n**3 + n**5.
4*n**3*(n + 1)**2
Let h(n) be the third derivative of -1/32*n**4 + 1/160*n**6 + 0*n + 18*n**2 + 1/4*n**3 + 0 - 1/40*n**5. Let h(y) = 0. What is y?
-1, 1, 2
Solve 4*h - 4/3*h**3 + 0 + 2/3*h**4 - 10/3*h**2 = 0.
-2, 0, 1, 3
Determine d, given that -36/7*d**3 + 432/7*d + 0 - 216/7*d**2 + 22/7*d**4 - 2/7*d**5 = 0.
-3, 0, 2, 6
Let y = 14 - -1. Factor -4*q**2 - q**4 + y - 10*q + 10*q**3 - 2*q**4 + 8*q**4 - 16*q**2.
5*(q - 1)**2*(q + 1)*(q + 3)
Let g = -35 + 42. Let 8*a + 10*a + 24*a**2 + 4*a**4 + 5*a + 16*a**3 + 4 - g*a = 0. Calculate a.
-1
Let z(i) be the first derivative of -343*i**6/9 + 6272*i**5/15 - 5719*i**4/6 - 13036*i**3/9 - 2020*i**2/3 - 400*i/3 + 293. Find c, given that z(c) = 0.
-2/7, 5
Let m be (-10)/4 - (-1581)/30. Let c = -49 + m. Suppose 0*y - c*y**2 - 2/5*y**3 + 8/5 = 0. What is y?
-2, 1
Let -48/5*q + 0 + 1/5*q**3 - 22/5*q**2 = 0. Calculate q.
-2, 0, 24
Find g, given that -32/5*g**4 + 1188/5*g + 304/5*g**3 - 936/5*g**2 - 108 = 0.
3/2, 5
Let y(j) be the second derivative of -4/5*j**2 + 0 - 8*j - 2/5*j**3 - 1/200*j**5 - 3/40*j**4. Factor y(c).
-(c + 1)*(c + 4)**2/10
Determine a, given that -124/21*a - 2/21*a**2 - 122/21 = 0.
-61, -1
Let x(c) be the first derivative of c**7/70 + 3*c**6/50 + 3*c**5/50 + 16*c - 29. Let o(z) be the first derivative of x(z). Factor o(q).
3*q**3*(q + 1)*(q + 2)/5
Factor 11*v - 2*v**2 - 55*v + 50*v**3 - 54*v**3 + 50*v**2.
-4*v*(v - 11)*(v - 1)
Let p = -22 + 31. Let m(x) be the first derivative of 2*x**3 - 8*x**2 + 22*x - 203. Let y(t) = -13*t**2 + 33*t - 45. Let j(q) = p*m(q) + 4*y(q). Factor j(g).
2*(g - 3)**2
Factor 0 + 2/21*o**2 - 172/21*o.
2*o*(o - 86)/21
Let m(s) = 2*s**2 - 8*s + 26. Let g(a) = a - 1. Let f(o) = 10*g(o) - m(o). Determine y so that f(y) = 0.
3, 6
Let n(w) be the third derivative of w**7/140 - w**6/30 + w**5/30 - 2*w**2 + 240*w. Suppose n(g) = 0. Calculate g.
0, 2/3, 2
Let s(u) = u**2 - 153*u + 1302. Let y be s(9). Factor -8/3*f**2 - 4/3 - y*f.
-2*(f + 2)*(4*f + 1)/3
Let p = 5653/3 + -1883. Factor 4/3 + p*t + 1/3*t**2.
(t + 2)**2/3
Factor -75/8*m**3 - 1485/8*m**2 - 57/2 - 144*m.
-3*(m + 19)*(5*m + 2)**2/8
Let b(o) = -63*o - 499. Let y be b(-8). Factor 0*w**3 + 0 + 4/13*w**4 - 4/13*w**2 - 2/13*w**y + 2/13*w.
-2*w*(w - 1)**3*(w + 1)/13
Factor -9/4*x**3 + 4 - 13*x + 12*x**2.
-(x - 4)*(3*x - 2)**2/4
Let r be 0*(4 + 21/(-6)). Let f be (-46)/(-8) + (-6)/(-24). Determine u, given that -3/2*u**3 - 9/2*u**2 + r*u + f = 0.
-2, 1
Suppose -4*d - 21 = -3*c, 3*c = 5*d + 7*c + 65. Let f be d/(-6) + 2/4. Find v such that -13*v**2 - v**4 + 2*v**3 - f*v + 1 + 13*v**2 = 0.
-1, 1
Let w be ((1296/(-100))/1)/(2/(-15)). Factor -6/5*a**2 - w + 108/5*a.
-6*(a - 9)**2/5
Let k(g) be the third derivative of g**5/210 - 7*g**4/6 + 97*g**3/21 + 60*g**2. Solve k(s) = 0.
1, 97
Factor -81/2*w - 3/2*w**3 + 27/2*w**2 + 81/2.
-3*(w - 3)**3/2
Let g(d) be the third derivative of -d**6/72 - d**5/4 - 5*d**4/3 - 7*d**3/3 + 30*d**2. Let f(i) be the first derivative of g(i). Find b such that f(b) = 0.
-4, -2
Let w = -49 + 51. Determine i, given that -101 + 125 + 5*i**2 + 0*i**w - i**2 - 20*i = 0.
2, 3
Let n be (3/5 + -1)*-10. Factor 15*k**3 + 7*k - 10 - 5*k**3 + 10*k**n - 40*k**2 - 5*k**5 + 15*k + 13*k.
-5*(k - 1)**4*(k + 2)
Let r(c) be the third derivative of c**6/30 - c**5/3 + c**4 + 48*c**2 + 2*c. Let r(n) = 0. What is n?
0, 2, 3
Let x(a) be the third derivative of a**5/40 + 29*a**4/8 - 30*a**3 + 722*a**2. Find p, given that x(p) = 0.
-60, 2
Let x(i) be the second derivative of -3*i**5/40 + 5*i**4/8 + 2*i**3 - 9*i**2 + 35*i. Factor x(j).
-3*(j - 6)*(j - 1)*(j + 2)/2
Let s(o) be the second derivative of 0 - 25/39*o**3 - 1/130*o**5 + 0*o**2 + 5*o + 5/39*o**4. Factor s(w).
-2*w*(w - 5)**2/13
Let i(b) be the third derivative of b**6/40 + b**5/80 - b**4/2 - b**3/2 - 355*b**2. Let i(p) = 0. Calculate p.
-2, -1/4, 2
Let s(a) = 10*a**5 + 5*a**4 - 15*a**3 - 5*a. Let m = 59 + -54. Let w(j) = -5*j**5 - 3*j**4 + 8*j**3 + 3*j.