t d be -1*(-19)/2280*-30*(1 + -1). Factor 0*x**2 + d*x + x**3 - 1/2*x**4 + 0.
-x**3*(x - 2)/2
Find w, given that 12076*w - 4*w**2 + 12235 - 3015 + 2860 = 0.
-1, 3020
Let x be (352/(-33))/(2016/(-108)). Factor -3/7 - 1/7*u**2 - x*u.
-(u + 1)*(u + 3)/7
Suppose 0 = 2*g + 2*m - 9802, -5*m = 26 - 6. Let i be (-2)/(-16) + (g/440 - 10). Determine d so that -i + 16/11*d - 2/11*d**2 = 0.
1, 7
Let l(b) be the third derivative of b**6/5 - 163*b**5/15 + 157*b**4/6 + 4207*b**2. Determine x so that l(x) = 0.
0, 1, 157/6
Let p(y) = -y**2 - 8*y + 20. Let v(z) be the third derivative of z**4/24 - z**3/3 + 318*z**2. Let g(o) = -2*p(o) - 10*v(o). Factor g(i).
2*(i - 2)*(i + 5)
Let c(v) = 4*v + 34. Let k be c(-8). Suppose -5*a = -5*d - k*a + 59, -2*a = -4. Factor -4 - 17*n - d + 2 - 3*n - 5*n**2.
-5*(n + 1)*(n + 3)
Suppose 2*i + 17 = y, 420*y - 416*y - 3*i - 38 = 0. Suppose 0 + 1/2*l**y + 0*l - 1/2*l**3 - 1/2*l**2 + 1/2*l**4 = 0. What is l?
-1, 0, 1
Let s = 802586 - 1605171/2. Determine j, given that 5 - 3/2*j - s*j**2 = 0.
-5, 2
Let z be 140/18*41868/122115. Solve 0*q**3 - 2/3*q**5 + 0 + 0*q**2 + z*q**4 + 0*q = 0.
0, 4
Let l(o) be the first derivative of 20 - 7/3*o**3 + 0*o + 0*o**2 - 1/18*o**4 - 1/60*o**5 - 1/540*o**6. Let z(t) be the third derivative of l(t). Factor z(f).
-2*(f + 1)*(f + 2)/3
Let d(u) be the second derivative of u**4/96 - 7*u**3/8 - u - 820. Factor d(o).
o*(o - 42)/8
Suppose 0 = 9*r - 25*r + 80. Factor 7*d**3 - r*d**4 - 375*d + 60*d - 98 - 149*d**2 - 13*d**3 + 69*d**3.
-(d - 7)**2*(d + 1)*(5*d + 2)
Factor -221/4*z + 73/2 + 19*z**2 - 1/4*z**3.
-(z - 73)*(z - 2)*(z - 1)/4
Let d(u) = -u**2 - 8*u - 4. Let j be d(-7). Suppose 3 = j*f, -n - f = -4*f - 5. Solve -39*y**3 - 55*y**3 + 82*y**3 - n*y + 20*y**2 = 0 for y.
0, 2/3, 1
Factor -164/7*c**3 - 4/7*c**4 - 2112/7*c + 0 - 160*c**2.
-4*c*(c + 4)**2*(c + 33)/7
Let b be (-2)/15*-3 - (-65)/25. Suppose -3*l = b*i - 9, 5*i + 1 - 4 = l. Determine u, given that u**5 - 3*u**4 + l*u**3 + 2*u**2 + 9 + u + 0*u - 8 - 4*u = 0.
-1, 1
Factor -1/4*q**2 - 239/2*q - 238.
-(q + 2)*(q + 476)/4
Determine w so that 105/4 + 3/8*w**2 + 51/8*w = 0.
-10, -7
Factor -5*y**2 + 184/5 + 38/5*y + 1/5*y**3.
(y - 23)*(y - 4)*(y + 2)/5
Let l(r) = -2*r**3 - 3*r - 1. Let y(p) = -4*p**3 - 38*p**2 + 87*p - 3. Let x(d) = 6*l(d) - 2*y(d). Find a, given that x(a) = 0.
0, 3, 16
Let x(u) = 349*u - 61420. Let o be x(176). Factor 1/2*w**3 - 3/2*w**2 + 1 - 1/2*w + 1/2*w**o.
(w - 1)**2*(w + 1)*(w + 2)/2
Let h = -1290 + 28387/22. Let f = 5/88 + h. Factor 3/4 + 11/8*v + f*v**2.
(v + 3)*(3*v + 2)/8
Let r be ((-12)/(-8))/((-1)/(-4)). What is b in -8*b**2 + 4 + 6*b + r*b**3 - 32*b**2 + 24*b**2 = 0?
-1/3, 1, 2
Let n(w) be the first derivative of 4*w**7/1575 + w**6/900 - 55*w**2/2 - 21. Let x(b) be the second derivative of n(b). Let x(v) = 0. What is v?
-1/4, 0
Factor 117*s - 15*s**3 + 72102 + 14*s**3 - 71697 - 9*s**2.
-(s - 9)*(s + 3)*(s + 15)
Let u be (93/(-1116))/((-3)/(-112))*(3072/(-14))/1. Factor -128/3*b**2 + 2/3*b**3 + 0 + u*b.
2*b*(b - 32)**2/3
Let f(q) = 3*q**2 - 63*q + 312. Let r(j) = 4*j**2 - 127*j + 624. Let v(m) = 5*f(m) - 3*r(m). Factor v(d).
3*(d - 4)*(d + 26)
Suppose -286*x**2 - 2312/3 - 2/3*x**4 - 76/3*x**3 - 2584/3*x = 0. What is x?
-17, -2
Let i(g) be the first derivative of -20/7*g + 2/21*g**3 + 14 + 9/7*g**2. Suppose i(v) = 0. What is v?
-10, 1
Let r(x) be the first derivative of x**6/30 - x**5/5 + x**4/2 - 2*x**3/3 + x**2/2 - x/5 - 817. Suppose r(j) = 0. What is j?
1
Let y(h) be the third derivative of h**5/150 + h**4/5 + 32*h**3/15 + h**2 - 815. Suppose y(g) = 0. What is g?
-8, -4
Factor h**5 + 115622*h**2 + 9*h**4 - 16*h**3 - h**4 + 3*h**4 - 115942*h**2.
h**2*(h - 5)*(h + 8)**2
Let t = -358742 + 358745. Find c such that -2/9*c**5 - 2/3*c**4 + 0*c**2 + 0*c + 0*c**t + 0 = 0.
-3, 0
Let c(m) be the second derivative of 0*m**2 + 0 + 1/294*m**7 - 3/7*m**3 + 1/30*m**6 - 1/28*m**4 - 67*m + 13/140*m**5. Determine v, given that c(v) = 0.
-3, -2, 0, 1
Suppose 0 = -t - 6*t + 105. Suppose 17*q - 10 = t*q. Factor -n - 5*n + q*n**2 - n**4 + 4*n**2 - 2*n**4.
-3*n*(n - 1)**2*(n + 2)
Solve 80*h**2 + 401 + 465 + 4*h**3 - h - 762 + 265*h + 34*h**2 = 0.
-26, -2, -1/2
Let r(c) = -1306*c**2 - 2 + 38*c - 1 + 1310*c**2. Let i(d) = 44*d**2 + 420*d - 32. Let j(x) = 3*i(x) - 32*r(x). Factor j(g).
4*g*(g + 11)
Let p(g) be the third derivative of -g**5/4 + 7*g**4/24 + 4*g**3/3 - g**2 - 280. Let p(i) = 0. Calculate i.
-8/15, 1
Let y be 2 + (-16)/7 + 132/21. Suppose 5*r = 3*p + y, 0 = r + p - 0*p - 6. Factor 4*m**4 + 210*m + 20 + 24*m**2 - 286*m + 80*m**2 + 4*m**5 - 56*m**r.
4*(m - 1)**4*(m + 5)
Suppose 0 = 5*j + 6*w - 3, 20*j = 21*j + 5*w + 7. Factor -2/7*h**j + 0 + 18/7*h + 0*h**2.
-2*h*(h - 3)*(h + 3)/7
Suppose 170*b - 2295 = 161*b. Suppose -b = -81*o - 4*o. Determine y so that -36/7 + 24/7*y**o - 3/7*y**4 + 12*y - 69/7*y**2 = 0.
1, 2, 3
Let x = 40210/69037 - 4/2227. Let q = 85/93 - x. Suppose 0 + 2/3*d**2 + 0*d**3 + q*d - 2/3*d**4 - 1/3*d**5 = 0. Calculate d.
-1, 0, 1
Let -428*x - 4*x**4 + 68*x - 52*x**2 + 1008*x + 80*x**3 - 416*x**2 = 0. What is x?
0, 2, 9
Suppose -67*l + 81*l - 3066 = 0. Let j = 219 - l. Suppose 3/7*f**5 + j - 5/7*f**2 - 2/7*f + 5/7*f**4 - 1/7*f**3 = 0. Calculate f.
-1, -2/3, 0, 1
Let 94*j**4 - 324*j**2 - 4*j**5 + 30933*j**3 + 230*j**4 - 30929*j**3 = 0. Calculate j.
-1, 0, 1, 81
Let k(c) be the second derivative of 47*c**5/140 - 703*c**4/84 + 596*c**3/21 + 26*c**2/7 - 56*c - 53. Determine i so that k(i) = 0.
-2/47, 2, 13
Let n = 24562/1771 - 1774/253. Factor 0 + 2/7*m**3 - n*m - 4/7*m**2.
2*m*(m - 6)*(m + 4)/7
Let b(m) be the second derivative of -m**8/2240 - m**7/210 - m**6/80 - 7*m**4/4 - 10*m + 4. Let q(z) be the third derivative of b(z). Factor q(w).
-3*w*(w + 1)*(w + 3)
Let r(f) be the third derivative of f**5/420 + 275*f**4/84 + 75625*f**3/42 - 12*f**2 - 60. Factor r(p).
(p + 275)**2/7
Solve 50091*c**2 + 1314*c - 50095*c**2 + 4726*c - 2280100 = 0 for c.
755
Let s(f) be the third derivative of 1/420*f**7 + 0*f**3 + 0*f**4 - 84*f**2 + 0 + 0*f**5 + 1/240*f**6 + 0*f. Factor s(r).
r**3*(r + 1)/2
Let w(r) be the second derivative of r**5/160 - r**4/96 - 5*r**3/48 - 3*r**2/16 - 5*r + 51. Suppose w(h) = 0. Calculate h.
-1, 3
Let y = -24807925040/959 + 25868532. Let h = -16/137 - y. Find l such that 16/7*l**2 + 0 + 4/7*l**3 - h*l = 0.
-5, 0, 1
Suppose 2 - 6 = 2*l, 2*b = -5*l - 112. Let k be ((-2)/(-4))/(b/(-136)*4). What is o in 0*o + k*o**2 + 0 = 0?
0
Let a(u) be the second derivative of 170*u - 1/36*u**4 + 0*u**2 + 1/2*u**3 + 0. Factor a(x).
-x*(x - 9)/3
Let j(i) be the first derivative of i**4/24 - i**3/18 - 3*i**2/4 + 3*i/2 + 15. Factor j(u).
(u - 3)*(u - 1)*(u + 3)/6
Let v be 28/6*123/(-2). Let m = v + 291. Factor 0 + 0*y + 42/5*y**m + 8/5*y**2 - 48/5*y**3 + 98/5*y**5.
2*y**2*(y + 1)*(7*y - 2)**2/5
Let a = 51 - -6. Find c, given that a*c + 2*c**2 + 7*c**2 - 106*c - 76*c - 4*c**2 = 0.
0, 25
Let l(u) be the first derivative of 5*u**6/12 - u**5/2 - 5*u**4/4 + 1750. Factor l(n).
5*n**3*(n - 2)*(n + 1)/2
Let t(b) be the second derivative of 1/60*b**5 - 5/24*b**4 + b**3 - 6*b + 0 - 11*b**2. Let q(n) be the first derivative of t(n). Find p, given that q(p) = 0.
2, 3
Let s(l) = 7*l**3 - 1031*l**2 + 2729*l - 7127. Let f(h) = h**3 - 150*h**2 + 390*h - 1018. Let c(n) = 41*f(n) - 6*s(n). Factor c(b).
-(b - 16)**2*(b - 4)
Let t(d) be the first derivative of -d**8/4200 + d**7/525 - d**6/180 + d**5/150 - 2*d**3 + 103. Let f(g) be the third derivative of t(g). Solve f(c) = 0.
0, 1, 2
Let v be (-85)/(-51) + 165/9. Suppose 0 = -v*i - 203 + 603. Find r such that -i + 50*r + 5*r**2 - 25/2*r**3 = 0.
-2, 2/5, 2
Let u(n) be the first derivative of -825*n**3 - 240*n**2 + 3*n - 1091. Solve u(f) = 0.
-1/5, 1/165
Factor 564634 - 425*l**2 - 175258 - 1188*l + 426*l**2 - 60*l.
(l - 624)**2
Let v be (2/(-2))/4 + (-54)/(-24). Factor 28*n + 20*n**v + 60*n + 422 - 206 - 184.
4*(n + 4)*(5*n + 2)
Let q = 127/11 + -337/33. Let v(r) be the first derivative of 0*r + q*r**4 + 0*r**2 + 8/9*r**3 - 13 - 2/3*r**5. Let v(m) = 0. What is m?
-2/5, 0, 2
Let i(d) be the first derivative of d**4/2 - 76*d**3/3 + d**2 - 73*d - 303. Let u be i(38). Factor -2*k - 4/3 + 2/3*k**2 + 2*k**u + 2/3*k**4.
2*(k - 1)*(k + 1)**2*(k + 2)/3
Let k(c) = 175*c + 700. Let r be k(-4). Let f(i) be the t