8*u + 79. Suppose -230 = -8*z - 214. Let r(q) = 5*q**3 + 18*q**2 - 43*q + 26. Let t(y) = z*i(y) - 7*r(y). Factor t(p).
-3*(p - 1)**2*(p + 8)
Determine z, given that 9602*z + 36*z**2 - 36 - 3*z**3 - 9737*z + 186 = 0.
2, 5
Let j(d) be the third derivative of -d**7/15 + 221*d**6/60 - 436*d**5/105 + 31*d**4/21 - 2270*d**2. Factor j(g).
-2*g*(g - 31)*(7*g - 2)**2/7
Let k = 207571 + -207568. Factor -1/2*j + 1/2*j**k - 7*j**2 + 7.
(j - 14)*(j - 1)*(j + 1)/2
Factor 513 - 12534*z + z**2 + 10485*z - 13*z**2.
-3*(z + 171)*(4*z - 1)
Suppose -18*x + 121 = -13*x + 4*m, -4*x + 3*m = -72. Let u be 22/x - 46/(-161). Factor 5/3*p**2 + 8/3*p + u + 1/3*p**3.
(p + 1)*(p + 2)**2/3
Let d(n) be the second derivative of -n**6/420 - n**5/210 + n**4/21 + 4*n**3/21 + 41*n**2 - 96*n. Let q(f) be the first derivative of d(f). Factor q(k).
-2*(k - 2)*(k + 1)*(k + 2)/7
Suppose -6*c - 20 + 32 = 0. Let t(s) = -s**3 + 1. Let y(x) = 2*x**4 - 6*x**3 + 6*x**2 - 2. Let n(r) = c*y(r) + 4*t(r). Factor n(u).
4*u**2*(u - 3)*(u - 1)
Solve -p - 107*p**2 - 35*p + 3*p**4 + 68*p**2 = 0.
-3, -1, 0, 4
Suppose 0 = -3*v + 4*c, 3*v + 3*c = -0 + 21. Factor -253*z**3 + 113*z**3 - 4*z**v + 124*z**3 - 12*z**2.
-4*z**2*(z + 1)*(z + 3)
Let u be ((-110)/385)/(288/(-28)). Let q(a) be the second derivative of -2/3*a**2 - 23*a - 2/9*a**3 - u*a**4 + 0. Factor q(y).
-(y + 2)**2/3
Let z(t) be the first derivative of -t**4/18 + 16*t**3/27 + 19*t**2/9 + 20*t/9 - 1446. Factor z(s).
-2*(s - 10)*(s + 1)**2/9
Let q(k) be the first derivative of k**4/4 + 31*k**3 + 1188*k**2 + 9680*k - 608. Factor q(u).
(u + 5)*(u + 44)**2
Let k(o) be the third derivative of 1/60*o**5 + 0 - 2*o**3 - 214*o**2 + 0*o + 11/24*o**4. Factor k(g).
(g - 1)*(g + 12)
Find t, given that -30*t + 66*t**2 + 262 - t**4 - 242 - 26*t**3 + 4*t + 3*t**4 - 36*t = 0.
1, 10
Let m be (24/44)/((-2401)/(-49049)) + 11/(-1). Factor 2/7*i - 3/7 + m*i**2.
(i - 1)*(i + 3)/7
Let y(p) = -8*p**3 - 46*p**2 + 65*p + 468. Let o(r) = 33*r**3 + 186*r**2 - 258*r - 1872. Let m(x) = -5*o(x) - 21*y(x). Let m(b) = 0. Calculate b.
-13, -3, 4
Let c(x) = 7*x**3 - 22*x**2 + 59*x - 168. Let y be c(3). Solve 76/7*k + 2/7*k**2 + y = 0.
-38, 0
Find t, given that 0 - 11/4*t**3 + 5/4*t**5 - 13/4*t**2 + 3/2*t + 13/4*t**4 = 0.
-3, -1, 0, 2/5, 1
Suppose -31*g + 25*g = -42*g. Let y(c) be the second derivative of 0*c**2 + g - 2*c**3 - 1/4*c**4 + 50*c. Factor y(t).
-3*t*(t + 4)
Determine g so that 6992/5*g + 2/5*g**4 + 1362/5*g**2 + 11552/5 + 92/5*g**3 = 0.
-19, -4
Let p be (-4250)/1250 - (4 + -3 - 5/1). Factor -3/5*u**3 + 12/5 - 12/5*u**2 + p*u.
-3*(u - 1)*(u + 1)*(u + 4)/5
Let p be 64/4*11/44. Factor 23*y + 20*y**2 - 10*y**3 - 3*y + 20*y - 5*y**p.
-5*y*(y - 2)*(y + 2)**2
Suppose -n - 3 = 5*s + 3*n, 4*s = -4*n - 4. Suppose 5*r - s = 34. Determine u so that 89*u**4 - 7*u**3 + 5*u**2 - 93*u**4 + r*u**2 - u**3 = 0.
-3, 0, 1
Let x(g) = -1 + 0 + 15*g**2 - 15*g + 6. Let u(v) = 8*v**2 - 8*v + 3. Suppose 10*n + 165 = -23*n. Let j(o) = n*u(o) + 3*x(o). Factor j(c).
5*c*(c - 1)
Let m(h) be the first derivative of h**6/2 - 4*h**5/15 - h**4/2 + 36*h**2 - 23. Let i(n) be the second derivative of m(n). Find y, given that i(y) = 0.
-1/3, 0, 3/5
Factor -200/19*s**3 + 0*s**2 + 0*s + 0 - 104/19*s**4 - 2/19*s**5.
-2*s**3*(s + 2)*(s + 50)/19
Factor -3/7*g**4 + 51/7*g**2 + 0 + 27/7*g + 3*g**3.
-3*g*(g - 9)*(g + 1)**2/7
Let i(b) be the third derivative of 1/3*b**3 + 33*b**2 + 0*b - 5/72*b**4 + 0 + 1/180*b**5. Factor i(f).
(f - 3)*(f - 2)/3
Let n(w) be the second derivative of -w**5/60 + 116*w**4 - 322944*w**3 + 449538048*w**2 - 14*w + 123. Factor n(b).
-(b - 1392)**3/3
Let z(w) be the first derivative of -w**5/5 - 5*w**4/2 - 11*w**3/3 + 35*w**2 + 1256. Factor z(o).
-o*(o - 2)*(o + 5)*(o + 7)
Let v = 11693/29245 + 1/5849. Determine c so that 24/5 - 2/5*c**2 + v*c = 0.
-3, 4
Suppose 23 = r - 3*g - 46, g + 275 = 5*r. Factor -338*o**3 - 328*o**3 - 26 - 55 - 108*o + 654*o**3 - r*o**2 - o**4.
-(o + 3)**4
Let q(c) be the third derivative of c**10/7560 + c**9/945 + c**8/420 + 35*c**4/24 + 78*c**2. Let o(y) be the second derivative of q(y). Factor o(t).
4*t**3*(t + 2)**2
Let i(r) be the second derivative of r**6/90 + r**5/60 - r**4/3 + r - 700. Determine a, given that i(a) = 0.
-4, 0, 3
Suppose -3*b + 37 = -62*h + 58*h, 6*b + 3 = -3*h. Solve 0*n - 12/5*n**b - 4/5*n**4 + 0 - 8/5*n**2 = 0.
-2, -1, 0
Let y(b) = -17*b**3 + 111*b**2 + 190*b. Let m(c) = 2*c**3 - 14*c**2 - 24*c. Let t(d) = -50*m(d) - 6*y(d). Factor t(w).
2*w*(w + 2)*(w + 15)
Let h(m) = -5*m**3 - 120*m**2 - 157*m + 114. Let c(t) = -2*t**3 - 47*t**2 - 52*t + 38. Let i(x) = 8*c(x) - 3*h(x). Factor i(r).
-(r - 2)*(r - 1)*(r + 19)
Factor 8605*d + 5715*d**2 - 1132*d**3 + 381*d**3 - 5730 + 362*d**3 + 379*d**3.
-5*(d - 573)*(d + 2)*(2*d - 1)
Let t(d) = -2*d**3 - 10*d**2 + 15*d + 20. Let g be t(-6). What is u in 82*u - 180*u**g - 41*u - 111*u**3 - 30*u**4 - 3*u**5 - 149*u = 0?
-3, -2, 0
Let m(i) be the second derivative of -i**7/168 - 11*i**6/72 - 5*i**5/3 - 10*i**4 + 34*i**3/3 - 27*i. Let f(b) be the second derivative of m(b). Factor f(t).
-5*(t + 3)*(t + 4)**2
Let l be (((-42)/(-33))/(-7) - (-18)/1188)*0. Solve 1/3*n**2 + 23/3*n + l = 0 for n.
-23, 0
Let l = 537 - 1052. Let g = l + 2577/5. Find w such that 0 + 0*w + 2/5*w**2 - g*w**3 = 0.
0, 1
Let z be 497 - 68 - (0 - 4). Let d = 437 - z. Determine h, given that 40/13*h + 74/13*h**3 - 34/13*h**d - 6*h**2 - 8/13 + 6/13*h**5 = 0.
2/3, 1, 2
Let c be 6 - 7 - (-6)/1. Factor 15*w - c*w**2 + 46 - 15*w**3 - 5*w**4 - 13 - 20 - 3.
-5*(w - 1)*(w + 1)**2*(w + 2)
Let n(i) = -12*i + 352. Let r be n(7). What is p in -113*p - 36*p**3 + 72*p**2 - 55*p + 24 + r*p = 0?
-2/3, -1/3, 3
Let y(n) = -16*n**4 + 72*n**3 + 652*n**2 - 756*n - 6. Let w(j) = -2*j**4 - 2*j**3 - 4*j**2 - 1. Let h(s) = -6*w(s) + y(s). Factor h(p).
-4*p*(p - 27)*(p - 1)*(p + 7)
Let g be 16/(-10) - 18/(-30). Let o be (-1 + 16)*(-2)/3. Let q(n) = n. Let p(y) = -5*y**2 - 30*y. Let v(f) = g*p(f) + o*q(f). Factor v(s).
5*s*(s + 4)
Find y, given that 68/3*y**3 + 34/3*y**4 - 4/3*y**5 - 74/3*y**2 + 40/3 - 64/3*y = 0.
-2, -1, 1/2, 1, 10
Factor -3221*u - 233*u**3 - 2167*u + 2186*u**2 + 16669*u**4 - 143 + 16667*u**4 - 2377 - 33331*u**4.
(u - 35)*(u - 6)**2*(5*u + 2)
Let b be 60 + 12*(-1)/2. Let 29*z**3 + 18*z**2 + z - 18 + 24*z**3 - b*z**3 = 0. What is z?
-1, 1, 18
Suppose -945*m**2 - 3526 - 2572*m + 10*m**3 - 1908*m + 6001 = 0. What is m?
-5, 1/2, 99
Determine i so that -1350*i + 671/2*i**3 + 1/2*i**5 + 53/2*i**4 - 941/2*i**2 + 1458 = 0.
-27, -2, 1, 2
Let u = 7363/36765 - 2/7353. Let h(g) be the second derivative of 0 - 1/5*g**3 - 1/50*g**5 + g + 1/10*g**4 + u*g**2. Factor h(n).
-2*(n - 1)**3/5
Let h = 106 + -346. Let r = -238 - h. Factor -4/11*i**3 + 2/11*i**4 + 2/11*i - 4/11*i**r + 2/11*i**5 + 2/11.
2*(i - 1)**2*(i + 1)**3/11
Let u be (19 - (-272)/(-14))*(-7 + (-6 - -6)). Find f, given that -2/3*f - 12 + 12*f**2 + 2/3*f**u = 0.
-18, -1, 1
Let q(j) be the second derivative of -j**4/6 + 176*j**3 - 1025*j. Let q(t) = 0. Calculate t.
0, 528
Suppose -64/7*o**4 + 288/7*o**3 - 4/7*o**5 + 456/7 + 188*o + 1208/7*o**2 = 0. What is o?
-19, -1, 6
Let i = 378 - 372. Let q be 3/(-4 + 15/6) + i. Factor -2/9*c + 2/9*c**5 + 0*c**3 + 4/9*c**2 - 4/9*c**q + 0.
2*c*(c - 1)**3*(c + 1)/9
Let u be (-1251)/(-1668) - (-23)/(-52). Let x(w) be the first derivative of -14/39*w**3 + 7/13*w**2 - u*w + 1/13*w**4 + 3. Factor x(j).
2*(j - 2)*(j - 1)*(2*j - 1)/13
Let u(r) be the second derivative of -r**4/6 + 86*r**3 + 259*r**2 + 690*r. Factor u(d).
-2*(d - 259)*(d + 1)
Let y be 9128/(-140)*(1342/1352 - 1). Let p = y - -3/169. Factor 0 + 0*i**3 + 0*i**2 - 1/4*i**5 + 0*i - p*i**4.
-i**4*(i + 2)/4
Let j(n) be the second derivative of -15*n**4/8 - 955*n**3/12 - 105*n**2/2 - 8681*n. Find m such that j(m) = 0.
-21, -2/9
Suppose 3*x - 30*x = -135. Find h such that 19*h**4 - 2*h + 16*h**4 - 10*h**3 + 0*h - 25*h**2 - 9*h**x + 15*h**5 - 4*h = 0.
-6, -1/2, -1/3, 0, 1
What is s in -88/15 - 38/3*s - 26/15*s**2 + 4/15*s**3 = 0?
-4, -1/2, 11
Let h(u) be the second derivative of u**5/75 - 8*u**4/3 + 640*u**3/3 - 103*u**2/2 + 16*u. Let s(d) be the first derivative of h(d). Factor s(j).
4*(j - 40)**2/5
Let c(u) be the second derivative of u**5/40 - 79*u**4/8 + 6241*u**3/4 - 493039*u**2/4 + 2970*u. Factor c(s).
(s - 79)**3