(w + 1)**2/4
Suppose 285*z - 156*z = 138 + 120. Solve 121/4*c**z + 4 + 22*c = 0.
-4/11
Suppose -216 = 5*k + 3*k. Let t = k - -30. Find s such that 21*s**3 - 6 - 42*s**3 + 9*s + 18*s**t = 0.
-2, 1
Suppose 0 = -i - 2*c + 9, -2*i - 9*c + 4*c = -21. Determine w so that 33*w**i + 8*w**2 - 234*w**4 - 13*w**3 + 242*w**4 = 0.
-2, -1/2, 0
Solve -54*o**4 + 1425*o + 250 + 2279/4*o**3 + 7/4*o**5 - 4385/2*o**2 = 0 for o.
-1/7, 1, 10
Let x(g) be the first derivative of -1/10*g**5 + 15/4*g**4 - 98*g + 105*g**2 + 25 - 253/6*g**3. Factor x(k).
-(k - 14)**2*(k - 1)**2/2
Let n be (534/9)/(1456/312) + -11. Determine w, given that -3*w**3 - 3/7*w**5 + 24/7*w + 15/7*w**4 - 3/7*w**2 - n = 0.
-1, 1, 2
Determine o so that -156 + 65 + o**2 + 572 + 43*o - 61 = 0.
-28, -15
Let n(t) = 57*t**2 - 9*t**3 - 112*t**2 + 55*t**2 - 2*t - 2. Let s be n(-2). Suppose 80 - 5*m - s - 2*m**2 + m = 0. What is m?
-3, 1
Let l(k) be the second derivative of 5/24*k**4 + 3*k**2 + 0 - 37*k - 1/12*k**5 - 1/2*k**3 + 1/72*k**6. Let h(z) be the second derivative of l(z). Factor h(c).
5*(c - 1)**2
Factor 0 - 1041/4*f**2 + 3/2*f**3 - 261/2*f.
3*f*(f - 174)*(2*f + 1)/4
Let c(j) be the second derivative of j**6/1080 - j**5/90 + j**3/6 + 3*j**2/2 - 11*j - 2. Let w(m) be the second derivative of c(m). Suppose w(l) = 0. What is l?
0, 4
Let b be (-1)/((-11)/(-4)) - (-5698)/1694. Determine i, given that -2/9*i**4 - 2*i**2 + 14/9*i - 4/9 + 10/9*i**b = 0.
1, 2
Let l(i) = -75*i + 227. Let t be l(3). Let b be (t/2*0)/(12/(-12)). Factor 3*x**2 + 9/4*x + b + 3/4*x**3.
3*x*(x + 1)*(x + 3)/4
Suppose 3716*s = 3709*s + 28. Let m(u) be the second derivative of 0 - 13*u + 0*u**2 + 1/9*u**s + 1/30*u**5 + 1/9*u**3. Factor m(x).
2*x*(x + 1)**2/3
Let s = 400 + -397. Find i such that 12*i**3 - s*i**3 - 5*i**3 - 200*i - 34*i**2 - 6*i**3 - 6*i**2 = 0.
-10, 0
Let w(a) = -a - 12. Let s be w(-6). Let u be (-2)/s + (-2 - 22/(-6)). Find k such that -3*k**u - 169 + 6*k + 169 = 0.
0, 2
Let r(g) be the third derivative of g**8/112 + 13*g**7/105 + 9*g**6/40 - 14*g**5/15 + 351*g**2. Factor r(y).
y**2*(y - 1)*(y + 7)*(3*y + 8)
Let b(g) = -7*g**2 + 4982*g - 1245009. Let z(n) = -36*n**2 + 24906*n - 6225047. Let v(t) = -11*b(t) + 2*z(t). Factor v(d).
5*(d - 499)**2
Let u = 3561 - 17801/5. Determine k, given that 2/5*k**3 + 4/5*k**2 - u - 2/5*k = 0.
-2, -1, 1
Let l(a) be the first derivative of -5*a**4/12 + 70*a**3/3 + 145*a**2/2 - 79*a - 204. Let v(y) be the first derivative of l(y). Factor v(r).
-5*(r - 29)*(r + 1)
Suppose -5*v - 2*g = -0*v - 14, -3*v + 10 = 2*g. Determine m so that 7*m + 594 + 30*m**4 - 290 - 5*m**3 - 2*m - 40*m**v - 294 = 0.
-1, -1/2, 2/3, 1
Suppose -73*k = 378*k. Factor 0*y + 1/3*y**5 + k + y**3 + 0*y**2 + 4/3*y**4.
y**3*(y + 1)*(y + 3)/3
Let s(x) be the third derivative of -x**9/120960 - x**8/40320 + x**7/5040 + 7*x**5/6 + x**2 + 5*x. Let p(q) be the third derivative of s(q). Factor p(v).
-v*(v - 1)*(v + 2)/2
Let p(z) be the third derivative of z**5/480 - 227*z**4/24 + 51529*z**3/3 + 357*z**2 + 4*z. Factor p(r).
(r - 908)**2/8
Let i(d) be the first derivative of -d**3/12 + 27*d**2/4 + 295*d/4 + 2133. Factor i(g).
-(g - 59)*(g + 5)/4
Let w = -9129 + 2802597/307. Let t = w + 5556/1535. Suppose 2/5*a**2 + 12/5*a + t = 0. What is a?
-3
Let h be 1257273/1935 + 8 + (-342)/43. Let -969/5*b**3 + 2526/5*b**2 + 1476/5*b + 216/5 - h*b**4 = 0. What is b?
-2/3, -6/19, 1
Factor 0 + 91/4*f**4 - 95*f**3 - 29*f**2 + 0*f.
f**2*(7*f + 2)*(13*f - 58)/4
Let p = 699 - 687. Suppose 0 = 5*r - 4*m - p + 17, 2*m - 7 = r. Factor -3/8*i**r + 0*i + 0 + 0*i**2.
-3*i**3/8
Factor -136/7 + 26/7*g + 2/7*g**2.
2*(g - 4)*(g + 17)/7
Let h(g) be the third derivative of -11/1575*g**7 + 8/225*g**5 + 0*g**3 + 0*g + 1/45*g**4 + 76*g**2 + 0 - 1/300*g**6 + 1/630*g**8. Suppose h(d) = 0. What is d?
-1, -1/4, 0, 2
Let v be (26/65)/(25/((-375)/(-9))). Let o be (-2)/5*(-15)/9. Factor -o + v*a**2 + 0*a.
2*(a - 1)*(a + 1)/3
Let p(o) be the first derivative of 4*o**5/5 - 37*o**4 + 416*o**3/3 - 136*o**2 - 10679. Factor p(s).
4*s*(s - 34)*(s - 2)*(s - 1)
Let t = 21324 - 21320. Let l(q) be the third derivative of 1/960*q**6 + 0*q**5 + 0*q + 0 + 1/1680*q**7 + 0*q**3 - 39*q**2 + 0*q**t. Factor l(s).
s**3*(s + 1)/8
Let q(u) = u**2 + 3*u + 2. Let m be q(-9). Let x = m - 47. Factor x*c - c**2 + 0*c + c**2 + 3*c**2.
3*c*(c + 3)
Let b(j) = 181*j**2 - 27*j + 174*j**2 + 54 - 6*j**3 - 560*j**2 + 157*j**2. Let a(i) = i**3 + 7*i**2 + 4*i - 8. Let s(v) = -27*a(v) - 4*b(v). Factor s(u).
-3*u**2*(u - 1)
What is v in 10/9*v**3 + 0*v + 8/9*v**2 + 2/9*v**4 + 0 = 0?
-4, -1, 0
Let f be (-2)/(-2)*(0 + 2). Let y be (-414)/115*((-8 - -1) + f). What is p in y*p + 3*p**3 - p**4 - 4*p**5 + 3*p**5 - 16*p + 5*p**2 = 0?
-1, 0, 2
Let a(b) = 47686*b - 190726. Let o be a(4). Find r such that 111/5*r - 3/5*r**3 - 18/5*r**2 - o = 0.
-10, 1, 3
Suppose -17/2*f**3 + 72 + 8*f - 153/2*f**2 + 9/2*f**4 + 1/2*f**5 = 0. What is f?
-9, -4, -1, 1, 4
Let v(u) be the first derivative of u**6/3 - 2*u**5/5 - u**4 + 1161. Let v(i) = 0. What is i?
-1, 0, 2
Suppose 25*f + 32*f + 109383 = 0. Let i = -13421/7 - f. Find x such that i*x**2 + 0*x + 0 - 3/7*x**3 = 0.
0, 4
Let a be 5*(6 - 7) + 7. Let 120*t**a + 30*t**4 + 54*t**4 - 132*t**2 + 60*t**5 - 81*t**3 + 12*t = 0. What is t?
-2, -2/5, 0, 1/2
Suppose 3*k = -4*d + 89, 2*k = -5*d + 69 - 12. Let i = 34 - k. Factor 19*f - 4*f**4 + 12*f**2 + 5*f**3 + 10*f**3 - i*f - 16 - 23*f**3.
-4*(f - 1)**2*(f + 2)**2
Suppose -456*s + 450*s = 2352. Let b = 829/2 + s. Factor -b*h + 405/4 + 5/4*h**2.
5*(h - 9)**2/4
Let h(y) = 14*y**4 - 296*y**3 + 778*y**2 - 622*y + 156. Let s(k) = 3*k**4 + k**3 + k**2. Let i(q) = -2*h(q) + 12*s(q). Find z, given that i(z) = 0.
-78, 1/2, 1
Let o = -2/39203 - -39363/3136240. Let c(j) be the second derivative of -12*j + 5/8*j**3 - j**2 + 0 - o*j**5 - 1/8*j**4. Solve c(l) = 0 for l.
-8, 1
Let d be 64/((-192)/(-15))*(2 + (-24)/15). Factor -4*n + 1/3*n**d + 20/3.
(n - 10)*(n - 2)/3
Let k(r) be the first derivative of -2*r**3/27 + 307*r**2/9 - 68*r + 1940. Solve k(d) = 0.
1, 306
Suppose 19*c - 575 = -537. Let g = 4162/13 - 320. Determine p so that -8/13*p - 6/13 - g*p**c = 0.
-3, -1
Let o(j) be the second derivative of -j**6/60 + 2*j**5/5 - 3*j**4 + 108*j**2 + 991*j. Find d such that o(d) = 0.
-2, 6
Let s(a) be the first derivative of -a**5/10 + 11*a**4/6 - 8*a**3 - 36*a**2 + 49*a + 17. Let d(i) be the first derivative of s(i). Factor d(c).
-2*(c - 6)**2*(c + 1)
Let b(x) be the second derivative of 12*x - 3 - 1/2*x**3 - 21*x**2 + 3/20*x**5 + 7/2*x**4. Factor b(w).
3*(w - 1)*(w + 1)*(w + 14)
Suppose 49*f = 46*f + 9. Let m(v) be the first derivative of 1/16*v**4 + 13 + 1/4*v**f + 3/8*v**2 + 1/4*v. Factor m(h).
(h + 1)**3/4
Let u(z) = 2*z**2 - 66*z - 2. Suppose 5*g - 3*v - 14 = 8, g + 5*v = -18. Let l(s) = -s**2 + 67*s + 3. Let b(p) = g*l(p) + 3*u(p). Factor b(t).
4*t*(t - 16)
Determine l so that -286*l**2 + 1602*l - 578 - 3916*l - 283*l**2 - 283*l**2 + 844*l**2 = 0.
-289, -1/4
Let r be (-366)/(-12) - (-115)/(-5). Let t(z) be the first derivative of -18 + r*z**2 + 0*z - 5/3*z**3. Factor t(y).
-5*y*(y - 3)
Find r such that 18/5*r**3 + 93/5*r**4 - 279/5 - 534/5*r**2 - 3/5*r**5 - 147*r = 0.
-1, 3, 31
Let o(u) be the first derivative of -2*u**5/45 - 13*u**4/18 - 22*u**3/9 - 31*u**2/9 - 20*u/9 - 3641. Factor o(j).
-2*(j + 1)**3*(j + 10)/9
Factor -7586/3*j - 7592*j**2 - 632/3 - 24*j**3.
-2*(j + 316)*(6*j + 1)**2/3
Let k(o) be the third derivative of 0*o**3 + 25/132*o**4 + 178*o**2 + 0*o + 49/330*o**5 + 23/660*o**6 - 1/1155*o**7 + 0. Factor k(v).
-2*v*(v - 25)*(v + 1)**2/11
Let u(b) = -2*b**2 - 11*b + 10. Let i be u(-6). Suppose -p - p + 6 = -q, -i*q - 3 = -p. Solve 3/4*w**2 + 3*w - p - 3/4*w**3 = 0 for w.
-2, 1, 2
Let u(p) = 172*p - 339. Let l be u(2). Let o(t) be the first derivative of 0*t**2 + 0*t - 1/2*t**6 + 0*t**3 + 26 + 6/5*t**l - 3/4*t**4. Factor o(x).
-3*x**3*(x - 1)**2
Suppose 94*q = 48*q + 276. Let a(v) be the third derivative of 0*v**3 - 18*v**2 + 0*v**4 + 0 + 0*v - 1/360*v**q + 0*v**5 + 1/630*v**7. Factor a(j).
j**3*(j - 1)/3
Let a(g) be the third derivative of g**6/1440 + 23*g**5/480 + 13*g**3/6 + g**2 - 5*g. Let o(y) be the first derivative of a(y). Factor o(q).
q*(q + 23)/4
Let a(y) be the third derivative of 121*y**6/240 + 5401*y**5/120 - 247*y**4/6 + 1