)*(r + 1)/15
Let p = 42574 - 42572. Factor 5488 - 1/4*y**3 + 21*y**p - 588*y.
-(y - 28)**3/4
Let b(c) = -2*c**3 - 3*c**2 - c - 8. Let j(q) = -4*q**3 - 1290*q**2 - 644*q - 40. Let l(v) = 5*b(v) - j(v). Find a such that l(a) = 0.
-1/2, 0, 213
Let n be (-678902)/(-63) - 2/9. Find x, given that -10776 + 8*x**2 + n + x**3 = 0.
-8, 0
Let -402 + 18 - 536*x**3 - 1533*x**2 + 36*x**5 - 1314*x**2 - 232036*x + 229764*x + 188*x**4 + 271*x**2 = 0. What is x?
-6, -2, -1, -2/9, 4
Suppose 8 = -4*g, -g = -0*h + 2*h. Suppose -3*q - 2*k - 4 + 2 = 0, -3*q + k = -h. Factor 3/2*y**3 - 9/2*y + q*y**2 + 3.
3*(y - 1)**2*(y + 2)/2
Suppose -64*q - 2*w + 14 = -63*q, -5*q + 40 = 4*w. Determine c, given that -6/5*c**q + 3/5*c**5 + 3/5*c**3 + 0*c + 0 + 0*c**2 = 0.
0, 1
Let r be 0/11 + 2 + -1. Let g be -6*r/(-21)*6/4. Factor -g*i**4 - 3/7*i**2 + 0*i + 0 + 6/7*i**3.
-3*i**2*(i - 1)**2/7
Let z(l) be the first derivative of -5*l**4/4 + 10*l**3 + 305*l**2/2 - 330*l - 12. Factor z(w).
-5*(w - 11)*(w - 1)*(w + 6)
Let w(p) be the first derivative of -p**5/10 - 4*p**4 + 17*p**3/3 + 8*p**2 - 33*p/2 - 3233. Factor w(m).
-(m - 1)**2*(m + 1)*(m + 33)/2
Let c(v) be the first derivative of -v**4/36 + 4*v**3/9 - 5*v**2/2 - 70*v - 48. Let b(n) be the first derivative of c(n). Factor b(w).
-(w - 5)*(w - 3)/3
Let d = -202 + 204. What is s in -3*s**d + 6*s**2 - 3*s**2 + s**2 + 10*s - 3*s**2 = 0?
0, 5
Factor -282*b**2 - 284*b**2 + 98*b**3 + 43*b**2 - 2160*b - 96*b**3 + 101*b**2.
2*b*(b - 216)*(b + 5)
Let s be (-836)/363 + 2/6 - 182/(-78). Let -s*d - 2/11 - 2/11*d**2 = 0. Calculate d.
-1
Let h(b) be the second derivative of -b**4/30 + 3*b**3 + 94*b**2/5 - 8858*b. Factor h(p).
-2*(p - 47)*(p + 2)/5
Let i(q) be the third derivative of q**5/270 - 91*q**4/54 - 185*q**3/9 + 2541*q**2. Find o, given that i(o) = 0.
-3, 185
Let h(z) be the first derivative of -1/900*z**6 - 5 + 1/20*z**4 + 0*z**2 + 1/150*z**5 + 0*z + 7/3*z**3. Let f(y) be the third derivative of h(y). Factor f(p).
-2*(p - 3)*(p + 1)/5
Let d = 138 + -136. Let i be (120/32)/(6/8). Determine b, given that 1941*b**2 + 5*b + 1 - 1942*b**d + i = 0.
-1, 6
Find p such that 1/5*p**2 - 9/5*p - 2 = 0.
-1, 10
Let a(u) be the second derivative of 1/10*u**5 + 1/30*u**6 + 0*u**2 - 4/3*u**3 + 39*u + 0 - 1/3*u**4. Factor a(j).
j*(j - 2)*(j + 2)**2
Suppose -7 - 9 = 2*x - 4*c, 13 = 4*x + c. Factor -48*d + 2*d**2 - 13*d**x + 8*d**2.
-3*d*(d + 16)
Let n(q) be the second derivative of 3*q**5/20 + 35*q**4/6 + 89*q**3/6 + 11*q**2 - 3*q + 142. Factor n(i).
(i + 1)*(i + 22)*(3*i + 1)
Let j(a) = -4*a**2 + 71*a + 1307. Let n be j(29). Factor -2/3*z**4 + 0*z - 1/3*z**n + 0 + 3/2*z**3.
-z**2*(z - 2)*(4*z - 1)/6
Suppose 33*c - 3*b = 36*c + 45, 5*b + 99 = 3*c. Factor -16/3*w**2 + 0 - 4/15*w**4 + 38/15*w**c - 10/3*w.
-2*w*(w - 5)**2*(2*w + 1)/15
Let v(x) be the third derivative of -x**5/330 + 25*x**4/44 + 574*x**3/33 + 2*x**2 - 146*x - 1. Solve v(m) = 0 for m.
-7, 82
Let v be 28/120*21 - 4. Let i(c) be the first derivative of 15/4*c**2 + 23 - c - 37/6*c**3 + 33/8*c**4 - v*c**5. Let i(z) = 0. Calculate z.
1/3, 1, 2
What is v in -1/4*v**2 - 1/12*v**3 + 9*v + 0 = 0?
-12, 0, 9
Suppose 3*w + t - 2 = 0, 5*w = -2*t + 2 + 2. Suppose -64*y + 67*y - 6 = w. Factor 3/7*f + 0 + 2/7*f**y.
f*(2*f + 3)/7
Let f be (3129/518 + -6)/(3852/23754). Solve -1/8*w**3 - f*w**4 + 0*w + 1/8*w**5 + 1/4*w**2 + 0 = 0.
-1, 0, 1, 2
What is v in 356/11*v**2 + 832/11 + 1014/11*v**4 - 4096/11*v + 13234/11*v**3 = 0?
-13, -2/3, 4/13
Suppose -60*j - 21 = -79*j - 2. Let u(m) be the first derivative of 5*m**2 + 2/3*m**3 + j + 8*m. Let u(b) = 0. Calculate b.
-4, -1
Let t = 176 - 173. Factor -7*y + 9*y**t + y**5 - 7*y**3 - 2 + 2*y**4 + y**3 - 8*y**2 - 5*y**3.
(y - 2)*(y + 1)**4
Let u(f) be the first derivative of f**3/27 + 49*f**2/6 + 146*f/9 - 172. Factor u(l).
(l + 1)*(l + 146)/9
Let b(c) = c**3 - 24*c**2 + 28*c + 159. Let d be b(24). Let y = 834 - d. Factor 0*o**y + 3/5*o + 0 + 7/10*o**2 - 1/10*o**4.
-o*(o - 3)*(o + 1)*(o + 2)/10
Suppose 0 = -l + 3*l. Suppose 4*x + 5 - 65 = l. Let 41*f**3 - 32*f**3 + 10*f**4 + f**5 - x*f**4 - 7*f**2 + 2*f = 0. Calculate f.
0, 1, 2
Let w be (141/3807*54/2)/((-3)/(-5)). Suppose -1/9*k**4 - 64/3 - 28/3*k**2 - 208/9*k - w*k**3 = 0. What is k?
-4, -3
Let f(u) be the second derivative of u**6/48 - 57*u**5/160 - 463*u**4/96 - 77*u**3/16 + 85*u**2/8 + 1237*u - 2. Suppose f(b) = 0. What is b?
-5, -1, 2/5, 17
Let a = -15423 + 15426. Let s(m) be the third derivative of 0*m**4 + 0 - 1/140*m**6 - 1/735*m**7 - 25*m**2 + 0*m + 0*m**a - 1/105*m**5. Factor s(z).
-2*z**2*(z + 1)*(z + 2)/7
Let o(r) be the first derivative of 32/15*r**3 + 32/5*r**2 - 64/5*r - 16/5*r**4 + 28/25*r**5 - 2/15*r**6 - 24. Suppose o(w) = 0. Calculate w.
-1, 2
Let h = 129569 - 129567. Find z such that 1/2*z**h - 1/2 + 1/4*z - 1/4*z**3 = 0.
-1, 1, 2
Let q(n) = -n**3 + n**2. Let u(b) = 2*b**3 + 20*b**2 - b + 25. Let l(m) = 3*q(m) + u(m). Let v be l(23). Factor -c**v - 1/5*c**3 + 9/5 - 3/5*c.
-(c - 1)*(c + 3)**2/5
Suppose 13*s = 11*s + 114. Let j be s/38*(-280)/(-3). Factor -j*z**4 + 8*z + 120*z**4 - 2*z**5 + 6*z**5 - z**3 + 37*z**3 - 28*z**2.
4*z*(z - 2)*(z - 1)**3
Let d be (-13144)/(-4929) - 4/6. Solve 1/2*r**d + 0 - r = 0 for r.
0, 2
Let q = 197 - 201. Let l be (-95)/35 + 3/(-4)*q. Determine g, given that -4/7*g**4 - 1/7*g**5 + 0*g - l*g**2 + 0 - 5/7*g**3 = 0.
-2, -1, 0
Let k be (12 - 13)/5 - 804/5. Let r be -8 + k/(-21) - -2. What is y in 19/3*y**3 + 14/3*y**2 - r*y**5 - 8/3*y**4 + 8/3 - 28/3*y = 0?
-2, 2/5, 1
Let n = 480 + -480. Suppose 0 = -4*u + g + 8, u - 1971*g - 19 = -1975*g. Factor 13/3*v**2 - 4/3*v + 4*v**u + n.
v*(3*v + 4)*(4*v - 1)/3
Let b be 16 + ((-1764)/14)/9. Let c(h) be the first derivative of -8/15*h**3 + 0*h**b - 2/25*h**5 - 2/5*h**4 + 17 + 0*h. Factor c(w).
-2*w**2*(w + 2)**2/5
Let a(v) = 9*v**3 + 40*v**2 - 111*v - 7386. Let i(x) = -2*x**3 - 2*x**2 - x - 5. Let j(k) = -3*a(k) - 12*i(k). Let j(u) = 0. What is u?
-23, 14
Let n be (49/((-735)/30))/(140/(-30)). Let 6/7*o**2 + 0*o**3 - n*o**4 - 3/7 + 0*o = 0. What is o?
-1, 1
Suppose -612 - 1710*f + 3*f**2 + 1010*f + 895*f = 0. Calculate f.
-68, 3
Factor -212*c - 16 + 129*c - 4*c**3 + 4*c**2 + 99*c.
-4*(c - 2)*(c - 1)*(c + 2)
Let p be 0 + (-9)/(27/(-12)). Suppose p*k - 12 = -3*b, -5 + 17 = -5*k + 3*b. Solve -2*i**2 + 8 + 4*i + k*i - 4*i = 0.
-2, 2
Factor -323/2*w**2 + 1/2*w**3 + 12960*w + 13122.
(w - 162)**2*(w + 1)/2
Let n(u) be the third derivative of -u**8/20160 - u**7/2520 + u**6/240 + u**5/4 - u**3/2 - 9*u**2 + 3. Let p(k) be the third derivative of n(k). Factor p(a).
-(a - 1)*(a + 3)
Suppose 1/4*y**4 - 105/4*y**2 - 13/4*y**3 + 0 - 171/4*y = 0. Calculate y.
-3, 0, 19
Suppose -283*p + 1204 = -27*p + 45*p. Let -16/5*i + 24/5*i**p + 48/5*i**2 - 52/5*i**3 - 4/5*i**5 + 0 = 0. What is i?
0, 1, 2
Let p(l) be the first derivative of -1/12*l**4 + 2*l**2 + 0*l**3 - 14*l - 8. Let r(i) be the first derivative of p(i). Suppose r(q) = 0. Calculate q.
-2, 2
Let c(h) be the second derivative of h**5/5 + 14*h**4/3 - 6*h**3 - 252*h**2 - 3*h + 278. Factor c(d).
4*(d - 3)*(d + 3)*(d + 14)
Suppose 11*a - 9 = 2*a. Let w(y) = 9*y + 3. Let z be w(a). Factor -10*l**3 - 4*l - 7*l**3 + 9*l**3 + z*l**2.
-4*l*(l - 1)*(2*l - 1)
Suppose -66*i = -4*h - 65*i - 6, -18 = 5*h - 3*i. Let o(d) be the second derivative of 1/15*d**5 + 7*d - 1/18*d**4 + 0 + 0*d**2 + h*d**3. Factor o(r).
2*r**2*(2*r - 1)/3
Find d, given that 106*d**2 - 308*d**2 + 101*d**2 + 45*d + 102*d**2 - 46 = 0.
-46, 1
Let t(k) be the second derivative of k**6/105 + 26*k**5/35 + 386*k**4/21 + 832*k**3/7 + 2304*k**2/7 + k - 13. Let t(o) = 0. Calculate o.
-24, -2
Let h(z) be the third derivative of 117/16*z**4 - 3*z**2 - 1/2*z**5 - 81/2*z**3 + 0*z - 6 + 1/80*z**6. Factor h(x).
3*(x - 9)**2*(x - 2)/2
Let i = -695 + 714. Let -8*v**2 + i*v**4 - 7*v**4 - 4*v**3 - 5*v**4 - 3*v**4 = 0. Calculate v.
-1, 0, 2
Let a be 5*4 - (2 - (-1 - -3)). Suppose 0 = n + 3*q - a, 2*q + 5 = 3*n - 0*n. Suppose n*u**4 - u**4 + 3*u**2 + 4*u**3 - 3*u**4 = 0. What is u?
-3, -1, 0
Let h be 26/8 + 2/(-8). Let u = 25337 + -228031/9. Factor 0 + u*a + 2/9*a**h + 4/9*a**2.
2*a*(a + 1)**2/9
Let f(r) = -4*r - 294. Let i be f(21). Let y = 382 + i. Solve 51/5*n**y - 9*n**5 + 6/5*n + 39/5*n**3 + 0 - 51/5*n**2 = 0 for n.
-1, 0, 2/15, 1
Let v(z) be the first de