(20). Suppose 12*d - a = 5. Factor -20*y - 5*y + 165*y**2 + 5*y**3 - 15 - 170*y**d.
5*(y - 3)*(y + 1)**2
Let f(o) be the first derivative of -3*o**5 - 55*o**4/4 - 40*o**3/3 + 10*o**2 - 1034. Factor f(p).
-5*p*(p + 2)**2*(3*p - 1)
Let y(i) be the first derivative of 1/18*i**2 + 10*i + 11/108*i**4 - 1/9*i**3 - 1/30*i**5 - 2. Let b(r) be the first derivative of y(r). Factor b(o).
-(o - 1)*(2*o - 1)*(3*o - 1)/9
Let q be (3*1 - 26/(-13)) + 176/(-36). Let n(o) be the third derivative of 0 + 9*o**2 + 1/72*o**4 - q*o**3 + 0*o + 1/60*o**5. Factor n(k).
(k + 1)*(3*k - 2)/3
Suppose -5 = 3*k + 7, 4*z - 3*k - 24 = 0. Factor 61*y**5 - 65*y**5 + y**3 + z*y**3.
-4*y**3*(y - 1)*(y + 1)
Let v be -8*6/(-6) + 37. Let d be (32/(-21))/((-30)/v). Factor 0 + d*n - 52/7*n**2 - 2*n**3.
-2*n*(n + 4)*(7*n - 2)/7
Let d(q) = 2*q**3 + 9*q**2 - 3*q - 57. Let c be d(9). Let m = c - 6211/3. Suppose 0 - 44*w**3 - 16/3*w + m*w**5 + 104/3*w**2 - 154/3*w**4 = 0. Calculate w.
-1, 0, 2/7, 2
Suppose -2*b = -10, 5*l - 259 = 3*b + 41. Determine t so that -35 - 52*t - 28*t - l*t + 5*t**3 - 45*t**2 + 218*t = 0.
1, 7
Let w(p) be the first derivative of -9/2*p**2 - 1/12*p**3 + 37/4*p - 236. Determine i so that w(i) = 0.
-37, 1
Suppose -4*s + 2*l + 208 = 3*l, 0 = -3*s + 2*l + 156. Factor -4*k + 2*k + s*k**2 - 50*k**2.
2*k*(k - 1)
Factor 850 - 995/3*v + 92/3*v**2 + 1/3*v**3.
(v - 5)**2*(v + 102)/3
Let g(o) be the third derivative of o**8/672 + 43*o**7/420 + 293*o**6/120 + 69*o**5/4 - 2025*o**4/16 + 1125*o**3/4 - 3*o**2 - 85*o. Factor g(c).
(c - 1)**2*(c + 15)**3/2
Factor -120/17*q - 2/17*q**4 + 20/17*q**3 - 72/17 - 26/17*q**2.
-2*(q - 6)**2*(q + 1)**2/17
Let j = 15 - 12. Suppose 0 = -5*l - v + 19, j*l - 8 = -l + v. Solve -z**l + 123 - 28*z**2 - 159 + 27*z + 33*z + 5*z**3 = 0 for z.
1, 3
Suppose -7 = -3*q + 2. Let y = -257 + 260. Determine o, given that 23*o**q - 7*o**y - 24*o**4 + 20*o**4 = 0.
0, 4
Let a(g) = -17*g**3 + 221*g**2 + 48*g - 621. Let m be a(13). Factor -3/2*f**m + 0 + 7*f**2 + 5/2*f.
-f*(f - 5)*(3*f + 1)/2
Let b be (-9)/6*(-9)/27*8. Find v such that -2*v**3 + 2*v**2 + 3*v**3 + b*v**3 - 6*v**2 - 48*v - v**3 = 0.
-3, 0, 4
Let i = -2165 + 2177. Let n(o) be the second derivative of 1/42*o**4 + 0 + i*o + 2/21*o**3 + 1/7*o**2. What is r in n(r) = 0?
-1
Let x(b) = b**2 - 5*b + 5. Let d be x(5). Suppose -2*n = d*n - 14. Suppose -i**3 - 5*i**3 - i**3 + 2*i**3 - 10*i**n = 0. Calculate i.
-2, 0
Let g(x) = 2*x - 1. Let u(w) = 52*w + 148*w + 968 + 21*w - 5*w**2 - 15*w - 3171. Let r(o) = -2*g(o) - u(o). Find l, given that r(l) = 0.
21
Let w(g) = 5*g**2 + 761*g - 712. Let b(a) = 15*a**2 + 2277*a - 2139. Let l(r) = 6*b(r) - 17*w(r). Suppose l(o) = 0. What is o?
-146, 1
Let h be (8 + 22 - 14 - 14)/6. Determine i, given that -10/3*i - 7/3*i**2 - h*i**3 + 0 = 0.
-5, -2, 0
Let j(l) be the first derivative of 6*l**3 - 3/2*l**5 + 0*l + 9/8*l**4 + 3*l**2 + 35. Find y such that j(y) = 0.
-1, -2/5, 0, 2
Let a(v) = v**3 - 7*v**2 + 4*v + 12. Let n be a(6). Suppose -9*l**3 - 233 + 6*l**2 + n*l**2 + 233 + 3*l**4 = 0. Calculate l.
0, 1, 2
Let i = -21 + 15. Let n be 20/(-30) + (-34)/i. Solve -3*z**5 + 3*z - z**5 - 20*z**2 + 12*z**3 + 9*z**4 + n*z - 5*z**4 = 0 for z.
-2, 0, 1
Let b = 719707/2 + -359841. Let -2 + b*w**3 - 45/2*w**2 + 12*w = 0. What is w?
2/5, 1
Determine x so that 368/11*x**3 - 34224/11*x - 2/11*x**4 - 17298/11 - 16556/11*x**2 = 0.
-1, 93
Let z be 27347/2829 + (-13 + 3/(-3))*(-3)/(-6). Factor -8/9*u + 2/9*u**3 + z - 2/3*u**2.
2*(u - 3)*(u - 2)*(u + 2)/9
Let g = -5619 - -112387/20. Let p(s) be the second derivative of 0*s**2 - 1/4*s**4 + 0 - 1/3*s**3 - 12*s - 5/42*s**7 + g*s**5 + 1/10*s**6. Solve p(o) = 0.
-1, -2/5, 0, 1
Determine q so that -1466*q**2 - 775/3*q**3 - 37/3*q**4 + 200/3 - 3460/3*q = 0.
-10, -1, 2/37
Solve 27990*q**2 + 94*q**4 - 7480 - 93575*q**3 + 5*q**4 + 174*q**4 - 30*q**4 + 7*q**4 + 22460*q = 0.
-1/2, 2/5, 374
Let q(o) be the first derivative of o**3/4 - 531*o**2/2 + 93987*o + 991. Factor q(g).
3*(g - 354)**2/4
Let x be ((12 - 15)*6/(-45))/5. Let o(l) be the second derivative of 1/5*l**4 + 0 - 8/5*l**2 + 3*l + 8/15*l**3 - 2/75*l**6 - x*l**5. Find g such that o(g) = 0.
-2, 1
Let c(h) = h. Let w(d) = -4*d**2 + 2972*d - 550564. Let l(b) = 4*c(b) - w(b). Factor l(k).
4*(k - 371)**2
Let b be ((-21)/105)/(1/(-2)). Let h(f) be the first derivative of -2*f**4 - b*f**5 - 4/3*f**3 + 4*f**2 - 5 + 6*f. Factor h(z).
-2*(z - 1)*(z + 1)**2*(z + 3)
Let s(h) be the first derivative of 45/16*h**2 + 1/2*h**3 + 25/4*h + 152 + 1/32*h**4. Factor s(k).
(k + 2)*(k + 5)**2/8
Determine n, given that 4*n**2 + 137824387 - 2392*n - 137824387 = 0.
0, 598
Suppose -24*i - 137*i + 578 = 128*i. Factor 0*y + 0 - 4/7*y**3 + 1/7*y**4 + 4/7*y**i.
y**2*(y - 2)**2/7
Let a(m) = 10*m**3 + 4660*m**2 + 1354898*m - 1359538. Let i(u) = u**3 + u + 3. Let s(b) = a(b) - 6*i(b). Let s(r) = 0. What is r?
-583, 1
Suppose -2346 = -19*c + 2*c. What is t in 110*t - 13*t**4 - c*t + 8 - 20*t**3 + 17*t**4 + 36*t**2 = 0?
1, 2
Determine n so that 5800418/11 + 2/11*n**2 - 6812/11*n = 0.
1703
Suppose 25*i = -4*g + 402, -2*g = 5*i - 422 + 356. Find n such that -i + 8*n - 2/3*n**2 = 0.
3, 9
Factor 73960 - 74304*m + 1722/5*m**2 - 2/5*m**3.
-2*(m - 430)**2*(m - 1)/5
Let m be 11 + (-121)/11 + 1/4. Let t(x) be the first derivative of -7 - 3*x - m*x**4 - 1/3*x**3 + 5/2*x**2. Solve t(r) = 0 for r.
-3, 1
Let a = 438 + -432. Let d be -4 + (3 - -9 - a). Suppose -1/2 - 5/8*j**d - 3/2*j = 0. Calculate j.
-2, -2/5
Let x(q) be the first derivative of 4/5*q**5 - 8*q - 4*q**3 - 10*q**2 + 61 + q**4. Factor x(c).
4*(c - 2)*(c + 1)**3
Find r such that -r**4 - 1/3*r**5 + 73/3*r**3 - 68*r - 140/3 + 11/3*r**2 = 0.
-10, -1, 2, 7
Let n(c) be the third derivative of 7/120*c**6 - 50*c**3 - 3/70*c**7 + 31/20*c**5 + 1/336*c**8 - 2*c**2 - 10/3*c**4 + 0 + 0*c. Factor n(o).
(o - 5)**2*(o - 3)*(o + 2)**2
Solve -3/2*k - k**2 - 1/6*k**3 - 2/3 = 0.
-4, -1
Let y be (2 - (1 - 18)) + -6. Suppose 4*a = -j + 10, y*j = 11*j - 3*a + 10. Factor -3/2*f**j + 1/2*f + 5/6*f**3 + 1/6.
(f - 1)**2*(5*f + 1)/6
Let z = -905613 - -905617. Factor -72 + 1/3*t**5 - 6*t**2 - 16/3*t**z - 108*t + 73/3*t**3.
(t - 6)**3*(t + 1)**2/3
Let q(k) be the second derivative of 1 + 0*k**3 + 0*k**2 + 28/3*k**4 + 33*k + 1/5*k**5. Factor q(j).
4*j**2*(j + 28)
Let o(x) = -6*x**3 + 2*x**2 + x - 1. Let h be o(-1). Factor 17*z**2 - 1 - h*z - 190*z**3 + 204*z**3 + 1.
z*(2*z + 3)*(7*z - 2)
Let n be 13 - 9/(18/22). Let s(w) be the first derivative of -25/2*w**n + 9 + 20*w**3 - 10*w. Find x, given that s(x) = 0.
-1/4, 2/3
Let p(i) = -35*i**3 + 5*i**2 + 3740*i - 10. Let f(t) = -3*t**3 - 3*t**2 + 2*t - 1. Let b(n) = -10*f(n) + p(n). Factor b(m).
-5*m*(m - 31)*(m + 24)
Let b = 442/253 + 294/253. Factor 80/11*x**2 - 50/11*x - b*x**3 + 0.
-2*x*(4*x - 5)**2/11
Let h(p) be the first derivative of 537289*p**3/4 - 19791*p**2/4 + 243*p/4 + 1226. Find o such that h(o) = 0.
9/733
Let x(t) = -t**3 + 12*t**2 + 22*t - 105. Let c be x(13). Suppose -2*u = m - 4, c = u - 4*u + 3*m. Factor -2/7*a**3 + u*a**4 + 0*a**2 + 1/7*a**5 + 1/7*a + 0.
a*(a - 1)**2*(a + 1)**2/7
Let n(y) = -3*y**2 - 21*y + 182. Let l(q) = q**2 - q - 14. Let b(u) = 4*l(u) + n(u). Let b(f) = 0. What is f?
7, 18
Factor -1308 - 69*i + i**3 + 397 + 405 + 314 + 381 - i**2.
(i - 7)*(i - 3)*(i + 9)
Factor 478/23*a - 2/23*a**2 + 964/23.
-2*(a - 241)*(a + 2)/23
Let a be 1 + ((-420)/(-14))/(-900) - 3/10. Determine s, given that 0 + a*s + 85/6*s**3 - 25/2*s**4 - 16/3*s**2 = 0.
0, 1/3, 2/5
Factor 0 + 4*j**4 + 0*j + 0*j**2 - 2/5*j**5 + 22/5*j**3.
-2*j**3*(j - 11)*(j + 1)/5
Let a = -76/5 + 418/15. What is l in -a*l - 361/3 - 1/3*l**2 = 0?
-19
Let h(k) be the second derivative of k**8/3360 + k**7/1680 - k**6/120 + 47*k**3/2 + 3*k - 48. Let c(u) be the second derivative of h(u). Factor c(d).
d**2*(d - 2)*(d + 3)/2
Let v(k) = -k**2 + 2*k - 1. Let b(w) = w**3 - 37*w**2 + 159*w - 207. Let x(z) = -2*b(z) + 18*v(z). Factor x(d).
-2*(d - 22)*(d - 3)**2
Suppose 0 = 2*v - 4*i + 4, -4 = 3*v + 10*i - 15*i. Suppose -t = 2*o - 8, -v*o - 3*o + 20 = 4*t. Factor -2/3*p**3 - 2/3*p**2 + t + 0*p.
-2*p**2*(p + 1)/3
Let b(g) be the third derivative of 5*g**8/336 + 113*g**7/42 + 3019*g**6/24 - 9745*g**5/12 + 6235*g**4/3 - 8410*g**3/3 - 129*g**2 + 1. Factor b(a).
5*(a - 1)**3*(a + 58)**2
Let x = 59912