**2 + 2/7*h + 8/7*h**4 + 0 + 8/7*h**5 - q*h**3 = 0.
-1, 0, 1/2
Determine p, given that -1274*p**4 + 8*p**5 + 65856 + 1354*p**4 + 12796*p**2 - 2019*p**3 + 80752*p - 9*p**5 = 0.
-3, -1, 28
Solve 40 + 12 - 160 - 51*d**2 - 4*d**3 + 7*d**3 - 12*d + 78*d**2 = 0.
-9, -2, 2
Suppose 42 = -10*n + 13*n. Suppose 52 = -n*b + b. Let h(x) = -x**2 - x + 2. Let z(q) = 6*q**2 + 6*q - 11. Let d(t) = b*z(t) - 22*h(t). Factor d(v).
-2*v*(v + 1)
Let a(f) = -11*f**4 - 57*f**3 + 54*f**2 + 47*f - 58. Let z(w) = -20*w**4 - 113*w**3 + 108*w**2 + 95*w - 115. Let j(v) = -9*a(v) + 5*z(v). Factor j(b).
-(b - 1)**2*(b + 1)*(b + 53)
Let x(c) be the second derivative of 1/100*c**5 + 4/5*c**2 + 46 + c - 1/2*c**3 + 1/10*c**4. Factor x(o).
(o - 1)**2*(o + 8)/5
Let f(b) = 5 + 21*b + 8 + 71*b**2 - 69*b**2. Let i(g) = -14*g**2 - 150*g - 92. Let y(a) = 44*f(a) + 6*i(a). Let y(q) = 0. Calculate q.
-5, -1
Suppose -69285*v + 221 + 51 = -69149*v. Factor -27/2*p**v - 507/2 + 117*p.
-3*(3*p - 13)**2/2
Suppose 0 = 8*i - 140 - 28. Let u = 23 - i. Determine y so that -2*y**u + 5 - 20 + 4*y + 3 + 10 = 0.
1
Let m(r) be the first derivative of 28 + 0*r**2 - 1/3*r**6 - 1/3*r**4 + 42*r + 7/10*r**5 + 0*r**3. Let k(l) be the first derivative of m(l). Factor k(u).
-2*u**2*(u - 1)*(5*u - 2)
Let r(l) be the third derivative of -l**7/315 + l**6/10 + 14*l**5/15 + 22*l**4/9 + 15*l**2 - 23. Determine s so that r(s) = 0.
-2, 0, 22
Determine i, given that 1480 + 4*i**3 - 762 - 87*i + 407*i - 324*i**2 - 718 = 0.
0, 1, 80
Let g(w) = -7*w**2 - 154*w - 361. Let p(c) = 11*c**2 + 244*c + 542. Let t(a) = -14*g(a) - 9*p(a). Factor t(u).
-(u - 4)*(u + 44)
Let t(n) = -5*n**2 - 34*n + 386. Let v be t(6). Let l(r) be the first derivative of r - 7/6*r**v + 2/9*r**3 + 38. Determine q so that l(q) = 0.
1/2, 3
Suppose -1764/5*f**2 - 768/5 - 2316/5*f - 27/5*f**3 = 0. What is f?
-64, -2/3
Let 236/5*g**2 - 68/5*g**3 - 48 + 68/5*g + 4/5*g**4 = 0. What is g?
-1, 1, 5, 12
Let o(k) = k**3 - 8*k**2 + 7*k + 7. Let f be o(7). Suppose -2*n = -5 - f. Factor -9 + 21*t**2 - n - 9 - 24 + 3*t**3 + 24*t.
3*(t - 1)*(t + 4)**2
Let g(n) = -4*n**4 + 2906*n**3 - 5781*n**2 + 30. Let l(c) = -4*c**4 + 2904*c**3 - 5782*c**2 + 20. Let o(u) = -2*g(u) + 3*l(u). Solve o(q) = 0.
0, 2, 723
Suppose -d = -2*i - 2*i + 32, 0 = 3*i + 5*d - 24. Suppose -11*u + 8*u = i*u. Let -2/15*z**5 + 0 + u*z + 2/5*z**3 + 0*z**4 + 4/15*z**2 = 0. Calculate z.
-1, 0, 2
Suppose 231*h = 237*h - 18. Factor -h*a**2 + 8 + 0*a**2 + 11 + 29 + 18*a.
-3*(a - 8)*(a + 2)
Let h(o) be the third derivative of -59*o**5/90 - 77*o**4/36 - 2*o**3 + 6730*o**2. What is q in h(q) = 0?
-1, -18/59
Let q(a) be the second derivative of a**7/420 - 22*a**6/75 - 181*a**5/200 + 11*a**4/15 + 3*a**3 - 4323*a. Determine n so that q(n) = 0.
-2, -1, 0, 1, 90
Factor 2207 + 0*r**3 - 133*r + 85*r - 2155 + r**3 + 9*r**2.
(r - 2)**2*(r + 13)
Suppose -152*u + 150*u + 4*o - 40 = 0, -o = -2*u - 40. Let i be (-22)/55*u/12. Factor i*z + 1/2 + 1/6*z**2.
(z + 1)*(z + 3)/6
Factor -756/5*q + 47628/5 + 3/5*q**2.
3*(q - 126)**2/5
Let c be ((-4)/(-22))/((-135)/(-495)). Solve -10/3 - 8/3*b + c*b**2 = 0.
-1, 5
Let b(i) = 20*i**5 + 74*i**4 - 1562*i**3 + 10368*i**2 - 23306*i - 11. Let a(u) = -2*u**5 + 2*u**4 - 2*u**3 - 2*u + 1. Let r(d) = 22*a(d) + 2*b(d). Factor r(f).
-4*f*(f - 18)**2*(f - 6)**2
Suppose -3*f + 4*v + 16 = 0, 5*f - 27*v = -28*v + 19. Factor 56 + 6*j**2 - f*j**2 + 32*j + 0*j**2 + 0*j**2.
2*(j + 2)*(j + 14)
Suppose -45*a = 11981 - 12116. Let g(w) be the third derivative of 0 + 5/3*w**a - 25*w**2 + 1/12*w**5 + 0*w - 5/8*w**4. Let g(t) = 0. Calculate t.
1, 2
Let z(m) = m**3 - 11*m**2 - m - 1. Let q(r) = -5*r**3 - 229*r**2 + 309*r + 1953. Let l(d) = -q(d) - 9*z(d). Factor l(s).
-4*(s - 81)*(s - 3)*(s + 2)
Let n(v) = v**2 + 38*v - 27. Let z(f) be the first derivative of 5*f**3/3 + 115*f**2 - 160*f - 102. Let x(h) = 25*n(h) - 4*z(h). Suppose x(w) = 0. Calculate w.
-7, 1
Let x(t) be the second derivative of -t**4/72 + 5*t**3/36 + 3*t + 86. Factor x(c).
-c*(c - 5)/6
Let o(m) = -12*m - 58. Let a be o(-5). Suppose -2*u**3 + 19*u + 8 - 24 - 20*u**a - 2*u**3 - 51*u = 0. What is u?
-2, -1
Let u = 69265 + -343653/5. Let m = u - 530. Determine v so that 7/5 + 24/5*v**2 + m*v + 2*v**3 + 1/5*v**4 = 0.
-7, -1
Let w(h) be the first derivative of -h**6/6 + 24*h**5/5 - 189*h**4/4 + 490*h**3/3 - 3085. Let w(j) = 0. Calculate j.
0, 7, 10
Let m(k) be the first derivative of 102*k**2 + 55 - 6936*k - 1/2*k**3. Factor m(y).
-3*(y - 68)**2/2
Let 0 + 2/9*g**2 - 164/9*g = 0. Calculate g.
0, 82
Let y(l) be the third derivative of -l**6/270 - 2*l**5/45 - 11*l**4/54 - 4*l**3/9 + 3*l**2 + 247. Factor y(j).
-4*(j + 1)*(j + 2)*(j + 3)/9
Let p(v) be the second derivative of 3*v**5/5 + 137*v**4/30 - 4*v**3/3 - 28*v**2/5 + 246*v. Determine u, given that p(u) = 0.
-14/3, -2/5, 1/2
Let m(y) = -54*y**2 - 2007*y + 500000. Let c(t) = 31*t**2 + 1004*t - 250000. Let s(l) = 7*c(l) + 4*m(l). What is h in s(h) = 0?
500
Let f = 372853 - 4834424/13. Let j = f + -973. Determine k so that 4/13*k**2 + 2/13*k**3 - 8/13*k - j = 0.
-2, 2
Let u(c) be the second derivative of -11/70*c**6 - 69/70*c**5 - 1/98*c**7 + 0 - 81/14*c**3 - 81/14*c**2 + 97*c - 45/14*c**4. Factor u(p).
-3*(p + 1)**2*(p + 3)**3/7
Let l(f) = -f + 42. Let z be l(10). Let h = z + -28. Factor -u**2 + 378*u**3 - 3*u**2 + 4*u**h - 386*u**3 + 8*u.
4*u*(u - 2)*(u - 1)*(u + 1)
Let i(u) = 10*u**3 + 274*u**2 + 1364*u - 482. Let b(v) = v**3 - 7*v**2 - 1. Let t(x) = -2*b(x) - i(x). Factor t(h).
-4*(h + 11)**2*(3*h - 1)
Let v(c) = 615*c - 2458. Let a be v(4). Suppose 3/2 + 4*m + a*m**3 - 15/2*m**2 = 0. What is m?
-1/4, 1, 3
Let b(g) be the first derivative of -3*g**4/4 + 48*g**3 - 1467*g**2/2 + 1326*g + 4356. Factor b(z).
-3*(z - 34)*(z - 13)*(z - 1)
Let v = -41530 + 41532. Determine q, given that -31/5*q**3 + 32/5*q - 1/5*q**5 + 2*q**4 + 22/5*q**v - 32/5 = 0.
-1, 1, 2, 4
Let j(x) be the first derivative of 5*x**4/12 - 10*x**3 + 325*x**2/6 + 42. Solve j(b) = 0 for b.
0, 5, 13
Let v be (-6)/(-3 - (12 - 6)). Let n(l) be the first derivative of -v*l - 26 - 2/9*l**3 - 2/3*l**2. Determine j so that n(j) = 0.
-1
Suppose -2262*i = -2261*i + 4*o - 36, -5*i - o + 9 = 0. Factor -1/6*y**3 - 1/6*y**5 + i - 1/3*y**4 + 0*y + 0*y**2.
-y**3*(y + 1)**2/6
Factor 44*f**4 + 215*f**3 - 194*f**2 + 181*f**4 - 266*f**2 + 42*f - 50*f + 28*f.
5*f*(f - 1)*(f + 2)*(45*f - 2)
Let d = 3844699/200245 + 1/40049. Factor 6/5*i**3 + d - 184/5*i + 56/5*i**2.
2*(i - 2)*(i + 12)*(3*i - 2)/5
Determine d, given that 256*d**3 + 427*d**3 + 77*d**3 - 80*d**4 - 120 - 910*d - 1525*d**2 = 0.
-1/4, 4, 6
Let b = 951 + -921. Suppose -6 + 39 + 17 - 18*l**2 - 7*l**3 + 5*l**3 - b*l = 0. Calculate l.
-5, 1
Let d = -758600 + 758600. Factor d - 1/3*x**2 + 31/3*x.
-x*(x - 31)/3
Let b = -120864 + 1571234/13. Let 16/13*z - b*z**2 - 30/13 = 0. What is z?
3, 5
Solve -410/17*w**2 - 3184/17*w - 2/17*w**3 - 6304/17 = 0 for w.
-197, -4
Let b = -59405/6 + 297029/30. Solve -2/5*p - b + 2/5*p**3 + 2/15*p**2 = 0.
-1, -1/3, 1
Let d(a) = -8*a**3 - 126*a**2 + 462*a - 422. Let u(j) = 18*j**3 + 253*j**2 - 929*j + 845. Let z(r) = 13*d(r) + 6*u(r). Let z(v) = 0. What is v?
2, 26
Let o = -190519/44 + 4330. Let i(m) be the second derivative of 0*m**5 - 1/33*m**3 + o*m**4 - 1/330*m**6 + 0*m**2 + 0 + 22*m. Factor i(q).
-q*(q - 1)**2*(q + 2)/11
Let u(t) be the second derivative of -t**8/168 + t**7/105 + t**6/60 - t**5/30 + 34*t**2 + 3*t + 13. Let k(r) be the first derivative of u(r). Factor k(l).
-2*l**2*(l - 1)**2*(l + 1)
Let r(o) be the third derivative of -o**5/90 - 241*o**4/36 - 80*o**3/3 + 3*o**2 - 48*o. Factor r(g).
-2*(g + 1)*(g + 240)/3
Let i(b) = -8*b + 12. Let n(s) = -s**2 + s + 1. Suppose 0*w = -4*w + 4. Let o = 3685 + -3689. Let r(a) = o*n(a) + w*i(a). Solve r(k) = 0 for k.
1, 2
Solve 39*r**2 + 96*r**2 - 515*r**3 - 10 + 35*r + 2174*r**5 - 2354*r**5 + 535*r**4 = 0.
-1/4, 2/9, 1
Let w(p) be the first derivative of -11 + 76/15*p**2 - 1/30*p**4 - 32/3*p - 32/45*p**3. Determine f so that w(f) = 0.
-20, 2
Let x(q) = -2*q**2 + 96*q - 1242. Let z = -145 - -136. Let f(a) = 4*a**2 - 191*a + 2482. Let h(d) = z*x(d) - 4*f(d). Find j such that h(j) = 0.
25
Solve 1236*a - a**2 - 628*a - 280 - 646*a = 0 for a.
-28, -10
Let y(c) be the second derivative of c**5/20 - 167*c**4/48 + 287*c**3/4 + 