. Let m(y) = -3*y**2 - 376*y + 375. Let r(n) = -4*j(n) + 7*m(n). Factor r(v).
-(v - 379)*(v - 1)
Let h be (-390744)/(-7504)*((-3)/(-8))/(27/84). Factor 69/2*d**2 + h + 3/4*d**4 - 108*d + 12*d**3.
3*(d - 1)**2*(d + 9)**2/4
Factor 536648/5 + 1038/5*l**2 - 1/5*l**3 - 270396/5*l.
-(l - 518)**2*(l - 2)/5
Let h(j) be the second derivative of -j**6/225 - 3199*j**5/75 - 3409067*j**4/30 + 4094720*j**3/9 - 2048000*j**2/3 - 11741*j. Factor h(r).
-2*(r - 1)**2*(r + 3200)**2/15
Let f(q) be the second derivative of -q**7/126 - 199*q**6/90 - 197*q**5/60 + 199*q**4/36 + 11*q**3 + 1770*q. Determine u so that f(u) = 0.
-198, -1, 0, 1
Let q(s) be the first derivative of s**4/4 - 4*s**3 - 47*s**2/2 + 32*s + 254. Let y be q(15). Solve -288/7*n - 324/7*n**y - 64/7 = 0 for n.
-4/9
Let t(s) = 19*s - 372. Let q be t(20). Suppose 4*r + 10 = 2*h, 4*h + 5*r = 5*h - q. Factor -1 - 1/3*x**h + 1/3*x + x**2.
-(x - 3)*(x - 1)*(x + 1)/3
Let w(c) be the second derivative of -c**4/21 - 860*c**3/21 - 92450*c**2/7 - 951*c. Factor w(b).
-4*(b + 215)**2/7
Let q(y) be the third derivative of -1/6*y**5 - 5/24*y**4 + 0*y + 0 + 0*y**3 + 5/336*y**8 + 0*y**6 + 1/21*y**7 - 22*y**2. Factor q(t).
5*t*(t - 1)*(t + 1)**3
Suppose -16*j - 374 + 1686 = 0. Suppose -j*h = -94*h + 24. Factor 3/8*s - 3/8*s**h + 0.
-3*s*(s - 1)/8
Solve 677834*r**2 + 1833633*r**2 - 965502760*r - 8670*r**3 + 2499793*r**2 + 5*r**4 = 0.
0, 578
Let o(j) be the second derivative of 1/30*j**6 + 8*j + 0*j**3 - 2 - 4/9*j**4 + 1/15*j**5 - 1/126*j**7 + 8/3*j**2. Factor o(d).
-(d - 2)**3*(d + 1)*(d + 2)/3
Let j = 312/5 + -916/15. Let v = -33 + 35. Factor 0*u + j*u**v + 0 + 2/3*u**3.
2*u**2*(u + 2)/3
Let s(o) = o. Let t(i) = 6*i + 2. Let a(z) = -3*s(z) + t(z). Let c be a(2). Factor -10*n**2 + 30*n**2 + 10 - 13*n - 4*n - c*n - 5*n**3.
-5*(n - 2)*(n - 1)**2
Let f(c) be the third derivative of -c**7/105 - c**6/2 - 221*c**5/30 + 10*c**4 + 300*c**3 + 10*c**2 + 2. Factor f(d).
-2*(d - 2)*(d + 2)*(d + 15)**2
Let 26/9*v - 2/9*v**2 + 28/9 = 0. What is v?
-1, 14
Let v(a) = -20*a**2 - 16*a + 16. Let r = -558 + 534. Let c(n) = n**2 + 1. Let s be c(0). Let y(g) = -g**2. Let p(j) = r*y(j) + s*v(j). Solve p(k) = 0.
2
Let a = -3655 - -3661. Let j(i) be the third derivative of 0 - 1/945*i**7 + 1/27*i**3 - 1/270*i**a + 1/54*i**4 + 0*i + 4*i**2 + 0*i**5. Let j(h) = 0. What is h?
-1, 1
Let x = 836 - 836. Let w be (-36)/252 - (-45)/168. Factor x*d - 1/2*d**2 + 0 - 1/2*d**3 - w*d**4.
-d**2*(d + 2)**2/8
Let q(t) be the second derivative of t**6/1020 - t**5/510 - t**4/17 - 36*t**2 - t + 7. Let f(y) be the first derivative of q(y). Let f(r) = 0. Calculate r.
-3, 0, 4
Let d(p) be the first derivative of p**7/42 + p**6/5 + 9*p**5/20 + p**4/3 + 109*p - 91. Let q(f) be the first derivative of d(f). Factor q(c).
c**2*(c + 1)**2*(c + 4)
Let o(p) = 3*p**2. Let w(h) = h**2 - 3*h - 19. Let g be w(6). Let q be o(g). Factor 6*u - 5*u**3 - u**q + 7*u**3 - 5*u**2.
u*(u - 3)*(u - 2)
Let u be ((-4)/60)/((-42)/420). Let s(o) be the first derivative of -14/25*o**5 + 0*o - 17 + 11/10*o**4 - u*o**3 + 0*o**2 + 1/15*o**6. Factor s(g).
2*g**2*(g - 5)*(g - 1)**2/5
Solve 3722*u - 2*u**2 + 465*u - 1858592 - 331*u = 0 for u.
964
Suppose 2*l = -w + 3 + 81, 209 = 5*l + 2*w. Find c such that -36 - c**4 - 24*c**3 - l*c - 69*c**2 - 43*c - c**4 - c**4 = 0.
-3, -2, -1
Let n(v) be the second derivative of v**4/30 - 62*v**3/15 - 128*v**2/5 - 30*v - 7. Factor n(y).
2*(y - 64)*(y + 2)/5
Let h(c) be the third derivative of 0*c**3 + 13*c**2 - 1/12*c**5 + 0 + 0*c - 5/24*c**4. Determine n so that h(n) = 0.
-1, 0
Let b(u) be the third derivative of -2*u**2 + 1/4*u**3 + 0*u - 32 + 1/120*u**5 + 1/12*u**4. Factor b(p).
(p + 1)*(p + 3)/2
Let s(b) be the first derivative of -2*b**6/3 - 28*b**5/5 + 3*b**4 + 76*b**3/3 - 28*b**2 + 429. Find p, given that s(p) = 0.
-7, -2, 0, 1
Let h(i) be the second derivative of -4*i**6/15 - 41*i**5/5 + 274*i**4/3 - 214*i**3 - 468*i**2 - 1388*i. Suppose h(b) = 0. Calculate b.
-26, -1/2, 3
Suppose 3*c + 2*h = 10, -3*h - 7 = c - 15. Let -8*u**4 + 2412 - 8*u**5 - 2412 - 12*u**3 - 10*u**4 - 2*u**c = 0. What is u?
-1, -1/4, 0
Let x be (162666/8)/9 - 3/12. Determine h so that -18*h**3 + x*h**2 - 20*h**4 - 4526*h**2 + 2263*h**2 - 6*h**5 = 0.
-2, -1, -1/3, 0
Let i(y) be the second derivative of y**6/255 + 2*y**5/85 + 2*y**4/51 + y + 377. Factor i(c).
2*c**2*(c + 2)**2/17
Let d(j) = 57*j**3 - 308*j**2 + 481*j + 275. Let u(i) = 84*i**3 - 463*i**2 + 722*i + 412. Let p(o) = -7*d(o) + 5*u(o). Suppose p(t) = 0. What is t?
-3/7, 3, 5
Let i(m) be the third derivative of m**7/105 + m**6/8 - 47*m**5/60 + 5*m**4/4 - 3401*m**2. Factor i(y).
y*(y - 1)*(y + 10)*(2*y - 3)
Let l be 0 - (-1492)/1170 - 3170/71325. Solve l*y + 24/13 - 2/13*y**3 - 2/13*y**2 = 0.
-2, 3
Let j(o) be the second derivative of 9/2*o**3 + 0 - 72*o - 3/20*o**5 - 21*o**2 + 3/2*o**4. Factor j(u).
-3*(u - 7)*(u - 1)*(u + 2)
Let t(f) be the first derivative of -f**4/14 - 16*f**3/7 - 65*f**2/7 - 12*f - 25. Let t(p) = 0. What is p?
-21, -2, -1
Let f(p) be the second derivative of p**4/24 - 16*p**3/3 - 345*p**2/4 + 520*p - 2. Suppose f(i) = 0. What is i?
-5, 69
Suppose 4*g + n = 7, 0 = g + g - 2*n - 6. Suppose -5*l = -g*j + 21, -3*j = 4*l - 9*l - 24. Solve -123*w**5 - 5*w**j + 4*w**3 - 2*w**4 + 2*w**2 + 124*w**5 = 0.
-1, 0, 1, 2
Let d = -451370 + 451375. Suppose -3/4*j**d - 5/4*j**4 + j**3 + 0 + j**2 + 0*j = 0. Calculate j.
-2, -2/3, 0, 1
Let z(r) be the first derivative of r**4/2 + 19*r**3/12 + 7*r**2/4 + 3*r/4 + 331. Factor z(q).
(q + 1)**2*(8*q + 3)/4
Let t = 3808 + -3806. Let s(i) be the second derivative of 0 + 10*i - i**4 - 2*i**t - 1/5*i**5 - 2*i**3. Let s(q) = 0. Calculate q.
-1
Suppose -5*d + 1710 = 5*z, 4*z = -d - 4*d + 1367. Let s = -340 + z. Suppose 0 - 3/5*b**s - 9/5*b**2 - 3/5*b**5 + 9/5*b**4 + 6/5*b = 0. What is b?
-1, 0, 1, 2
Determine y, given that 146039*y**2 - 148*y - 146043*y**2 + 1192 - 440*y = 0.
-149, 2
Suppose 0 = 4*l + 2*l. Suppose l = 2*f - 4 - 0. Solve 12*y**3 - 12*y**4 + 4*y**4 - f*y**2 + 2*y + 2*y**5 - 6*y**2 = 0.
0, 1
Let q(o) be the first derivative of 8*o - 9 - 2*o**2 - 4/3*o**3. Factor q(x).
-4*(x - 1)*(x + 2)
Factor 3*y**3 + 39 - 58*y**2 + y**3 + 1 + 6786*y + 3*y**3 - 6910*y.
(y - 10)*(y + 2)*(7*y - 2)
Let w(j) be the third derivative of j**5/75 + 17*j**4/6 - 172*j**3/15 + 1163*j**2. Let w(v) = 0. Calculate v.
-86, 1
Let n(i) be the first derivative of i**4/6 + 32*i**3/9 - 271*i**2/3 - 572*i/3 + 51. Suppose n(m) = 0. What is m?
-26, -1, 11
Let t = 794/2151 + 18/239. Factor -t*p**2 + 2/3*p**3 - 2/9*p**5 + 0 + 0*p**4 + 0*p.
-2*p**2*(p - 1)**2*(p + 2)/9
Find d such that 548/3*d + 2/3*d**3 + 118/3*d**2 + 144 = 0.
-54, -4, -1
Let f(q) = 12*q**2 - 355*q + 16185. Let g(c) = 17*c**2 - 533*c + 24279. Let z(x) = -7*f(x) + 5*g(x). Solve z(n) = 0.
90
Determine g so that 116*g + 465/4 - 1/4*g**2 = 0.
-1, 465
Let a(b) be the second derivative of 2*b**6/45 - 313*b**5/45 + 8519*b**4/27 - 12274*b**3/9 + 1156*b**2 - b - 7. Find d such that a(d) = 0.
1/3, 2, 51
Let f(g) be the third derivative of g**5/12 + 5*g**4/8 - 325*g**3/3 - 7945*g**2. Factor f(h).
5*(h - 10)*(h + 13)
Let f = 61 + -39. Suppose t - 20 = 5*j - 52, 5*t = 2*j - f. Let i(d) = -d**2 + d + 1. Let l(w) = 5*w**2 + 2*w - 22. Let y(u) = j*i(u) + l(u). Factor y(k).
-(k - 4)**2
Let 118*l + 630*l**2 + 309*l**3 - 213*l**4 - 375*l**3 + 43*l + 190*l + 51*l**5 - 81 = 0. What is l?
-1, 3/17, 3
Let p(m) = m**2 + 5*m + 1. Let g(a) = -5*a**2 + 92*a - 436. Let q(t) = 5*g(t) + 20*p(t). Let q(b) = 0. Calculate b.
4, 108
Let g(s) be the first derivative of -s**7/210 + s**6/45 - 28*s**3/3 - 101. Let m(a) be the third derivative of g(a). Factor m(t).
-4*t**2*(t - 2)
Let t(s) be the first derivative of -3*s**5/20 + 171*s**4/8 - 4833*s**3/4 + 33858*s**2 - 470448*s + 4773. Determine a, given that t(a) = 0.
24, 33
Let q = -1588882 + 1588948. Suppose 1/2*v**2 - q*v + 2178 = 0. What is v?
66
Let x(i) be the third derivative of 0 - 1/540*i**6 + 100/27*i**3 - 65/108*i**4 + 7/135*i**5 + 2*i + 11*i**2. Factor x(h).
-2*(h - 5)**2*(h - 4)/9
Let o(s) be the first derivative of s**3/2 + 912*s**2 + 554496*s - 40. Let o(f) = 0. What is f?
-608
Let c(j) be the second derivative of j**4/30 - 8*j**3/15 - 33*j**2/5 + 214*j. Factor c(s).
2*(s - 11)*(s + 3)/5
Let s = 91 - 86. Suppose 0 