*(t + 2)**2/5
Let w(s) be the first derivative of -3*s**4/7 + 4*s**3/21 + 216*s**2/7 - 144*s/7 + 413. Factor w(t).
-4*(t - 6)*(t + 6)*(3*t - 1)/7
Let x(l) = 30*l**2 - 67 - 4*l + 3*l**3 + 127 + 16*l - 75. Let g(f) = f**2 - 1. Let o(c) = 15*g(c) - x(c). Factor o(w).
-3*w*(w + 1)*(w + 4)
Let v(s) = -s**4 - 23*s**3 - 84*s**2 - 102*s + 2. Let u(b) = -b**4 - 25*b**3 - 83*b**2 - 101*b + 3. Let r(y) = 2*u(y) - 3*v(y). Factor r(q).
q*(q + 2)*(q + 4)*(q + 13)
Let d(z) be the third derivative of z**6/270 - 1262*z**5/135 + 1261*z**4/54 - 6*z**2 - z + 145. Factor d(x).
4*x*(x - 1261)*(x - 1)/9
Suppose -4*x + 8*x = -8, 4*u + 2*x = 12. Let c be 6552/10530*(-1)/(49/(-21)). Factor -c*o**3 + 2/15*o**2 + 0*o + 2/15*o**u + 0.
2*o**2*(o - 1)**2/15
Let r(c) be the second derivative of -1/24*c**4 + 25/12*c**3 - 208*c - 2 - 23/2*c**2. Factor r(u).
-(u - 23)*(u - 2)/2
Let k(m) = 7 - m**2 + 13*m + 0*m**2 - 17. Let g be k(12). Factor 9*s**g - 3*s + 16*s**2 - 22*s**2.
3*s*(s - 1)
Suppose -10*y = -54 - 66. Let d - 5*d + 0*d - y*d**3 + 20*d**4 + 0*d**2 + 16*d**5 - 20*d**2 = 0. What is d?
-1, -1/4, 0, 1
Suppose 60*h = 134 + 46. Suppose -2 - h*r**2 - 9/2*r - 1/2*r**3 = 0. What is r?
-4, -1
Let i(w) = -w**2 - 169*w + 3698. Let g be 5/20*8 + -9. Let b(c) = 3*c**2 + 337*c - 7396. Let r(u) = g*i(u) - 3*b(u). Factor r(d).
-2*(d - 43)**2
Factor -r**5 - 242*r**4 + 493*r**4 + 3*r**5 - 289*r**4 + 36*r**3.
2*r**3*(r - 18)*(r - 1)
Let i be 55/(-20)*(-7 - -2)*(-113)/((-678)/12). Find a, given that 0*a - 2 + i*a**5 + 197/2*a**3 + 79/2*a**2 + 177/2*a**4 = 0.
-1, -2/5, 2/11
Let p = 10646 + -10643. Let v(m) be the third derivative of -29*m**2 - 1/600*m**6 + 2/15*m**p + 0*m + 1/50*m**5 + 0 - 3/40*m**4. Factor v(a).
-(a - 4)*(a - 1)**2/5
Let g(n) = 624*n - 3117. Let s be g(5). Solve -9/4*v**5 + 0*v - 1/2*v**2 + 1/2*v**4 + 9/4*v**s + 0 = 0 for v.
-1, 0, 2/9, 1
Let h(c) be the first derivative of -5*c**6/27 - 4312*c**5/45 - 38951*c**4/3 - 555560*c**3/27 - 46225*c**2/9 - 8157. Suppose h(z) = 0. What is z?
-215, -1, -1/5, 0
Let v(u) be the second derivative of 5*u**7/42 - 3*u**6/2 + 7*u**5/4 + 15*u**4/4 - 20*u**3/3 + 1626*u. Determine g, given that v(g) = 0.
-1, 0, 1, 8
Let s(u) = -77*u + 8. Let h be s(0). Suppose 2*d = 2*c + h, 0 = 4*c + 14*d - 12*d - 8. Factor c*r + 2/13*r**5 + 0 + 0*r**2 - 6/13*r**4 + 0*r**3.
2*r**4*(r - 3)/13
Let y = -85169 - -255509/3. Determine d so that d - y - 1/3*d**2 = 0.
1, 2
Let n(j) be the second derivative of -j**5/4 + 25*j**4/2 + 625*j**3/2 + 2500*j**2 + 1241*j - 1. Factor n(f).
-5*(f - 40)*(f + 5)**2
Let x(r) = 2*r**2 + r + 2. Let n = -248 - -247. Let j(s) = 7*s**2 + 22*s + 8. Let h(i) = n*j(i) + 4*x(i). Let h(t) = 0. Calculate t.
0, 18
Let w(a) be the first derivative of 0*a + 1/33*a**3 - 1/66*a**4 + 21*a**2 + 1/330*a**5 - 45. Let x(y) be the second derivative of w(y). Factor x(c).
2*(c - 1)**2/11
Let g(x) be the first derivative of -1/900*x**6 + 1/100*x**5 - 1/30*x**4 + 7 - 16/3*x**3 + 0*x**2 + 0*x. Let z(v) be the third derivative of g(v). Factor z(w).
-2*(w - 2)*(w - 1)/5
Let v(l) = 7*l + 72. Let m be v(-10). Suppose 0*w + 3*w = 24. Factor 4*c**3 + 3*c**2 - w*c**m + c**2.
4*c**2*(c - 1)
Suppose z + 3*x - 7 = -4, 4*z - 57 = -3*x. Factor c**2 - c**2 + 72 - 87 - 3*c**2 + z*c.
-3*(c - 5)*(c - 1)
Let w(b) be the second derivative of b**5/20 + 5*b**4/4 - 87*b**3/2 - 275*b**2/2 - 153*b + 1. Let w(m) = 0. What is m?
-25, -1, 11
Let x = 448298/39 - 34484/3. Factor 0 + x*f**3 + 22/13*f - 24/13*f**2.
2*f*(f - 11)*(f - 1)/13
Let u = -53/3720 + 7/310. Let q(z) be the third derivative of -1/15*z**3 + 0 + 0*z + 1/300*z**5 + u*z**4 + 5*z**2. Determine c, given that q(c) = 0.
-2, 1
Factor 818 + 33*w + 628*w - 1481*w + 2*w**2.
2*(w - 409)*(w - 1)
Factor -570 + 3/2*c**2 - 42*c.
3*(c - 38)*(c + 10)/2
Let 48*u**4 + 0 - 16/5*u + 452/5*u**3 - 64/5*u**2 = 0. What is u?
-2, -2/15, 0, 1/4
Let a(p) be the third derivative of -p**7/630 - 148*p**6/45 - 29402*p**5/15 - 174640*p**4/9 - 696200*p**3/9 - 2*p**2 + 3*p + 1533. Factor a(b).
-(b + 2)**2*(b + 590)**2/3
Factor 555 - 168 - 144 - 2*m**2 - 187 - 76*m - 130.
-2*(m + 1)*(m + 37)
Let v(y) be the first derivative of -y**4/4 + 5*y**3/24 + 3*y**2/16 - 102. Let v(a) = 0. Calculate a.
-3/8, 0, 1
Let f(h) be the first derivative of 39 + 1/2*h**4 - 6*h**2 + 0*h - 10/3*h**3. Let f(i) = 0. What is i?
-1, 0, 6
Let q(k) be the first derivative of 30*k - 5/3*k**3 - 5/2*k**2 + 98. Factor q(l).
-5*(l - 2)*(l + 3)
Let d(h) = 2*h**3 - 2*h**2 - 18*h + 35. Let o be d(2). Suppose -4*c + 4 = 0, -2*j - 15*c + o = -12*c. Determine t so that 14/9*t + 4/9 + 2/3*t**j = 0.
-2, -1/3
Factor -90 + 85*f - 784*f**3 + 787*f**3 + 206*f - 64*f**2.
(f - 15)*(f - 6)*(3*f - 1)
Let a(v) be the first derivative of -13/2*v**4 - 44/3*v**3 + 64*v + 16/5*v**5 + 32*v**2 + 42 - 1/3*v**6. Solve a(w) = 0 for w.
-1, 2, 4
Suppose 4*q - 11 = -4*u + 9, 5*u = 3*q + 9. Suppose q*x + 2*p = 0, 9 = 2*x + 3*x + 2*p. Solve -18*c**5 + 6*c**5 - x*c**5 - 10*c**3 - 25*c**4 = 0 for c.
-1, -2/3, 0
Suppose c + 0*f - 3*f = 23, -3*f = 6. Factor -15*x**2 - 12*x + 11 - x**2 + c*x**2.
(x - 11)*(x - 1)
Let r(u) be the third derivative of 8/105*u**7 + 0*u**4 + 2/15*u**5 + 1/6*u**6 + 0*u**3 - 2*u**2 + 0*u + 1/84*u**8 - 15. Factor r(m).
4*m**2*(m + 1)**2*(m + 2)
Let v(k) be the first derivative of -k**5/90 + 5*k**4/6 - 25*k**3 + 375*k**2 + 5*k + 44. Let j(x) be the first derivative of v(x). Factor j(f).
-2*(f - 15)**3/9
Factor w - 162*w**2 + 16*w**4 + 2*w - 410*w**5 - 45*w**3 + 409*w**5 - 3*w.
-w**2*(w - 9)**2*(w + 2)
Let t(a) = a**2 + a + 2. Let c be t(-5). Suppose c - 12 = 5*f. Solve 8*u**2 - 5*u**4 - 3*u**2 + 9*u**f + 4*u - 2*u**2 + 3*u**3 = 0.
-1, -2/5, 0, 2
Suppose 3*k**3 - 3423*k + 1479*k - 28672 - 2*k**2 + 2428 + 29*k**2 = 0. What is k?
-18, 27
Let u be (12 + -12)*(0 + -3)*52/312. Let t(j) be the second derivative of 30*j + u + 16/3*j**3 - 1/3*j**4 - 14*j**2. Solve t(f) = 0.
1, 7
Let b(s) be the first derivative of s**6/360 - 3*s**5/8 - s**3/3 - 3*s**2/2 - 220. Let m(z) be the third derivative of b(z). Let m(g) = 0. What is g?
0, 45
Factor 3448/13 - 10/13*l**2 - 8616/13*l.
-2*(l + 862)*(5*l - 2)/13
Suppose 8*q - q = 14. Let p be (-9 - 1)/((-6 - q) + 6). Suppose -43*u**3 + 107*u**3 - 46*u**3 + 3*u**4 - 3*u**p = 0. What is u?
-2, 0, 3
Suppose 6*j - 63*j + 754 = 320*j. Find c such that -8/11*c**3 + 26/11*c**4 - 6/11*c**5 + 0*c**j + 0 + 0*c = 0.
0, 1/3, 4
Let l(o) be the first derivative of -5*o**3 - 1665*o**2/2 + 3150*o - 285. Let t(g) = -g**2 - 128*g + 242. Let i(j) = -3*l(j) + 40*t(j). Let i(m) = 0. What is m?
2, 23
Let v(j) = j**2 + 4*j + 4. Let p(k) = -4*k - 114. Let b be p(-28). Let w be v(b). Factor 0 + 0*d + w*d**2 + 0*d**3 - 2/5*d**4.
-2*d**4/5
Factor 62*r**4 - 8263 - 228*r**3 + 8287 - 68*r + 282*r**2 - 75*r + 3*r**5.
(r - 1)**3*(r + 24)*(3*r - 1)
Factor 13341*i - 6665*i - i**3 - 6676*i - 47*i**2.
-i**2*(i + 47)
Let h = 72 + -30. Solve 4340 + 212*t + 25*t**2 - h*t - 4051 = 0 for t.
-17/5
Suppose 0 = 8*g + 2 - 10. Let r be (5 - -1)/((-1 - -3)*g). Factor r*w**3 - 4*w**2 + w**2 - 23*w - 17*w + 3*w**4 + 37*w.
3*w*(w - 1)*(w + 1)**2
Let s(u) = 7*u**2 - 160*u - 173. Let z(a) = -516 - 216*a**2 - 394*a + 214*a + 236*a**2 - 300*a. Let i(n) = -8*s(n) + 3*z(n). Find k such that i(k) = 0.
-1, 41
Suppose 2*n + 63 = 9*n. Factor -2*w**3 - 16*w**2 - 12*w**2 + n*w - 40*w - 67*w.
-2*w*(w + 7)**2
Let i be 17/(-5)*70/42*-3. Suppose 5*y - 21 = 26*o - 24*o, -4*o = -5*y + i. Solve 72/5 + 2/5*n**o + 24/5*n = 0.
-6
Determine u, given that -28/15*u**3 - 68/15*u - 24/5*u**2 - 2/15*u**4 - 22/15 = 0.
-11, -1
Factor 7/2*d**3 + 58890*d - 909*d**2 + 16900.
(d - 130)**2*(7*d + 2)/2
Suppose -2*p = 6, -3*s + 3 = -0*s + p. Suppose 2*d + 2*r = 12 - 2, -d - 4 = -s*r. Solve -4/5*z + 2*z**3 - 6/5*z**d + 0 = 0.
-2/5, 0, 1
Let n(x) be the first derivative of x**6/2 - 63*x**4/2 + 152*x**3 - 549*x**2/2 + 216*x - 418. Determine d so that n(d) = 0.
-8, 1, 3
Factor -2/5*u**2 - 368 - 468/5*u.
-2*(u + 4)*(u + 230)/5
Let j(t) = -20*t**2 - 78*t + 918. Let g(y) = -26*y**2 - 76*y + 918. Let h(i) = -3*g(i) + 4*j(i). Factor h(b).
-2*(b - 9)*(b + 51)
Let v(g) = 141*g**2 - 3403*g + 1362. Let o(f) = 384*f**2 - 10208*f + 4086. Let h(k) = 4*o(k) - 11*v(k). Factor h(c).
-3*(c + 227)*(5*c - 2)
Determine o so that 0 - 27/4*o**4 - 51/4*o**2 - 1/2*o + 20*o**