be the first derivative of j**8/10080 - j**7/2520 - 19*j**3 + 19. Let f(r) be the third derivative of v(r). Factor f(c).
c**3*(c - 2)/6
Let k(g) be the first derivative of g**6/5 + 4*g**5/5 - g**4/2 - 4*g**3 + 4*g**2 + 72*g + 114. Let t(m) be the first derivative of k(m). Factor t(v).
2*(v - 1)*(v + 2)**2*(3*v - 1)
Let t = -300101 - -300103. Suppose 40/7*l**2 - 2/7*l**5 + t*l**4 - 16/7*l + 0 - 36/7*l**3 = 0. Calculate l.
0, 1, 2
Determine t, given that -71*t**4 - 4*t**5 - 200*t**3 - 313*t**4 + 1632*t**2 + 3200*t - 23*t**4 - t**4 - 584*t**3 = 0.
-100, -2, 0, 2
Let d(s) be the first derivative of 2*s**5/15 + 19*s**4/6 + 76*s**3/3 + 224*s**2/3 + 256*s/3 - 958. Suppose d(r) = 0. What is r?
-8, -2, -1
Let r(l) = -2*l**2 - 33*l + 110. Let t be r(3). Let u be t/((-147)/28)*2/12. Suppose 0*g**2 + 2/9*g**4 + 0*g + 4/9*g**3 - u*g**5 + 0 = 0. What is g?
-1, 0, 2
Let y(w) be the first derivative of w**5/80 - 7*w**4/32 - 9*w**3/4 - 84*w**2 - 174. Let z(x) be the second derivative of y(x). Factor z(s).
3*(s - 9)*(s + 2)/4
Let c be 21/(-3) - -45*340/2142. Find r such that c*r**3 + 4/7*r - 3/7*r**4 + 8/7*r**2 + 0 = 0.
-1, -2/3, 0, 2
Let w(j) = -j**2 - 53*j - 245. Let s be w(-40). Let u = -545/2 + s. Factor u*a**3 - 5/2*a**5 + 5/2*a**4 + 0 + 0*a - 5/2*a**2.
-5*a**2*(a - 1)**2*(a + 1)/2
Factor 86143*v - 5*v**2 - 172312*v - 150 + 86254*v.
-5*(v - 15)*(v - 2)
Let p(y) = -16*y + 69. Let q be p(4). Factor 6*j**3 - 2286*j**5 + 5*j**4 - 2*j**4 + 2283*j**q.
-3*j**3*(j - 2)*(j + 1)
Let a(v) be the second derivative of -v**4/24 + 44*v**3/3 - 4*v + 259. Factor a(l).
-l*(l - 176)/2
Let d be 2 - 2 - (0 - 238)/2. Let b = 374 - d. Determine f so that -279*f**4 - 426*f - 4974*f + 306*f**3 + b*f**2 + 1500 + 717*f**3 + 21*f**5 = 0.
-2, 2/7, 5
Let b(f) = 4*f**2 - 15*f + 3. Let v(u) = 3*u**2 - 13*u + 2. Suppose 0 = 13*r + 17 + 9. Let p(c) = r*b(c) + 3*v(c). Solve p(q) = 0 for q.
0, 9
Let n(s) be the first derivative of 0*s + 0*s**2 + 3/20*s**5 + 0*s**3 + 0*s**4 + 110 - 1/24*s**6. Find w, given that n(w) = 0.
0, 3
Let -65/2 - 65/4*m**3 - 1/4*m**4 + 3/4*m**2 + 193/4*m = 0. Calculate m.
-65, -2, 1
Let a(q) be the second derivative of 2*q**7/21 - 4*q**6/5 + 9*q**5/5 - 4*q**4/3 - 2*q + 611. Factor a(f).
4*f**2*(f - 4)*(f - 1)**2
Let i(d) = -19*d**3 + 230*d**2 + 548*d - 4. Let j(m) = -18*m**3 + 228*m**2 + 546*m - 6. Let p(n) = 3*i(n) - 2*j(n). Find o, given that p(o) = 0.
-2, 0, 92/7
Let p(n) be the first derivative of 2*n**2 + 2/5*n**5 - 140 - 9/4*n**4 + 0*n + 1/2*n**6 + 0*n**3. Suppose p(a) = 0. Calculate a.
-2, -2/3, 0, 1
Let p be (0 - 2)*(-16)/(-3 - -7). Let d be (-4)/16 + 9*2/p. What is l in -12 - 24*l + 61*l**2 - 76*l**d - 3*l**3 + 0 = 0?
-2, -1
Let q be (-6)/(-9)*9/2. Let l be ((-132)/(-8)*6 - 1)/1. Determine m, given that 3*m**q - 10*m + 2*m**3 + 93*m**2 + 0*m**3 - l*m**2 = 0.
-1, 0, 2
Let l(y) be the third derivative of y**7/140 - y**6/8 + 2*y**5/5 - 1543*y**2. Suppose l(w) = 0. Calculate w.
0, 2, 8
Determine x so that 32*x + 0 - 2/3*x**3 + 4/3*x**2 = 0.
-6, 0, 8
Suppose 5*y**2 + 39*y - 460 - 112*y - 147*y = 0. Calculate y.
-2, 46
Suppose 4*b = -17*j + 22*j - 70, 4*j - 56 = -5*b. Solve b + 2/7*t - 2/7*t**3 + 0*t**2 = 0.
-1, 0, 1
Let a be (3/1 - (-459)/(-162))*(-93)/(-62). Determine u so that a*u + 1/4*u**4 + 3/4*u**3 + 3/4*u**2 + 0 = 0.
-1, 0
Factor 0 - 1359/2*v + 3/2*v**2.
3*v*(v - 453)/2
Let f be (-11)/(550/60)*(-25)/2. Suppose f*h = -b + 20*h + 12, 0 = -5*b - h + 8. Factor 3/5*j**3 + 0 + 3*j**b - 3/5*j**4 + 9/5*j.
-3*j*(j - 3)*(j + 1)**2/5
Let g(h) = h**3 + 2*h**2 + h - 1. Let q(a) = -4*a**5 - 88*a**4 - 148*a**3 + 104*a**2 + 168*a - 8. Let y(x) = 8*g(x) - q(x). Determine l so that y(l) = 0.
-20, -2, -1, 0, 1
Let j(n) be the first derivative of 5*n**6/6 + 99*n**5 - 515*n**4/4 - 1495*n**3/3 + 255*n**2 + 1000*n - 1164. Solve j(v) = 0.
-100, -1, 1, 2
Suppose -w + 4 = -5*n + 63, 3*n - 5*w = 31. Let z(d) be the first derivative of -49*d - 1/3*d**3 + 7*d**2 + n. Factor z(v).
-(v - 7)**2
Let s(b) be the third derivative of -b**5/270 - 193*b**4/54 + 43*b**3/3 - 1749*b**2. Factor s(j).
-2*(j - 1)*(j + 387)/9
Suppose 0 = 5*g + 10, -2*p + 4*g + 2 = -12. Factor 78*a**2 + 20*a + 125*a**4 - 16*a**2 + 225*a**p + 58*a**2.
5*a*(a + 1)*(5*a + 2)**2
Let w(d) = 11*d - 28. Let l be w(4). Factor 9*g**5 - 20*g**2 + 9*g**3 + 20*g**4 + 10*g**5 - l*g - 15*g**5 + 3*g**3.
4*g*(g - 1)*(g + 1)**2*(g + 4)
Let i = -26 - -26. Suppose 2*u - 6 + 0 = i. Solve -s**2 + 5*s**u - s**2 - 6*s**3 - s**2 = 0 for s.
-3, 0
Let r(y) be the third derivative of 3*y - 1/180*y**5 - 1/24*y**4 + 0*y**3 + 13*y**2 + 0. Factor r(s).
-s*(s + 3)/3
Let x = 544 - 539. Suppose 4*u - x*u = 5*u. Factor u + 6/5*p - 3/5*p**2.
-3*p*(p - 2)/5
Let k(a) = -25*a**4 - 64*a**3 + 528*a**2 - 534*a - 142. Let v(x) = 399*x**4 + 1026*x**3 - 8448*x**2 + 8547*x + 2271. Let f(t) = -33*k(t) - 2*v(t). Factor f(d).
3*(d - 2)**2*(d + 6)*(9*d + 2)
Let w(o) = 2*o**3 + o**2 - o + 1. Let l(b) = -b**4 + 268*b**3 - 21904*b**2 + 84108*b - 82956. Let v(q) = 5*l(q) + 60*w(q). Solve v(m) = 0.
2, 144
Let k(x) be the second derivative of -x**7/231 + 7*x**6/165 - x**5/11 - x**4/33 + x**3/3 - 5*x**2/11 + 510*x - 1. Solve k(t) = 0.
-1, 1, 5
Factor 7/2*v**2 + 72 - 9/2*v**3 + 325*v.
-(v - 9)*(v + 8)*(9*v + 2)/2
Let l(o) = o**3 + 19*o**2 - 21*o - 9. Let m(g) = -g**3 - g**2 - g + 3. Let b(c) = 2*l(c) + 6*m(c). What is d in b(d) = 0?
0, 2, 6
Let p(r) be the second derivative of 0*r**3 - 1 + 0*r**2 - 1/5*r**5 - 2*r - 5/3*r**4. What is m in p(m) = 0?
-5, 0
Let a(v) be the third derivative of -v**8/252 + 2*v**7/21 + 13*v**6/10 + 37*v**5/9 + 14*v**4/3 + 2079*v**2. Determine d, given that a(d) = 0.
-4, -1, 0, 21
Let o(k) = 31*k**2 + 56*k. Let z(j) = -20*j**2 - 56*j. Let n(s) = 4*o(s) + 6*z(s). Find m, given that n(m) = 0.
0, 28
Let 9 - 202 - 119 + 242*z - 152 + 462*z - 244*z**2 + 4*z**3 = 0. Calculate z.
1, 2, 58
Let m(v) be the third derivative of -v**6/40 - 91*v**5/20 - 45*v**4/4 + 7686*v**2. Factor m(i).
-3*i*(i + 1)*(i + 90)
Suppose 4*g = -4*g + 96. Suppose -5*r + 2 = 2*n, 0*r + g = -2*r - 4*n. Factor 4*y + 4*y**3 - 3*y**3 - 3*y**r - y**2 + 0*y**2.
y*(y - 2)**2
Let q(z) = z**2 + 1256*z + 387986. Let g be q(-548). Factor -44/15*b**g - 8/3 + 82/15*b + 2/15*b**3.
2*(b - 20)*(b - 1)**2/15
Solve -579 + 1651337*m**2 - 786 - 1651342*m**2 + 170*m = 0 for m.
13, 21
Let k(l) be the first derivative of -l**4/26 + 2*l**3/3 - 54*l**2/13 + 144*l/13 - 4013. Factor k(u).
-2*(u - 6)*(u - 4)*(u - 3)/13
Let l(x) be the second derivative of x + 1/39*x**3 - 20 - 7/195*x**6 + 31/78*x**4 + 11/130*x**5 - 12/13*x**2. Let l(q) = 0. Calculate q.
-1, 4/7, 3
Let u(r) be the first derivative of -r**6/3 - 14*r**5/5 + 9*r**4 - 4*r**3/3 - 17*r**2 + 18*r + 1713. Find o, given that u(o) = 0.
-9, -1, 1
Let k(m) = 25*m**4 + 785*m**3 - 450*m**2 - 3490*m. Let u(j) = 4*j**4 + 124*j**3 - 71*j**2 - 551*j. Let n(d) = 11*k(d) - 70*u(d). Factor n(q).
-5*q*(q - 2)*(q + 2)*(q + 9)
Let w = 1578 - 1575. Suppose 2*g + 20 = 12*g. Factor -6/17*m**w - 4/17*m**g + 0 - 2/17*m**4 + 0*m.
-2*m**2*(m + 1)*(m + 2)/17
Let s = 6036/6325 - 26/575. Factor 0*c + 12/11*c**2 - 2*c**4 + 0 + s*c**3.
-2*c**2*(c - 1)*(11*c + 6)/11
Factor 115/8*t**4 + 1/8*t**5 + 630*t**3 + 12740*t**2 + 230496 + 109760*t.
(t + 3)*(t + 28)**4/8
Factor 3/5*d**3 + 57/5*d**2 + 297/5*d + 243/5.
3*(d + 1)*(d + 9)**2/5
Let m(l) be the first derivative of 2/5*l**2 + 2/5*l**3 + 0*l - 135 + 1/10*l**4. Factor m(k).
2*k*(k + 1)*(k + 2)/5
Let j = 659 + -661. Let a be j/(-3) + 640/(-1320). Factor -6/11*k - 4/11 - a*k**2.
-2*(k + 1)*(k + 2)/11
Let o = -35868 + 2259548/63. Let z = o - -22/9. Let z*r + 0 + 4/7*r**3 + 6/7*r**2 = 0. What is r?
-1, -1/2, 0
Let v(t) be the third derivative of t**8/10080 - t**7/630 - t**6/72 - t**5/20 + 7*t**4/12 + 70*t**2. Let s(o) be the third derivative of v(o). Factor s(l).
2*(l - 5)*(l + 1)
Let a(k) be the third derivative of k**7/1470 + 2*k**6/105 - 3*k**5/35 - 18*k**2 - 169. Factor a(y).
y**2*(y - 2)*(y + 18)/7
Suppose -499 - 425 = -11*k. Let y be (k/210)/(2/6). Factor 2/5*g**5 + 0 + 6/5*g**4 + 2/5*g**2 + 0*g + y*g**3.
2*g**2*(g + 1)**3/5
Solve 8 + 264*m**5 - 2479*m + 224*m**4 + 5032*m - 2521*m - 166*m**3 - 102*m**2 = 0 for m.
-1, -2/3, -2/11, 1/2
Factor 34*p**3 + 81*p**2 + 87*p**4 - 84*p**4 + 39*p + 31*p**3 - 20*p**3.
3*p*(p + 1)**2*(p + 13)