Factor b(t).
-2*(t + 2)*(t + 3)**2/3
Let p(m) be the second derivative of 2*m + 4/11*m**2 - 3/110*m**5 + 1/165*m**6 - 5/66*m**4 + 1/11*m**3 + 60. Suppose p(o) = 0. What is o?
-1, 1, 4
Let c = -13 - -37. Let j = c + -21. Factor 13*t**5 - 2*t**3 + 5*t**j - 16*t**5.
-3*t**3*(t - 1)*(t + 1)
Let m(t) be the first derivative of 3*t**4/4 - 26*t**3 + 60*t**2 + 576*t + 5205. Factor m(q).
3*(q - 24)*(q - 4)*(q + 2)
Let o(q) be the third derivative of -q**8/560 + 6*q**7/175 - 19*q**6/100 + 13*q**5/25 - 33*q**4/40 + 4*q**3/5 + 931*q**2 + 1. Let o(a) = 0. Calculate a.
1, 8
Let i be 468/40*(-7112)/(-8001). Find c, given that 72/5*c - i*c**2 - 32/5 + 12/5*c**3 = 0.
1, 4/3, 2
Let f(n) = 145*n**3 - n**5 - n**4 - 74*n**3 - 72*n**3 + 2*n. Let k(g) = g**5 - 37*g**4 - 165*g**3 - 256*g**2 - 172*g - 44. Let r(q) = f(q) - k(q). Factor r(d).
-2*(d - 22)*(d + 1)**4
Let q(a) = a**4 + 10*a**3 + 7*a**2 - 10*a - 14. Let m = 69 - 84. Let i(f) = -6*f**4 - 69*f**3 - 48*f**2 + 69*f + 99. Let t(p) = m*q(p) - 2*i(p). Factor t(s).
-3*(s - 1)*(s + 1)*(s + 2)**2
Let w(d) be the second derivative of 7*d**6/15 + 43*d**5/5 - 55*d**4/2 + 44*d**3/3 + 28*d**2 - 1779*d. Suppose w(i) = 0. Calculate i.
-14, -2/7, 1
Suppose -2*x - 92 = -2*w, -4*x - 210 = 5*w + 19. Let z be (-4)/12*x + 3. Factor 20*s + 5*s**2 + z*s - 35*s.
5*s*(s + 1)
Let c(s) = s**2 + 20*s - 186. Suppose -4*a - 2*w = -26, 0 = 61*a - 62*a + 4*w + 11. Let h be c(a). Factor 82/11*q**2 - 98/11 - 6/11*q**h - 266/11*q.
-2*(q - 7)**2*(3*q + 1)/11
Let s(p) be the first derivative of p**6/72 + 7*p**5/24 + 5*p**4/4 + 7*p**3 + 26. Let n(b) be the third derivative of s(b). Let n(j) = 0. Calculate j.
-6, -1
Let d be (-2)/(-4)*((-111)/6 + 19). Let l(r) be the second derivative of -5/6*r**3 - 1/60*r**5 - r + 25/6*r**2 + 0 - d*r**4. Factor l(w).
-(w - 1)*(w + 5)**2/3
Let q(j) = 239*j + 40. Let y be q(12). Factor 2*u**2 + 2*u**5 - 5818*u**4 + 2908*u**4 + y*u**4 - 6*u**3 + 4*u.
2*u*(u - 2)*(u - 1)*(u + 1)**2
Let u(y) = -77*y**2 + 510*y - 4320. Let g(m) = -5*m**2 + 34*m - 288. Let b(t) = -62*g(t) + 4*u(t). What is r in b(r) = 0?
16, 18
Let s(c) be the second derivative of 1/6*c**3 + 0*c**2 + 13/80*c**5 + 1/8*c**6 - 187*c - 2/3*c**4 + 0. Factor s(w).
w*(w - 1)*(w + 2)*(15*w - 2)/4
Let w = -8780634/5 - -1756127. Find x, given that -w*x**5 + 2/5*x**4 + 0*x + 1/5*x**3 - 2/5*x**2 + 0 = 0.
-1, 0, 1, 2
Let g = -9012604/94785 - -20183/213. Let z = 2/445 - g. Let 0*t + 0 + 1/6*t**3 + z*t**2 = 0. Calculate t.
-2, 0
Factor 1070/9 - 224/9*a + 2/9*a**2.
2*(a - 107)*(a - 5)/9
Let a(g) be the first derivative of 1/100*g**5 - 6 + 19*g + 0*g**2 + 1/60*g**4 - 1/15*g**3. Let q(o) be the first derivative of a(o). Factor q(x).
x*(x - 1)*(x + 2)/5
Suppose 5*p = -10 - 0. Let c be p*(2 - 57/6). Suppose c*w - w**2 - 11*w + 5*w**2 = 0. What is w?
-1, 0
Let w = 1412/187 + -52/11. Let g = w + -590/221. Factor 16/13*q + 0 - g*q**2.
-2*q*(q - 8)/13
Let c(t) be the second derivative of 0 + 86*t + 7/18*t**3 + 0*t**2 - 1/36*t**4. Factor c(z).
-z*(z - 7)/3
Let i be 75893/36638 + 38/7. Factor -19*x - 1/4*x**3 + i*x**2 + 14 - 1/4*x**4.
-(x - 2)**3*(x + 7)/4
Let f(z) be the third derivative of -z**8/4032 - z**7/24 - 49*z**6/16 + 7*z**5/10 + 42*z**2 + 1. Let q(k) be the third derivative of f(k). Factor q(j).
-5*(j + 21)**2
Suppose 0 = -311*p - 913*p + 490*p - 610*p. Solve -361/3*i**2 + 0 + p*i - 1/3*i**4 - 38/3*i**3 = 0.
-19, 0
Let f(n) be the third derivative of 0 - n**2 + 66*n + 0*n**3 + 1/392*n**8 + 0*n**4 + 0*n**5 - 1/280*n**6 - 1/490*n**7. Factor f(a).
3*a**3*(a - 1)*(2*a + 1)/7
Let c be 14/15*(-58 + (-85610)/(-1470)). Suppose -2*v + c*v**2 + 0 = 0. What is v?
0, 9
Suppose -19*y + 14*y = -3*f - 639, 4*f = y - 138. Let a be (-20)/y - (-16)/36. What is t in 18/7 + 2*t**2 + a*t**3 + 30/7*t = 0?
-3, -1
Let w(o) be the second derivative of -o**4/6 + 225*o**3 - 1346*o**2 - 10597*o + 1. Determine v, given that w(v) = 0.
2, 673
Suppose 519 + 57 = 12*f + 12*f. Let w(y) be the second derivative of 0*y**2 + 1/96*y**4 - f*y + 1/24*y**3 + 0. Factor w(o).
o*(o + 2)/8
Let j(s) be the second derivative of s**4/42 - 37*s**3/21 + 186*s**2/7 + 6*s + 181. Factor j(m).
2*(m - 31)*(m - 6)/7
Let q(o) = o**2 - 596*o + 40660. Let u be q(78). Solve u*x + 0 + 1/4*x**3 + 16*x**2 = 0.
-32, 0
Let d(o) be the second derivative of -o**6/24 + 15*o**5/8 - 1265*o**4/48 + 175*o**3/2 - 245*o**2/2 - 31*o. Factor d(s).
-5*(s - 14)**2*(s - 1)**2/4
Let n = -293 + 294. Let a(i) = i**3 - i**2 + i. Let f(d) = 98*d**4 - 732*d**3 - 1318*d**2 - 572*d - 72. Let y(o) = n*f(o) + 4*a(o). Factor y(q).
2*(q - 9)*(q + 1)*(7*q + 2)**2
Let r(y) be the second derivative of -y**4/6 + 5*y**3/21 + 2*y**2/7 - 4750*y. Factor r(x).
-2*(x - 1)*(7*x + 2)/7
Let r(a) be the first derivative of 18*a**2 - 215 + 16/5*a**3 + 1/5*a**4 + 216/5*a. What is h in r(h) = 0?
-6, -3
Suppose -5*i - 2*g = -2, 0*g + 4*g + 16 = 0. Let c be 6 + (-12)/(4 + 0). Factor 4*w**2 + 2*w**i + w**3 - 3*w - 4*w**c.
-3*w*(w - 1)**2
Factor 1/3*d**3 + 100/3 + 7*d**2 + 40*d.
(d + 1)*(d + 10)**2/3
Suppose 31 = -j - 39. Let i = -65 - j. Let p(y) = 15*y**2 - 4*y - 6. Let g(t) = 14*t**2 - 3*t - 5. Let r(n) = i*p(n) - 6*g(n). Factor r(m).
-m*(9*m + 2)
Suppose 2345*h = 2138*h. Let -8/9*l**4 + 2/3*l**2 + h + 22/9*l**3 + 0*l = 0. What is l?
-1/4, 0, 3
Let w(b) be the third derivative of -b**6/40 + b**5/10 + b**4/8 - b**3 - 1521*b**2. Suppose w(v) = 0. What is v?
-1, 1, 2
Let p(c) = 3*c**4 - c**3 + c**2 + c. Let s(f) = -10*f**4 - 69*f**3 + 875*f**2 - 2883*f + 2075. Let r(d) = 3*p(d) + s(d). Find n such that r(n) = 0.
-83, 1, 5
Let p = -3/71545 - -71554/214635. Factor -19/3*r - p*r**2 + 0.
-r*(r + 19)/3
Let f be (7 - 2) + 2 - (11 - 8). Factor 2*p**2 - 717*p + 24 - 5*p**3 - 14*p**2 + 745*p - 7*p**3 + f*p**4.
4*(p - 3)*(p - 2)*(p + 1)**2
Let v be 153/51*(1 + 2215/(-2217)). Let d = 2221/1478 - v. Factor -d*j**2 + 15*j**3 + 0 + 0*j.
3*j**2*(10*j - 1)/2
Suppose 3*n = -3*w - 0*w + 18, 3*w + 6 = 5*n. Solve 2*q**2 - 8*q**w + 9*q**3 + 3*q + 2*q**2 = 0 for q.
-3, -1, 0
Let t be ((-11)/3 + 4)*9. Solve -72*k + 224*k**3 - 44 - 1277*k**t + 445*k**2 + 676*k**4 + 48 = 0 for k.
2/13, 1/4, 1
Let b be ((-30)/2 - -3)*(-76)/95. Factor 4*y - b - 2/5*y**2.
-2*(y - 6)*(y - 4)/5
Let n(d) be the first derivative of d**4 + 0*d + 70 + 2/3*d**3 + 0*d**2 + 2/5*d**5. Let n(a) = 0. Calculate a.
-1, 0
Suppose -4*g + 63 = 11. Suppose -5*y + g = -7. Determine k so that -11*k**2 + 7*k**2 + 8*k**2 - y*k**4 = 0.
-1, 0, 1
Let p = -5410591/15 + 360707. Find d such that -p*d + 14/15*d**3 + 0 + 2/15*d**2 - 2/15*d**4 = 0.
-1, 0, 1, 7
Let i(d) be the first derivative of -2*d**6/15 + 17*d**5/5 - 30*d**4 + 72*d**3 + 432*d**2 + 47*d - 54. Let g(j) be the first derivative of i(j). Factor g(l).
-4*(l - 6)**3*(l + 1)
Determine a so that -4*a**4 + 110*a**3 + 12*a**3 - 52*a + 240 - 140*a**2 - 166*a**3 = 0.
-5, -4, -3, 1
Find z such that -89*z**3 + 1936 + 31*z**3 + 60*z**2 + 29*z**3 + 31*z**3 + 594*z = 0.
-11, -8
Suppose -160*l = 696165 - 696485. Factor -19/3*j + l - 7/3*j**2.
-(j + 3)*(7*j - 2)/3
Let l be -1 + (-1 - 2) + (22 - -95)/13. Solve 0*o + 15/2*o**3 + 7/2*o**2 + 9/2*o**4 + 0 + 1/2*o**l = 0 for o.
-7, -1, 0
Suppose -2*i + 5*u + 176 = 0, u + 4*u - 475 = -5*i. Let t = -175 - -177. Suppose x**t - x**2 + 2*x**2 + 3*x**3 + 92*x**5 - i*x**5 = 0. Calculate x.
-1, 0, 2
Suppose -9*m + 7*m + u + 1 = 0, 3*u - 11 = -m. Suppose 164*q**2 - 1167*q - 2588*q + 1235*q - m*q**3 - 2088*q + 28*q**2 = 0. What is q?
0, 48
Let n(x) = -36*x**4 + 1963*x**3 - 476*x**2 + 10*x + 40. Let d(m) = 12*m**4 - 654*m**3 + 159*m**2 - 3*m - 12. Let f(y) = 10*d(y) + 3*n(y). Factor f(c).
3*c**2*(c - 54)*(4*c - 1)
Solve 42/13 + 20/13*h + 2/13*h**2 = 0 for h.
-7, -3
Factor -100*z + 37*z - 3*z**2 + 990 - 2*z**2 - 72*z.
-5*(z - 6)*(z + 33)
Let h = -200 - -202. Factor -14*o**3 - h*o**5 + 5*o**5 + o**5 - 4*o**4 + 6*o**3.
4*o**3*(o - 2)*(o + 1)
Suppose 0*g**2 - 1153 + 1592*g + 3277 - 530 - 2*g**2 = 0. What is g?
-1, 797
Let s(a) be the third derivative of a**9/15120 - a**8/3360 + a**7/2520 + a**4/8 + 2*a**3/3 + 35*a**2. Let i(m) be the second derivative of s(m). Factor i(y).
y**2*(y - 1)**2
Suppose 4*i = -3*a + 7963, 3*a - 2686 = 3*i + 5291. Solve a + 2494 + 4849 + 4*x**2 + 400*x + 0*x**2 = 0.
-50
Suppose -j - 26 = -3*j. Suppose -12 = -j*g + 14. Factor 2*o**3 - 4*o**3 +