3
Let n(u) be the second derivative of u**5/90 - 575*u**4/54 + 1147*u**3/27 - 191*u**2/3 + 576*u - 1. Factor n(f).
2*(f - 573)*(f - 1)**2/9
Factor -19/8*h - 11 - 1/8*h**2.
-(h + 8)*(h + 11)/8
Let v be (-252)/196 - (-30)/7. Let f(x) be the second derivative of 0*x**v - 23*x - 7/10*x**5 + 1/15*x**6 + 0*x**2 - 4/3*x**4 + 0. Factor f(h).
2*h**2*(h - 8)*(h + 1)
Let m(n) = 6*n**4 - 9*n**3 - 85*n**2 - 35*n + 7. Let r(a) = 4*a**4 - 5*a**3 - 57*a**2 - 23*a + 5. Let h(g) = 5*m(g) - 7*r(g). Factor h(d).
2*d*(d - 7)*(d + 1)**2
Let w(h) be the third derivative of -1/18*h**4 - 1/3*h**3 + 0*h - 1/45*h**5 - 1/270*h**6 + 0 - 22*h**2. Let u(y) be the first derivative of w(y). Factor u(p).
-4*(p + 1)**2/3
Suppose 87*z**2 + 31*z**3 - 78*z**3 - 165*z + 22*z**3 + 81 + 22*z**3 = 0. What is z?
1, 27
Let v(r) = -2*r**3 + 3*r**2 + 4*r - 2. Let b be v(4). Let s = b - -94. Factor -20*o**4 - o - o - 8*o**2 - s*o**3 + 2*o.
-4*o**2*(o + 1)*(5*o + 2)
Let h(b) be the third derivative of b**8/168 - b**7/21 + b**6/30 + 4*b**5/15 - 34*b**2 - 5*b. Determine f, given that h(f) = 0.
-1, 0, 2, 4
Let y(t) be the second derivative of -2/9*t**2 + 0 - 63*t + 7/9*t**3 + 23/54*t**4. Factor y(u).
2*(u + 1)*(23*u - 2)/9
Let m(a) be the third derivative of a**8/840 - a**7/75 - 17*a**6/150 + 4*a**5/15 - 1892*a**2. Find h such that m(h) = 0.
-4, 0, 1, 10
Let p(z) be the first derivative of 2*z**6/3 - 4*z**5 - z**4 + 20*z**3/3 + 96. Factor p(j).
4*j**2*(j - 5)*(j - 1)*(j + 1)
Let a = 326811/217876 - -3/217876. Determine v so that 15/2*v**4 + 0*v**2 + 0*v**3 + 0*v + 0 - a*v**5 = 0.
0, 5
Let h = -20025 - -40059/2. Let z(q) be the first derivative of -2*q - h*q**2 + 25/16*q**4 - 8 - 5/2*q**3. Factor z(a).
(a - 2)*(5*a + 2)**2/4
Suppose 3*m + 4*m = 1085. What is h in -20 - 130*h**4 + 35*h**2 - 5*h**5 + 115*h**4 - m*h**3 + 160*h**3 = 0?
-2, -1, 1
Let q(h) = 828*h**2. Let m be q(-1). Suppose -x - 8*x = -m. Factor 94*b**2 - x*b**2 + 16 - 16*b + 4 - 6*b.
2*(b - 10)*(b - 1)
Let w(u) be the third derivative of u**6/600 - 22*u**5/25 + 1179*u**4/8 - 17161*u**3/15 - 2*u**2 + 16*u - 22. Factor w(i).
(i - 131)**2*(i - 2)/5
Suppose 1764*i = -621*i + 4770. Solve 4/7 + b**4 + 25/7*b**i - 19/7*b**3 - 16/7*b - 1/7*b**5 = 0 for b.
1, 2
Let a(j) be the first derivative of 0*j + 2/3*j**3 - 217 - 7/3*j**2 + 1/24*j**4. Factor a(q).
q*(q - 2)*(q + 14)/6
Let n(h) be the second derivative of 13/140*h**5 - 1/210*h**6 + 0*h**2 + 1/6*h**4 + 4*h + 0*h**3 + 4. Factor n(o).
-o**2*(o - 14)*(o + 1)/7
Suppose -3*v - 7*o - 4229 = -5*o, -o - 4234 = 3*v. Let i = 1417 + v. Factor -13/2*f**2 + 3*f**3 - 1/2*f**i + 6*f - 2.
-(f - 2)**2*(f - 1)**2/2
Let r(f) = -86*f**3 + 21*f**2 + 1384*f - 270. Let c(v) = 29*v**3 - 14*v**2 - 461*v + 90. Let q(a) = 11*c(a) + 4*r(a). Solve q(t) = 0.
-6, 1/5, 3
Let j(x) be the third derivative of -74*x**2 + 1/8*x**4 + 0 + 1/100*x**5 + 0*x + 3/5*x**3. Solve j(c) = 0 for c.
-3, -2
Solve -2*q**3 - 73*q - 59 + 39*q**2 - 55*q**2 - 176*q**2 + 463*q - 137 = 0 for q.
-98, 1
Let c(y) be the third derivative of 11/30*y**6 - 2/3*y**3 - 2*y + 8/105*y**7 + 1/6*y**4 - 55*y**2 + 0 + 3/5*y**5. Factor c(l).
4*(l + 1)**3*(4*l - 1)
Let t(c) be the first derivative of c**8/2520 - c**6/270 + c**4/36 + 33*c**3 - 83. Let p(z) be the third derivative of t(z). Factor p(y).
2*(y - 1)**2*(y + 1)**2/3
Suppose 4*h + 3016 = -4*t, -8*h - 567 = t + 187. Let l = -752 - t. Factor 1/2*m + 1 - 1/2*m**l.
-(m - 2)*(m + 1)/2
Let v(u) be the second derivative of 38/15*u**3 - 1/75*u**6 + 0 - 1/25*u**5 + 13/30*u**4 + 117*u + 24/5*u**2. Determine o, given that v(o) = 0.
-3, -2, -1, 4
Let h be (2/(-12))/((-2)/(-3189)). Let p = 267 + h. Let p*y**2 + 0 - 1/2*y**5 - 9/4*y**3 - 1/4*y + 7/4*y**4 = 0. Calculate y.
0, 1/2, 1
Let h be (-16)/28 - (1 - (-354)/42). Let u be (-1 - (9 + h))/2. Solve -1/3*p**5 + u*p**4 + 1/3*p**3 + 0 + 0*p + 0*p**2 = 0 for p.
-1, 0, 1
Let f(c) be the first derivative of c**6/27 + 104*c**5/9 - 262*c**4/9 + 4*c**3/27 + 523*c**2/9 - 524*c/9 - 3253. Find d such that f(d) = 0.
-262, -1, 1
Let u(r) be the second derivative of 5*r**7/42 - 13*r**6/6 + 59*r**5/4 - 595*r**4/12 + 90*r**3 - 90*r**2 + 59*r + 2. Suppose u(d) = 0. What is d?
1, 2, 3, 6
Let l(p) = p**2 - 1. Let z(i) = 5*i**2 + 0*i**2 - 39 + 8 + 22 - 4*i. Let q(t) = 6*l(t) - z(t). Determine u so that q(u) = 0.
-3, -1
Let j(q) be the first derivative of -4*q**3/15 + 398*q**2/5 + 160*q - 7278. Solve j(r) = 0.
-1, 200
Let v(m) be the third derivative of -m**6/200 + m**5/100 + m**4/5 - 6*m**3/5 + m**2 + 413*m. Solve v(n) = 0.
-3, 2
Let j(f) = 54*f**4 + 334*f**3 + 199*f**2 - 8383*f + 8000. Let v(w) = 13*w**4 + 83*w**3 + 48*w**2 - 2096*w + 2000. Let n(a) = 4*j(a) - 17*v(a). Factor n(u).
-5*(u - 4)*(u - 1)*(u + 10)**2
Let m(k) be the second derivative of k**7/10080 + k**6/180 + k**5/32 - 2*k**4/3 - 2*k - 15. Let f(d) be the third derivative of m(d). Factor f(v).
(v + 1)*(v + 15)/4
Let t(d) be the second derivative of -d**6/12 - d**5/20 + 395*d**4/24 + 194*d**3/3 + 96*d**2 + 3*d + 859. Let t(q) = 0. Calculate q.
-8, -1, 48/5
Let f be (-25)/(-350)*-4 - (-312)/14. Suppose 0 = 2*o + 3 - 5, -u - 4*o = -6. Factor -5*g**3 + 35*g - 18*g - f*g + u - 20*g**2 + 28.
-5*(g - 1)*(g + 2)*(g + 3)
Suppose 0 = 20*m + 1598 + 2. Let g be ((-102)/85)/((-207)/m + -3). Suppose g*p - 128/11 - 2/11*p**2 = 0. What is p?
8
Let p(s) be the third derivative of s**7/84 + s**6/12 + s**5/12 - 5*s**4/12 - 5*s**3/4 + 1287*s**2. Suppose p(b) = 0. What is b?
-3, -1, 1
Let c(u) = 288*u + 3970. Let m be c(-6). Suppose 0*q + 2*s - 30 = -5*q, 2*q - 28 = -4*s. Factor 36*w**2 + 3*w**q - 28*w**3 - 7*w**4 + m*w - 32 - 2214*w.
-4*(w - 1)**2*(w + 1)*(w + 8)
Let v(l) = 6*l - 26. Let d be v(5). Suppose j = 3*c + 19, 0*j - d*c - 12 = 2*j. Factor -60*m**3 - 2179*m**4 + 2204*m**j + 45*m**2 - 3*m - 7*m.
5*m*(m - 1)**2*(5*m - 2)
Factor 7*p - 60*p**2 + 30*p**2 + 2*p + 33*p**2.
3*p*(p + 3)
Let k(d) = -23*d - 75 + 27*d + 11*d. Let n be k(5). Solve -4/3*w**4 + 0*w + 0*w**2 + n + 4/3*w**3 = 0.
0, 1
Let f(m) be the third derivative of 121*m**8/3192 - 241*m**7/665 + 239*m**6/190 - 466*m**5/285 - 2*m**4/19 - 8*m**2 + 3*m + 9. Find p such that f(p) = 0.
-3/121, 0, 2
Let n = 12721/24 + -12689/24. What is w in 10/9*w**2 + n*w + 2/9 = 0?
-1, -1/5
Let y be ((-2)/(-16))/((-84)/(-576)*(4 + 560/(-147))). Suppose y + 1/4*k**2 - 11/4*k = 0. What is k?
2, 9
Suppose -w + 20 = 6*w + 3*w. Let k(r) be the first derivative of w*r + 2/3*r**3 + 21 - 2*r**2. Factor k(i).
2*(i - 1)**2
Let t(s) be the second derivative of -s**6/150 + 55*s**5/4 - 117992*s**4/15 - 236672*s**3/15 + 648*s. Factor t(k).
-k*(k - 688)**2*(k + 1)/5
Let u be (-119)/(-28) - (-3 + 7) - (-4)/16. Let a(x) be the first derivative of u*x**4 - 7/3*x**3 - x**2 + 7/5*x**5 + 0*x - 27. Find g such that a(g) = 0.
-1, -2/7, 0, 1
Let c(q) be the second derivative of -8*q + 50/27*q**3 + 8/9*q**2 - 73/54*q**4 + 1/6*q**5 + 0. Solve c(h) = 0 for h.
-2/15, 1, 4
Let a = -7245/4140998 + -2/8249. Let h = 1007/1506 + a. Suppose -h*n - 2/9*n**2 + 8/9 = 0. Calculate n.
-4, 1
Let y be 10*(-99)/(-33) + -25. Solve 0 + 0*t**3 - 6/5*t**4 + 3/5*t + 6/5*t**2 - 3/5*t**y = 0.
-1, 0, 1
Let b(n) be the second derivative of 1/2*n**3 + 0*n**2 + 176*n + 1/40*n**5 + 0 - 5/24*n**4. Factor b(l).
l*(l - 3)*(l - 2)/2
Suppose 0 = k + z - 5*z - 10, 4*z - 8 = 4*k. Let b be 6 + (k - -3) + -1. Determine g so that -g**2 - 65 + 65 + b*g + g = 0.
0, 3
Let p be 47/(-95) + (-5 - 112/(-20)). Suppose -779*u + 970 = -588. Factor -p*c**u - 12/19*c - 18/19.
-2*(c + 3)**2/19
Suppose -11*x - 28 = -39*x. Let m be (-1 - x) + (-312)/(-52). Determine b so that 4/11*b**2 + 0 - 2/11*b**3 - 2/11*b**m + 0*b = 0.
-2, 0, 1
Factor -20*u**3 - 658*u - 105928*u**2 + 266*u - 192 + 106140*u**2.
-4*(u - 8)*(u - 3)*(5*u + 2)
Let t be ((-12)/36)/(3/(-189)). Let i be (-64)/(-28) - 6/t. Solve 12*k - i*k**3 - 2*k**3 + 0*k**2 + 8*k**2 = 0.
-1, 0, 3
Let f(o) = -o**3 + 4*o**2 + 14*o - 10. Let q be f(5). Factor -27*x**4 - 55*x**3 - 6*x - 5*x + 6*x - q*x**2 + 2*x**4.
-5*x*(x + 1)**2*(5*x + 1)
Let l(m) = m**3 - 35*m**2 - 35*m - 32. Let d be l(36). Solve -3*n**2 - 4*n**2 + d*n**2 - 2*n**2 + 60*n = 0 for n.
0, 12
Let f(w) = 6*w**3 + 2*w**2 + 26*w. Suppose -p - 3*h + 7*h = -23, 4*h = -p - 17. Let y(c) = -2*c**3 - c**2 - 8*c. Let l(a) = p*f(a) + 10*y(a). Factor l(m).
-2*m*(m + 1)*