 - 36. Let l(t) be the first derivative of s(t). What is a in l(a) = 0?
0, 4
Let a(j) = 25*j**2 + 89*j + 40. Let u(o) = 19*o**2 + 63*o + 30. Let w(c) = -8*a(c) + 11*u(c). Factor w(t).
(t - 1)*(9*t - 10)
Let v be -9827*(-67)/68541 - (-3)/(-11). Factor -29/3 + v*w + 1/3*w**2.
(w - 1)*(w + 29)/3
Let o(p) be the first derivative of 72 - 1/26*p**4 + 14/39*p**3 - 11/13*p**2 + 10/13*p. Factor o(c).
-2*(c - 5)*(c - 1)**2/13
Let q(f) = -f**3 + 11*f**2 + 273*f - 2368. Let u be q(8). Factor 0*g + u - 1/2*g**2.
-(g - 4)*(g + 4)/2
Let v(h) be the first derivative of 0*h + 3/2*h**4 - 1/6*h**6 - 1/5*h**5 - 4*h**2 + 4/3*h**3 + 95. Factor v(y).
-y*(y - 2)*(y - 1)*(y + 2)**2
Let d(y) be the second derivative of y**5/4 - 415*y**4/12 - 215*y**3 + 1425*y. Factor d(m).
5*m*(m - 86)*(m + 3)
Suppose -3*j**2 + 91386*j - 91152*j - 297 + 66 = 0. Calculate j.
1, 77
Let i(m) be the second derivative of 0 + 2/3*m**3 - 1/6*m**5 - 11/2*m**2 + 11*m - 1/4*m**4. Let c(y) be the first derivative of i(y). Factor c(x).
-2*(x + 1)*(5*x - 2)
Let i(y) be the first derivative of -y**6/18 + 10*y**5/3 - 89*y**4/6 - 280*y**3/9 + 179*y**2/6 + 230*y/3 - 7525. Let i(u) = 0. Calculate u.
-1, 1, 5, 46
Suppose 0 = -2*g + 3*c - 127, 289 = -5*g + 6*c - 8*c. Let i = g + 77. Let 5*r**2 - r**2 + i - 10*r**2 + 35*r - 2*r = 0. Calculate r.
-1/2, 6
Let g be (-130)/(-14) + 2/2. Let j be (-8)/(-100) + 134196/111300. Let -6*d**3 - g*d**2 + 0 + 27/7*d + 48/7*d**4 - j*d**5 = 0. What is d?
-1, 0, 1/3, 3
Let h(w) be the second derivative of 17/18*w**3 - 1/90*w**6 - 17/60*w**5 - w - 3*w**2 + 19/36*w**4 + 44. Factor h(g).
-(g - 1)**2*(g + 1)*(g + 18)/3
Let m = 7/3702 + 1823/14808. Let v(w) be the third derivative of 0*w + 0*w**3 + m*w**4 + 1/180*w**5 + 0 - 24*w**2. Solve v(o) = 0.
-9, 0
Let o(r) be the second derivative of -32*r**7/21 - 256*r**6/5 + 47*r**5 + 1945*r**4/6 + 279*r**3 + 98*r**2 - 8*r - 2. Let o(a) = 0. Calculate a.
-49/2, -1, -1/4, 2
Factor 14*h**2 + 62 - 19*h**2 - 4 - 23 + 30*h.
-5*(h - 7)*(h + 1)
Let j be ((-165)/(-66))/(-5)*(-13 - (-1 + -5)). Suppose -j*d**2 + 13/4*d + 1/4 = 0. Calculate d.
-1/14, 1
Let y(p) be the first derivative of -5 + 0*p - 45/8*p**4 - 3/4*p**2 - 39/10*p**5 - 7/2*p**3 - p**6. Factor y(x).
-3*x*(x + 1)**3*(4*x + 1)/2
Factor -412/3*x**4 - 628864/3 - 28562/3*x**3 - 1285472/3*x - 2/3*x**5 - 684760/3*x**2.
-2*(x + 1)**2*(x + 68)**3/3
Let g(z) be the first derivative of -z**5/5 - 5*z**4 - 33*z**3 + 10*z**2 + 100*z - 1078. Factor g(x).
-(x - 1)*(x + 1)*(x + 10)**2
Let r(y) = 5*y**3 + 91*y**2 - 2309*y - 2395. Let w(x) = x**3 - x**2 - x + 1. Suppose 11 = 10*o + 71. Let m(f) = o*w(f) + r(f). Let m(d) = 0. Calculate d.
-1, 49
Let m be 78/104 - (-10)/8. Let 36 - 2*d**2 + 30*d - 201 + d**m - 60 = 0. Calculate d.
15
Let o(k) be the first derivative of k**6/51 + 108*k**5/85 - 56*k**4/17 + 8650. Suppose o(j) = 0. Calculate j.
-56, 0, 2
Suppose 3*t - 5*g - 11 = 0, -4*g + 12 = 5*t - 31. Let z be t*(-40)/(-336)*(-3)/(-5). Factor z*p**4 + 9/2*p**3 + 0 + 27/2*p + 27/2*p**2.
p*(p + 3)**3/2
Let b = -1084 + 1087. Let a(k) be the third derivative of 1/30*k**5 + 0 - 4*k**2 + 1/3*k**4 + k**b + 0*k. Factor a(x).
2*(x + 1)*(x + 3)
Suppose 2 - 17/4*h - 1/4*h**3 + 5/2*h**2 = 0. Calculate h.
1, 8
Let h(z) be the first derivative of -3/5*z**5 - 27*z - 22*z**3 + 6*z**4 - 71 + 36*z**2. Factor h(a).
-3*(a - 3)**2*(a - 1)**2
Let z(i) be the first derivative of i**3/6 + 73*i**2/2 + 5329*i/2 - 1719. Factor z(r).
(r + 73)**2/2
Suppose -52*k + 47*k + 10 = 0. Let d = -80 - -80. Solve -2/5*n**k + d*n + 2/5 = 0 for n.
-1, 1
Let f(r) be the third derivative of 0 - 24/35*r**7 + 0*r + 0*r**3 + 10*r**2 + 49/20*r**6 - 9/8*r**4 + 1/16*r**8 - 12/5*r**5. What is w in f(w) = 0?
-1/7, 0, 1, 3
Determine d so that 0 + 242/19*d**3 + 1540/19*d**2 + 2450/19*d = 0.
-35/11, 0
Let u be 14*(3/2 - 0). Let i be ((-64)/6)/((-14)/u). Find h such that -2*h**2 - 16 - 18 - 20*h - i = 0.
-5
Let w be ((-8)/10)/(8/(-40)). Suppose 0 = -2*a - o + 7 + 3, 0 = -2*a + w*o - 10. Suppose 8/3 + 12*q**a - 20/3*q - 8*q**2 = 0. What is q?
-2/3, 1/3, 1
Let l(p) be the second derivative of -p**7/63 + 4*p**6/15 - 16*p**5/15 + 171*p. Factor l(a).
-2*a**3*(a - 8)*(a - 4)/3
Let f(c) be the second derivative of 7*c**6/24 - 10*c**5/3 - 305*c**4/24 - 35*c**3/3 - 81*c**2 + 64*c. Let w(g) be the first derivative of f(g). Factor w(j).
5*(j - 7)*(j + 1)*(7*j + 2)
Let k(n) be the first derivative of -n**6/6 + 6*n**5/5 + 3*n**4 - 56*n**3/3 - 48*n**2 + 3705. Factor k(y).
-y*(y - 6)*(y - 4)*(y + 2)**2
Factor -h**2 + 3*h**2 - 16*h - 36*h + 262921 - 3*h**2 - 262076.
-(h - 13)*(h + 65)
Let d be ((-135)/6)/(-9)*6/5. Suppose v - d*v = -4*v. Factor 0*o + v*o - 191*o**3 + 195*o**3 + 4*o**4 - 8*o**2.
4*o**2*(o - 1)*(o + 2)
Let u(z) = z**2 + z - 1. Let m(b) = b**3 + 7*b**2 + 25*b - 74. Let c(h) = m(h) + 2*u(h). Let v(i) be the first derivative of c(i). Suppose v(o) = 0. What is o?
-3
Let c(b) be the first derivative of b**5/100 - 11*b**4/40 + 12*b**3/5 + 151*b**2/2 + 20. Let v(m) be the second derivative of c(m). Solve v(f) = 0 for f.
3, 8
Let i(f) be the first derivative of -f**3/9 + 1619*f**2/3 - 2621161*f/3 - 7269. Factor i(j).
-(j - 1619)**2/3
Let 4/3*g**5 - 76/3*g**2 - 244/3*g**4 + 772/3*g - 767/3*g**3 - 256/3 = 0. Calculate g.
-2, 1/2, 64
Let h be 393/15 - (-461)/(-2305). Factor -4 + 77*r**2 + h*r - 1089/2*r**3.
-(9*r + 2)*(11*r - 2)**2/2
Let y(u) be the second derivative of -1/7*u**6 + 0 - 9/7*u**2 - 10/7*u**4 + 9/14*u**5 + 25/14*u**3 + 1/98*u**7 - 324*u. Factor y(k).
3*(k - 6)*(k - 1)**4/7
Let t(k) be the second derivative of -k**7/252 - k**6/20 + 7*k**5/8 + 1421*k**4/72 + 343*k**3/3 + 4*k - 247. Factor t(w).
-w*(w - 12)*(w + 7)**3/6
Let q(o) = 6*o**3 - 3*o**2 - 5*o + 5. Let t(g) = g**3 - g + 1. Let w(z) = q(z) - 5*t(z). Let n be w(0). Factor n*i + 0 - 2/3*i**3 - 2/3*i**2.
-2*i**2*(i + 1)/3
Suppose -702*s = -705*s + 171. Suppose 3*i - s*g = -60*g, 3*i = -5*g. Let -13/4*h**4 + h**3 + h**2 + i + 5/4*h**5 + 0*h = 0. Calculate h.
-2/5, 0, 1, 2
Let 4*w**5 - 215*w**4 - 2243*w**2 - 1453*w**3 - 107*w**3 + 71*w**4 - 429*w**2 - 1260*w = 0. Calculate w.
-7, -1, 0, 45
Let r(w) = w**4 + w**3 - 18*w**2 - 8*w - 8. Let c(n) = -4*n - 1 + 4 + 6*n**2 + 7*n. Let s be 0 + (1/(-6))/(51/54 - 1). Let l(t) = s*r(t) + 8*c(t). Factor l(k).
3*k**2*(k - 1)*(k + 2)
Let w(u) be the second derivative of u**6/50 + 33*u**5/50 + 141*u**4/20 + 22*u**3 + 30*u**2 - 59*u - 3. Factor w(j).
3*(j + 1)**2*(j + 10)**2/5
Let 7*c**3 + 20*c + 4481*c**4 + 16*c**2 + 5*c**3 - 4485*c**4 + 20*c**2 = 0. Calculate c.
-1, 0, 5
Suppose 5*x = 25, -14*r = -11*r - 5*x + 49. Let u be 12/(-81)*6/r*6. Factor u*m - 2/9 - 2/3*m**2 + 2/9*m**3.
2*(m - 1)**3/9
Determine d, given that 804*d - 77*d - 1296 - 4*d**3 + 989*d - 325*d**2 - 91*d**2 = 0.
-108, 1, 3
Suppose -48*n - 16 = 32. Let s be n - (2 - (-15)/(-3)). Factor 7/4*j**3 + 5/4*j**s - 1/2*j + 0.
j*(j + 1)*(7*j - 2)/4
Let s(h) = -h**3 - h**2 + 2*h. Suppose -8*x + 71 = -49. Let l(u) = 4*u**3 - 19*u**2 + 115*u. Let j(d) = x*s(d) + 5*l(d). Determine i so that j(i) = 0.
0, 11
Let r(q) be the third derivative of 17/240*q**6 + 7/48*q**5 + 0*q - 3/280*q**7 + 0 - 3/2*q**3 - 13/8*q**4 - 31*q**2. Let r(u) = 0. Calculate u.
-2, -2/9, 3
Solve 100352/17*m + 0 + 2/17*m**3 - 896/17*m**2 = 0 for m.
0, 224
Let q(y) be the third derivative of y**8/1344 + 17*y**7/120 - 121*y**6/240 + y**5/120 + 241*y**4/96 - 121*y**3/24 - 1397*y**2. Factor q(o).
(o - 1)**3*(o + 1)*(o + 121)/4
Suppose 2*g - 5*g + 18 = 0. Let s be 1456/496 - (-6)/93. Let g*t + 2*t - t**2 + s*t**3 - 11*t**2 + t = 0. What is t?
0, 1, 3
Let y(c) be the third derivative of -c**9/16632 - c**8/420 - c**7/220 - 52*c**3/3 - 162*c**2. Let s(k) be the first derivative of y(k). Factor s(a).
-2*a**3*(a + 1)*(a + 21)/11
Suppose 262 = 12*a - 602. Factor z - 76*z**2 + 64 + a*z**2 + 23*z.
-4*(z - 8)*(z + 2)
Let c(d) be the first derivative of -3/2*d**2 + 39 + 1/4*d**3 + 0*d. Factor c(q).
3*q*(q - 4)/4
Let w = 9992/1305 - 44/435. Factor 1156/9 + 1/9*x**2 - w*x.
(x - 34)**2/9
Let j(i) = 9*i**2 + i - 4. Let o(d) = 36*d**2 - 48*d**2 + 12 - 9. Let s(k) = 3*j(k) + 2*o(k). What is l in s(l) = 0?
-2, 1
Let u(p) = 16792*p**2 - 10320*p + 1350. Let o(h) = -2399*h**2 + 1474*h - 195. Let x(v) = 15*o(v) + 2*u(v). Factor x(c).
-(49*c - 15)**2
Suppose 3*i**5 - i**5