z + 1)
Let d be -116*2/5*15/(-12). Let l = d - 53. Factor 30*o**4 - 25*o**l + 9*o**2 + 57*o**3 - o**2 - 21*o**3.
-o**2*(o - 2)*(5*o + 2)**2
Let o(x) be the second derivative of -x**6/105 + 23*x**5/35 - 709*x**4/42 + 1380*x**3/7 - 8100*x**2/7 - 1156*x. Find r, given that o(r) = 0.
5, 18
Factor 16/3*x**2 + 17/3 + 67/6*x - 1/6*x**3.
-(x - 34)*(x + 1)**2/6
Let j(z) = 7*z**2 - 999*z - 136215. Let w(y) = -4*y**2 + 497*y + 68106. Let c(h) = -5*j(h) - 9*w(h). Solve c(n) = 0.
-261
Factor -1188/7 - 135/7*n - 3/7*n**2.
-3*(n + 12)*(n + 33)/7
Let u(x) be the second derivative of 5/6*x**4 - 5/2*x**3 - 3*x - 11 + 1/4*x**5 + 0*x**2. Factor u(q).
5*q*(q - 1)*(q + 3)
Let i(j) be the third derivative of 0*j - 33*j**2 - 8/33*j**3 + 0 + 3/44*j**4 - 1/330*j**5. Factor i(r).
-2*(r - 8)*(r - 1)/11
Factor 2507/3*f**3 + 0 + 99856/9*f - 52456/9*f**2 + 1/9*f**5 - 166/9*f**4.
f*(f - 79)**2*(f - 4)**2/9
Suppose 39*v - 603 - 177 = 0. Factor 45 + z**2 - 25 - 15*z - v.
z*(z - 15)
Suppose 9320 + 1409*q + 345*q**3 - 9320 + 9937*q + 6435*q**2 + 4989*q + 5*q**4 = 0. Calculate q.
-33, -3, 0
Let m(x) be the second derivative of x**4/4 + 2*x**3 - 2175*x**2/2 - 4914*x. What is u in m(u) = 0?
-29, 25
Let i be 90/36 + (-2 - (-93)/30). Let h(k) be the first derivative of -i*k**5 - 6*k + 27/2*k**2 + 21/2*k**4 + 1/2*k**6 - 16*k**3 + 8. Factor h(f).
3*(f - 2)*(f - 1)**4
Let t = 699931/5 - 141142. Let v = 1160 + t. Factor -v*i**3 + 12/5 + 3*i**2 + 48/5*i.
-3*(i - 2)*(i + 1)*(7*i + 2)/5
Let h be (16/(-10))/((-4)/3). Factor o + h + 1/5*o**2.
(o + 2)*(o + 3)/5
Let g(r) be the first derivative of 7*r**6/2 + 132*r**5/5 + 225*r**4/4 + 18*r**3 - 1122. Factor g(d).
3*d**2*(d + 3)**2*(7*d + 2)
Let p(j) be the third derivative of 6/25*j**5 - 37/150*j**6 + 0 - 1/168*j**8 - 2*j**2 - 18/5*j**3 + 9/4*j**4 - 38/525*j**7 - 11*j. Solve p(c) = 0 for c.
-3, 2/5, 1
Let g(o) = 2*o**2 + o. Let y(h) = -35*h**2 - 330*h + 990. Let b(c) = 15*g(c) + y(c). Factor b(v).
-5*(v - 3)*(v + 66)
Let r = -14 + 33. Suppose v - 28 = -5*f, 2*f - 5*v - r = -8*v. Factor k**2 - 2*k**2 - f*k**2 + 2*k**2.
-4*k**2
Suppose 0 = 12*w + 56 - 236. Let i be (w/3 - 171/(-63)) + -6. Find j such that -2/7*j**2 + 0 - i*j = 0.
-6, 0
Let b = -23 - -21. Let q(p) be the first derivative of -5*p**3 - 33*p**2/2 - 10*p + 11. Let k(w) = 30*w**2 + 65*w + 20. Let d(i) = b*k(i) - 5*q(i). Factor d(j).
5*(j + 2)*(3*j + 1)
Find y such that 170/3*y + 2/21*y**3 - 4/21 - 598/21*y**4 + 598/7*y**2 = 0.
-1, 1/299, 2
Let l(q) be the first derivative of 4/9*q**3 + 58 + 1/6*q**4 + 0*q + 1/3*q**2. Factor l(o).
2*o*(o + 1)**2/3
Let p(n) be the third derivative of n**8/6720 + n**7/168 + 3*n**6/80 + n**5/60 + 79*n**4/24 + 137*n**2. Let q(f) be the third derivative of p(f). Factor q(j).
3*(j + 1)*(j + 9)
Let s(k) be the second derivative of 1/2*k**2 - 1/2*k**3 + 19 - 1/3*k**4 + k. Factor s(n).
-(n + 1)*(4*n - 1)
Let w(i) be the first derivative of -i**3/6 - 71*i**2/4 - 69*i + 587. Factor w(g).
-(g + 2)*(g + 69)/2
Let i be 144/(-1680)*5/(-18). Let m(r) be the second derivative of i*r**4 - 4/7*r**2 + 0 - 8*r - 1/7*r**3. Factor m(u).
2*(u - 4)*(u + 1)/7
Let r = 368722209923/510815 - 1099/102163. Factor 60453363/5 + 804/5*l**3 + r*l + 3/5*l**4 + 80802/5*l**2.
3*(l + 67)**4/5
Suppose -4*c = -3*a + 2, -3*c = -c - 2. Let g be a + (0/(-19))/(0 + -1). Factor -3*j**3 + 15*j**g + 5*j**2 + 13*j**3 - 5*j**3 - 15*j - 90.
5*(j - 2)*(j + 3)**2
Let t = 1783/3046 + -130/1523. Determine p so that 0*p**2 - t*p**5 + 0*p + 0 + 3*p**3 + 1/2*p**4 = 0.
-2, 0, 3
Let u be -8 - (572/(-104))/(5/10). What is o in 6/13*o**2 + 6/13*o**u - 2/13*o**4 - 14/13*o - 12/13 = 0?
-1, 2, 3
Factor -7/2*w**2 - 95/6*w - 25/2 - 1/6*w**3.
-(w + 1)*(w + 5)*(w + 15)/6
Suppose -2*a = 5*d - 1, -5*a + 119*d - 121*d + 34 = 0. Factor -1/2 - 3*z - a*z**3 - z**5 - 9/2*z**4 - 7*z**2.
-(z + 1)**4*(2*z + 1)/2
Let s(y) be the third derivative of -y**5/540 - 19*y**4/54 - 61*y**2 + 1. Solve s(h) = 0 for h.
-76, 0
Let g(v) be the first derivative of 127*v**3/3 + 65*v**2 + 3*v - 1331. Factor g(n).
(n + 1)*(127*n + 3)
Factor 58943 + 189*i + 3*i**5 - 42*i**4 + 96*i**3 - 58943 + 330*i**2.
3*i*(i - 9)*(i - 7)*(i + 1)**2
Let r(d) be the third derivative of d**6/360 + 197*d**5/30 + 9735*d**4/2 + 348100*d**3/9 - 2148*d**2. Suppose r(t) = 0. What is t?
-590, -2
Let f(n) be the first derivative of -n**3/3 + 284*n**2 + 10114. Factor f(y).
-y*(y - 568)
Let l = -132 + 139. Suppose -d - 3 = 0, 4*w + d = l*w - 9. Find x such that -6/7*x**w + 0 + 15/7*x**3 + 0*x - 9/7*x**4 = 0.
0, 2/3, 1
Let l(i) = 48*i - 94. Let s be l(2). Let n(x) be the first derivative of -4/3*x**3 + 0*x - 6*x**s - 10. Factor n(z).
-4*z*(z + 3)
Determine p, given that 76/5*p**3 + 2864/5*p**2 - 2/5*p**4 - 21294/5 + 18356/5*p = 0.
-13, 1, 63
Let b(c) = 5*c**3 + c + 5. Let p(x) = -102*x**3 + 90*x**2 + 426*x + 255. Let s(a) = 21*b(a) + p(a). Let s(k) = 0. Calculate k.
-24, -5, -1
Find j such that 132*j - 68 + 12*j**3 + 807*j**4 - 49*j**2 - 806*j**4 - 28*j**2 = 0.
-17, 1, 2
Suppose -2*j - 96 = -10*j. Let h = -248/21 + j. Factor -10/21*s**2 + 8/21*s**3 + h*s + 0 - 2/21*s**4.
-2*s*(s - 2)*(s - 1)**2/21
Let p(z) = 3*z**5 + 15*z**4 + 96*z**3 + 111*z**2 - 36. Let i(a) = -a**5 - 7*a**4 - 48*a**3 - 56*a**2 + 16. Let x(t) = 9*i(t) + 4*p(t). Factor x(v).
3*v**2*(v - 5)*(v + 2)**2
Let o(w) be the first derivative of 3*w**3/4 - 75*w**2/8 + 21*w + 778. Factor o(m).
3*(m - 7)*(3*m - 4)/4
Let c(b) = 318 - 9*b + 77*b - 99 - 37*b. Let s be c(-7). Find g such that s*g**2 + 8/5 - 16/5*g - 2/5*g**3 = 0.
1, 2
Let q(u) be the second derivative of 190*u + 1/48*u**4 + 0 + 2209/8*u**2 + 47/12*u**3. Solve q(t) = 0 for t.
-47
Factor -768 - 1/6*k**3 - 160*k - 28/3*k**2.
-(k + 8)*(k + 24)**2/6
Let m(z) = 30*z**2 - 10*z - 5. Let f(k) = -k**3 + 28*k**2 - 11*k - 4. Let g be (-20)/5 - -2 - -7. Let l(h) = g*f(h) - 4*m(h). Factor l(j).
-5*j*(j - 3)*(j - 1)
Find v, given that 2/11*v**5 + 1556/11*v**3 - 1558/11*v + 722 - 98/11*v**4 - 7844/11*v**2 = 0.
-1, 1, 11, 19
Let c(d) = d**2 - 3*d - 5. Let r be c(5). Suppose 789*h + 11 - 619 = 970. Factor -6/13*g**3 + 8/13*g**h + 0 - 4/13*g**4 + 8/13*g + 2/13*g**r.
2*g*(g - 2)**2*(g + 1)**2/13
Let j = -5876390/7 + 839486. Solve j*z**2 - 16/7*z**4 + 6/7*z**5 + 0*z + 0 - 10/7*z**3 = 0 for z.
-1, 0, 2/3, 3
Suppose -3*r + 8*r - 185 = 0. Let -118*m**4 + 115*m**4 + 7*m**2 - r*m**2 + 8*m + 19*m**3 = 0. What is m?
0, 1/3, 2, 4
Let l(i) be the first derivative of -i**6/2 - 393*i**5 - 159405*i**4/2 + 322750*i**3 - 972195*i**2/2 + 324723*i - 3062. Let l(y) = 0. What is y?
-329, 1
Let w(l) be the first derivative of l**6/21 - 16*l**5/7 + 12*l**4 + 500*l**3/21 - 169*l**2/7 - 60*l - 5256. What is q in w(q) = 0?
-1, 1, 6, 35
Determine a, given that 64/7 + 148/7*a**3 - 576/7*a**2 + 528/7*a = 0.
-4/37, 2
Let x = -278 - -234. Let b be 11 + 429/x + -3 + 2. Factor 1/4*p**2 - 1/4*p + b*p**3 - 1/4.
(p - 1)*(p + 1)**2/4
Let x(d) be the third derivative of -d**7/140 + d**6/40 + 7*d**5/40 + d**4/4 + 6*d**2 - 43*d. Find w such that x(w) = 0.
-1, 0, 4
Let j(m) be the third derivative of -7/160*m**6 + 0*m**3 + 0*m**4 - 1 + 0*m - 1/56*m**7 + 2*m**2 - 3/80*m**5 - 1/448*m**8. Determine c, given that j(c) = 0.
-3, -1, 0
Solve -185/2*s**2 + 5/2*s**3 - 845/2*s + 1025/2 = 0 for s.
-5, 1, 41
Suppose 2*m = m + 5*v - 7, -3*m + 15 = 3*v. Factor -5*z**2 - 24 + 24*z**2 - 6*z**2 + 4*z**3 + m*z**2 + 4*z.
4*(z - 1)*(z + 2)*(z + 3)
Let x(k) be the second derivative of -k**6/75 + 209*k**5/50 + k**4/10 - 125*k**3/3 - 418*k**2/5 + 409*k - 11. Determine a so that x(a) = 0.
-1, 2, 209
Let o = -89 - -109. Suppose 80 = -15*f + o*f. What is z in 0*z**3 + 47*z + 64*z**2 - 5*z**5 - 17*z**4 + f + 4*z**3 + 17*z = 0?
-2, -1, -2/5, 2
Suppose 0 = 428*f - 405*f. Let b(v) be the second derivative of -1/100*v**5 + 0 + f*v**2 + 1/60*v**4 + 1/15*v**3 - 27*v. Suppose b(s) = 0. Calculate s.
-1, 0, 2
Let t(d) be the third derivative of -4*d**7/525 - d**6/60 + 21*d**5/50 - 16*d**4/15 - 4*d**3/3 + 1811*d**2 + 2. Find h such that t(h) = 0.
-5, -1/4, 2
Let a = 4248 - 4244. Let n(g) be the first derivative of -4*g - 5*g**2 - 8/3*g**3 + 21 - 1/2*g**a. Suppose n(c) = 0. Calculate c.
-2, -1
Let r(x) = 14493*x - 14293. Let m be r(1). Let -20*h**3 - 2000/3*h - m*h**2 + 0 - 2/3*h**4 = 0. Calculate h.
-10, 0
Suppose -5*b = 3*f + 6, -4*b + 517 = f + 519