)**2/7
Let f be 131/5 + 9/(-180)*-16. Factor -33 - f*k - 4*k**2 - 7*k**2 + 8*k + 29 + 4*k**3.
(k - 4)*(k + 1)*(4*k + 1)
Let b(q) be the third derivative of -q + 1/15*q**5 - 1/30*q**6 - 27*q**2 + 1/336*q**8 + 0 + 0*q**4 + 0*q**3 - 1/210*q**7. Solve b(j) = 0.
-2, 0, 1, 2
Let q(n) = 7*n**2 + 206*n + 1347. Let l(t) = -2*t**2 - 66*t - 450. Let w(c) = 10*l(c) + 3*q(c). Factor w(s).
(s - 51)*(s + 9)
Let z(o) be the second derivative of -o**9/4200 + o**8/5600 + o**7/3150 + 35*o**4/12 + 54*o. Let n(c) be the third derivative of z(c). Factor n(r).
-2*r**2*(3*r - 2)*(3*r + 1)/5
Let z(g) be the third derivative of 39*g**2 + 0 - 8/45*g**5 + 11/36*g**4 - 2/9*g**3 + 0*g + 7/180*g**6. Factor z(q).
2*(q - 1)**2*(7*q - 2)/3
Let w(j) = -j**5 + j**4 - j**3 - j**2 + j - 2. Let o be 7 - (-2)/4*-26. Let x(z) = -5*z**5 + 2*z**3 - 3*z - 12. Let c(a) = o*w(a) + x(a). Factor c(s).
s*(s - 3)**2*(s - 1)*(s + 1)
Let a = -43 - -45. Factor -7 + 14 + 2*o**2 - 34 + 25*o + 2*o - 8*o**a.
-3*(o - 3)*(2*o - 3)
Let k = -48073 + 624951/13. What is b in k*b**2 + 6/13*b - 20/13 = 0?
-5, 2
Suppose 52 = -13*x - 0*x. Let y(t) = t**2 + 4*t + 5. Let w be y(x). Determine d so that 3*d + w*d**2 + 807 - 28*d - 787 = 0.
1, 4
Let r(m) be the first derivative of 2*m**3/3 + 2338*m**2 + 2733122*m - 442. What is a in r(a) = 0?
-1169
Let c(j) be the third derivative of -j**8/448 + 11*j**7/84 - 21*j**6/160 - 27*j**5/20 - j**4/24 + 6*j**3 - 4*j**2 - 5*j + 22. What is w in c(w) = 0?
-1, 2/3, 2, 36
Let w(o) = o**3 + 17*o**2 - 14*o + 73. Let p be w(-18). Let k(t) = -t**2 + 14*t + 3. Let c(s) = -s - 1. Let h(m) = p*k(m) + 3*c(m). Let h(z) = 0. Calculate z.
0, 11
Suppose 312/5*p**3 + 88*p**2 - 160*p + 46/5*p**4 + 0 + 2/5*p**5 = 0. What is p?
-10, -4, 0, 1
Let z(w) = -10*w**2 - 91*w + 41. Let v(h) = -5*h**2 - 46*h + 21. Let r(a) = a. Let i be r(-5). Let p(t) = i*v(t) + 3*z(t). Factor p(g).
-(g + 9)*(5*g - 2)
Let w = -2085493 - -14598456/7. Solve w*q**3 + 1767/7*q - 27*q**2 + 361/7 = 0.
-1/5, 19
Let q(s) be the third derivative of s**5/20 - 169*s**3/2 + 11254*s**2. Suppose q(b) = 0. Calculate b.
-13, 13
Let q(s) be the second derivative of s**6/75 + 44*s**5/25 + 86*s**4/15 - 21*s - 2. Factor q(p).
2*p**2*(p + 2)*(p + 86)/5
Let b = -567 + 241. Let i = 328 + b. Factor 16/3*k + 0*k**i + 0 - 4/3*k**3.
-4*k*(k - 2)*(k + 2)/3
Let l(z) be the second derivative of -5*z**7/42 - 23*z**6/6 - 2901*z. Determine f so that l(f) = 0.
-23, 0
Factor -1951*h**3 + 16*h + 971*h**3 + 982*h**3 + 18*h**2.
2*h*(h + 1)*(h + 8)
Let d = -186110 + 186112. Factor 6/5*p**4 - 4*p**d - 3/5*p**3 + 0 + 1/5*p**5 - 12/5*p.
p*(p - 2)*(p + 1)**2*(p + 6)/5
Let y(k) = -k**5 + 8*k**4 - 14*k**3 - 32*k**2 + 66*k. Let q(f) = f**5 - 2*f**4 + f**3 - f. Suppose 62 - 30 = -32*o. Let w(v) = o*y(v) - 2*q(v). Factor w(i).
-i*(i - 2)**2*(i + 4)**2
Solve 299/2*n - 89401/4 - 1/4*n**2 = 0 for n.
299
Suppose -8*j - r = -13*j + 5, -2*r = 2*j - 14. Factor -26*q**2 + 4*q**3 + 20*q + 98*q**2 - 56 - 30*q**j - 10*q**2.
4*(q - 1)*(q + 2)*(q + 7)
Let c = -12 + 12. Suppose -2*j + 3 + 5 = c. Find d such that 3*d**4 - 3*d**4 + 5*d**3 - 18*d**2 - 4*d**j + 17*d**2 = 0.
0, 1/4, 1
Let i(c) be the first derivative of c**5/5 + 15*c**4/4 - 4*c**3/3 - 30*c**2 - 7054. What is k in i(k) = 0?
-15, -2, 0, 2
Solve 363*q**4 + 366*q**4 + 160*q**3 + 1596*q**2 - 160*q - 1091*q**4 + 366*q**4 - 1600 = 0 for q.
-20, -1, 1
Factor 1869*n**3 + 2*n**2 - 1868*n**3 - 42*n + 216 - 37*n**2.
(n - 36)*(n - 2)*(n + 3)
Let g(h) = -h**3. Let i(d) = d**3 - 21*d**2 + 42*d - 24. Let z(n) = 2*g(n) - i(n). Factor z(y).
-3*(y - 4)*(y - 2)*(y - 1)
Let l = -12595 + 604565/48. Let w(r) be the third derivative of -l*r**5 + 1/96*r**6 + 5/12*r**4 - 5/6*r**3 + 0 - 4*r**2 + 0*r. Find v, given that w(v) = 0.
1, 2
Let x = 256203 + -3330635/13. Suppose -2/13*z + x*z**2 + 0 - 2/13*z**3 = 0. Calculate z.
0, 1
Let l be ((-500)/(-1575)*-3)/(-2*5/70). Solve l*i - 1/3*i**2 - 19/3 = 0.
1, 19
Let l(s) = -22*s - 106. Let b be l(-32). Suppose 0 = -0*x + 2*x - 4. Factor -b + 592 - u**x - u**2 + 8*u.
-2*(u - 3)*(u - 1)
Suppose -10*w = -332 + 322. Let j be (-4)/(-51)*(w - -5). Factor 2/17*r**2 - j*r + 6/17.
2*(r - 3)*(r - 1)/17
Let i(u) be the first derivative of u**6/540 - u**5/90 - u**4/12 - 7*u**3/3 - 37. Let d(w) be the third derivative of i(w). What is n in d(n) = 0?
-1, 3
Suppose -8*r + 52 = 5*r. Factor 48*b + 62*b**2 - 10*b + 82*b**2 + 10*b + 14*b**r - 4*b**2 - 94*b**3.
2*b*(b - 4)*(b - 3)*(7*b + 2)
Factor q + 25*q**3 - 20*q**4 - 10*q**2 + 10409*q**5 - q - 10404*q**5.
5*q**2*(q - 2)*(q - 1)**2
Let v(y) be the second derivative of -16/25*y**5 - 1/105*y**7 - 16/5*y**2 - 28/15*y**4 - 16/5*y**3 - 3/25*y**6 - y + 169. Factor v(o).
-2*(o + 1)*(o + 2)**4/5
Let a be 112/(-105)*3/(-2). Let q(z) = -8*z - 48. Let k be q(-6). Let k + 12/5*v**2 - 4/5*v**3 - a*v = 0. Calculate v.
0, 1, 2
Let b(p) be the first derivative of p**4/8 + p**3/6 - p**2/2 + 988. Factor b(a).
a*(a - 1)*(a + 2)/2
Let f be 933/5 - (-10 + 48/5). Factor -187 - 3*j**2 + 3*j**3 + f + 0*j**3.
3*j**2*(j - 1)
Factor -4106046*t**2 - 45*t**5 - 13201002*t - 983030*t**3 - 24181104*t**2 - 5200*t - 5325923*t - 3070625 - 11505*t**4.
-5*(t + 85)**3*(3*t + 1)**2
Let g(d) be the third derivative of 5/9*d**4 - 100/9*d**3 - 8 - 1/90*d**5 + 0*d - 3*d**2. Factor g(s).
-2*(s - 10)**2/3
Let u be 30/(-23)*(-1)/(-3)*(-184)/460. Factor 0*b - 10/23*b**4 - u*b**3 + 0 + 0*b**2.
-2*b**3*(5*b + 2)/23
Suppose 9*n - 66 = -3. Factor 22*o**2 + 0 - 20 - 16 - n*o**2 - 12*o.
3*(o - 2)*(5*o + 6)
Suppose 3*r - 2*o - 11 = -2*r, 4*r - 2 = 5*o. Suppose 3*u + 2*q = 3, 4*u + r*q - 24 = 7*q. Factor 4*a + 1 + a**3 + u*a**2 + 4*a - 9*a + 4*a.
(a + 1)**3
Let c(p) = -5*p**2 - 35*p + 2. Let i(j) = -3*j + 70. Let n be i(24). Let t(d) = -35*d**2 - 250*d + 15. Let b(x) = n*t(x) + 15*c(x). Factor b(y).
-5*y*(y + 5)
Let x = 44409/103523 - 6/14789. Let -x*f**3 - 27/7*f**2 - 81/7*f - 81/7 = 0. What is f?
-3
Let s = 10/333 - -434/333. Let d(l) be the second derivative of 1/10*l**5 - 1/24*l**4 + 0 - s*l**3 + 5*l + l**2. Solve d(f) = 0 for f.
-2, 1/4, 2
Let a = -214034/45 + 57736/9. Let b = 1659 - a. Factor 1/5*i**5 - b*i**3 + 0*i + 0 - 2/5*i**4 + 2/5*i**2.
i**2*(i - 2)*(i - 1)*(i + 1)/5
Suppose 0 = -8*l + 3*l + 3*k + 70, 0 = -4*l - 4*k + 56. Solve -84*d**4 - 20*d - 20 + 79*d**4 - 5*d**5 + 39*d**3 - l*d**3 + 25*d**2 = 0 for d.
-2, -1, 1, 2
Let m(y) = -y**3 + 24*y**2 + 37*y - 6. Let p(i) = -20*i**2 - 36*i + 8. Let o(n) = 4*m(n) + 3*p(n). Let o(v) = 0. What is v?
-1, 0, 10
Factor -4*a**2 - 550564 - 19*a - 1917*a - 2135*a + 1103*a.
-4*(a + 371)**2
Let q(a) be the first derivative of a**6/27 - 4*a**5/9 + 7*a**4/18 + 4*a**3/3 - 1353. Determine p so that q(p) = 0.
-1, 0, 2, 9
Let j(p) = -7*p**3 - 40*p**2 + 19*p + 32. Let q(s) = -20*s**3 - 119*s**2 + 53*s + 97. Let g(d) = 11*j(d) - 4*q(d). Suppose g(o) = 0. Calculate o.
-12, -1, 1
Suppose 2*g = -4*p + 76, 82*g + 2*p + 46 = 83*g. Let t(i) be the first derivative of -5/4*i**4 + g - 15/2*i**2 + 5*i + 5*i**3. Factor t(y).
-5*(y - 1)**3
Let p = -4576 + 4576. Let s(j) be the second derivative of p - 10*j - 1/40*j**5 + 1/12*j**3 + 5/24*j**4 - 5/4*j**2. Suppose s(w) = 0. What is w?
-1, 1, 5
Let r = -9707 + 9709. Let y(z) be the first derivative of -1/2*z**6 + 0*z - 25 + 0*z**5 + r*z**3 + 0*z**2 + 9/4*z**4. Factor y(x).
-3*x**2*(x - 2)*(x + 1)**2
Let f(u) be the second derivative of -u**4/96 - 119*u**3/48 - 87*u**2/4 - 555*u - 2. Factor f(x).
-(x + 3)*(x + 116)/8
Let u(m) be the first derivative of -2*m**5/35 + 4*m**4/7 - 2*m**3/21 - 6*m**2 + 1156. Factor u(o).
-2*o*(o - 7)*(o - 3)*(o + 2)/7
Determine u so that 28*u**5 - 36*u**3 + 0 + 18*u + 397*u**2 + 0 - 57*u**4 - 330*u**2 = 0.
-1, -1/4, 0, 9/7, 2
Let o be -3 - (-1)/3*147/13. Let f = o + -31/91. Find w such that 1/7 + f*w + 3/7*w**2 + 1/7*w**3 = 0.
-1
Let p(z) = z**4 - z**3 - 2*z**2 - z. Let t(k) = -2*k**4 + 29*k**3 + 259*k**2 + 419*k + 192. Let o(g) = p(g) - t(g). Factor o(h).
3*(h - 16)*(h + 1)**2*(h + 4)
Let j(p) be the first derivative of 1/16*p**4 + 0*p**5 + 0*p - 1/240*p**6 - 10*p**2 + 1/6*p**3 + 7. Let a(w) be the second derivative of j(w). Factor a(o).
-(o - 2)*(o + 1)**2/2
Suppose 0 = -1785*o + 1786*o + 26. Let w be (-6)/4*o/52. What is q in -w*q**2 - 12 - 6*q = 0?
-4
Let q(d) = 0*d**2 + 2*d - 7*d**2 + d**2 + 4. Let t(g) = 9 - 2*g