*f**2 + 157*f - 13. Let h be 25/10 - 28/(-8). Let b(a) = -716*a**2 + 158*a - 14. Let o(v) = h*m(v) - 5*b(v). Factor o(k).
-2*(19*k - 2)**2
Solve -248*b + 65*b**2 - 4*b**4 + 160 + 19*b**2 + 8417*b**3 - 8409*b**3 = 0 for b.
-5, 1, 2, 4
Let z(d) be the third derivative of -7/720*d**6 + 0*d**3 + 1/252*d**7 + 1/24*d**4 + 23*d**2 + 1/2016*d**8 + 0 - 1/72*d**5 + 0*d. Factor z(a).
a*(a - 1)**2*(a + 1)*(a + 6)/6
Suppose 3*x + 2*a - 109 = 0, -5*a + 8*a - 145 = -4*x. Factor 35*o + 6*o**4 - o**4 - x + 84 + 45*o**2 + 25*o**3 - 37.
5*(o + 1)**3*(o + 2)
Let k(a) = -a**2 - 6*a - 1. Let r = -19 - -14. Let h be k(r). Factor -2*d**4 - h*d**3 + 8*d**4 + 2 + 4*d**5 + 3*d**4 - 3*d**4 - 8*d**2.
2*(d - 1)*(d + 1)**3*(2*d - 1)
Let j be ((-114)/95)/((-4)/50). Factor -j*l**2 + 1667*l**3 + 5*l**2 - 1672*l**3.
-5*l**2*(l + 2)
Let d = -27844/77 - -2544/7. Suppose 16/11*o**2 + 38/11*o - 2/11*o**3 + d = 0. What is o?
-1, 10
Let x(b) be the second derivative of b**7/168 + b**6/60 - b**5/40 - b**4/12 + b**3/24 + b**2/4 + 7*b - 4. Suppose x(d) = 0. Calculate d.
-2, -1, 1
Let f(i) be the third derivative of i**11/83160 + i**10/9450 + i**9/5040 - 23*i**5/60 - i**2. Let k(y) be the third derivative of f(y). Factor k(v).
4*v**3*(v + 1)*(v + 3)
Let a = 36 + -32. Factor -9 + 1 - a - 4*u**2 - 16*u.
-4*(u + 1)*(u + 3)
Let d(r) = 29*r**2 - 7*r - 22. Let z(q) = -7*q**2 + 2*q + 5. Let o = -6 - 0. Let b(l) = o*d(l) - 26*z(l). Factor b(x).
2*(x - 1)*(4*x - 1)
Suppose -r + 5 = 5*i, -r + 2*r = 2*i - 2. Let m(v) = 2*v**3 + v**2 - 2*v + 1. Let a be m(i). Find y such that -12*y**a - 3*y**3 - y + 3 + 7*y**2 - 2 = 0.
-1, 1/3
Let b(s) = -4*s**2 - 2*s - 55. Let z(v) = -v**2 - 8. Let n(p) = -b(p) + 5*z(p). Factor n(g).
-(g - 5)*(g + 3)
Factor 0 - 9/7*y**3 - 2/7*y - 11/7*y**2.
-y*(y + 1)*(9*y + 2)/7
Let j be 12*(-12)/180*(2 - (-18)/(-8)). Let 0 - j*h**2 + h = 0. Calculate h.
0, 5
Let u(z) be the third derivative of z**8/336 - z**7/84 - z**6/72 + z**5/12 + 8*z**3/3 + 6*z**2. Let q(p) be the first derivative of u(p). Factor q(r).
5*r*(r - 2)*(r - 1)*(r + 1)
Let c(h) be the first derivative of h**4/4 - 40*h**3/3 - 83*h**2/2 - 42*h - 167. Find u, given that c(u) = 0.
-1, 42
Let f be 320/675 - 4/54. Let p(t) be the first derivative of 2/3*t**3 - f*t**5 - 1/5*t**6 - 2/5*t**2 + 0*t - 12 + 1/2*t**4. Find q, given that p(q) = 0.
-2, -1, 0, 1/3, 1
Suppose 7*f - 5*f = -6. Let a be -1 - (3 + f) - -7. Solve 0*q + a*q + 0*q**2 - 3 - 3*q**2 = 0.
1
Let w(z) be the third derivative of 0*z + 3*z**2 + 1/315*z**7 - 7/36*z**4 + 0 + 1/10*z**5 - 1/36*z**6 + 2/9*z**3. Factor w(l).
2*(l - 2)*(l - 1)**3/3
Let u(b) be the third derivative of -1/36*b**4 + 4/45*b**6 + 8/45*b**5 - 1/9*b**3 + 0 + 2*b**2 + 0*b. Suppose u(c) = 0. What is c?
-1, -1/4, 1/4
Let x be (-17)/(-85)*(7 - 5). Determine j, given that 2/15*j**5 + x*j**2 + 0*j + 14/15*j**3 + 0 + 2/3*j**4 = 0.
-3, -1, 0
Let m(p) = p**2 - 21*p. Suppose 3*h - 15 - 18 = 0. Let s(u) = -4*u. Let x(k) = h*s(k) - 2*m(k). Factor x(z).
-2*z*(z + 1)
Let g = -1306 - -2615/2. Factor -g*h**2 + 3/2 + 3/4*h**3 - 3/4*h.
3*(h - 2)*(h - 1)*(h + 1)/4
Let y(b) be the first derivative of -128/15*b**3 + 1/5*b**4 - 19 + 88/5*b**2 + 12/25*b**5 - 64/5*b. Solve y(m) = 0.
-4, 2/3, 1, 2
Let l(k) be the third derivative of k**7/105 + 3*k**6/20 + k**5/3 - 3*k**4 - 56*k**3/3 - 40*k**2 + k. Factor l(n).
2*(n - 2)*(n + 2)**2*(n + 7)
Let j = 36 - 33. Factor -j*y**4 + 50*y - 38*y + 7 - 18*y**2 + 17 - 15*y**3.
-3*(y - 1)*(y + 2)**3
Suppose 1132 = -20*a + 1192. Factor 1/3*r - 1/3*r**a + 0*r**2 + 0.
-r*(r - 1)*(r + 1)/3
Determine j, given that -196/5*j + 0 - 2*j**4 + 136/5*j**3 - 434/5*j**2 = 0.
-2/5, 0, 7
Let u(s) be the second derivative of -10985*s**7/112 + 11323*s**6/40 - 39*s**5/20 - 173*s**4/2 + 35*s**3 - 6*s**2 + 381*s. What is t in u(t) = 0?
-2/5, 2/13, 2
Solve -15/4 + 3/4*f**2 - 3*f = 0 for f.
-1, 5
Let b = 51 + -42. Factor -b - n**4 + 6*n + 3*n**4 - 6*n**3 - 5*n**4 + 12*n**2.
-3*(n - 1)**2*(n + 1)*(n + 3)
Let k be 2 + -2 + (-20)/(-4). Let 15*q**3 - 45*q**4 + 180 - 6*q**5 + 2*q**k + 365*q**2 + 480*q + 9*q**5 = 0. What is q?
-1, 6
Let i(w) be the third derivative of 2/15*w**3 + 0 + 1/150*w**5 + 8*w**2 + 1/20*w**4 + 0*w. What is u in i(u) = 0?
-2, -1
Let q = -133 - -667/5. Let r be 9 + 121/(-11) - (-36)/15. Find p, given that r - q*p**2 + 0*p = 0.
-1, 1
Factor -1/2*k**3 - 1/4*k - 5/8*k**2 + 0 - 1/8*k**4.
-k*(k + 1)**2*(k + 2)/8
Let h(o) be the first derivative of -o**6/90 - o**5/6 - 11*o**4/12 - 20*o**3/9 - 8*o**2/3 - 15*o + 16. Let y(r) be the first derivative of h(r). Factor y(m).
-(m + 1)**2*(m + 4)**2/3
Let a(t) be the second derivative of 2*t**7/63 - 8*t**6/45 - 19*t**5/15 - 14*t**4/9 - 82*t - 2. Find r such that a(r) = 0.
-2, -1, 0, 7
Let d(l) = -4*l**3 - 2*l**2. Let y = 1 + 0. Suppose 48 = 21*k - 15. Let h(i) = i**4 + i**2. Let n(q) = k*h(q) + y*d(q). Factor n(s).
s**2*(s - 1)*(3*s - 1)
Let w(t) be the second derivative of 2*t**4/3 - 71*t**3 + 53*t**2 + 13*t - 2. Factor w(n).
2*(n - 53)*(4*n - 1)
Let i be (-4)/1 + 41/((-410)/(-60)). Let o(a) be the second derivative of 1/50*a**5 + 0*a**i + 1/30*a**4 + 0*a**3 - 5*a + 0. Factor o(t).
2*t**2*(t + 1)/5
Let l(u) = -u**2 + 9*u + 74. Let t be l(14). Let g(r) = 3*r**3 - 12*r**2 + r - 4. Let d be g(t). Suppose 1/2*o**2 - o + d = 0. What is o?
0, 2
Factor -44/7*j + 242/7 + 2/7*j**2.
2*(j - 11)**2/7
Let w(j) be the third derivative of j**6/240 - 7*j**5/120 - 7*j**4/6 - 4*j**3 - 63*j**2 - 2*j. Factor w(n).
(n - 12)*(n + 1)*(n + 4)/2
Let o(k) be the first derivative of 2*k**6/9 + 44*k**5/15 + 15*k**4 + 36*k**3 + 36*k**2 - 54. Factor o(n).
4*n*(n + 2)*(n + 3)**3/3
Let z(f) be the second derivative of f**7/2520 - 7*f**6/360 + 49*f**5/120 + 4*f**4/3 - 19*f. Let k(y) be the third derivative of z(y). Factor k(u).
(u - 7)**2
Determine p so that 4/5*p**2 - 38/5 - 74/5*p = 0.
-1/2, 19
Factor 2/15*y**3 + 18/5*y - 12/5 - 4/3*y**2.
2*(y - 6)*(y - 3)*(y - 1)/15
Let o(r) be the second derivative of -r**5/150 + r**4/6 - 3*r**3/5 + 13*r**2/15 - 5*r - 3. Factor o(m).
-2*(m - 13)*(m - 1)**2/15
Suppose 4*p - 15 = -p. Suppose p*j = -j + 8. Find i, given that i**j - 13 + i + 11 + 0*i**2 = 0.
-2, 1
Let w be (-2 - (-1)/1)/((-170)/48586). Let t = -284 + w. Determine f so that -t - 6/5*f - 1/5*f**2 = 0.
-3
Suppose -8*m + 11*m = -24. Let j be 13 + -3 + m + 6. What is i in -2*i**3 - 4*i**2 - j*i + 20*i**2 + i**4 - 8*i**3 + i**4 = 0?
0, 1, 2
Factor 0 - 40/3*a + 1/3*a**4 - 4/3*a**2 + 10/3*a**3.
a*(a - 2)*(a + 2)*(a + 10)/3
Let c(s) be the first derivative of s**3/2 - 87*s**2/4 - 45*s - 130. Factor c(j).
3*(j - 30)*(j + 1)/2
Let q(t) = -t**3 + 4*t**2 - 4*t + 1. Let i be q(3). Let h be i/5 - ((-104)/20)/13. Solve 1/2*r**2 + r + h = 0 for r.
-2, 0
Factor 4*s + 1/2*s**2 - 6 - 1/2*s**3.
-(s - 2)**2*(s + 3)/2
Suppose -u + 1 = -0. Let x be u/(-4)*2*-6. Suppose -5*s**x - 3*s - 8*s**2 - 3*s + 2*s + s**4 - 2*s**4 = 0. Calculate s.
-2, -1, 0
Let k(p) be the second derivative of 21/20*p**5 + 15/4*p**4 + 6*p**2 + 11*p + 0 + 1/10*p**6 + 13/2*p**3. Factor k(z).
3*(z + 1)**3*(z + 4)
Let n = 4210005937/3912736594 - -213/6903205. Let l = 1/1090 + n. Solve 4/13 + l*p - 14/13*p**3 - 4/13*p**2 = 0 for p.
-1, -2/7, 1
Let r(q) be the first derivative of -9*q**5/5 + 39*q**4/4 + 10*q**3 - 48. Factor r(t).
-3*t**2*(t - 5)*(3*t + 2)
Suppose 2*r = 10, 47*f + r + 5 = 52*f. Factor -2/15*j**f - 4/15*j - 2/15.
-2*(j + 1)**2/15
Suppose -8*n + 2 = -2*u + 10, -4 = 4*n. Factor 0 + u*x + 2/5*x**2.
2*x**2/5
Let q(y) be the third derivative of -y**5/40 + y**4/16 + 3*y**3 - 101*y**2. Factor q(n).
-3*(n - 4)*(n + 3)/2
Let p = -22955/3 + 7652. Factor -2 - 5/3*a - p*a**2.
-(a + 2)*(a + 3)/3
Suppose 14/9*c**2 + 208/9*c**4 + 0 + 32/9*c**5 + 0*c - 110/9*c**3 = 0. Calculate c.
-7, 0, 1/4
Let b be 897/245 - 3 - 12/20. Let c = 58/147 - b. Determine m, given that 0 - c*m**4 + 0*m + 0*m**3 + 1/3*m**2 = 0.
-1, 0, 1
Factor -8/3*f**2 + 8*f**3 + 0 + 2/9*f.
2*f*(6*f - 1)**2/9
Suppose p - c = -2, -4*c + 28 = 12. Suppose -5*g + 14 = p*y, -3*y + g - 5*g = -14. Let -1/4*n + 0 + 1/4*n**y = 0. What is n?
0, 1
Suppose 0 = -w - 6 + 12. Factor 2*g**2 + w*g**3 + 8*g**3 - 16*g**3 + 4*g.
-2*g*(g - 2)*(g + 1)
Factor 12/5*a + 0 + 3/5*a**4 - 12/5*a**3 - 3/5*a**2.
3*a*(a - 4)*(a - 1)*(a + 1)/5
Let d(l) be the third derivative of -l**6/780 - 7*l**5/390 + l**4/