e the first derivative of l**9/3528 - l**8/1176 + l**7/1470 + 9*l**3 - 37. Let o(f) be the third derivative of t(f). Factor o(x).
2*x**3*(x - 1)*(3*x - 2)/7
Let v(h) = h**2 + 6*h - 4. Let i be v(17). Factor -12*d**4 + 2*d**5 - 24*d**2 + 8*d + 26*d**3 - 387 + i.
2*d*(d - 2)**2*(d - 1)**2
Let p(z) be the second derivative of -z**3/6 + 3*z**2/2 + 2*z. Let g be p(-5). Factor -4*r + 0*r**5 - 8*r**4 + 4*r**5 + 16*r**2 - g*r**2.
4*r*(r - 1)**3*(r + 1)
Let y(t) be the third derivative of -t**7/525 + 19*t**6/300 + 2*t**5/15 + 192*t**2. Factor y(g).
-2*g**2*(g - 20)*(g + 1)/5
Suppose -5*z = 4*w - 157, -3*w + 14 = z - 13. Let u(g) = 5*g**2 + 34*g + 110. Let a(o) = -81*o**2 - 543*o - 1761. Let n(l) = z*u(l) + 2*a(l). Factor n(x).
3*(x + 6)**2
Let b(x) = x**3 - x**2. Let r(d) = -16*d**3 - 104*d**2 + 324*d - 84. Let w(l) = -5*b(l) + r(l). Factor w(i).
-3*(i - 2)*(i + 7)*(7*i - 2)
Factor -5*m + 13/3*m**2 + 2/3.
(m - 1)*(13*m - 2)/3
Let f(q) be the first derivative of 18*q**5/5 + 2*q**4 - 38*q**3/3 - 14*q**2 - 455. Determine y, given that f(y) = 0.
-1, 0, 14/9
Let t(l) be the first derivative of 0*l**2 - 3/14*l**4 + 0*l - 2/35*l**5 - 4/21*l**3 - 5. Factor t(a).
-2*a**2*(a + 1)*(a + 2)/7
Let x(h) = 15*h - 3. Let y be x(1). Factor 26*o**3 + 32 - 16*o**3 + y*o**4 - 24*o**2 + 18*o**3 - 48*o.
4*(o - 1)*(o + 2)**2*(3*o - 2)
Let s(d) be the first derivative of -2*d**3/33 - 5*d**2/11 + 12*d/11 + 21. Factor s(y).
-2*(y - 1)*(y + 6)/11
Let b(m) be the third derivative of -7/39*m**4 + 0 - 4/13*m**3 + 3*m**2 - 1/260*m**6 + 0*m - 17/390*m**5. Let b(h) = 0. Calculate h.
-3, -2, -2/3
Let q(t) be the first derivative of -1/5*t - 1/5*t**4 - 1/2*t**2 - 8/15*t**3 + 2. Find a such that q(a) = 0.
-1, -1/2
Let w = -956 + 956. Factor 0 - 2/3*c**3 - 2/3*c**2 + w*c.
-2*c**2*(c + 1)/3
Factor 21/2*z**3 - 6*z**4 + 0 + 0*z - 9/2*z**2.
-3*z**2*(z - 1)*(4*z - 3)/2
Let q(a) = -4*a + 12. Let o be q(2). Factor -7 + 23 + o*b**2 - 4*b**3 - 16*b**2.
-4*(b - 1)*(b + 2)**2
Let k(v) = 2735*v - 13673. Let o be k(5). What is q in 0*q**o + 2/3*q**4 + 0 + 0*q - 2/3*q**3 = 0?
0, 1
Determine g, given that 1/3*g**3 - 22/3*g**2 + 121/3*g + 0 = 0.
0, 11
Let b(j) = j**3 - j. Let y(s) = s**4 - 110*s**3 + 4374*s**2 - 78730*s + 531441. Let m(q) = -2*b(q) - y(q). Suppose m(x) = 0. What is x?
27
Let c(m) = 8*m**2 + 11*m - 30. Let r(u) = -6*u**2 - 12*u + 32. Let v(w) = 4*c(w) + 6*r(w). Factor v(d).
-4*(d - 2)*(d + 9)
Let z(w) = -4*w**4 - 20*w**3 + 4*w**2 - 20. Let o(m) = m**3 + 1. Let g(u) = -20*o(u) - z(u). Determine k so that g(k) = 0.
-1, 0, 1
Let q(v) = v**3 - 52*v**2 - 52*v - 48. Let y be q(53). Let s(u) be the second derivative of 0 + 5/6*u**3 + 1/3*u**4 + 1/20*u**y + u**2 - 7*u. Factor s(k).
(k + 1)**2*(k + 2)
Let c(k) be the first derivative of k**4/24 - k**3 + 9*k**2 - 36*k - 24. Solve c(o) = 0.
6
Let j(l) = l**2 + 3*l - 28. Let i be j(4). Let d(s) be the third derivative of i - 1/100*s**5 + 0*s - 1/20*s**4 + s**2 - 1/10*s**3. Factor d(h).
-3*(h + 1)**2/5
Let t(a) be the third derivative of -a**5/4 - 5*a**4/3 - 10*a**3/3 + a**2 + 101. Factor t(n).
-5*(n + 2)*(3*n + 2)
Let t be -4 - (-14 + 5) - -4. Let c be (t + (-20)/4)/10. Determine u, given that -4/5 - c*u**4 + 2/5*u + 6/5*u**2 - 2/5*u**3 = 0.
-2, -1, 1
Suppose 42*p**3 + 4*p**4 + 4 + 337/4*p**2 + 69/2*p = 0. What is p?
-8, -2, -1/4
Let k(l) be the second derivative of 16*l**4/15 - 127*l**3/30 - l**2/5 + 106*l. Factor k(i).
(i - 2)*(64*i + 1)/5
Let o(b) be the third derivative of -b**6/24 - 17*b**5/60 - b**4/4 + 103*b**2. Determine z so that o(z) = 0.
-3, -2/5, 0
Suppose 10*i - 30 + 10 = 0. Suppose -5*z = 5*v - 10 - 20, i*z = 3*v - 3. Solve 10/7*b - 4/7 - 6/7*b**4 - 10/7*b**v + 10/7*b**2 = 0 for b.
-2, -1, 1/3, 1
Let g(k) be the first derivative of 10*k**6/3 + 41*k**5 + 15*k**4/2 - 205*k**3/3 - 25*k**2 - 67. Determine c, given that g(c) = 0.
-10, -1, -1/4, 0, 1
Suppose -16*k = -15*k + 64. Let n = 66 + k. Factor 0*o - 1/3*o**3 + 0 + 1/3*o**4 - 2/3*o**n.
o**2*(o - 2)*(o + 1)/3
Let f be (2/(-5))/((-2)/10). Let g be (4/2 - 3)/(6/(-30)). Factor -f*c**2 + 3*c**4 - c**4 - 2*c**5 + c**g + c.
-c*(c - 1)**3*(c + 1)
Suppose m = 9*b - 4*b - 19, -11 = -b + m. Factor -8/3 + 4/9*d**b + 4/9*d.
4*(d - 2)*(d + 3)/9
Let m(g) be the first derivative of 1 + 1/15*g**5 + 5/2*g**2 + 2/3*g**3 + 1/3*g**4 + 0*g. Let a(y) be the second derivative of m(y). Factor a(p).
4*(p + 1)**2
Let m(n) = -n**3 + 9*n**2 + n - 6. Let z be m(9). Let x(l) = -l**3 + 4*l**2 - 3*l. Let q be x(2). Factor 13*v + 4*v**2 + z*v**q - 7*v - 4*v**2.
3*v*(v + 2)
Let o(f) be the first derivative of 2*f**3/3 - 55*f**2 - 112*f + 3. Suppose o(z) = 0. Calculate z.
-1, 56
Let c(f) be the first derivative of 2*f**5/5 + 5*f**4/2 + 4*f**3 + 145. Let c(a) = 0. Calculate a.
-3, -2, 0
Suppose 506 = -6*j - 112. Let k = 722/7 + j. Factor k*x**2 - 3/7*x + 3/7*x**3 - 1/7.
(x - 1)*(x + 1)*(3*x + 1)/7
Factor 89*v + 5*v**2 - 300*v + 269*v + 71*v + 106*v.
5*v*(v + 47)
Let t(d) be the first derivative of -d**4/4 + 38*d**3/3 - 361*d**2/2 - 105. Find p, given that t(p) = 0.
0, 19
Let c(w) be the third derivative of w**2 + 1/30*w**4 + 0*w - 1/300*w**5 + 0 - 1/10*w**3. Factor c(v).
-(v - 3)*(v - 1)/5
Let z(a) be the second derivative of -a**7/42 - a**6/6 + 23*a**5/80 + 5*a**4/2 - 6*a**3 + 76*a. Find b such that z(b) = 0.
-4, 0, 3/2
Suppose -138 = -7*r + r. Solve 16*m**3 + 7*m**2 + 52*m - r - 71*m**2 + 11 = 0.
1/2, 3
Let a be (-54)/(-18) + 1/1. Let p(o) = -o**3 - 1. Let b(x) = -24*x**3 + 48*x**2 + 16*x + 4. Let t(z) = a*p(z) + b(z). Factor t(h).
-4*h*(h - 2)*(7*h + 2)
Let a(b) be the second derivative of b**4/20 - 3*b**3 - 93*b**2/10 + b - 115. Suppose a(q) = 0. Calculate q.
-1, 31
Let w(t) be the third derivative of 2/195*t**6 - 1/30*t**5 + 0*t**3 - 1/1365*t**7 + 0*t + 0 + 13*t**2 + 1/26*t**4. Suppose w(k) = 0. What is k?
0, 1, 6
Let s(u) be the first derivative of -5*u + 28 - 5*u**2 - 5/3*u**3. Factor s(i).
-5*(i + 1)**2
Determine t, given that 1 + 15/4*t**2 + 13/4*t + 1/4*t**4 + 7/4*t**3 = 0.
-4, -1
Let 0 + 3/5*k - 3/5*k**3 + 0*k**2 = 0. What is k?
-1, 0, 1
Let t(h) = -h**3 + h**2 - h. Let r(q) = 2*q**3 - 2*q**2 + 4*q. Let m be ((3*2)/2)/(7 - 4). Let i(c) = m*r(c) + 4*t(c). Find z, given that i(z) = 0.
0, 1
Factor -10*j - 2*j - 2187*j**4 + 4*j**2 + 8 + 2186*j**4 - 2*j**2 + 3*j**3.
-(j - 2)**2*(j - 1)*(j + 2)
Let f be 6/4*80/15. Let u be (-10 + f)*(0 + -1). Let z(i) = -2*i**3 - i**2 + i - 3. Let l(n) = 2*n**3 + 2*n**2 + 2. Let h(a) = u*z(a) + 3*l(a). Factor h(y).
2*y*(y + 1)**2
Let h(k) be the second derivative of k**5/10 + 9*k**4/2 + 56*k**3 - 196*k**2 - 4*k. Solve h(s) = 0.
-14, 1
Let r(p) be the second derivative of -p**6/135 - p**5/90 + p**4/54 + p**3/27 - 281*p. Suppose r(y) = 0. What is y?
-1, 0, 1
Let i be 184/115 - 4/(-10). Suppose 3*z = -0*z - i*o + 4, z + 4*o + 2 = 0. Suppose -9/2*t**z - 6*t + 6 - 3/2*t**4 + 6*t**3 = 0. What is t?
-1, 1, 2
Let x(a) = a**2 + 4*a + 2. Suppose 0 = -2*f + f - 4. Let v be x(f). Solve 10*l + 4*l**2 + 0*l**2 + v*l**2 + 4 = 0 for l.
-1, -2/3
Let d be (17/51)/((-5)/(-3)). Let p(k) be the first derivative of 1/15*k**6 + 4/25*k**5 - d*k**2 - 4/15*k**3 + 0*k**4 - 5 + 0*k. Factor p(l).
2*l*(l - 1)*(l + 1)**3/5
Let u(x) = -13 + x**3 + 202*x**2 + 7*x**4 - 18*x**4 - 179*x**2. Let s(b) = 5*b**4 - 11*b**2 + 6. Let z(c) = -13*s(c) - 6*u(c). Find h such that z(h) = 0.
0, 1, 5
Let x be ((-32)/10)/(40/(-300)). What is z in -x*z**3 - 5*z**4 + 3*z**5 + 3*z**4 + 3*z**5 + 4*z**4 - 8*z**2 = 0?
-2, -1/3, 0, 2
Let l = -7932 + 71410/9. Factor l*a**4 + 0 - 2*a**3 + 2/9*a**2 - 8/9*a**5 + 2/9*a.
-2*a*(a - 1)**3*(4*a + 1)/9
Let r(j) be the first derivative of j**6/9 - 23*j**5/45 - 7*j**4/18 + 43*j**3/27 - 2*j**2/3 + 691. Solve r(o) = 0 for o.
-3/2, 0, 1/3, 1, 4
Determine a, given that 1737*a**5 + 33*a**4 + 6 - 6 - 54*a**3 - 324*a**2 + 648*a - 1740*a**5 = 0.
-3, 0, 2, 6
Let f(n) = -20*n**4 + 44*n**2 - 17*n - 17. Let c(m) = -7*m**4 + 15*m**2 - 6*m - 6. Let k(a) = 17*c(a) - 6*f(a). Factor k(u).
u**2*(u - 3)*(u + 3)
Let l(h) be the third derivative of 121/60*h**6 - 8/3*h**3 + 6*h**2 + 0 - 143/15*h**5 + 0*h + 23/3*h**4. What is r in l(r) = 0?
2/11, 2
Let i be (-18)/(-63) - 38/(-14). Factor 4*z**3 + 4 + i*z - 19*z - 6*z**2 - 2 - 8.
2*(z - 3)*(z + 1)*(2*z + 1)
Let b = -12619/240 - -263/5. Let y(c) be the third derivative of 4