 such that a(q) = 0.
-1, 0
Let d(x) be the second derivative of x**9/2160 - 11*x**8/2100 + x**7/56 - x**6/100 + 7*x**3/3 + 8*x. Let o(w) be the second derivative of d(w). Factor o(b).
b**2*(b - 3)**2*(7*b - 2)/5
Let z(j) be the first derivative of 54/5*j + 2/25*j**5 + 24/5*j**3 - 54/5*j**2 - j**4 + 21. Factor z(u).
2*(u - 3)**3*(u - 1)/5
Let a(p) be the first derivative of 5/14*p**4 + 0*p - 2/5*p**5 + 15 + 4/21*p**3 + 0*p**2. Factor a(x).
-2*x**2*(x - 1)*(7*x + 2)/7
Let u be 69/3 - 4/(-4). Suppose -7*j + u = -3*j. Factor 1 + k**4 - 4 - 6*k + j*k**3 + 3*k**4 - k**4.
3*(k - 1)*(k + 1)**3
Let q(z) be the second derivative of -1/66*z**4 + 0 - 50*z + 4/11*z**2 + 4/33*z**3 - 1/110*z**5. Suppose q(n) = 0. What is n?
-2, -1, 2
Let o = -11 + 16. Solve -368*g + o*g**3 + 10*g**4 + 368*g = 0 for g.
-1/2, 0
Let j(s) be the second derivative of s**7/147 - 4*s**5/35 + s**4/7 + s**3/3 - 6*s**2/7 - 23*s. Suppose j(r) = 0. What is r?
-3, -1, 1, 2
Suppose 2*i = 3*i - 2*a - 33, -2*a - 2 = 0. Suppose 43 = 3*t - 5*h, -4*t = 3*h - i - 7. Factor -t*b + 3*b**3 - 3 + 8*b + 3.
3*b*(b - 1)*(b + 1)
Let j(t) be the first derivative of 5*t**5/9 - 23*t**4/36 - 52*t**3/27 - 2*t**2/9 - 523. Suppose j(y) = 0. What is y?
-1, -2/25, 0, 2
Let m(o) be the first derivative of o**9/12096 - o**7/1120 + o**6/720 + 17*o**3/3 + 11. Let l(z) be the third derivative of m(z). Factor l(u).
u**2*(u - 1)**2*(u + 2)/4
Factor 2*s - 4*s + 10*s - 4*s**2 - 12*s + 4*s**3 + 4.
4*(s - 1)**2*(s + 1)
Let z(j) be the first derivative of 2*j**3/3 - 13*j**2 + 60*j + 213. Solve z(w) = 0 for w.
3, 10
Let k(z) = z**2 - 11*z - 24. Suppose 10*x = 12 - 32. Let i be k(x). Let 1 + 1/4*r**i - 5/4*r = 0. Calculate r.
1, 4
Let b(j) be the first derivative of -56/3*j**3 + 32*j + 8*j**2 + 20 - 12/5*j**5 - 13*j**4. Determine a so that b(a) = 0.
-2, -1, 2/3
Suppose 0 = -2*g - 2*g + 20. Let m be g + (2/1 - 3). Let -8*v**2 + 1 + m*v**2 + 3*v**2 = 0. Calculate v.
-1, 1
Let l = -18/569 + -9612/19915. Let t = -8/21 - l. Factor 0*m + 2/15*m**5 + 2/15*m**2 - 2/15*m**3 + 0 - t*m**4.
2*m**2*(m - 1)**2*(m + 1)/15
Factor -2/11*v + 0 + 2/11*v**3 - 2/11*v**4 + 2/11*v**2.
-2*v*(v - 1)**2*(v + 1)/11
Suppose -3*g + 15 = -3*u, 4*g + 4*u + 0 = 4. Determine i, given that 4*i**2 - 3*i**2 - 3*i**g + 0*i**2 + 2*i**2 = 0.
0, 1
Suppose -19*s = -21*s + 16. Factor 0 - 12*l**2 + 12*l + 5 - 4*l**3 - s*l + 7.
-4*(l - 1)*(l + 1)*(l + 3)
Find r, given that r**2 - 10733 + 36*r**3 + 10736 + 42*r + 74*r**2 = 0.
-1, -1/12
Let i(c) be the third derivative of -c**5/42 - c**4/28 + 2*c**3/21 - 40*c**2. Factor i(b).
-2*(b + 1)*(5*b - 2)/7
Let s(h) = h**5 - 2*h**4 + 11*h**2 + 2*h. Let a(g) = 4*g**5 - 8*g**4 - g**3 + 43*g**2 + 6*g. Let t(y) = 6*a(y) - 22*s(y). Factor t(p).
2*p*(p - 2)*(p - 1)**2*(p + 2)
Let n be (1428/8)/(-17)*1/(-14). Let i(d) be the first derivative of -n*d**2 + 0*d + 3/4*d**4 - 1/4*d**3 + 9/20*d**5 - 1. Factor i(k).
3*k*(k + 1)**2*(3*k - 2)/4
Let s be -1 - (-4 + 5 + 30/(-6)). Let b = 15 + -59/4. Factor 1/4 - 1/4*v + 1/4*v**s - b*v**2.
(v - 1)**2*(v + 1)/4
Let p(d) = 9*d**2 - 154*d + 405. Let z(v) = 6*v**2 - 103*v + 270. Let t(k) = 5*p(k) - 8*z(k). Determine q so that t(q) = 0.
3, 15
Suppose 0 = -20*b + 16*b - 68. Let q(x) = 84*x**2 + 45*x. Let k(h) = 142*h + 17*h - 24*h + 252*h**2 + 1. Let i(r) = b*q(r) + 6*k(r). Solve i(o) = 0.
-2/7, -1/4
Let d(o) be the third derivative of 2*o**7/315 + 2*o**6/45 + 4*o**5/45 + 22*o**2 + 4. Factor d(m).
4*m**2*(m + 2)**2/3
Let o(c) be the first derivative of 2*c**3/3 - 5*c**2 - 12*c + 153. Factor o(f).
2*(f - 6)*(f + 1)
Let b(y) be the third derivative of y**6/60 - y**5/30 - y**4/3 + 4*y**3/3 - y**2 - 15. Determine u so that b(u) = 0.
-2, 1, 2
Factor -237*t**3 + 121*t**3 + 114*t**3.
-2*t**3
Let s(h) = -5*h**2 - 20*h - 5. Let v(n) = -n. Let o(m) = -s(m) + 10*v(m). Factor o(r).
5*(r + 1)**2
Suppose 4*l - 5 + 17 = 0. Let t(m) be the first derivative of 9*m**4/4 - 9*m**2/2 + 69. Let o(u) = -u**4 - u**3 + u + 1. Let a(j) = l*o(j) - t(j). Factor a(h).
3*(h - 1)**3*(h + 1)
Let q(g) = 5*g - 34. Let k be q(7). Let y be 5/15*(k - -3). Determine w, given that 2/3*w**3 + 0*w**2 - 2*w + y = 0.
-2, 1
Let d(y) be the second derivative of 0*y**2 + 1/4*y**5 + 0*y**3 + 0 - 1/24*y**6 - 5/12*y**4 + 3*y. Suppose d(w) = 0. What is w?
0, 2
Suppose 9*k - 22*k = -9*k. Let a(i) be the third derivative of -1/30*i**3 - 1/150*i**5 + k + i**2 + 0*i + 1/40*i**4. Determine q, given that a(q) = 0.
1/2, 1
Let i(b) = 2*b**3 + 6*b**2 + 2*b - 2. Let m(k) = k**4 + 7*k**3 + 20*k**2 + 7*k - 7. Let q(u) = 7*i(u) - 2*m(u). Find l, given that q(l) = 0.
-1, 0, 1
Let f(m) = -5*m**2 + 8*m - 15. Let w(k) = 11*k**2 - 17*k + 33. Let l(n) = -9*f(n) - 4*w(n). Find x such that l(x) = 0.
1, 3
Determine s so that 9/4*s**5 + 39/4*s**4 + 57/4*s - 1/2*s**3 - 9/4 - 47/2*s**2 = 0.
-3, 1/3, 1
Factor 13/5*n**4 + 1/5*n**5 + 48/5*n**3 - 32/5*n**2 - 512/5*n - 768/5.
(n - 3)*(n + 4)**4/5
Let w be (-11)/(-2)*(0 - (-4 - 0)). Solve -60*k - w*k**3 + 54*k**2 + 3*k**4 + k**3 + 5 + 23 - 4 = 0.
1, 2
Let s be 8 + -12 + (9 - 1). Let t(c) be the third derivative of 1/15*c**5 - 1/3*c**3 + 0 + 0*c**6 - s*c**2 - 1/105*c**7 + 0*c**4 + 0*c. Factor t(p).
-2*(p - 1)**2*(p + 1)**2
Let m(q) = -1. Let c(y) = y**3 - 11*y**2 + 35*y - 27. Let w be 5/20 + 2*(-6)/(-16). Let l(b) = w*c(b) - 2*m(b). Suppose l(s) = 0. What is s?
1, 5
Let l(r) = 49*r**4 - 324*r**3 + 172*r**2 - 24*r. Let q(h) = -147*h**4 + 973*h**3 - 516*h**2 + 72*h. Let p(f) = 14*l(f) + 4*q(f). Factor p(j).
2*j*(j - 6)*(7*j - 2)**2
Let p(g) be the second derivative of 13*g**6/210 + 3*g**5/28 - 2*g**4/7 - 2*g**3/21 + 63*g. Factor p(x).
x*(x - 1)*(x + 2)*(13*x + 2)/7
Let i(b) be the second derivative of b**4/18 - 58*b**3/9 - 59*b**2/3 + 219*b. Factor i(o).
2*(o - 59)*(o + 1)/3
Suppose 35/9*d - 2/3 - 5/3*d**3 + d**4 - 47/9*d**2 = 0. What is d?
-2, 1/3, 3
Let m be 2 + 5/(20/(-7)). Let i be 18/24*8/6*0. Factor 0 + m*w**3 - 1/4*w**2 + i*w.
w**2*(w - 1)/4
Let l be 12/(2 - -1) - (-4 - -3). Factor -3*s**4 + 1201*s**2 - 1177*s**2 + l + 12*s**3 + 5*s**4 + 1 + 20*s.
2*(s + 1)**3*(s + 3)
Factor 7 + 35*y - 21*y + 5*y**2 + 3 - 29*y.
5*(y - 2)*(y - 1)
Let f(r) be the second derivative of 0 + 12/5*r**2 - 30*r - 1/50*r**5 + 7/30*r**4 - 16/15*r**3. Factor f(o).
-2*(o - 3)*(o - 2)**2/5
Let r(m) = -m**2 + 1780*m + 127896. Let y(q) = -q**2 + 892*q + 63948. Let i(u) = 4*r(u) - 7*y(u). Solve i(p) = 0.
-146
Suppose j - 114 + 18 = 0. Determine p so that 95*p**3 + p**2 - j*p**3 - 4*p**2 = 0.
-3, 0
Let q(t) be the first derivative of 2*t**5/45 - 11*t**4/18 + 16*t**3/27 + 20*t**2/9 - 361. Factor q(n).
2*n*(n - 10)*(n - 2)*(n + 1)/9
Let o(r) be the first derivative of 2*r**3/3 + 11*r**2/4 + 5*r/4 - 55. Factor o(s).
(2*s + 5)*(4*s + 1)/4
Let i(l) be the first derivative of -l**6/120 + 9*l**5/40 - l**4 + 15*l**3 - 17. Let x(a) be the third derivative of i(a). Factor x(v).
-3*(v - 8)*(v - 1)
Let d(x) be the first derivative of 11 + 1/15*x**5 + 0*x - 1/6*x**4 + 0*x**3 + 0*x**2. Let d(a) = 0. Calculate a.
0, 2
Solve 315*y + 534*y - 1104*y - 5*y**2 = 0 for y.
-51, 0
Factor -4 - 15*y**2 - 5*y**3 - 983*y - 1 + 968*y.
-5*(y + 1)**3
Let p = -32/87 - -2303/348. Factor -p*a**2 - 5 - 10*a - 5/4*a**3.
-5*(a + 1)*(a + 2)**2/4
Solve -2/15*o**2 - 2/3*o - 4/5 = 0.
-3, -2
Let g(i) be the first derivative of -2/33*i**3 - 1/330*i**5 - 1/44*i**4 - 5 + 0*i - 3*i**2. Let y(d) be the second derivative of g(d). Factor y(t).
-2*(t + 1)*(t + 2)/11
Let q(r) = r**2 + 10*r - 1. Let d be q(-10). Let x be (d/4)/(-2 + 115/60). Factor 1/5*p**4 + 1/5*p**x - 1/5*p**2 - 1/5*p + 0.
p*(p - 1)*(p + 1)**2/5
Suppose n - 4 = -1. Suppose 2*i - 3*b - 10 = 0, -b = n*i - 8*i + 12. Determine m, given that -2*m**4 + i*m**2 + 3*m**5 + 10*m**3 - 9*m**5 + 0*m**4 - 4*m = 0.
-1, 0, 2/3, 1
Suppose -3*l = -t - 0*t - 6, 9 = 2*t + l. Suppose -3*k + 6 + t = 0. Factor 2*j**k - 3*j**3 + 43*j - 39*j.
-j*(j - 2)*(j + 2)
Let n = 13545 - 67724/5. Factor 4/5*k**2 + 0 + n*k.
k*(4*k + 1)/5
Find c such that -8*c + 3*c**2 + 5*c**3 - c**2 - 18313*c**4 + 18314*c**4 = 0.
-4, -2, 0, 1
Let h(z) be the third derivative of 0*z + 0 + 1/6*z**4 + 1/30*z**5 - 3*z**2 + 1/3*z**3. Factor h(r).
2*(r + 1)**2
Suppose -14*c - 27 = -4*g - 11*c, c = 3*g - 14. Factor -18/7 - 39/7*s - g*s**3 + 78/7*s**2.
-3*(s - 3)*(s - 1)*(7*s + 2)/7
Let f be (-20)/(