3. Factor o(m).
-2*(m - 3)**2*(m - 2)*(m - 1)
Let b(r) be the third derivative of r**6/315 + r**5/70 + r**4/42 + r**3/63 - 6*r**2 + 1. Factor b(j).
2*(j + 1)**2*(4*j + 1)/21
Suppose 4*f = 4*k + 24, f = 3*f + 4*k + 6. Let b(l) be the second derivative of 0 - f*l - 1/2*l**2 + 1/12*l**4 + 0*l**3. Factor b(p).
(p - 1)*(p + 1)
Let k(u) be the first derivative of -4 + 2/3*u**3 - 1/2*u**2 + 0*u - 1/4*u**4. Determine v so that k(v) = 0.
0, 1
Let o be 1 + (3 - -1) + 0. Let a(l) = 3*l - 25. Let p be a(10). Factor o*f**3 - f**3 - 5*f**5 - 2*f**4 - f**p.
-2*f**3*(f + 1)*(3*f - 2)
Let h be (-52)/(-30) - 44/33. Suppose 0*x = 3*x - 9. Determine f so that -8/5*f - 12/5*f**2 - 2/5*f**4 - h - 8/5*f**x = 0.
-1
Solve 1/8*r**2 + 1/8*r**3 + 0 - 3/4*r = 0 for r.
-3, 0, 2
Suppose -5*u + 97 = 3*d, u + u - 3*d = 22. Let y = -15 + u. What is f in 6/5 + 3/5*f - 3/5*f**y = 0?
-1, 2
Let o(b) = -55*b + 13 + 20*b**2 - 12*b + 137*b**2. Let d(x) = 79*x**2 - 34*x + 7. Let z(u) = -7*d(u) + 4*o(u). What is y in z(y) = 0?
1/5
Let r be (-7 + 2)*(0 - 1). Let l(k) be the first derivative of 2/21*k**3 + 1/21*k**6 + 0*k - 2 - 2/35*k**r + 0*k**2 - 1/14*k**4. Factor l(n).
2*n**2*(n - 1)**2*(n + 1)/7
Factor -3*s**2 - 1 + 2 + 4*s**2 - 5.
(s - 2)*(s + 2)
Factor 5*r**2 + 10*r**5 - 5*r**5 + 20 - 5*r**4 + 7*r - 25*r**3 + 33*r.
5*(r - 2)**2*(r + 1)**3
Let f(k) be the second derivative of 1/180*k**6 + 0 + k + 1/6*k**3 + 0*k**4 - 1/30*k**5 + 0*k**2. Let h(n) be the second derivative of f(n). Factor h(j).
2*j*(j - 2)
Let d(n) be the second derivative of 0*n**3 + 1/16*n**4 + 0 + 1/40*n**5 + 2*n - 1/8*n**2. Find b, given that d(b) = 0.
-1, 1/2
Let v(y) = -y**2 - 7*y - 4. Let t be v(-6). Let z(s) be the third derivative of -2/9*s**3 + 0 + 2/15*s**5 - 7/180*s**6 + 0*s - 1/12*s**4 + t*s**2. Factor z(o).
-2*(o - 1)**2*(7*o + 2)/3
Suppose 9*u + 0*u = 27. Let w(x) be the first derivative of 1/10*x**5 + 0*x + 1/2*x**u - 3 + 1/4*x**2 + 3/8*x**4. Find j, given that w(j) = 0.
-1, 0
Let z(k) be the second derivative of -k**4/28 - k**3/7 + 10*k. Suppose z(o) = 0. What is o?
-2, 0
Let x(l) be the first derivative of -l**4/2 + 2*l**3 - 3*l**2 + 2*l - 9. Factor x(k).
-2*(k - 1)**3
Let -88*d**4 - 590*d**2 - 451 + 83*d**4 + 900*d + 46 + 100*d**3 = 0. Calculate d.
1, 9
Suppose -3/2*w - 3/8*w**2 + 9/2 = 0. Calculate w.
-6, 2
Let x(l) = -3*l**3 - 3. Let o(h) = 3*h**3 + h**2 + 4. Let r(m) = -3*o(m) - 4*x(m). Find p such that r(p) = 0.
0, 1
Let q(o) be the first derivative of o**7/1400 - o**6/1800 - o**5/200 + o**4/120 - 3*o**3 - 4. Let g(p) be the third derivative of q(p). Factor g(n).
(n - 1)*(n + 1)*(3*n - 1)/5
Let k = -5 + 8. Let q(c) be the first derivative of 0*c**2 - 1/6*c**6 - 2 + 3/4*c**4 - 2/3*c**k + 0*c**5 + 0*c. Let q(j) = 0. Calculate j.
-2, 0, 1
Let u(x) be the first derivative of -x**6/45 - x**5/6 - x**4/2 - 7*x**3/9 - 2*x**2/3 - 6*x - 2. Let n(w) be the first derivative of u(w). Solve n(m) = 0.
-2, -1
Let p be 40/22 + 2/11. What is q in -q - p + 2*q + 2*q**2 - q = 0?
-1, 1
Let t(y) = y - 2. Let m(u) = 3*u**2 - 22*u + 32. Let n(q) = -m(q) - 4*t(q). Determine g, given that n(g) = 0.
2, 4
Let a(n) = n**3 - 3*n**2 - 3*n - 1. Let s(b) = 6*b**3 - 15*b**2 - 15*b - 5. Let d be (-4)/(12/33) + 3. Let l = 3 - d. Let y(r) = l*a(r) - 2*s(r). Factor y(v).
-(v + 1)**3
Let r(c) be the first derivative of -c**7/84 + c**6/60 + 4*c - 5. Let d(f) be the first derivative of r(f). Determine v, given that d(v) = 0.
0, 1
Let x(t) be the second derivative of t**5/4 + 5*t**4/12 - 25*t**3/6 + 15*t**2/2 + 10*t. Suppose x(r) = 0. Calculate r.
-3, 1
Let q(l) = l + 15. Let j be q(-11). Suppose -v = j*v - 10. Solve 6*r**3 + 2*r**v + 0*r**2 - 3*r**4 + 5*r**4 + 2*r + 4*r**2 = 0 for r.
-1, 0
Let d(b) = 2*b**2 + b + 1. Let u be d(-1). Determine h so that h**4 - 2*h - h**u - h**3 - h**3 + 5*h - h = 0.
-1, 0, 1, 2
Determine c so that -17*c**5 + 4 + 30*c**5 - 4*c + 8*c**3 + 4*c**4 - 8*c**2 - 17*c**5 = 0.
-1, 1
Let s(p) be the third derivative of p**8/10080 - p**7/1890 + p**6/1080 + p**4/8 + 2*p**2. Let g(r) be the second derivative of s(r). Factor g(m).
2*m*(m - 1)**2/3
Let n(j) be the first derivative of j**5/20 - j**4/12 + 3*j - 4. Let y(r) be the first derivative of n(r). Let y(g) = 0. Calculate g.
0, 1
Factor 3*k**3 - k**3 - 239*k**2 + 237*k**2.
2*k**2*(k - 1)
Suppose 4*u + a - 20 = 0, 0 = 2*u + 2*a - 1 - 3. Solve 0*t**4 + 2*t**3 + t**3 - 3*t**5 + 6*t**4 - u*t**2 = 0 for t.
-1, 0, 1, 2
Let l = 570 - 45599/80. Let z(w) be the second derivative of 0*w**3 + 0*w**4 + l*w**5 - 3*w + 0*w**2 + 0. Find s such that z(s) = 0.
0
Let v(q) be the first derivative of -q**4/18 - 8*q**3/27 - q**2/9 + 4*q/3 + 48. Let v(s) = 0. Calculate s.
-3, -2, 1
Let m = 8 + -8. Factor -3 + 3*h**2 + 2*h - 2*h**3 - h**2 + 1 + m.
-2*(h - 1)**2*(h + 1)
Let j = -148 - -89. Let l = j - -239/4. What is z in 0 + 0*z - 3/4*z**4 + l*z**2 + 3/4*z**3 - 3/4*z**5 = 0?
-1, 0, 1
Let q be (-22)/(-33) - (-4 - (-3 + 1)). Factor q*c - 4/3*c**4 + 8/3*c**2 + 0 - 2*c**3 + 2/3*c**5.
2*c*(c - 2)**2*(c + 1)**2/3
Let a(c) be the third derivative of 0*c - 1/60*c**4 + 0 + 1/50*c**5 - 1/150*c**6 + 0*c**3 - 2*c**2. Factor a(s).
-2*s*(s - 1)*(2*s - 1)/5
Let r(m) = -13*m**5 + 73*m**4 - 85*m**3 + 19*m**2 + 5. Let p(g) = g**5 - g**4 - g**3 - g**2 + 1. Let l(k) = 5*p(k) - r(k). Factor l(v).
2*v**2*(v - 3)*(3*v - 2)**2
Suppose 4/13*c**4 + 2/13*c**2 + 0 + 0*c - 6/13*c**3 = 0. Calculate c.
0, 1/2, 1
Let i(j) = 36*j - 286. Let l be i(8). Let 0*o**l + 9/5*o - 3/5*o**3 + 6/5 = 0. Calculate o.
-1, 2
Suppose 0 = -3*i - 6*i + 18. Let r(d) be the second derivative of 2/7*d**i + 4*d + 1/42*d**4 - 1/7*d**3 + 0. Factor r(a).
2*(a - 2)*(a - 1)/7
Let q be (-70)/(-90) + 4/18. Let r(c) be the first derivative of -1/6*c**3 - q + 1/4*c + 1/8*c**2. Suppose r(m) = 0. What is m?
-1/2, 1
Let t be 32/12 - 2/3. Factor -2*r**3 - 4*r**5 - 2*r**4 - t*r + 2*r + 8*r**4.
-2*r**3*(r - 1)*(2*r - 1)
Let m(i) = 4*i + 4*i**2 + 14*i**2 - 10*i - 17*i**2 + 2. Let s be m(6). Find l such that -2/7*l**3 + 4/7*l**s + 2/7*l - 4/7 = 0.
-1, 1, 2
Let g(l) = 7*l**2 - 13*l - 4. Let c(s) = 15*s**2 - 27*s - 9. Let r(k) = 4*c(k) - 9*g(k). Factor r(d).
-3*d*(d - 3)
Let n(m) = m. Let d be n(5). Suppose 7*a = 3*a - 3*o + d, -3*a = 2*o - 4. Suppose -a*r**4 - 2*r**2 + r - 6*r**3 - 4*r**2 - 3*r = 0. Calculate r.
-1, 0
Let h(u) = -6*u**2 + 73*u - 54. Let v(m) = 3*m**2 - 36*m + 27. Let w(l) = -6*h(l) - 13*v(l). Solve w(y) = 0 for y.
1, 9
Let g(v) = -6*v**2 - 8*v. Let r(a) = -4*a**2 - 4*a + 5. Let h(b) = 5*b**2 + 5*b - 6. Let m(s) = -5*h(s) - 6*r(s). Let t(n) = -g(n) + 8*m(n). Factor t(q).
-2*q**2
Let r = -20 + 24. Factor -4*d**3 - r + 4*d**3 - 4*d + 5*d**3 - d**3 + 4*d**2.
4*(d - 1)*(d + 1)**2
Let f(g) be the second derivative of 0*g**3 - 4*g + 0*g**6 - 1/42*g**7 + 0*g**4 + 0*g**2 + 0 + 1/20*g**5. What is t in f(t) = 0?
-1, 0, 1
Suppose 11 = -y - 5*t, -2*t = -6*t - 12. Let -2*u + 2*u**5 + 3*u**4 - 3*u**4 + y*u**4 - 4*u**2 = 0. Calculate u.
-1, 0, 1
Factor 2/7*c**3 + 24/7 - 16/7*c - 2/7*c**2.
2*(c - 2)**2*(c + 3)/7
Let v(z) be the first derivative of 4*z + 5/4*z**4 + 3 - 2*z**3 - 3/2*z**2. Suppose v(j) = 0. What is j?
-4/5, 1
Determine t so that -2*t**3 + 0*t**2 + 8/7*t - 6/7*t**4 + 0 = 0.
-2, -1, 0, 2/3
Let t = -16 + 19. Let o be (t - 0 - 4) + 1. Let 0*g**4 + 3/2*g**3 + 0*g + o*g**2 + 0 - 3/2*g**5 = 0. What is g?
-1, 0, 1
Factor -23*g - 8 - 67*g**3 - 44*g**2 - 4*g**5 - 24*g**4 - 20*g**2 - 13*g + 11*g**3.
-4*(g + 1)**4*(g + 2)
Let l(d) be the second derivative of -3*d**8/2240 - d**7/168 + d**6/120 + d**4/3 - 7*d. Let j(y) be the third derivative of l(y). Solve j(n) = 0 for n.
-2, 0, 1/3
Let m(w) = -2*w**3 + 2*w**2 - 1. Let y be m(-1). Factor -r - 1 - 8*r**2 + r**3 + 9*r**2 + 0*r**y.
(r - 1)*(r + 1)**2
Factor 31 - 17 - 4*n**2 - 4*n + 4*n**3 - 10.
4*(n - 1)**2*(n + 1)
Let r be (10/(-1) - 0) + -1. Let l = r - -11. Determine d, given that 1/3*d**4 - 1/3*d**2 + 0*d + l*d**3 + 0 = 0.
-1, 0, 1
Factor 2 - l**2 + 6*l**2 + 0*l**2 - 7*l**2.
-2*(l - 1)*(l + 1)
Let x(p) be the third derivative of -p**8/1008 + p**7/105 - 11*p**6/360 + p**5/30 - 9*p**2. Find z, given that x(z) = 0.
0, 1, 2, 3
Let a(w) = -w**3 + 2. Let o be a(0). Let 16 + 54*s**3 + 45*s**2 + 88*s - 4*s**3 + 54*s**o + 41*s**2 = 0. What is s?
-2, -2/5
Let d(k) be the second derivative of -2*k**7/147 - 2*k**6/3