21. Factor m(r).
2*(r - 6)**2*(r + 3)/3
Suppose -4*s = 5*o - 17, -3*s - 3 = -4*o - 8. Suppose 2*m = 4*c - c - 4, -s*c + 5*m = 8. Factor 2/5*f**c + 2/5*f**2 - 6/5*f - 4/5 + 6/5*f**3.
2*(f - 1)*(f + 1)**2*(f + 2)/5
Let t(w) be the third derivative of -w**6/540 + w**5/45 - w**4/12 + 19*w**3/6 + 20*w**2. Let a(d) be the first derivative of t(d). Factor a(u).
-2*(u - 3)*(u - 1)/3
Factor -2 - 43/3*z - 55/3*z**2 + 16/3*z**4 + 88/3*z**3.
(z - 1)*(z + 6)*(4*z + 1)**2/3
Find z such that 250/9*z + 110/3*z**3 + 4/9*z**5 + 0 - 62/9*z**4 - 650/9*z**2 = 0.
0, 1/2, 5
Let p(j) be the first derivative of -j**9/1008 + j**7/280 + 13*j**3/3 - 21. Let r(a) be the third derivative of p(a). Let r(s) = 0. Calculate s.
-1, 0, 1
Let r(d) = 9*d**3 - d**2 - 14*d + 4. Let o(i) = 35*i**3 - 5*i**2 - 55*i + 15. Let f be 3/2*88/33. Let n(v) = f*o(v) - 15*r(v). Find b such that n(b) = 0.
-1, 0, 2
Suppose -20/9*s + 4/9*s**2 + 8/3 = 0. Calculate s.
2, 3
Let s = 2 - 6. Let w be (-4)/(0 + s/3). Factor 12*t**4 + w*t + 5*t**5 + t**5 - 2*t**5 - t**5 + 18*t**3 + 12*t**2.
3*t*(t + 1)**4
Let d(n) be the second derivative of -n**4/6 + 3*n**3/2 + 7*n**2/2 + 5*n. Let g be d(5). Let -g*z + 4*z - z**3 - z = 0. Calculate z.
-1, 0, 1
Let k(z) be the third derivative of z**5/210 + z**4/7 + 11*z**3/21 - z**2 + 2*z. Suppose k(m) = 0. Calculate m.
-11, -1
Let b(h) = -5*h**2 + 23*h + 32. Suppose -19 = -w - 4*c, 3*w + w = 3*c + 19. Let k(o) = -4*o**2 + 22*o + 32. Let u(q) = w*k(q) - 6*b(q). Factor u(z).
2*(z + 4)**2
Let g(d) = 2*d**3 - 13*d**2 - 26*d + 19. Let j be g(8). Find o such that 0 - 1/6*o**2 + 1/6*o**4 + 1/6*o**j - 1/6*o = 0.
-1, 0, 1
Let f(d) be the first derivative of -185/4*d**4 - 100/3*d**3 - 30*d**5 - 15/2*d**6 + 0*d - 10*d**2 + 14. Let f(b) = 0. What is b?
-1, -2/3, 0
Find l, given that -17 - 60*l - 80*l - 3*l**5 - 170*l**3 + 63*l**5 + 55*l**4 - 285*l**2 - 3 = 0.
-1, -2/3, -1/4, 2
Factor 4/9*a**2 + 0*a - 2/9*a**5 + 0 + 8/9*a**4 - 10/9*a**3.
-2*a**2*(a - 2)*(a - 1)**2/9
Suppose -8*u + 10*u + 2 = 0. Let b(j) = 1. Let o(a) = a**2 - 6*a + 5. Let c(v) = u*o(v) - 4*b(v). Determine f so that c(f) = 0.
3
Suppose -i = 0, 3*g + g + 4*i = 3*i + 16. Find j, given that 3/4*j**g + 1/4*j**3 - 7/4*j**2 - 1/4*j**5 + 1 + 0*j = 0.
-1, 1, 2
Let i = 111/436 + -1/218. Let o(c) be the first derivative of 3 + 1/12*c**3 - i*c**2 + 0*c. Factor o(m).
m*(m - 2)/4
Let g(d) be the second derivative of -5*d**4/12 - 10*d**3 - 90*d**2 - d + 138. Factor g(f).
-5*(f + 6)**2
Suppose -64/3 - 100/9*o - 2/9*o**2 = 0. What is o?
-48, -2
Factor 343*x**2 - 10*x - 345*x**2 + 2*x.
-2*x*(x + 4)
Suppose 132 = 65*a - 32*a. Let c(u) be the first derivative of -3/7*u**2 + 4/7*u - 16/21*u**3 - 9 - 3/14*u**a. Determine k, given that c(k) = 0.
-2, -1, 1/3
Let d be -1*(3 + 8) + 11. Factor d + 1/6*y - 1/12*y**2.
-y*(y - 2)/12
Let v = -98 - -96. Let w be (v/(-1))/(-16 + 17). Factor 1/4*q**w + 1/4 - 1/2*q.
(q - 1)**2/4
Let u = -2834 + 2837. Determine y, given that 1/6*y**u - 1/6*y**5 + 1/4*y**4 - 1/3*y**2 + 0*y + 1/12 = 0.
-1, -1/2, 1
Let z(g) = -5*g. Let i be z(-4). Factor 8*l + 12*l**3 - i*l**3 - 12*l**4 + 8*l**4 + 4*l**2.
-4*l*(l - 1)*(l + 1)*(l + 2)
Let h(g) be the first derivative of 0*g + 1/9*g**2 + 1/18*g**4 + 4/27*g**3 - 53. Solve h(n) = 0.
-1, 0
Factor -9*t**3 - 30*t**5 + 4*t**4 + 2*t**4 + 33*t**5.
3*t**3*(t - 1)*(t + 3)
Let g(z) be the third derivative of -z**7/735 - z**6/420 + z**5/35 + z**2 + 13. Solve g(h) = 0 for h.
-3, 0, 2
Let i(y) = 2*y**2 - 2*y - 1. Let v be i(0). Let d be (18/20 + v)/(4/(-30)). Let -d*r + 0 - 3/4*r**2 = 0. Calculate r.
-1, 0
Let u(m) be the second derivative of 4*m**7/315 - 11*m**6/225 + 3*m**5/50 - m**4/90 - m**3/45 + m - 30. Find o, given that u(o) = 0.
-1/4, 0, 1
Let w(k) = -5*k - 155. Let t be w(-31). Let h(m) be the second derivative of 0 - 1/80*m**5 + 0*m**2 + 1/24*m**3 + t*m**4 + 4*m. What is l in h(l) = 0?
-1, 0, 1
Let l(p) be the second derivative of -p**7/84 - p**6/30 + p**4/12 + p**3/12 + 11*p + 1. Determine i, given that l(i) = 0.
-1, 0, 1
Let t be (8/(-3))/(-2)*12/40. Let k(d) be the first derivative of 2*d**3 - t*d**5 + 4*d + 1 + 5*d**2 - 1/2*d**4. Factor k(u).
-2*(u - 2)*(u + 1)**3
Let l(p) be the first derivative of -p**4/4 + 5*p**3/3 - 2*p**2 + 77. Factor l(b).
-b*(b - 4)*(b - 1)
Let n = 1033/6 - 172. Let f(u) be the first derivative of 4 - 1/2*u**2 + n*u**3 + 0*u. Find p, given that f(p) = 0.
0, 2
Suppose -75*h + 12 = -71*h. Solve 0 - 4/9*v**h - 2/9*v**4 - 2/9*v**2 + 0*v = 0.
-1, 0
Let q(a) be the second derivative of -a**6/600 - 2*a**5/75 - 2*a**4/15 - 9*a**2/2 - 3*a. Let d(j) be the first derivative of q(j). Factor d(b).
-b*(b + 4)**2/5
Suppose 20*x - 14 = -14. Let b(d) be the third derivative of -1/240*d**5 + 4*d**2 + x + 1/48*d**4 + 0*d - 1/480*d**6 + 0*d**3. Determine k so that b(k) = 0.
-2, 0, 1
Let q = -15 + 18. Suppose -2*v + k + 5 = 0, -2*k + q*k - 19 = -4*v. Determine r, given that -2*r + 6*r + 2*r - 2*r**2 - v = 0.
1, 2
Let 2/7*d**2 + 0 - 2/7*d = 0. What is d?
0, 1
Let r(i) be the first derivative of -i**3 + 12*i**2 + 60*i - 325. Factor r(y).
-3*(y - 10)*(y + 2)
Suppose d - 20 = 90. Suppose -5*o + d = i, 0 = o + 2*o + 3*i - 78. Let -2*k**5 + 4*k**3 - 21 + o - 2*k = 0. Calculate k.
-1, 0, 1
Let y(p) be the first derivative of 10*p**6/3 - 11*p**5 + 5*p**4/4 + 65*p**3/3 - 25*p**2/2 - 10*p - 176. Suppose y(h) = 0. Calculate h.
-1, -1/4, 1, 2
Let v = -2527/12 + 2617/12. Solve -63/2*m - 1/2*m**3 - 49/2 - v*m**2 = 0.
-7, -1
Let b(m) be the second derivative of -35*m - 1/4*m**4 + 12*m**2 - m**3 + 0. Factor b(q).
-3*(q - 2)*(q + 4)
Factor 21/2*s - 3/4*s**2 - 147/4.
-3*(s - 7)**2/4
Let t(i) be the first derivative of 7*i**6/540 + i**5/90 - i**3 + 2*i + 44. Let h(j) be the third derivative of t(j). Find y such that h(y) = 0.
-2/7, 0
Suppose -5*a - 112 = 2*c, -3*c + 3*a - 168 = a. Let z = c + 842/15. Find q such that 2/15*q**2 - z*q - 4/15 = 0.
-1, 2
Let n(g) = -4*g**2 + 12*g + 160. Let r be n(8). Factor 4/7*j**2 + 0 - 12/7*j**3 + 12/7*j**4 + r*j - 4/7*j**5.
-4*j**2*(j - 1)**3/7
Let r(f) be the first derivative of f**3/3 + 3*f**2/2 - 6*f + 4. Let n be r(-5). Factor 4*h - h**5 + 6*h**n - 6*h**2 - h - 2*h**5 + 0*h.
-3*h*(h - 1)**3*(h + 1)
Let c(r) be the third derivative of r**9/7560 - r**7/420 + r**6/180 + r**4/6 + 8*r**2. Let n(x) be the second derivative of c(x). Factor n(u).
2*u*(u - 1)**2*(u + 2)
Let j(v) = 2*v**2 + 2*v + 2. Let f be j(-1). Solve -3*l**4 + 0*l**f - l**2 + 0*l**2 + 4*l**2 = 0 for l.
-1, 0, 1
Let r = -45 + 47. Let 71 - w**r + 4*w + 2*w**2 - 68 = 0. What is w?
-3, -1
Let i(n) be the first derivative of 5*n**6/6 + 7*n**5 + 85*n**4/4 + 85*n**3/3 + 15*n**2 - 118. Factor i(y).
5*y*(y + 1)**2*(y + 2)*(y + 3)
Find v such that 64 + 6*v - 231*v**2 - 5*v**5 + v**5 + 16*v**4 + 151*v**2 - 22*v + 20*v**3 = 0.
-2, -1, 1, 2, 4
Let w(q) = q**2 + q - 12. Let t(p) = -12*p**2 - 42*p + 64. Let j(d) = -t(d) - 10*w(d). Let j(m) = 0. What is m?
-14, -2
Factor i**3 + 28*i**2 - 176*i**2 + 5*i**3 - 3468 + 1564*i - 2*i**3.
4*(i - 17)**2*(i - 3)
Let c(n) = 3*n**3 + 11*n**2 + 5*n. Let v be c(-4). Let s be (v/1)/4*-1. Solve -13*t**2 - 12 - 15*t + s*t**2 + t**2 = 0 for t.
-4, -1
Let k = -45 + 79. Let a = -32 + k. Determine i, given that -1/3 + a*i**2 - 5/3*i = 0.
-1/6, 1
Let w(m) be the third derivative of m**6/60 - m**5/10 + m**4/4 - m**3/3 + 2*m**2 + 42. Find o such that w(o) = 0.
1
Let x(d) = -5*d**3 - 40*d**2 - 80*d - 45. Let g(h) = -7*h**3 - 59*h**2 - 120*h - 68. Let z(w) = -5*g(w) + 8*x(w). Let z(b) = 0. Calculate b.
-2, -1
Let d be 26/66*-4 - (-16)/24. Let a = 72/55 + d. Let -a - 1/5*v**3 + 3/5*v**2 + 1/5*v - 1/5*v**4 = 0. What is v?
-2, -1, 1
Let x be (33/(-6) - -1)*30/(-8). Let k(r) be the first derivative of -3*r + 25/2*r**3 + 15/4*r**2 - 189/10*r**5 - 4 - x*r**4. Find v such that k(v) = 0.
-1, -1/3, 2/7, 1/3
Let p = -369 - -371. Let w(m) be the second derivative of 0*m**p - 7/36*m**4 + 7/90*m**6 - 1/9*m**3 + 1/30*m**5 + 0 - 6*m. Solve w(v) = 0.
-1, -2/7, 0, 1
Let m be 32/14 + (104/28 - 4). Let j be ((-3)/(-4))/((-27)/(-12) - m). Find y such that -1/3*y - 1/3 + 2/3*y**j + 2/3*y**2 - 1/3*y**5 - 1/3*y**4 = 0.
-1, 1
Let r(t) be the second derivative of -1/160*t**6 - 4*t - 7/32*t**4 + 0 + 3/8*t**3 - 3*t**2 + 1/16*t**5. Let h(j) be the first derivative of r(j). Factor h(b).
-3*(b - 3)*(b - 1