he first derivative of c**5/90 + c**4/36 + 7*c**2 + 6. Let o(i) be the second derivative of m(i). Factor o(f).
2*f*(f + 1)/3
Let v(i) be the second derivative of -i**6/6 + 13*i**5/4 - 5*i**4 + 229*i. Factor v(u).
-5*u**2*(u - 12)*(u - 1)
Let o(r) be the third derivative of 2*r**7/21 - 17*r**6/30 + 7*r**5/5 - 11*r**4/6 + 4*r**3/3 + 372*r**2. Solve o(g) = 0 for g.
2/5, 1
Suppose 68*m - 71*m + 21 = 0. Suppose -37 + m = -15*j. Determine b, given that 2/5*b**j - 4/5*b + 2/5 = 0.
1
Let h(o) be the first derivative of -10*o**2 + 5*o**4 + 20/3*o**3 - 8*o + 20 - 12/5*o**5. Let h(r) = 0. Calculate r.
-1, -1/3, 1, 2
Let d(q) = 15*q**3 + 45*q**2 + 42*q + 12. Let l(t) = -6*t**3 - 18*t**2 - 17*t - 5. Let g be (0 + (-6)/4)*20/6. Let y(c) = g*d(c) - 12*l(c). Factor y(s).
-3*s*(s + 1)*(s + 2)
Let m be (111/27 - 4)*51 - -2. Determine s so that 4/3*s + 20/3*s**2 + 0 + m*s**3 + 7/3*s**4 = 0.
-2, -1, -2/7, 0
Let f(k) be the third derivative of -k**6/60 - k**5/6 - k**4/6 + 8*k**3/3 + 34*k**2. Let f(r) = 0. What is r?
-4, -2, 1
Let w(b) be the second derivative of 0*b**2 + 0*b**3 - 3/50*b**5 + 0 + 14*b - 1/75*b**6 - 1/15*b**4. Factor w(m).
-2*m**2*(m + 1)*(m + 2)/5
Let u(l) be the second derivative of 1/8*l**4 + 1/20*l**5 - l**3 + 0 - 1/2*l**2 - 9*l. Let k(a) be the first derivative of u(a). What is w in k(w) = 0?
-2, 1
Let v(f) be the second derivative of 12*f + 5/6*f**4 + 0 + 7/3*f**3 + 1/10*f**5 + 3*f**2. Factor v(b).
2*(b + 1)**2*(b + 3)
Factor 7/4 + 1/8*u**3 - 1/8*u - 7/4*u**2.
(u - 14)*(u - 1)*(u + 1)/8
Let y(g) be the first derivative of 6*g + 27/2*g**2 + 8 + 9/5*g**5 + 15*g**3 + 33/4*g**4. Factor y(v).
3*(v + 1)**3*(3*v + 2)
Let g = 2258 - 2258. Let t(o) be the third derivative of -1/105*o**5 + g + 0*o**4 - 1/1176*o**8 + 0*o - 1/84*o**6 - 6*o**2 - 4/735*o**7 + 0*o**3. Factor t(q).
-2*q**2*(q + 1)**2*(q + 2)/7
Let b(k) be the first derivative of -k**3/2 + 237*k**2/4 + 120*k + 646. Factor b(h).
-3*(h - 80)*(h + 1)/2
Factor -12 + 1/2*o**2 - o.
(o - 6)*(o + 4)/2
Factor 432*k + 20*k**2 - 53*k**2 + 20*k**2 + 4783 + 16*k**2 + 10769.
3*(k + 72)**2
Let x(o) be the first derivative of 0*o**3 + 0*o - o**2 + 1/2*o**4 - 38. Factor x(a).
2*a*(a - 1)*(a + 1)
Suppose -5*o + 39 = 3*u, 0 = 3*o - 5*u + 2*u - 9. Let y be (-9)/20*(o - 156/18). Find k such that 4/5*k - y*k**3 + 0 - 2/5*k**2 + 2/5*k**5 + 2/5*k**4 = 0.
-2, -1, 0, 1
Let i(c) be the first derivative of -2*c**5/5 + 29*c**4/8 - 31*c**3/6 + 3*c**2/2 + 178. Determine j so that i(j) = 0.
0, 1/4, 1, 6
Let l = -23 - -13. Let n = l + 14. Determine w so that -w**4 - 2*w**3 + 3*w**4 - w**4 + w**n = 0.
0, 1
Let f(z) = -11*z**4 + 29*z**3 + 126*z**2 + 76*z - 4. Let s(g) = 9*g**4 - 28*g**3 - 126*g**2 - 75*g + 3. Let p(u) = 3*f(u) + 4*s(u). Factor p(k).
k*(k - 12)*(k + 3)*(3*k + 2)
Factor -1/5*w**2 + 3/5 + 2/5*w.
-(w - 3)*(w + 1)/5
Let r be 3*(0 + (-28)/(-126)). Find m, given that -2*m - 2/3*m**4 + 4/3 + 2*m**3 - r*m**2 = 0.
-1, 1, 2
Factor 8*i**4 + 7*i**2 - 16*i + i**2 - 2*i**5 - 15*i + 29*i - 12*i**3.
-2*i*(i - 1)**4
Let d(f) be the first derivative of f**6/27 + 34*f**5/45 + 29*f**4/9 + 164*f**3/27 + 53*f**2/9 + 26*f/9 + 88. Solve d(p) = 0 for p.
-13, -1
Let l(s) = -s + 7. Let x be (24/10)/((-16)/(-40)). Let u be l(x). Suppose u + 0 + b**2 + 2*b - 1 = 0. What is b?
-2, 0
Let q be ((-207)/54)/((-22)/80). Let s = 168/11 - q. Suppose s*u + 2/3*u**2 + 2/3 = 0. Calculate u.
-1
Let r(z) = 1. Let t be 3/8 - 1150/80. Let n(i) = i**2 + 8*i + 9. Let p(k) = t*r(k) - 2*n(k). Solve p(m) = 0 for m.
-4
Let j(q) = q**3 - 22*q**2 + 146*q - 344. Let c(o) = 5*o - 2*o - 6*o + 4*o + 1 + o**2. Let z(v) = 2*c(v) + 2*j(v). Suppose z(s) = 0. Calculate s.
7
Let g = 2128/1355 + 8/271. Factor 8/5 + 4/5*u - g*u**2 - 4/5*u**3.
-4*(u - 1)*(u + 1)*(u + 2)/5
Let z(v) be the first derivative of -1/2*v**4 - 13/9*v**3 - 4/3*v - 1/15*v**5 - 2*v**2 - 14. Factor z(h).
-(h + 1)**2*(h + 2)**2/3
Let y(r) = 2*r**2 - 2*r. Let d(m) = -4*m**2 + 238*m + 6728. Let n(l) = -2*d(l) - 6*y(l). Determine z, given that n(z) = 0.
-58
Let u(x) be the third derivative of -11*x**6/30 + 36*x**5/5 + 10*x**4/3 - 63*x**2 - 2. Determine p so that u(p) = 0.
-2/11, 0, 10
Suppose -2*x**3 + 74*x**2 - 192*x**2 + 88*x**2 + 55*x - 30 + 7*x**3 = 0. What is x?
1, 2, 3
Let x be 737/201 - ((-10)/(-2) - 2). Factor x + 1/3*h**3 - 1/3*h - 2/3*h**2.
(h - 2)*(h - 1)*(h + 1)/3
Let p = -12 - -15. Suppose -w = -p*w + 8. Factor a**5 - a**2 + 2*a**3 + 3*a**5 - 2*a**w + 3*a**2 - 6*a**5.
-2*a**2*(a - 1)*(a + 1)**2
Let y(k) be the first derivative of 0*k**2 - 1/2*k**4 + 0*k - 33 + 4/3*k**3 - 2/5*k**5. Factor y(u).
-2*u**2*(u - 1)*(u + 2)
Let f(j) be the second derivative of -2*j**6/45 + 2*j**5/3 - 8*j**4/9 - 20*j**3/9 + 6*j**2 + j + 72. Let f(h) = 0. Calculate h.
-1, 1, 9
Let r(c) = -c**3 - c**2 + 53*c - 24. Let v be r(-8). Let f = 2/3 + 0. Suppose f*m - 7/3*m**5 + v - 19/3*m**4 - 5*m**3 - 1/3*m**2 = 0. Calculate m.
-1, 0, 2/7
Let p = -3676 + 18914/5. Let z = 108 - p. Let -z*x - 3/5*x**2 - 3/5 = 0. What is x?
-1
Suppose 3*q + 3*c = 21, -5*c + 10*c = 20. Let f(z) be the second derivative of 8*z**2 + 0 + 3*z - 8/3*z**q - z**4. Suppose f(h) = 0. Calculate h.
-2, 2/3
Let m(v) be the first derivative of -7 + 0*v**3 + 0*v**2 - 3/16*v**4 + 0*v - 3/20*v**5. Let m(z) = 0. Calculate z.
-1, 0
Let l(k) = -3*k**2 - 29*k - 145. Let m(x) = -x**2 - 16*x - 73. Let z(r) = -2*l(r) + 5*m(r). Factor z(y).
(y - 25)*(y + 3)
Let w be (-24)/(-144) + (-1 - 1202/(-60)). Let n = w - 92/5. Find y such that 8/5*y**2 + n - 2/5*y**3 - 2*y = 0.
1, 2
Determine a so that 88*a - 52*a**3 + 250*a**3 + 22*a**2 + 2*a**5 - 40*a**4 + 5*a**2 - 288*a + 13*a**2 = 0.
-1, 0, 1, 10
Let r be 19/(-38)*(-8)/(-814). Let j = 401/1221 - r. Determine l, given that 0 - j*l**2 + 4/3*l**3 + 0*l = 0.
0, 1/4
Let x(m) be the third derivative of -m**8/6720 - m**7/840 + m**6/80 + m**5/5 + 10*m**2. Let u(v) be the third derivative of x(v). Determine n so that u(n) = 0.
-3, 1
Let v be (2 - 1)/((-11)/(-11)). Suppose -5*k - v = -16. Find u such that 10*u**4 - u**3 - 13*u**k + 9 - 18*u**2 - 1 + 6*u**5 + 8*u = 0.
-2, -1, -2/3, 1
Factor -7*r + r**3 - 54 - 50 + 231 - 61 - 60.
(r - 2)*(r - 1)*(r + 3)
Let f(j) be the second derivative of j**6/210 + 9*j**5/140 + j**4/3 + 6*j**3/7 + 8*j**2/7 + 143*j. Factor f(x).
(x + 1)*(x + 2)**2*(x + 4)/7
Let k(y) = -6*y**3 - 30*y**2 + 23*y - 7. Let f(o) = -5*o**3 - 30*o**2 + 23*o - 8. Let c = 104 - 107. Let m(z) = c*f(z) + 4*k(z). Factor m(s).
-(s + 4)*(3*s - 1)**2
Suppose -157 - 71 = -114*u. Let 0*s**3 + 0 + 2/5*s**4 + 0*s**u + 0*s = 0. Calculate s.
0
Let g(q) = 5*q**2 + 2*q - 2. Let y be g(1). Let f be (-2)/6 - (-10)/3. Determine m, given that m**5 - f*m**5 + 2*m**3 + 0*m**y = 0.
-1, 0, 1
Let d(q) = 2*q**3 - 52*q**2 + q - 24. Let h be d(26). Let u be (-1 - (-6)/4)*(-108)/(-117). Determine i, given that 2/13 + u*i**h + 2/13*i**3 + 6/13*i = 0.
-1
Suppose -5*v + 125 = -20. Let s = v - 26. Find z, given that -4*z**3 + 4*z + 6*z + s*z**2 - 4*z**2 - 4 - z**2 = 0.
-2, 1/2, 1
Factor 2511 - 2553 + 15*b + 3*b**2 + 0*b.
3*(b - 2)*(b + 7)
Let a(u) = u**5 + u**4 + u**3 - u. Let n(y) = -4*y**5 - 6*y**3 + y**2 + 3*y. Let i(l) = -6*a(l) - 2*n(l). Factor i(m).
2*m**2*(m - 1)**3
Suppose 37*x - 12 = 34*x. Suppose -5*n + x*h - h + 22 = 0, 5*n = -2*h + 2. Suppose 2*m**3 + 61 - 61 - 6*m - 4*m**n = 0. What is m?
-1, 0, 3
Let o(i) = -86*i**3 + 100*i**2 - 14*i. Let n be (2/11)/((-1)/(-11)). Let w(k) = -17*k**3 + 20*k**2 - 3*k. Let y(j) = n*o(j) - 11*w(j). Factor y(d).
5*d*(d - 1)*(3*d - 1)
Let b = 43261/51918 + 2/25959. Factor b*f**2 + 0 + 0*f.
5*f**2/6
Let w(v) be the first derivative of 5*v**4/4 + 85*v**3/3 + 140*v**2 + 260*v - 509. Solve w(o) = 0.
-13, -2
Solve -672*w + 7*w**3 + 784 + 10*w**3 + 2*w**3 - 108*w**2 - 23*w**3 = 0.
-14, 1
Let w(v) be the first derivative of v**7/2730 + v**6/2340 - 15*v**3 - 19. Let m(q) be the third derivative of w(q). Factor m(b).
2*b**2*(2*b + 1)/13
Determine a so that -2/7*a**4 + 0 + 50/7*a - 10*a**2 + 22/7*a**3 = 0.
0, 1, 5
Suppose -r = 2*r - 4*z - 67, 0 = -3*r + z + 82. Let g be (-1)/10*-2 - r/(-145). Factor 0*f + 4/5*f**2 + 0 - 6/5*f**3 + g*f**5 + 0*f**4.
2*f**2*(f - 1)**2*(f + 2)/5
Let w = 40 - 37. Factor 4*n + 0*n + 0*n**w - n**3 - 3*n.
-n*(n - 1)*(n + 1)
Let k(h) = -2*h**2 + 43*h - 38. Let z(c) = 65*c - 3*c**2 + 24*c - 116 + 39 -