- 206. Let p be t(42). Let s(r) be the second derivative of 0 + r + 4/27*r**3 - 1/54*r**p - 4/9*r**2. Factor s(o).
-2*(o - 2)**2/9
Let p = -14697/280 - -421/8. Let y = p + 3/20. Solve 128/7 + y*n**3 + 24/7*n**2 + 96/7*n = 0.
-4
Suppose -7*f - 240 = -5*i - 3*f, -f = 0. Let o = i + -48. Factor 6/5*c**2 + o + 3/5*c + 0*c**3 - 3/5*c**5 - 6/5*c**4.
-3*c*(c - 1)*(c + 1)**3/5
Let p = -75 - -75. Factor 5*c + p*c**2 - 149 - c**2 - c**3 + 146.
-(c - 1)**2*(c + 3)
Suppose -5*m = -11*m - 16*m + 4*m. Suppose 0*j - 8/9*j**5 - 26/9*j**4 + m - 4/9*j**2 - 22/9*j**3 = 0. Calculate j.
-2, -1, -1/4, 0
Let 9*w - w**2 + 5*w**2 + 55*w - 40 - 28 = 0. What is w?
-17, 1
Let x(s) = 6*s**2 + 12*s + 28. Let b(l) = -14*l**2 - 22*l - 54. Let g(n) = 2*b(n) + 5*x(n). Factor g(q).
2*(q + 4)**2
Determine g, given that -72/5 - 2*g**2 - 2/5*g**3 + 64/5*g = 0.
-9, 2
Let k = -124469/135 + 922. Let s(l) be the second derivative of 3*l - 1/90*l**5 - 1/54*l**4 + 0*l**2 + 0 + k*l**6 + 1/27*l**3. Let s(r) = 0. What is r?
-1, 0, 1
Suppose 0 = 2*r - 5*w - 72, r - 2*w - 45 = -10. Let b be 6/33 + r/11. Suppose -4*u**3 - b - 2*u - u + 7*u**3 + 3*u**2 = 0. Calculate u.
-1, 1
Let o(g) be the first derivative of -19 + 4/7*g + 4/21*g**3 - 4/7*g**2. Determine b so that o(b) = 0.
1
Let m = 88/65 - 2/13. Suppose -9/5*x**3 + 3/5*x**2 + 0 + m*x**4 + 0*x = 0. Calculate x.
0, 1/2, 1
Let s(i) be the second derivative of 2*i**6/105 - 64*i**5/35 + 362*i**4/7 - 3968*i**3/21 + 1922*i**2/7 - i - 17. Find q such that s(q) = 0.
1, 31
Let h(r) be the third derivative of 0 - 1/420*r**7 - 12*r**2 + 0*r - 1/12*r**4 - 1/3*r**3 + 1/120*r**6 + 1/40*r**5. Factor h(k).
-(k - 2)**2*(k + 1)**2/2
Let h(f) be the first derivative of 2*f**3/21 - 6*f**2/7 + 16*f/7 - 72. Factor h(z).
2*(z - 4)*(z - 2)/7
Let -10/3*z - 1/3*z**2 + 11/3 = 0. What is z?
-11, 1
Suppose 0 = 12*h - 7*h - 30. Let j be (h/(-6))/((-2)/8). Factor 3*t**5 - 3*t**j + 9*t**5 - 9*t**5 + 15*t**2 - 6*t - 9*t**3.
3*t*(t - 1)**3*(t + 2)
Let h(u) be the second derivative of u**4/84 - u**3/21 - 4*u**2/7 - 6*u - 2. Factor h(g).
(g - 4)*(g + 2)/7
Let a(r) = 6*r**4 - 6*r**2 - 24*r + 4. Let u(p) = -p**4 + p**3 + 6*p - 1. Let t(m) = -a(m) - 4*u(m). Factor t(k).
-2*k**2*(k - 1)*(k + 3)
Let -133435*j**2 + 133447*j**2 + 60*j**3 + 47*j**4 + 21*j**5 + 22*j**4 = 0. Calculate j.
-2, -1, -2/7, 0
Let u(h) be the first derivative of h**8/168 - 2*h**7/105 + h**6/60 + 6*h**2 - 12. Let f(d) be the second derivative of u(d). Suppose f(c) = 0. Calculate c.
0, 1
Let p = -4 + 6. Suppose -12 = -p*i - 4. Factor -2*z**4 - 5*z - 9*z**3 + z - 12*z**2 + z**i - z**4.
-z*(z + 2)**2*(2*z + 1)
Let i = 5 - 41. Let v(b) = -16*b**3 - 20*b - 18. Let g(a) = -a**3 - a - 1. Let t(s) = i*g(s) + 2*v(s). What is f in t(f) = 0?
-1, 0, 1
Let q(d) = 60*d**3 - 106*d**2 - 23*d + 58. Let z(r) = -20*r**3 + 36*r**2 + 8*r - 20. Let y(n) = -4*q(n) - 11*z(n). Factor y(b).
-4*(b - 1)**2*(5*b + 3)
Let a(w) be the first derivative of 189*w**4/4 - 60*w**3 + 57*w**2/2 - 6*w - 136. Factor a(q).
3*(3*q - 1)**2*(7*q - 2)
Let k(g) be the first derivative of 3*g**4/4 + 70*g**3 + 3675*g**2/2 - 86. Factor k(l).
3*l*(l + 35)**2
Let m be (10/(-15))/((-2)/9). Suppose m*v - 48 = 3*h, -h = 7 - 2. Let 4*w**2 + 9 + 9*w - 36 + v*w**2 + 3*w**3 = 0. Calculate w.
-3, 1
Let z(m) = m**2 + 11*m. Let t(y) = y**2 + 10*y - 1. Let d(r) = -5*t(r) + 4*z(r). Let q be d(-5). Factor q + 2*b + b**2 - 10.
b*(b + 2)
Let a = 96 - 57. Suppose a = 8*m + 15. Find b, given that -1/5*b**m + 0 + 1/5*b + 1/5*b**2 - 1/5*b**4 = 0.
-1, 0, 1
Let b(l) = -4*l**2 - 99*l + 1152. Let q(j) = 10*j**2 + 199*j - 2304. Let y(d) = -14*b(d) - 6*q(d). Determine k, given that y(k) = 0.
24
Let g be 3/(-2) + (-1)/2*-9. Suppose 0 = 3*a - 2*a + 2*n - 2, 0 = -3*n + g. Factor a + 7/4*k**2 - 1/4*k**5 - 1/2*k + 5/4*k**4 - 9/4*k**3.
-k*(k - 2)*(k - 1)**3/4
Let o(y) be the first derivative of -y**7/420 + y**6/160 - y**4/96 - y**2/2 + 10. Let m(i) be the second derivative of o(i). Factor m(x).
-x*(x - 1)**2*(2*x + 1)/4
Suppose 0*k = -2*k - y + 53, 2*k + 5*y - 73 = 0. Factor -3*t**4 + 12*t**4 + 27*t**5 - k*t**5.
3*t**4*(t + 3)
Let a(f) = -8*f + 25. Let v be a(3). Let x be 3/(-45)*v*(-30)/9. Solve 4/9*o**4 + 0 - 2/9*o**3 - x*o**5 + 0*o + 0*o**2 = 0.
0, 1
Let q(c) be the second derivative of -7*c + 0*c**3 - 1/15*c**4 - 1/25*c**5 + 0*c**2 + 0 - 1/150*c**6. What is n in q(n) = 0?
-2, 0
Let a(i) = -41*i**2 - 346*i - 332. Let r(u) = 9*u**2 + 86*u + 83. Let h(q) = -4*a(q) - 18*r(q). Factor h(g).
2*(g - 83)*(g + 1)
Let n(p) be the first derivative of -p**6/420 + p**5/70 - 4*p**3/21 - 7*p**2 - 31. Let g(q) be the second derivative of n(q). Find l such that g(l) = 0.
-1, 2
Let j(l) = -19*l**3 + 125*l**2 + 248*l + 104. Let s(p) = -18*p**3 + 125*p**2 + 246*p + 103. Let d(v) = -3*j(v) + 4*s(v). Factor d(w).
-5*(w - 10)*(w + 1)*(3*w + 2)
Let g(y) = -8*y**2 + 9*y - 8. Let v(f) = 4*f**2 - 4*f + 4. Let t(w) = -w**3 - 6*w**2 + 7*w + 4. Let x be t(-7). Let o(i) = x*g(i) + 7*v(i). Factor o(d).
-4*(d - 1)**2
Let p(s) be the third derivative of s**7/1470 - s**6/280 + s**5/140 - s**4/168 - 329*s**2. Find y such that p(y) = 0.
0, 1
Suppose 0 = -2*h + 14, -141*s + 280 = -136*s - 5*h. Let s*v + 12 + 18*v**3 + 159/2*v**2 - 21/2*v**4 = 0. What is v?
-1, -2/7, 4
Let l be 2625/(-250)*2/(-56). Factor 0*m**2 - 3/4*m**3 + l - 3/8*m**4 + 3/4*m.
-3*(m - 1)*(m + 1)**3/8
Let m(i) = i + 19. Let y = 59 - 78. Let r be m(y). Let r - 2/7*x - 3/7*x**2 = 0. Calculate x.
-2/3, 0
Let r(n) be the second derivative of 3*n**5/80 - 27*n**4/8 + 243*n**3/2 - 2187*n**2 - 156*n - 3. Find i such that r(i) = 0.
18
Let h(g) = 20*g**2 - 25*g + 5. Let p(v) = -v**4 + v**3 - v**2 + 1. Let m(a) = -h(a) - 5*p(a). Factor m(y).
5*(y - 1)**3*(y + 2)
Let j(r) be the second derivative of -r**5/150 + r**4/30 + r**3/5 + 2*r**2 + r. Let z(o) be the first derivative of j(o). What is g in z(g) = 0?
-1, 3
Suppose 3*q - a - 6 = 14, 3*q + a = 10. Let f(m) be the first derivative of -m**6 - 2/3*m**2 + 11/6*m**4 + m**q + 4/3*m - 19/9*m**3 - 2. Solve f(k) = 0.
-1, -1/2, 2/3, 1
Determine a so that -4447*a**5 + 4446*a**5 + 11*a**4 + 5*a**2 - 19*a**3 + 4*a**2 = 0.
0, 1, 9
Let p = 3099/2 - 1624. Let j = p + 76. Solve -9/4 + 2*a**2 + 1/4*a**4 + j*a**3 - 3/2*a = 0.
-3, -1, 1
Let w = -1415 - -1419. Factor -5/3*u**3 + 5/6*u**w + 5/3*u**2 - 5/6*u + 1/6 - 1/6*u**5.
-(u - 1)**5/6
Let v be (0/(-2))/(-20 - -22). Let u(m) be the first derivative of 0*m**2 + v*m - 1/2*m**5 + 3 + 0*m**3 - 1/4*m**4. Factor u(o).
-o**3*(5*o + 2)/2
Let a = 9 - 3. Suppose a*c - 1185 = c. Suppose 13*i**2 + 7*i**2 + c*i**5 - 12*i**3 - 8*i - 233*i**5 - 4*i**4 = 0. Calculate i.
-2, 0, 1
Let r(b) be the third derivative of b**6/960 + b**5/160 + b**4/64 + 25*b**3/6 - 23*b**2. Let q(f) be the first derivative of r(f). Solve q(a) = 0.
-1
Let o(h) be the second derivative of 0*h**5 + 34*h + 1/33*h**3 + 0 - 2/165*h**6 - 1/231*h**7 + 0*h**2 + 1/33*h**4. Let o(f) = 0. What is f?
-1, 0, 1
Let b be -6*7/(-147) - 180/(-350). Determine u, given that 4/5*u - 4/5 - 4/5*u**3 + b*u**2 = 0.
-1, 1
Solve 46/3*a**2 + 14 + 86/3*a + 2/3*a**3 = 0.
-21, -1
Suppose -24/11 - 10/11*n**3 + 34/11*n - 2/11*n**4 + 2/11*n**2 = 0. What is n?
-4, -3, 1
Let w be 104/48 - (19/6 - 3). Let x(u) be the first derivative of -3/2*u**w - 3*u**3 + 0*u + 2. Suppose x(f) = 0. What is f?
-1/3, 0
Let d(l) be the second derivative of l**5/50 - l**4/15 - 7*l**3/15 - 4*l**2/5 - 2*l. Let d(h) = 0. Calculate h.
-1, 4
Let f(x) be the first derivative of 48*x**5/5 + 78*x**4 - 183*x**3 + 213*x**2/2 - 24*x - 60. Factor f(r).
3*(r - 1)*(r + 8)*(4*r - 1)**2
Let u be (-136)/7 - (-16)/(-28). Let p = -18 - u. Solve 5*v**2 - 11*v**2 + 2*v**3 + 2*v**p = 0.
0, 2
Let s(r) be the third derivative of -r**6/10 + 17*r**5/20 + 10*r**4 - 21*r**3/2 - 11*r**2. Find d such that s(d) = 0.
-3, 1/4, 7
Let d(n) be the first derivative of 3*n**4/4 - 7*n**3 + 21*n**2/2 + 45*n + 788. Factor d(g).
3*(g - 5)*(g - 3)*(g + 1)
Let i(j) be the first derivative of j**7/357 + j**6/255 - j**5/170 - j**4/102 + 2*j + 5. Let t(z) be the first derivative of i(z). Factor t(n).
2*n**2*(n - 1)*(n + 1)**2/17
Let k = -3 + 6. Let m(a) be the first derivative of 3*a**2 + 3*a**3 + 2*a**3 + 5*a**k - 3*a**3 + 7. Factor m(c).
3*c*(7*c + 2)
Let i(x) = 7*x**2. Let c be i(1). Suppose -8*u**4 + 6*u**3 - 2*u**5 +