ine d, given that o(d) = 0.
5
Let h = 455/3 - 149. Determine f, given that h*f + 4/3 - 7/3*f**2 - 5/3*f**3 = 0.
-2, -2/5, 1
Let k = -19488 + 4910911/252. Let l = -1/28 - k. Factor -2/9*a**2 + l - 2/9*a**3 + 2/9*a.
-2*(a - 1)*(a + 1)**2/9
Let w(q) be the second derivative of 7/18*q**4 - 1/12*q**3 - 1/12*q**2 - q - 1. Find z, given that w(z) = 0.
-1/7, 1/4
Let t(c) be the third derivative of c**6/40 + 2*c**5/5 + 458*c**2. Factor t(i).
3*i**2*(i + 8)
Let o = 121 + -1209/10. Let l(u) be the first derivative of 1/8*u**4 + 6 + 1/6*u**3 - 1/12*u**6 - o*u**5 + 0*u**2 + 0*u. Factor l(m).
-m**2*(m - 1)*(m + 1)**2/2
Suppose -2*c + 2 - 8 = 0, 0 = -r + c + 6. Let q(k) be the first derivative of 2/3*k - 1/2*k**2 + 1/9*k**3 - r. Factor q(m).
(m - 2)*(m - 1)/3
Let t(c) be the first derivative of -3*c**4/4 - 3*c**3 + 9*c**2 + 24*c + 61. Factor t(l).
-3*(l - 2)*(l + 1)*(l + 4)
Let s(i) be the third derivative of -i**7/60 + i**6/90 + 7*i**5/60 - i**4/6 - 11*i**3/6 - 9*i**2. Let g(x) be the first derivative of s(x). Solve g(d) = 0.
-1, 2/7, 1
Let f(w) be the second derivative of -w**4/8 + 137*w**3/2 - 56307*w**2/4 + 82*w - 2. Factor f(j).
-3*(j - 137)**2/2
Let s(v) = -v**3 - v**2 - 2*v + 43. Let r be s(0). Determine q, given that r*q**3 + q**4 + q**2 + q**2 - 46*q**3 = 0.
0, 1, 2
Suppose 10*f + 78 = 23*f. Suppose -q + f = 2*q. Let 45/2*i**q + 1/4 + 27*i**3 + 17/4*i - 54*i**4 = 0. Calculate i.
-1/6, 1
Let n(u) be the second derivative of u**4/120 + u**3/30 - 195*u. Factor n(s).
s*(s + 2)/10
Factor 42 - 52 - 5*t**2 + 42 + 13.
-5*(t - 3)*(t + 3)
Let o(l) be the first derivative of 4/9*l**3 - 8/3*l**2 - 7 + 4*l. Factor o(v).
4*(v - 3)*(v - 1)/3
Factor 1/6*u**3 + 0 + 0*u + 1/2*u**2.
u**2*(u + 3)/6
Suppose 2*u + 73*u = 159 - 9. Let 8/3*h**u + 10/3*h + 4/3 + 2/3*h**3 = 0. Calculate h.
-2, -1
Let m(f) = 2*f - 6. Let j be m(5). Suppose 4 = j*l - 4, 0 = b - 5*l + 8. Factor 3*u**b - 3*u**4 + 3*u**2 - 6*u**2 - 3*u**5.
-3*u**4*(u + 1)
Let s(d) be the third derivative of d**5/20 + 7*d**4/4 + 13*d**3/2 + 24*d**2 - d. Factor s(w).
3*(w + 1)*(w + 13)
Let s(k) be the second derivative of -k**2 - 1/2*k**3 + 0 - 5*k + 3/20*k**5 + 1/6*k**4. Find j such that s(j) = 0.
-1, -2/3, 1
Let q(x) be the first derivative of x**8/140 + 2*x**7/105 + x**6/75 + 7*x**2 - 18. Let o(c) be the second derivative of q(c). Factor o(i).
4*i**3*(i + 1)*(3*i + 2)/5
Suppose 505*b = 610*b. Let u(w) = w**2 + w + 1. Let i be u(-2). Factor 0*k**2 + 0*k + 2/7*k**i + b.
2*k**3/7
Let r(d) be the third derivative of d**5/90 + 65*d**4/18 + 4225*d**3/9 + 2*d**2 + 84. Factor r(s).
2*(s + 65)**2/3
Let a(v) be the first derivative of 3*v**2 + 5*v**4 - v - 2 + 13/2*v**3 + 27/20*v**5. Let y(m) be the first derivative of a(m). Suppose y(i) = 0. What is i?
-1, -2/9
Factor 346*j + 521*j + 3*j**5 - 1632*j**2 - 40298*j**3 + 96*j**4 + 40964*j**3.
3*j*(j - 1)**2*(j + 17)**2
Suppose -18*o**2 + 5/2*o**3 + 18*o + 0 + 2*o**4 - 1/2*o**5 = 0. Calculate o.
-3, 0, 2, 3
Let q be (-2 + 3/2)/(-1). Let u be 488/(-122) + 27/4. Factor 11/4*z - u*z**2 - 3/4 + 1/4*z**3 + q*z**4.
(z - 1)**2*(z + 3)*(2*z - 1)/4
Let u(x) be the first derivative of -1/30*x**3 - 3 - 1/300*x**5 - 1/60*x**4 + 0*x - x**2. Let k(z) be the second derivative of u(z). Let k(y) = 0. Calculate y.
-1
Let s(r) = 2*r**3 + 2*r**2 + 4*r + 6. Let v be s(-3). Let m be (-8)/(-10)*(-35)/v. Factor -m*a**2 + 10/3*a**3 + 0 + 0*a + 2*a**5 - 14/3*a**4.
2*a**2*(a - 1)**2*(3*a - 1)/3
Let z(k) be the third derivative of k**7/210 + k**6/24 - 11*k**5/20 + 9*k**4/8 + 17*k**2 - 8. Factor z(u).
u*(u - 3)*(u - 1)*(u + 9)
Suppose 8*c + 0*c - c = 0. Let w(u) be the third derivative of 0*u**4 + 0*u + 0*u**3 + 0*u**6 + 1/35*u**7 + 3*u**2 + c*u**5 - 3/112*u**8 + 0. Factor w(y).
-3*y**4*(3*y - 2)
Let m be (160/280)/(23/7). Factor 0 + 2/23*b**2 + m*b.
2*b*(b + 2)/23
Factor 3 + b**3 - 16 - 4455*b - 15*b**2 + 4482*b.
(b - 13)*(b - 1)**2
Let q(k) = k**2 + 144*k - 441. Let u be q(3). Find i, given that 4/5*i + u - 4/5*i**2 = 0.
0, 1
Suppose -1/4*r**4 - 1/2*r**5 + 1/2*r**2 + r**3 - 1/4 - 1/2*r = 0. What is r?
-1, -1/2, 1
Let s(m) be the third derivative of -m**5/10 + 23*m**4/8 - 11*m**3/2 + 227*m**2. Factor s(a).
-3*(a - 11)*(2*a - 1)
Let j(x) be the first derivative of -3*x**5/20 + x**4/2 + x**3/2 - 3*x**2 + 17*x + 15. Let v(m) be the first derivative of j(m). Determine a so that v(a) = 0.
-1, 1, 2
Let m be ((-4)/2)/((-6)/39). Let p = -8 + m. Factor 4*z**4 - 4*z + 4*z**2 - 5*z**2 + 2*z**2 - p*z**2 + 4*z**3.
4*z*(z - 1)*(z + 1)**2
Let y be 150/(-45)*6/(-5). Let b = -6 + 8. Find o such that -15*o**2 - 3*o**y + b*o**3 - 6*o - 13*o**3 - o**3 + 0*o**4 = 0.
-2, -1, 0
Let l(y) = -y**3 + 3*y**2 - y - 2. Let t be 1*(3 - 0) + -1. Let p be l(t). Suppose -3/5*o**3 + p*o - 3/5*o**2 + 0 = 0. Calculate o.
-1, 0
Suppose -15*v + 7 = -8. Let n be (v - (-2)/6)/(44/6). Determine g so that 2/11*g**2 + 4/11*g + n = 0.
-1
Let q(f) be the third derivative of -4/105*f**5 - 4/21*f**3 + 10*f**2 + 1/210*f**6 + 0 + 5/42*f**4 + 0*f. Factor q(y).
4*(y - 2)*(y - 1)**2/7
Let m be 23/8 - (7 + 114/(-16)). Solve 0*t**2 + 2/7*t**m + 0*t + 0 = 0.
0
Suppose 2*x + 6 = 14. Suppose -5*l + n + 2 = -35, 0 = l - x*n + 4. Suppose l*s**3 - 10*s**3 + s**3 - s + 2*s**2 = 0. What is s?
0, 1
Let t(i) be the third derivative of i**8/672 + i**7/420 - i**6/80 - i**5/120 + i**4/24 - 162*i**2. Factor t(g).
g*(g - 1)**2*(g + 1)*(g + 2)/2
Let -4/7*u**4 + 40/7*u**3 - 16*u + 12/7*u**2 - 80/7 = 0. What is u?
-1, 2, 10
Let k = 1033/277 - 752552/239605. Let j = k - -2/173. Factor 12/5*b**4 + 12/5*b**2 + j*b + 3/5*b**5 + 18/5*b**3 + 0.
3*b*(b + 1)**4/5
Let f(a) = -2*a**5 - 17*a**4 + 49*a**3 + 40*a**2 - 122*a - 98. Let c(j) = -j**5 - j**4 + j**3 - j. Let y(u) = -3*c(u) + f(u). Factor y(n).
(n - 7)**2*(n - 2)*(n + 1)**2
Let i = 17409 - 17409. Factor -9/5*a**4 - 3/5*a**5 + 0*a + i*a**3 + 12/5*a**2 + 0.
-3*a**2*(a - 1)*(a + 2)**2/5
Factor 2/9*o**2 + 1058/9 + 92/9*o.
2*(o + 23)**2/9
Let v = 28 - 24. Factor -3*u**2 + 12*u - 11*u + v*u**2.
u*(u + 1)
Let x = 938 - 938. Factor -2/3*z**4 + 0*z**2 - 4/9*z**5 + x*z + 0 - 2/9*z**3.
-2*z**3*(z + 1)*(2*z + 1)/9
Let k be (-3)/(-2*(-9)/(-24)). Let d(p) = -p**2 + 5*p - 1. Let j be d(k). Factor t - t + 0*t**j + 2*t**3 + 6*t**2.
2*t**2*(t + 3)
Solve 71/2*u**3 - 143/3*u**4 - 26/3*u**2 + 121/6*u**5 + 2/3*u + 0 = 0 for u.
0, 2/11, 1
Let v(d) be the third derivative of -d**6/120 + 4*d**5/15 + 13*d**4/8 - 9*d**3 + 28*d**2. Factor v(x).
-(x - 18)*(x - 1)*(x + 3)
Suppose 2*b - 4*n + 265 = 69, 5*n - 380 = 4*b. Let s be (-8)/(-60) - 11*3/b. Determine a so that 0 + 0*a + 0*a**3 + s*a**2 - 1/2*a**4 = 0.
-1, 0, 1
Let s be (371 + -375)*(-53)/20. Suppose -4/5 + 33/5*z**4 + 31/5*z**2 + s*z**3 + 7/5*z**5 + 0*z = 0. What is z?
-2, -1, 2/7
Let z(r) be the third derivative of 7*r**7/60 - 203*r**6/80 - 3*r**5 - 13*r**4/12 - r**2 - 28. Let z(u) = 0. Calculate u.
-2/7, 0, 13
Suppose 0 = 5*y + 3*j - 1, 46*y - 43*y = -j + 7. Determine q, given that 0*q + 2/5*q**3 - 4/5*q**4 + 4/5*q**2 - 2/5*q**y + 0 = 0.
-2, -1, 0, 1
Solve -50*o**5 + 70*o**3 + 1357*o**2 - 15*o - 1332*o**2 + 10*o**5 - 100*o**4 = 0 for o.
-3, -1/2, 0, 1/2
Let h(y) be the second derivative of -y**6/75 - y**5/25 + 14*y**4/15 - 46*y**3/15 + 21*y**2/5 - 252*y + 2. Let h(a) = 0. What is a?
-7, 1, 3
Find a, given that 76*a**2 + 84 - 42*a + 4*a**3 - 61*a + 0*a**3 - 61*a = 0.
-21, 1
Let v(g) = -5*g**2 - 108*g - 6. Let p(q) = -2*q**2 - 36*q - 2. Let n(x) = -11*p(x) + 4*v(x). Let b be n(19). Factor b*s - 36 + 4/3*s**3 - 12*s**2.
4*(s - 3)**3/3
Let t(w) be the first derivative of w**6/2 - 13*w**5/5 + 2*w**4 + 4*w**3 + 36. Factor t(q).
q**2*(q - 3)*(q - 2)*(3*q + 2)
Factor -2/9*k**2 - 8 - 8/3*k.
-2*(k + 6)**2/9
Let f be -2*(6 - 6 - 1). Let q be -1 - ((-2)/(-4))/(f/(-4)). Factor -2/7*n**3 + 2/7*n + q*n**2 + 0.
-2*n*(n - 1)*(n + 1)/7
Suppose 2*h + 28 + 43*h**2 - 32*h + 7 - 48*h**2 = 0. What is h?
-7, 1
Let d(b) be the second derivative of 0 - 1/2*b**2 + 0*b**3 - b + 1/12*b**4. Suppose d(r) = 0. What is r?
-1, 1
Determine z, given that 46*z**2 + 16 - 17*z + 39*z - 47*z**2 - 16*z = 0.
-2, 8
Suppose a + 0*a + 16 = 5*z, -4*a + 32 = 4*z. Suppose 0*m + z*m**3 + m**4 - 7*m**4 + 4*m + 14*m**2 = 0. Calculate m.
-1, -1/3, 0, 2
Let l = 149 - 147. Factor -803*z + 4*z**l + 803*z - 16.
4*(z - 2)*(z + 2)
Let v(b) = -b**5 + 