50). Determine d so that -6/7*d**2 + 3/7*d + 6/7*d**l - 3/7*d**5 + 0*d**3 + 0 = 0.
-1, 0, 1
Let a(v) = 2*v**3 + 25*v**2 + 23*v - 3. Let i(m) = m**3 + 25*m**2 + 24*m - 4. Let j(x) = -4*a(x) + 3*i(x). Determine u so that j(u) = 0.
-4, -1, 0
Let 15/2*u**2 + 0 - 1/2*u**4 + 0*u + u**3 = 0. What is u?
-3, 0, 5
Let v(d) be the second derivative of -d**7/126 + d**6/30 + d**5/6 - 74*d. Determine a so that v(a) = 0.
-2, 0, 5
Let h(n) be the second derivative of -n**7/84 + n**5/20 - n**3/12 - 288*n. Let h(l) = 0. Calculate l.
-1, 0, 1
Suppose -19*z = -16*z - 15. Factor z*l + 3 + 7*l - 11 - 7*l**3 + 3*l**3.
-4*(l - 1)**2*(l + 2)
Let k(p) be the first derivative of -12 + 2/3*p**3 + 4*p**2 + 6*p. Factor k(n).
2*(n + 1)*(n + 3)
Let a(w) be the second derivative of 1/18*w**5 + 1/54*w**4 + 1/63*w**7 + 0 + 0*w**2 + 0*w**3 - 16*w + 7/135*w**6. Determine q so that a(q) = 0.
-1, -1/3, 0
Let f = -1905 + 5719/3. Let l(u) be the first derivative of -10/9*u**3 + 9 - u**2 + f*u. Let l(k) = 0. What is k?
-1, 2/5
Suppose 1 = -4*s + 2*k + 11, -s - 10 = -3*k. Solve -16/5*o**2 - 24/5*o**3 - 16/5*o**4 + 0 - 4/5*o**s - 4/5*o = 0.
-1, 0
Let k(g) be the second derivative of 0*g**3 + 0 + 0*g**2 + 1/135*g**6 + 8*g + 1/6*g**4 - 1/15*g**5. Determine d, given that k(d) = 0.
0, 3
Let d = -1630 - -1630. Determine s, given that -1/5*s**2 + 1/5*s**4 - 1/5*s**3 + 1/5*s**5 + 0 + d*s = 0.
-1, 0, 1
Factor -73 - 156 + 4*k**3 - 52*k**2 - 21 + 19 - 21 + 204*k.
4*(k - 7)*(k - 3)**2
Let w(b) = -2*b**2 - b + 12. Let j be w(4). Let d be (-1 + (-28)/(-21))*j/(-22). Suppose 2/11*h**4 + 2/11*h**2 - 6/11*h**3 + 6/11*h - d = 0. What is h?
-1, 1, 2
Let u(v) be the third derivative of -v**2 + 6/175*v**7 + 0*v**5 - 1/210*v**8 + 1/30*v**6 + 0*v**4 + 0 + 0*v**3 + 2*v. Solve u(g) = 0.
-1/2, 0, 5
Let q(w) be the first derivative of w**4/10 - 4*w**3/15 - w**2/5 + 4*w/5 + 511. Let q(h) = 0. Calculate h.
-1, 1, 2
Suppose 4*h - 97 = -5*f, 3*h = 3*f - 68 - 1. Let k be ((-4)/3)/(175/f - 9). Factor 8/3 + 0*l - 2/3*l**k.
-2*(l - 2)*(l + 2)/3
Let h(i) be the first derivative of i**6/200 - i**5/50 - i**4/40 + i**3/5 + 3*i**2 - 4. Let g(a) be the second derivative of h(a). Factor g(s).
3*(s - 2)*(s - 1)*(s + 1)/5
Let u = -1679 - -1679. Let k(m) be the second derivative of 0 + 0*m**3 - 3/4*m**4 + u*m**2 - 5*m - 3/20*m**5. Factor k(i).
-3*i**2*(i + 3)
Let j(g) = g**3 + g + 3. Let z(q) = -4*q**5 - 20*q**4 + 180*q**2 - 20*q - 492. Let m(i) = -20*j(i) - z(i). Suppose m(v) = 0. Calculate v.
-3, 2
Let y(t) = -19*t**2 - 56*t - 48. Let k(d) = -8 - 14*d - 1 - 5*d**2 + 7 - 10. Let h(p) = 22*k(p) - 6*y(p). Let h(c) = 0. What is c?
-6, -1
Let w(j) be the third derivative of 11/24*j**4 - 7/30*j**5 - 1/30*j**6 + 8/105*j**7 + 12*j**2 + 0 - 1/48*j**8 + 0*j - 1/3*j**3. Suppose w(o) = 0. What is o?
-1, 2/7, 1
Let n = 28 + -26. Factor -d**4 - 13*d**2 + d + d + n*d - 6*d**3 - 16*d - 4.
-(d + 1)**2*(d + 2)**2
Let a(m) be the third derivative of m**6/30 + 14*m**5/15 + 32*m**4/3 + 64*m**3 - 15*m**2 - 21*m. Find j, given that a(j) = 0.
-6, -4
Let o(v) = -2*v**3 - 23*v**2 - 80*v - 39. Let y(a) = a**3 + 25*a**2 + 79*a + 39. Let r(h) = -4*o(h) - 5*y(h). Determine s so that r(s) = 0.
-1, 13
Let n(d) be the first derivative of d**3/3 - 131*d**2/2 + 130*d - 94. Solve n(g) = 0.
1, 130
Let z be (-4)/(-6) - (-30)/9. Suppose 0 = l, z*q - 3*l + 2*l = 24. Determine y so that 7*y**2 - y**4 - 5*y**3 - 4*y - q*y**2 - 9*y**2 = 0.
-2, -1, 0
Let l be (-16)/(-28)*(-7)/(-2). Factor 8*k + 6*k**2 - 2*k**3 - l*k**2 - 10*k.
-2*k*(k - 1)**2
Let u = -1972/3 + 658. Find o, given that 2/3*o**3 - 2/3*o**4 - u*o + 0 + 2/3*o**2 = 0.
-1, 0, 1
Let u(p) = -5*p - 37. Let j be u(-8). Determine g so that -22*g**3 - 4*g**2 + g**3 + g**2 - j*g**2 = 0.
-2/7, 0
Suppose 4*g + 0*g = 2*j - 316, 3*g + 237 = -j. Let l = g + 82. Factor h**l + h - 1/4 - 3/2*h**2 - 1/4*h**4.
-(h - 1)**4/4
Let h(v) = v**3 + 5*v**2 - 19*v - 17. Let f be h(-7). Factor 27*a**4 + f*a**3 - 23*a**3 - 7*a**4.
5*a**3*(4*a - 1)
Let j(d) be the third derivative of d**5/30 - d**4/12 - 2*d**3/3 + 11*d**2 + 3. Factor j(c).
2*(c - 2)*(c + 1)
Let s(m) be the first derivative of -m**5/15 + 7*m**4/12 - 2*m**3/3 + 118. Factor s(u).
-u**2*(u - 6)*(u - 1)/3
Let p = -481 + 486. Let c(m) be the first derivative of -8 + 0*m + 0*m**2 - 1/2*m**4 + 0*m**3 - 2/5*m**p. What is k in c(k) = 0?
-1, 0
Factor 128/19*w + 0 + 2/19*w**3 - 32/19*w**2.
2*w*(w - 8)**2/19
Suppose -18 = -100*k + 49*k + 645. Let 7*n**3 - 1/2*n**4 - 5/2 - 1/2*n**5 + 19/2*n - k*n**2 = 0. What is n?
-5, 1
Let u(v) be the first derivative of v**4/108 - 5*v**3/54 - v**2/3 - 6*v - 7. Let g(o) be the first derivative of u(o). What is q in g(q) = 0?
-1, 6
Suppose -13 = -2*f + 53. Suppose 2*u - 25 - f = 0. Let 5*d**2 - 3*d**2 + 6*d**4 - 35*d**3 + u*d**3 - 2*d**5 = 0. Calculate d.
0, 1
Suppose 14*l - 12*l - 16 = 0. Factor 55 - 55 + 4*u**2 + l*u.
4*u*(u + 2)
Suppose 23 = 5*j + n, 4*j - 4 - 18 = -2*n. Let u be (-12)/9 - j/(-6)*3. Let -4/3*w**5 - 10/3*w**2 - 14/3*w**4 - u*w + 0 - 6*w**3 = 0. What is w?
-1, -1/2, 0
Suppose -428/5*a - 6/5*a**4 + 142/5 + 428/5*a**3 - 136/5*a**2 = 0. What is a?
-1, 1/3, 1, 71
Let v(y) be the third derivative of y**8/252 + y**7/30 + 37*y**6/360 + 2*y**5/15 + y**4/18 - 2*y**2 - 4. Let v(d) = 0. What is d?
-2, -1, -1/4, 0
Let 19*y**4 - 19*y**2 - 10*y**3 - 15*y**2 - 32*y - 41*y**2 + 11*y**2 - 3*y**5 = 0. What is y?
-1, -2/3, 0, 4
Suppose 0*m + 0*m**2 - 1/7*m**5 - 2/7*m**3 - 3/7*m**4 + 0 = 0. Calculate m.
-2, -1, 0
Let f(n) be the first derivative of 1/5*n**4 - 2/5*n**2 - 4/15*n**3 + 0*n + 19 + 4/25*n**5. Factor f(x).
4*x*(x - 1)*(x + 1)**2/5
Let h(r) be the third derivative of 0*r**3 + 0*r + 2/35*r**7 + 1/30*r**6 - 2*r**2 + 1/84*r**8 - 1/3*r**4 - 1/5*r**5 + 0. Determine q so that h(q) = 0.
-2, -1, 0, 1
Factor 0 - 8/3*q**2 - 7/3*q**4 - 5*q**3 + 0*q.
-q**2*(q + 1)*(7*q + 8)/3
Let s be 11 + (0 - 3) + 6*(-3 - -2). Determine k so that -4/9 - 2/9*k**4 + 2/9*k**3 + 2/3*k**s - 2/9*k = 0.
-1, 1, 2
Let w(a) be the first derivative of 37 + 0*a - 1/10*a**4 + 0*a**2 - 2/15*a**3. Factor w(z).
-2*z**2*(z + 1)/5
Suppose 0 = -3*f - 0 - 6. Let s(w) = -w**3 - w**2 - 2*w - 4. Let p be s(f). Factor i + 3*i**2 + i**2 - i - 4*i**p.
-4*i**2*(i - 1)*(i + 1)
Let z = 1891 - 1888. Factor 6*h - 3/2*h**2 - 8 + 1/8*h**z.
(h - 4)**3/8
Let m(c) be the first derivative of c**7/63 - 4*c**6/45 + c**5/5 - 2*c**4/9 + c**3/9 - 6*c + 2. Let v(l) be the first derivative of m(l). Factor v(g).
2*g*(g - 1)**4/3
Let b(q) be the second derivative of q**3/6 - 2*q**2 - q. Let c be b(6). Solve 5*t - c*t**2 - t - 2*t**3 - 4*t = 0 for t.
-1, 0
Let d(q) be the third derivative of q**7/1890 + 19*q**6/540 + 277*q**5/540 - 133*q**4/18 + 98*q**3/3 + 212*q**2. Find v such that d(v) = 0.
-21, 2
Find n such that 12/11*n + 2*n**2 + 0 - 2/11*n**4 + 8/11*n**3 = 0.
-1, 0, 6
Suppose 0 = 7*u + 117 - 131. Factor -u*r**3 + 5/4*r**4 + 0*r + 0 - r**2.
r**2*(r - 2)*(5*r + 2)/4
Suppose 35 = 32*w - 29. Let c(v) be the first derivative of 6*v**w + 1/2*v**4 - 10 - 3*v**3 - 4*v. Determine t, given that c(t) = 0.
1/2, 2
Let a(p) be the second derivative of 5*p**4/12 - 10*p**3 + 175*p**2/2 + 347*p. Find r such that a(r) = 0.
5, 7
Let a(d) be the second derivative of -2*d**4/3 - 11*d**3/3 - 6*d**2 - 946*d. Solve a(j) = 0.
-2, -3/4
Let l = -8 - -11. Let t(m) be the second derivative of -1/63*m**7 + 1/3*m**l - 1/15*m**6 + 0 + 1/9*m**4 - 1/15*m**5 + 1/3*m**2 - 12*m. Solve t(y) = 0.
-1, 1
Let 8/5*v + 2*v**2 + 0 = 0. Calculate v.
-4/5, 0
Factor -7*r**3 + r**5 - 8*r + 2*r + 38*r**4 - 2*r**2 - 37*r**4 - 11*r**2.
r*(r - 3)*(r + 1)**2*(r + 2)
Suppose 0 = 9*g - 8 - 478. Let c be 24/g*2/(8/6). Suppose 0*z**4 - c*z**5 - 2/3*z + 0*z**2 + 4/3*z**3 + 0 = 0. Calculate z.
-1, 0, 1
Let o(r) = -r**2. Let m(f) = -8*f**3 - 9*f**2 + 8*f. Let l(c) = -m(c) - 3*o(c). Factor l(s).
4*s*(s + 2)*(2*s - 1)
Let f be (4 - 38/8)*31/((-186)/24). Factor 24/5*t**2 + 6*t + 6/5*t**f + 12/5.
6*(t + 1)**2*(t + 2)/5
Let z(o) be the first derivative of o**6/1440 - 2*o**3 + 9. Let t(r) be the third derivative of z(r). Factor t(p).
p**2/4
Let -225/4*s - 1/4*s**5 - 83/2*s**3 - 7*s**4 + 105*s**2 + 0 = 0. What is s?
-15, 0, 1
Let p = 36341/11 - 3301. Factor -p*d - 6/11 - 24/11*d**2.
-6*(d + 1)*(4*d + 1)/11
Let p(s) be the third derivative of -s**7/11340 + s**4/24 + 11*s**3