*h**4/12 - 49*h**3/6 + h**2 - 43*h. Determine b, given that d(b) = 0.
7
Let w(f) = 2*f - 28 - 8*f**2 - 2*f**3 - 21 + 47. Let t(u) = -3*u**3 - 9*u**2 + 3*u - 3. Let z(s) = 5*t(s) - 6*w(s). Suppose z(o) = 0. What is o?
-1, 1
Let y(x) be the second derivative of -37*x + 1/7*x**4 + 38/21*x**3 - 4*x**2 + 0. Factor y(b).
4*(b + 7)*(3*b - 2)/7
Let n(y) be the third derivative of y**5/240 - y**4/32 - y**3/6 + y**2 - 24*y. Factor n(i).
(i - 4)*(i + 1)/4
Let y(c) = 22*c**2 - 940*c - 22090. Let h(n) = -4*n**2 + 188*n + 4418. Let x(w) = 16*h(w) + 3*y(w). Factor x(z).
2*(z + 47)**2
Let p(y) = -20*y**2 - 39*y + 43. Let f(d) = -321*d**2 - 624*d + 687. Let x(s) = 2*f(s) - 33*p(s). Solve x(j) = 0.
-3, 5/6
Let n = -25/41 - -291/410. Let t(s) be the first derivative of 7/4*s**2 + s + 5/8*s**4 - 3 + 3/2*s**3 + n*s**5. Suppose t(a) = 0. Calculate a.
-2, -1
Let d be (-4)/(4*(-3)/(-36)). Let f = 15 + d. Solve -145*g**2 - 99*g**4 + 49*g**5 - f - 76*g**4 + 12*g - 1 + 28*g + 235*g**3 = 0 for g.
2/7, 1
Let k(n) be the second derivative of -1 - 1/20*n**5 + 3*n - 1/12*n**4 + 1/3*n**3 + 0*n**2. Factor k(i).
-i*(i - 1)*(i + 2)
Let u be 1*12/15*10/4. Factor -u*g**2 + 0*g + 2*g**4 + 0*g.
2*g**2*(g - 1)*(g + 1)
Let m(h) be the second derivative of h**7/2520 - h**6/80 - h**5/12 + h**4/12 + 7*h. Let c(r) be the third derivative of m(r). Let c(i) = 0. Calculate i.
-1, 10
Let x(p) = p - 1. Let v be x(4). Suppose -a + v*h - h = 5, -3*h = 5*a - 27. Factor -1/2*t**5 - 3*t**a - 2*t**4 + 0 - 1/2*t - 2*t**2.
-t*(t + 1)**4/2
Let h(o) be the second derivative of -o**5/10 + 8*o**4/3 - 52*o**3/3 + 48*o**2 - 141*o. Factor h(r).
-2*(r - 12)*(r - 2)**2
Let x(f) be the second derivative of -f**5/390 + f**4/156 - 37*f**2/2 + 30*f. Let o(v) be the first derivative of x(v). Suppose o(m) = 0. What is m?
0, 1
Let t(u) be the third derivative of -2/75*u**5 - 2/15*u**4 + 2/5*u**3 + 0 + 29*u**2 - 2/525*u**7 + 2/75*u**6 + 0*u. Find a such that t(a) = 0.
-1, 1, 3
Let l be (342/(-36) - -12)/(-2*10/(-24)). Factor 6/7*g + 2/7 - 4/7*g**l - 6/7*g**4 + 4/7*g**2 - 2/7*g**5.
-2*(g - 1)*(g + 1)**4/7
Let u be 24/(-18)*2/(-4). Suppose -2*c + 4 = -2*k + 2, -4*c + 14 = k. Determine h so that 0 - 1/3*h**4 + 0*h**2 - u*h**c + 0*h = 0.
-2, 0
Let w(c) be the first derivative of -c**4/42 + 2*c**3/21 + 3*c**2/7 - 29*c - 3. Let a(f) be the first derivative of w(f). Factor a(k).
-2*(k - 3)*(k + 1)/7
Let z(x) be the third derivative of x**8/2856 - x**7/595 + x**6/340 - x**5/510 - 2*x**2 + 35*x. Factor z(y).
2*y**2*(y - 1)**3/17
Let t(p) be the first derivative of p**5/25 - 2*p**4/5 - 195. Let t(g) = 0. What is g?
0, 8
Let h = -10 + 13. Let j(o) = -18*o**3 - 134*o**2 - 63*o - 6. Let c(x) = x**3 - x**2 - x - 1. Let y(u) = h*j(u) + 6*c(u). Factor y(p).
-3*(p + 8)*(4*p + 1)**2
Suppose -12*y + 246 = 222. Let w(o) be the first derivative of -2/15*o**3 + 4/5*o + 8 - 1/5*o**y. Determine x so that w(x) = 0.
-2, 1
Let j(y) be the third derivative of 33*y**2 + 0 - 1/20*y**5 + 0*y - 6*y**3 - y**4. Let j(g) = 0. What is g?
-6, -2
Let f(n) = 52*n**2 - 140*n + 16. Suppose 33 = -6*c - 15. Let k(v) = 35*v**2 - 93*v + 11. Let m(q) = c*k(q) + 5*f(q). Factor m(u).
-4*(u - 2)*(5*u - 1)
Suppose 13*x + 173 = 212. Let 9/2*h**4 + 12 + 59*h**2 - 46*h - 57/2*h**x = 0. What is h?
2/3, 2, 3
Suppose 4*q = -0*q + 55*q - 102. Factor 4/5 - 12/5*p + 13/5*p**q + 1/5*p**4 - 6/5*p**3.
(p - 2)**2*(p - 1)**2/5
Let x(i) be the first derivative of -4/3*i + 4 - 11/3*i**3 - 11/3*i**2 - 7/30*i**5 - 37/24*i**4. Find o, given that x(o) = 0.
-2, -1, -2/7
Let b = -47/2 + 24. Let w be -2 + (-21)/(-9) - 2/12. Factor -1/6*z**2 + 1/3*z**4 + 1/2*z - b*z**3 - w.
(z - 1)**2*(z + 1)*(2*z - 1)/6
Suppose -200*n + 402*n - 173*n = 0. What is d in 8/5*d**3 + 16/5*d**2 + 1/5*d**4 + 0 + n*d = 0?
-4, 0
Let q(c) be the first derivative of c**4/8 + 2*c**3/3 + c**2 + 138. Factor q(y).
y*(y + 2)**2/2
Let h(n) be the second derivative of n**6/6 + 15*n**5/4 - 355*n**4/12 + 155*n**3/2 - 95*n**2 - 220*n - 2. Let h(c) = 0. What is c?
-19, 1, 2
Factor 0*o**2 + 0 - 1/2*o**3 + 1/2*o.
-o*(o - 1)*(o + 1)/2
Let x be 5 + 40/(-48)*3. What is o in -1/2*o**3 + x*o**2 + 2 - 4*o = 0?
1, 2
Let x(d) be the first derivative of 2*d**3/21 + 51*d**2/7 + 543. What is v in x(v) = 0?
-51, 0
Suppose 2*s + o - 10 = -s, 0 = 2*s + 2*o. Suppose -s = 2*x - 5*q, 0*x - 3 = -5*x - 3*q. What is n in 0 - 1/6*n**2 + x*n = 0?
0
Suppose 0*z = -15*z. Let d(i) be the first derivative of z*i - 4 + 2/15*i**3 + 0*i**2 + 6/25*i**5 - 3/10*i**4 - 1/15*i**6. Factor d(m).
-2*m**2*(m - 1)**3/5
Suppose -881 + 628 = 18*h - 397. Solve 0 + 0*w - 4*w**5 + 52/3*w**3 + 16/3*w**4 + h*w**2 = 0 for w.
-1, -2/3, 0, 3
Suppose 150*w**5 - 125*w**5 + 12*w**2 - 4*w**3 + 9*w**3 - 40*w**4 - 2*w**2 = 0. Calculate w.
-2/5, 0, 1
Let o(u) be the first derivative of u**5/20 - 3*u**4/4 + 5*u**3/2 + 25*u**2/2 - 375*u/4 - 53. Suppose o(k) = 0. What is k?
-3, 5
Let -2/5*s**2 + 8 - 38/5*s = 0. Calculate s.
-20, 1
Let l(i) = 2*i**4 + 2*i**3 + i - 1. Let g(a) = -9*a**4 + 18*a**3 + 69*a**2 + 36*a + 6. Let b(t) = -g(t) - 6*l(t). Factor b(k).
-3*k*(k + 1)*(k + 2)*(k + 7)
Suppose -x + 4 = -0*x - 4*h, 3*h + 3 = 4*x. Suppose x*b = 3*b - 4*c + 6, -c - 7 = -5*b. Let z + 0*z**b - 3*z + 1 - 2 - z**2 = 0. What is z?
-1
Let h(a) be the third derivative of 1/70*a**7 - 33*a**2 - 3/20*a**5 + 0 + 0*a + 1/40*a**6 + a**3 - 1/8*a**4. Factor h(m).
3*(m - 1)**2*(m + 1)*(m + 2)
Factor 25/2*k**2 + 3*k + 0 - 25/2*k**3.
-k*(5*k - 6)*(5*k + 1)/2
Let i be (10 + -14)/((-8)/10). Let j(y) be the third derivative of -1/4*y**4 - 1/20*y**i + 0 + 0*y + 1/40*y**6 + 2*y**2 + 0*y**3. Find v such that j(v) = 0.
-1, 0, 2
Find q such that 1/2*q**5 + 0 + 5/2*q**3 - 2*q**4 + 0*q - q**2 = 0.
0, 1, 2
Let v be (3515/750)/(-19) - (-3)/12. Let d(h) be the third derivative of 1/120*h**4 + h**2 - v*h**5 + 0*h + 0 + 1/15*h**3. Factor d(g).
-(g - 2)*(g + 1)/5
Let x(m) = 2*m**3 - 3*m**3 + m - 5 + 0*m + 0*m + 7*m**2. Let h be x(7). Factor -10*n**3 + 0*n**3 + 5*n**2 + h*n + 3*n**3.
-n*(n - 1)*(7*n + 2)
Let r(j) be the first derivative of -j**6/5 + 192*j**5/25 - 573*j**4/5 + 4104*j**3/5 - 13851*j**2/5 + 17496*j/5 + 559. Suppose r(g) = 0. What is g?
1, 4, 9
Let j(y) be the first derivative of -13*y**4/2 - 84*y**3 - 285*y**2 + 200*y + 994. What is q in j(q) = 0?
-5, 4/13
Factor -1/4*w**2 - 21/4*w - 5.
-(w + 1)*(w + 20)/4
Factor -54/7*d**2 + 3/7*d**3 + 0 + 96/7*d.
3*d*(d - 16)*(d - 2)/7
Let x(y) be the first derivative of -y**6/12 - 17*y**5/10 - 53*y**4/4 - 145*y**3/3 - 325*y**2/4 - 125*y/2 + 137. Let x(b) = 0. Calculate b.
-5, -1
Let t = 282 + -282. Let b(c) be the first derivative of t*c + 0*c**3 - 3 + 1/16*c**4 - 1/8*c**2. Factor b(n).
n*(n - 1)*(n + 1)/4
Factor -17/3 + 1/3*k**4 - 16*k**2 + 14/3*k**3 + 50/3*k.
(k - 1)**3*(k + 17)/3
Let f(a) = -65*a**2 + 84*a - 18. Let z(j) = 31*j**2 - 42*j + 9. Let q(l) = -6*f(l) - 11*z(l). Suppose q(k) = 0. Calculate k.
3/7
Let p(k) = k - 9. Let f be p(11). Determine a, given that -31*a + 0 - 2 - f*a**2 + 63*a - 28*a = 0.
1
Suppose 4*l + 3*j = 5*j - 2, -2*j = l - 12. Suppose 3*p - 8*p**3 - 3*p**3 + 3*p**3 + 3*p**5 + l*p**3 = 0. Calculate p.
-1, 0, 1
Let f(h) be the third derivative of h**7/525 - 19*h**6/300 - 7*h**5/25 - 251*h**2. Determine w so that f(w) = 0.
-2, 0, 21
Suppose 18 - 48 = -3*r. Let d = r - 7. Factor 8*v**4 + 3*v**d + 7*v**4 - 3*v**4.
3*v**3*(4*v + 1)
Suppose -2*i + u - 11 = 4*u, 4*u = 3*i + 25. Let m be 14/(-3)*4/i. Factor 0 + 2/3*r**2 + m*r.
2*r*(r + 4)/3
Let j(m) = m**5 + m**3 - m**2 - m - 1. Let u(h) = -15*h**5 - 15*h**4 + 27*h**3 - 3*h**2 + 6*h + 6. Let x(s) = -6*j(s) - u(s). Determine a, given that x(a) = 0.
-3, 0, 1/3, 1
Let y be 108/882*(-112)/(-24). Solve 2/7 - y*g**2 + 4/7*g**3 - 2/7*g + 2/7*g**4 - 2/7*g**5 = 0 for g.
-1, 1
Suppose 64 = -17*p + 64. Let k = 2 - 0. Let 0*i - 3/7*i**4 + p + 0*i**k + 1/7*i**3 = 0. What is i?
0, 1/3
Let y(h) be the first derivative of -h**4/8 + 95*h**3/2 - 27075*h**2/4 + 857375*h/2 + 382. Factor y(i).
-(i - 95)**3/2
Let h(f) be the second derivative of 1/3*f**3 + 3*f - 1/42*f**7 + 5/12*f**4 - 1/30*f**6 + 0*f**2 + 3/20*f**5 + 0. Factor h(y).
-y*(y - 2)*(y + 1)**3
Let h(v) = 7*v**4 - 33*v**3 + 36*v**2 + 10*v. Let z(l) = 7*l**4 - 33*l**3 + 38*l**2 + 9*l. Let c(p) = -3*h(p) + 2*z(p). Factor c(y).
-y*(y - 3)*(y - 2)*(7*y + 2)
Determine f,