15. Let b be r(15). Let w(k) be the first derivative of b*k - 3/5*k**5 + 2 + 1/2*k**4 + 1/6*k**6 + 0*k**3 + 0*k**2. Solve w(u) = 0.
0, 1, 2
Let r(i) be the first derivative of 5 + 3*i**2 - 3/2*i**4 + 3/5*i**5 - 3*i + 0*i**3. Solve r(p) = 0.
-1, 1
Let n(j) be the first derivative of 49 + 4/7*j**2 + 0*j + 1/7*j**4 - 4/7*j**3. What is h in n(h) = 0?
0, 1, 2
Suppose -9*o - 2*l + 4 = -5*o, -31 = -5*o + 4*l. Let x(c) be the first derivative of 1/12*c**2 - 1/18*c**o + 13 + 0*c. Factor x(y).
-y*(y - 1)/6
Let u(b) be the first derivative of 2*b**6/15 - 4*b**4/5 - 8*b**3/15 + 6*b**2/5 + 8*b/5 + 79. Factor u(k).
4*(k - 2)*(k - 1)*(k + 1)**3/5
Let q(g) = g**2 - 7*g + 5. Suppose 0*h - h - 5 = 0. Let l(u) = 2372*u + 0*u**2 - 2378*u + 4 + u**2. Let j(s) = h*l(s) + 4*q(s). Find w, given that j(w) = 0.
0, 2
Let t be 3*2/(-9) - 196/(-6). Factor -38*m**3 + t*m + 8 + 42*m**3 + 8 + 20*m**2.
4*(m + 1)*(m + 2)**2
Let v(y) be the third derivative of -1/80*y**6 + 0*y**3 + 0*y - 1/16*y**4 + 0 - 25*y**2 - 1/20*y**5. Determine f, given that v(f) = 0.
-1, 0
Let j(y) = y**2 - 5*y + 64. Let s(l) = l**2 - 2*l + 4. Let c(p) = j(p) - 2*s(p). Find q, given that c(q) = 0.
-8, 7
Let o(b) be the first derivative of 7*b**6/12 + 4*b**5/5 + b**4/8 - 672. Factor o(a).
a**3*(a + 1)*(7*a + 1)/2
Factor 2/3*w**2 + 20/3*w - 22/3.
2*(w - 1)*(w + 11)/3
Suppose 6*i**2 - 72*i + 288 - 1/6*i**3 = 0. What is i?
12
Let i(m) be the first derivative of m**3 + 45*m**2/2 + 78*m - 41. Factor i(f).
3*(f + 2)*(f + 13)
Let g = 71 - 134. Let y be (g/42)/((-6)/16*1). Solve 1/2 + 3/4*n**2 + 7/4*n**3 - 5/4*n**y - 7/4*n = 0.
-1, 2/5, 1
Let o(l) be the second derivative of -2*l**6/15 + 3*l**5 - 12*l**4 - l - 61. Determine f so that o(f) = 0.
0, 3, 12
Let b = 84 + -20. Factor -4*i**4 - b + 32*i**2 + 22*i - 5*i + 23*i + 2*i**5 - 8*i - 16*i**3.
2*(i - 2)**3*(i + 2)**2
What is b in 100*b**3 + 85/2*b**4 + 5/2*b**5 + 0*b + 0 - 750*b**2 = 0?
-10, 0, 3
Suppose 7*o - 3*o - 8 = s, 0 = -3*o + 2*s + 1. Suppose -3*j + 26 = 4*d, 4 - 3 = -2*j + d. Factor 2*h - 4*h**3 + 2*h - 5*h**j + 12 - 4 - o*h**2.
-4*(h - 1)*(h + 1)*(h + 2)
Let s(j) = -4*j - 6*j**2 - 8*j**3 + 60 - 60. Let t(g) = g**4 - 9*g**3 - 6*g**2 - 5*g. Let r(o) = -6*s(o) + 4*t(o). What is b in r(b) = 0?
-1, 0
Let m = -24 - -28. Let y(d) be the first derivative of d**3 - 5/2*d**2 + 2 + 2*d + 1/4*d**m - 1/5*d**5. Solve y(g) = 0.
-2, 1
Let a = 2225/7 - 19955/63. What is z in -4/3 - 2/9*z**2 + a*z = 0?
2, 3
Let z be 2*15/(-90) - 26/(-24). Suppose -3/2 - z*v**2 + 9/4*v = 0. What is v?
1, 2
Let q(o) be the third derivative of -o**8/1008 + o**7/630 + o**6/120 - o**5/180 - o**4/36 + 2*o**2 - 21. Let q(t) = 0. Calculate t.
-1, 0, 1, 2
Let t = 12849/44 - 171/22. Let j = -282 + t. Factor 3/4*f + j*f**2 - 3/2.
3*(f + 1)*(3*f - 2)/4
Determine b, given that 692/9 + 2426/9*b + 14/9*b**2 = 0.
-173, -2/7
Let y(n) be the first derivative of -n**4/10 + 6*n**3/5 - 24*n**2/5 + 8*n - 490. Factor y(t).
-2*(t - 5)*(t - 2)**2/5
Suppose -3*q + 7*q = 28. Let r(p) = 13*p**2 + 7. Let l(g) = 4*g**2 + 2. Let n(b) = q*l(b) - 2*r(b). Let n(y) = 0. Calculate y.
0
Solve 3*j - j**2 + 15 + 17*j - 31 - 3*j**2 = 0.
1, 4
Let m(t) = t**3 + 10*t**2 - 13*t - 20. Let h be m(-11). Let u**h - 8 - 4*u + 8 + u**2 = 0. Calculate u.
0, 2
Let s(k) = -k**3 + 3*k**2 - 3*k + 5. Let t be s(2). Let b(l) be the first derivative of 6/5*l**2 - 5 - 2/3*l**t - 2/5*l. Find y, given that b(y) = 0.
1/5, 1
Let h(x) be the second derivative of x**8/560 + x**7/56 + x**6/20 - x**3/3 - 3*x**2/2 + 49*x. Let c(k) be the second derivative of h(k). What is s in c(s) = 0?
-3, -2, 0
Let y be (9 + 510/(-54))/((-28)/72). Solve y*i - 2/7*i**2 - 8/7 = 0.
2
Let a(n) be the first derivative of -n**6/2 + 6*n**5 - 45*n**4/2 + 40*n**3 - 75*n**2/2 + 18*n - 349. Solve a(h) = 0.
1, 6
Let f(x) be the second derivative of 2*x**7/21 + 2*x**6/15 - 7*x**5/5 - x**4/3 + 4*x**3 + x - 28. Solve f(s) = 0.
-3, -1, 0, 1, 2
Suppose 0 = f - 2 - 1. Suppose 0*t = o - t - f, -2*o + 3 = t. Factor 2*k**4 + 2*k**3 + k**o - 2*k**5 - 5*k**2 + 2*k**2.
-2*k**2*(k - 1)**2*(k + 1)
Let d(l) be the first derivative of 2/7*l**2 + 2/21*l**3 + 2/7*l - 8. Factor d(s).
2*(s + 1)**2/7
Let r = -122030/358187 + 2/7621. Let w = 488/329 + r. Find s such that 8/7*s - 2/7*s**2 - w = 0.
2
Let a = 978529/9 - 108842. Let c = a + 117. Factor c*k**3 + 2/9*k**5 - 2/3*k - 4/9*k**2 - 2/9 + 2/3*k**4.
2*(k - 1)*(k + 1)**4/9
Let z(h) = -h + 1. Let c(i) = -3*i**2 + 54*i - 111. Let g(o) = c(o) - 15*z(o). Factor g(k).
-3*(k - 21)*(k - 2)
Let q be -9*((-20)/75)/(4/(-10)). Let k be (-2)/q - (-14)/147. Determine f, given that -1/7 + 4/7*f**2 + k*f = 0.
-1, 1/4
Let c(v) be the second derivative of -v**9/45360 + v**8/10080 - v**7/7560 - v**4 - 19*v. Let h(a) be the third derivative of c(a). What is g in h(g) = 0?
0, 1
Let j(w) be the first derivative of -3*w**5/5 - 9*w**4/2 - 3*w**3 + 15*w**2 + 150. Factor j(b).
-3*b*(b - 1)*(b + 2)*(b + 5)
Let r(p) be the first derivative of 0*p**3 + 0*p + 1/2*p**4 - 16 + 0*p**2. Factor r(c).
2*c**3
Determine t, given that 1/4*t**3 + 0*t - 1 + 3/4*t**2 = 0.
-2, 1
Let x(m) be the third derivative of 10*m**2 + 1/20*m**5 + 0 + 0*m + 1/4*m**4 - 3/2*m**3. Factor x(v).
3*(v - 1)*(v + 3)
Let m be 59 + (-16)/12*3. Let q = m - 107/2. Factor -3 - 9/2*l**2 + q*l**3 + 3/2*l**4 - 15/2*l.
3*(l - 2)*(l + 1)**3/2
Suppose g = 2*x + 2, -3*g = -7*g + 5*x + 8. Let n(y) be the first derivative of 2/9*y**g - 2/27*y**3 - 4 + 0*y - 1/18*y**4. Factor n(c).
-2*c*(c - 1)*(c + 2)/9
Let y = 1185 + -1182. Suppose 0*g + 12 = 3*g. Factor 44/3*a**2 + 6 - 16/3*a**y - 16*a + 2/3*a**g.
2*(a - 3)**2*(a - 1)**2/3
Let q(i) = 9*i**2 + 25*i + 6. Let n(w) be the first derivative of -w**3/3 + w**2/2 + 13. Let t(x) = -n(x) - q(x). What is v in t(v) = 0?
-3, -1/4
Let u(z) be the second derivative of z**7/63 - z**6/45 - z**5/15 - 135*z. Factor u(s).
2*s**3*(s - 2)*(s + 1)/3
Let v(r) be the second derivative of -r**4/114 - 41*r**3/57 - 40*r**2/19 + r + 26. Factor v(o).
-2*(o + 1)*(o + 40)/19
Let d(c) be the second derivative of -c**7/23940 - c**6/2280 + c**5/285 - 3*c**4/4 + 6*c. Let x(f) be the third derivative of d(f). What is a in x(a) = 0?
-4, 1
Let r(k) = -4*k**3 + 138*k**2 + 5476*k + 5. Let o(j) = -j**3 - 2*j**2 + 1. Let c(d) = 15*o(d) - 3*r(d). Factor c(f).
-3*f*(f + 74)**2
Let r(t) be the second derivative of t**6/90 + 13*t**5/30 + 73*t**4/36 - 208*t**3/3 + 384*t**2 - 4*t - 27. Suppose r(f) = 0. What is f?
-16, 3
Let v(d) be the first derivative of -3*d**4 + 16/3*d**3 + 2/3*d**6 - 8/5*d**5 + 0*d + 8*d**2 + 10. Let v(m) = 0. What is m?
-1, 0, 2
Let -1/8*a**2 - 3/8*a**3 + 0 + 1/4*a = 0. What is a?
-1, 0, 2/3
Let h(l) = 10*l**3 + 62*l**2 - 138*l - 62. Let n(z) = z**2 + z - 1. Let v(r) = -h(r) - 2*n(r). Factor v(o).
-2*(o - 2)*(o + 8)*(5*o + 2)
Let g(k) = -3*k**3 - 9*k**2 - 3*k + 3. Let j(b) = -5*b**3 - 17*b**2 - 6*b + 6. Suppose -y = -0*y - 6. Let a(h) = y*j(h) - 11*g(h). Solve a(p) = 0 for p.
-1, 1
Let v(w) = w**3 - 6*w**2 - 19*w + 28. Let s be v(8). Let y(z) be the second derivative of 1/48*z**s + 0 + z + 1/4*z**3 + 9/8*z**2. Factor y(b).
(b + 3)**2/4
Let i = 52 + -49. Suppose -26 = -2*x - 2*b - 2*b, 3*b = 3*x - i. Determine g so that 2/7*g**x + 0*g + 0*g**2 + 0 - 2/7*g**4 + 0*g**3 = 0.
0, 1
Suppose 96 - 91 = -t. Let a(w) = 6*w**2 + 5*w - 7. Suppose 4*s = 132 + 8. Let f(l) = l**2 + l - 1. Let z(o) = s*f(o) + t*a(o). Factor z(c).
5*c*(c + 2)
Let t(k) = -k**2 - 10*k + 29. Let p be t(-12). Let l be 1/4 + (-15)/(-4). Solve -p - 10*g**2 + l*g + 2*g + 9 = 0.
-2/5, 1
Let x(d) be the first derivative of d**6/3 + 12*d**5/5 + d**4/2 - 16*d**3 + 16*d**2 + 131. Determine l so that x(l) = 0.
-4, 0, 1
Let v(k) = -k**3 + 10*k**2 + k. Let h be v(10). Let p = h - 8. Factor 2*a + 6 + 5*a**2 - 2*a**p - 11*a.
3*(a - 2)*(a - 1)
Let h be (3 + -7)*(2 - 6/2). Factor -z**3 - 1 + 2*z - 2 - z**3 + h*z**2 - 1.
-2*(z - 2)*(z - 1)*(z + 1)
Let p(a) = -a + 10. Let g be p(18). Let k be 6/225*-6*20/g. Factor 0 + 0*c - k*c**4 + 6/5*c**3 - 4/5*c**2.
-2*c**2*(c - 2)*(c - 1)/5
Let y = -41 - 43. Let v = 86 + y. Factor 48 + 9*i**v + 3/4*i**3 + 36*i.
3*(i + 4)**3/4
Let y(p) be the first derivative of p**5/30 + p**4/24 - 2*p**3/9 - p**2/3 + 71. Determine o, given that y(o) = 0.
-2, -1, 0, 2
Let r(t) be the second derivative of t**5/180 - 4*t**4/27 + 7