9*j**3 + 1/3*j - p*j**4 - 5. Find i, given that h(i) = 0.
1, 2
Suppose -12*a**5 + 117*a**3 + 78*a**4 - a**2 + 31*a**2 + 3*a**5 - 1 + 1 = 0. Calculate a.
-1, -1/3, 0, 10
Let u(c) be the third derivative of 14*c**2 + 0*c - 5/8*c**4 + 0*c**3 + 0 + 1/12*c**5. Factor u(m).
5*m*(m - 3)
Solve 5*h**2 - 7/2*h**3 - 3/2*h**4 + 4 + 14*h = 0.
-2, -1/3, 2
Let s(f) be the third derivative of -f**10/264600 - f**9/84672 - f**8/141120 - 11*f**5/60 - 13*f**2. Let z(h) be the third derivative of s(h). Factor z(x).
-x**2*(x + 1)*(4*x + 1)/7
Let u(p) = 9*p**3 + 63*p**2 + 54*p + 17. Let d(h) = 218 + 11*h**3 + 24*h - 212 - 6*h - 8*h**3 + 21*h**2. Let k(s) = -17*d(s) + 6*u(s). Factor k(c).
3*c*(c + 1)*(c + 6)
Let i(t) be the third derivative of t**7/210 - 31*t**2. Solve i(x) = 0 for x.
0
Let w(o) = -o - 15. Let p be w(-6). Let b be 2 + 4 + p/3. Find f, given that 3*f**4 + 9*f**b - f**2 - 54*f + 57*f + 2*f**2 + 8*f**2 = 0.
-1, 0
Let h(v) be the third derivative of -v**9/3024 + v**8/672 - v**4/6 + 9*v**2. Let n(y) be the second derivative of h(y). Suppose n(c) = 0. What is c?
0, 2
Factor 459/2*y**2 + 3/4 + 267/8*y.
3*(17*y + 2)*(36*y + 1)/8
Suppose -6 = -4*a + 14. Suppose -a*u + 2 = -8. Factor -15*g**2 - 3*g + 9*g**2 - 2 + 5*g**u.
-(g + 1)*(g + 2)
Let h(b) be the second derivative of b**6/105 + b**5/10 + 3*b**4/7 + 20*b**3/21 + 8*b**2/7 - 62*b - 3. Factor h(c).
2*(c + 1)*(c + 2)**3/7
Factor 2/7*k**2 + 338/7 + 52/7*k.
2*(k + 13)**2/7
Suppose -5*m + 3*q - 9 = -4*m, -20 = -4*q. Suppose m*t = t. Determine r so that 20*r**2 + 7*r**3 + 9*r**3 + 0 + 8*r + 4*r**4 + t = 0.
-2, -1, 0
Let h be (-112)/(-180) + -7 + 366/54. Solve 2/5*q**5 + 0 - h*q**2 + 0*q - 2/5*q**3 + 2/5*q**4 = 0 for q.
-1, 0, 1
Suppose -o + 18 = -5*i, -4*o + 7*o - 18 = 3*i. Let s(p) be the first derivative of 1/9*p**o + 1/3*p + 1/3*p**2 + 1. Factor s(y).
(y + 1)**2/3
Let u(t) be the second derivative of -t**6/90 - t**5/30 + t**4/36 + t**3/9 - 4*t - 4. Let u(z) = 0. What is z?
-2, -1, 0, 1
Let x(q) be the first derivative of -4/11*q - 2/11*q**3 - 2 - 7/11*q**2. Suppose x(f) = 0. What is f?
-2, -1/3
Let g be (-1)/(-4) + 11/4. Let j(k) be the second derivative of 1/12*k**4 + 0 - 4/15*k**g - 2/5*k**2 - k. Suppose j(c) = 0. Calculate c.
-2/5, 2
Let p(o) be the second derivative of 0*o**2 + 1/48*o**4 + 0 - 18*o + 0*o**3. Factor p(r).
r**2/4
Let v(s) = 2*s - 27. Let y be v(22). Find w, given that 4*w**4 + 20*w**3 + 32 - 6*w**2 - 8*w**4 - w**2 - y*w**2 - 16*w = 0.
-1, 2
Suppose -1/5*n**2 + 3 - 2/5*n = 0. What is n?
-5, 3
Let d(r) be the first derivative of r**6/48 - 3*r**5/8 + 83*r**4/32 - 209*r**3/24 + 15*r**2 - 25*r/2 + 31. Find g such that d(g) = 0.
1, 2, 5
Let u(y) be the first derivative of 0*y**3 + 5/4*y**4 - 15/2*y**2 - 10*y + 8. Factor u(x).
5*(x - 2)*(x + 1)**2
Determine z so that 33 + 47*z - 5*z**3 + 37 - 11*z**2 + 31*z**2 + 48*z = 0.
-2, -1, 7
Let c(r) be the third derivative of r**5/600 - r**4/80 - 37*r**2 - 1. Find l such that c(l) = 0.
0, 3
Suppose -57 = -105*s + 104*s. Solve -4*j**3 - 23*j**2 - 6*j**4 + s*j**2 - 28*j**2 + 4*j = 0.
-1, -2/3, 0, 1
Let b(k) be the first derivative of 3*k**7/1120 + k**6/96 - k**5/40 - k**4/8 - 13*k**3/3 - 1. Let i(g) be the third derivative of b(g). Factor i(o).
3*(o - 1)*(o + 2)*(3*o + 2)/4
Suppose 15*q + 4 = 17*q. Find d, given that -3*d**4 + 4*d**4 + 2*d**3 - 4*d**3 + 1 - q + 2*d = 0.
-1, 1
Let f be -318*2/(-1) - -3. Suppose 6*j + 153 = f. Suppose -3/2*i**4 - j*i**2 - 162*i - 243/2 - 18*i**3 = 0. Calculate i.
-3
Suppose -4*g = 3*c - 28 - 10, -2*g + 26 = 5*c. Let o be (-5 - -3) + g/2. What is p in -22*p**3 + 8*p - 9*p**3 - 5*p**3 - 28*p**o = 0?
-1, 0, 2/9
Let m(r) be the third derivative of -r**8/70560 + r**6/2520 - 19*r**5/60 + 19*r**2. Let l(v) be the third derivative of m(v). Factor l(x).
-2*(x - 1)*(x + 1)/7
Let c(l) be the third derivative of -l**7/490 - l**6/35 - 23*l**5/140 - l**4/2 - 6*l**3/7 - 103*l**2. Solve c(i) = 0 for i.
-3, -2, -1
Let l = -72778/42201 + 140/81. Let q = l + 1024/4689. Factor 8/9*m - q*m**2 - 8/9.
-2*(m - 2)**2/9
Let t(c) be the first derivative of c**4/18 + 8*c**3/27 - 19*c**2/9 + 28*c/9 + 111. Find q, given that t(q) = 0.
-7, 1, 2
Let z(j) = 3*j + 52. Let l be z(-16). Let k(f) be the third derivative of 0 + 1/240*f**5 - 1/48*f**l + 0*f**3 + 3*f**2 + 0*f. Let k(t) = 0. Calculate t.
0, 2
Suppose -5*l + 4 = -4*l. Let x be l/(-6) - (-24)/9. Factor 117*s + 4*s**x - 12*s**2 + 32 + 12*s**3 - 165*s.
4*(s - 2)*(s + 2)*(3*s - 2)
Let c = 63 + -61. Suppose 5*i - 5 = 5*n, 2*i - n + 1 = -c*n. Factor 6/7*k + i + 2/7*k**2.
2*k*(k + 3)/7
Let n(r) be the third derivative of -61*r**6/30 + 2*r**5/15 + 61*r**4/6 - 4*r**3/3 + 46*r**2. Solve n(d) = 0 for d.
-1, 2/61, 1
Let l(j) be the first derivative of -j**6/48 - j**5/5 - 21*j**4/32 - 3*j**3/4 + 396. Factor l(u).
-u**2*(u + 2)*(u + 3)**2/8
Let y be 9*6/324 - 8/48. Factor y + 6/11*r**4 + 0*r + 0*r**2 - 12/11*r**3.
6*r**3*(r - 2)/11
Suppose 2*n + 12 = r, 4*r - 2 = -3*n + 2. Let u be ((-13)/((-195)/18))/((-6)/(-20)). Factor r*b**2 + 8*b + b - b + u.
4*(b + 1)**2
Let b(i) be the second derivative of -i**4/4 - 17*i**3/2 - 99*i**2 + i - 13. Factor b(v).
-3*(v + 6)*(v + 11)
Let o = 1412 + -1410. Factor 6 + 3/2*d**3 + 15/2*d**o + 12*d.
3*(d + 1)*(d + 2)**2/2
Factor -132/5 + 1/5*a**3 - 128/5*a - 29/5*a**2.
(a - 33)*(a + 2)**2/5
Let y = 43 - 41. What is n in 8*n**2 - 24*n**2 - 5*n + 10*n**2 + 11*n**y = 0?
0, 1
Let p(i) = 21*i**2 - 18*i. Let l(m) = 5*m**2 - 5*m. Let d(y) = -2*y + 18. Let q be d(10). Let u(b) = q*p(b) + 9*l(b). Let u(k) = 0. What is k?
0, 3
Suppose 21*y = 17*y + 8. Determine q so that 2*q**2 - 5*q**y + 155*q - 27 - 137*q = 0.
3
Let w = 378 - 376. Let n = -2 + 2. Determine c, given that 4/5*c**3 + 2/5*c**5 + n*c**w + 6/5*c**4 + 0*c + 0 = 0.
-2, -1, 0
Let g be ((-4)/(40/(-45)))/(6/56). What is z in -31*z + 68*z + 0*z**2 - g*z + 5*z**2 = 0?
0, 1
Let a = -2433 - -2436. Factor 0*k - 4/11*k**a - 2/11*k**4 - 2/11*k**2 + 0.
-2*k**2*(k + 1)**2/11
Let o(d) be the second derivative of 15*d**2 - 55/6*d**3 + 25*d - 1/6*d**6 + 3/4*d**5 + 0 + 5/4*d**4. Factor o(y).
-5*(y - 3)*(y - 1)**2*(y + 2)
Let n(s) = s**2 - 6*s - 7. Let g(a) = -10 - 2 + 6 - 6*a. Let y(m) = -4*g(m) + 3*n(m). Factor y(q).
3*(q + 1)**2
Suppose -i - 7 = 2*t, t = -146*i + 148*i - 11. Solve -4/5*k**4 + 16/5*k**2 + 0*k - 12/5*k**i + 0 = 0 for k.
-4, 0, 1
Let b(r) be the first derivative of r**6/8 - 9*r**5/20 - 15*r**4/16 + 3*r**3/4 + 3*r**2/2 + 234. Solve b(n) = 0 for n.
-1, 0, 1, 4
Let f(c) be the first derivative of -10*c - 19 + 5/2*c**2 + 5/6*c**6 - 5/2*c**4 + 20/3*c**3 - 2*c**5. Solve f(i) = 0 for i.
-1, 1, 2
Factor 2*c**2 - 5*c - 20*c**2 + 7*c**2 + 10*c**2 + 84 + 0*c**2.
-(c - 7)*(c + 12)
Determine y so that 8 + 36*y**2 - 47*y - 20*y**3 + 41*y - 3*y**4 - 22*y + 7*y**4 = 0.
1, 2
Let h(l) be the first derivative of l**5/40 - 3*l**4/8 + 35*l**3/24 + 3*l**2/4 - 9*l/2 + 407. Factor h(t).
(t - 6)**2*(t - 1)*(t + 1)/8
Let s be (3 - 4) + 9/3. Let k be 154/21 - s/(-3). Solve -k + 0*l**2 + 6*l**2 + 10 - 3*l**4 - 5 = 0 for l.
-1, 1
Let a(r) be the second derivative of r**7/14 - 9*r**6/5 + 81*r**5/5 - 54*r**4 - 366*r. What is u in a(u) = 0?
0, 6
Let q(c) = 3*c**4 - 77*c**3 - 69*c**2 + 70*c + 59. Let z(p) = -p**4 + 25*p**3 + 23*p**2 - 23*p - 20. Let n(o) = -2*q(o) - 7*z(o). Factor n(u).
(u - 22)*(u - 1)*(u + 1)**2
Suppose -5*c + m + 10 = 0, -620*c + 2*m = -623*c + 6. Factor 4/5*o**4 - 16 + 16/5*o + 12*o**c - 32/5*o**3.
4*(o - 5)*(o - 2)**2*(o + 1)/5
Let b(w) = w + 1 - 6 + 3. Let n be b(7). Factor 0*d**3 + 0*d + 3/2*d**4 + 0 + 1/2*d**n - 2*d**2.
d**2*(d - 1)*(d + 2)**2/2
Let w(c) be the third derivative of -5*c**9/24192 - c**8/3360 + c**7/6720 - 2*c**3/3 + 10*c**2. Let q(g) be the first derivative of w(g). Factor q(h).
-h**3*(h + 1)*(5*h - 1)/8
Let s be (-4)/16 - 125/(-20). Let b(r) be the first derivative of 0*r + 0*r**2 - 2 - 16/3*r**3 - s*r**4 - 12/5*r**5 - 1/3*r**6. Factor b(a).
-2*a**2*(a + 2)**3
Let r(h) be the second derivative of -h**4/12 - 21*h**3/2 - 427*h. Determine q so that r(q) = 0.
-63, 0
Let u(i) = -i**3 + i**2 - i + 1. Let f(r) = -7*r**3 + 24*r**2 - 39*r + 22. Let w(o) = -f(o) + 6*u(o). Factor w(t).
(t - 16)*(t - 1)**2
Let f be (((-2)/10)/((-2)/(-4)))/(96/(-400)). Factor f*n**3 + 40/3*n**4 + 25/3*n**5 - 10/3*n**2 + 0 + 0*n.
5*n**2*(n + 1)**2*(5*n