) be the third derivative of -2/3*q**3 + 0*q + 1/60*q**5 - 16*q**2 + 0 + 0*q**4. Factor y(n).
(n - 2)*(n + 2)
Suppose 158*x - 153*x - 10 = 0. Factor 0 + 1/3*g + g**x.
g*(3*g + 1)/3
Let j(k) be the third derivative of 16*k**2 - 1/240*k**6 - 1/24*k**3 + 0*k + 0 + 1/96*k**4 + 1/1344*k**8 - 1/840*k**7 + 1/120*k**5. Find t, given that j(t) = 0.
-1, 1
Factor 7/2*t**2 - 7/2*t**4 + 1/2*t**5 + 0 + 4*t - 9/2*t**3.
t*(t - 8)*(t - 1)*(t + 1)**2/2
Let 5*t**2 + 1 - 16 - 190*t + 362*t - 182*t = 0. Calculate t.
-1, 3
Suppose -7*k - 24 = -11*k. Let t be 27/33*k/9. Let -6/11*w**3 + 2/11*w**2 - 2/11 + t*w = 0. What is w?
-1, 1/3, 1
Suppose -4*a + 3 = -5. Determine b, given that -4*b**3 + b**3 - 8*b**2 + 4*b**2 - a*b**2 - 3*b = 0.
-1, 0
Let y = 250 + -250. Let b(q) be the second derivative of -1/2*q**3 + 3*q**2 - q + 1/10*q**6 + 3/20*q**5 + y - 3/4*q**4. Factor b(d).
3*(d - 1)**2*(d + 1)*(d + 2)
Let a(y) be the first derivative of 0*y**3 + 1/390*y**5 + 2 + 0*y - 1/78*y**4 + 5/2*y**2. Let p(m) be the second derivative of a(m). Factor p(w).
2*w*(w - 2)/13
Let z(r) = -r**3 - r**2 + r - 2. Let o(h) = 2*h**3 - 4*h**2 + h + 10. Let j(f) = -o(f) - z(f). Factor j(g).
-(g - 4)*(g - 2)*(g + 1)
Let x be 2/(-14)*6*(-147)/42. Solve 5/2*y - 1/2*y**4 - y**2 + 3/2 + 1/2*y**5 - x*y**3 = 0.
-1, 1, 3
Suppose -t**3 - 20*t**2 - 24*t - 69*t - 123 - 69 + 66 = 0. What is t?
-14, -3
Let b be ((-1)/(-24))/((-62)/(-496)). Let p(w) be the second derivative of 0*w**2 + 0 + 2*w + b*w**3 + 1/6*w**4. Suppose p(n) = 0. Calculate n.
-1, 0
Suppose 4*d - 8 = g + 2*g, 2*d - 4 = -4*g. Suppose -d*r = -4*r + 8. What is x in -x**2 + 2*x**2 + 3*x**3 + 0*x**2 - r*x**2 = 0?
0, 1
Let y(p) = 2*p**2 + 329*p - 618. Let r(o) = -12*o**2 - 1648*o + 3088. Let h(z) = -3*r(z) - 16*y(z). Find q such that h(q) = 0.
2, 78
Let n(m) be the first derivative of -m**6/600 - m**5/150 + m**4/120 + m**3/15 - 7*m**2 + 3. Let a(j) be the second derivative of n(j). Solve a(k) = 0 for k.
-2, -1, 1
Let o(v) be the second derivative of v**9/1512 + v**8/840 - v**7/210 + 2*v**3/3 - v. Let a(j) be the second derivative of o(j). Factor a(g).
2*g**3*(g - 1)*(g + 2)
Let q(f) be the first derivative of -1/12*f**4 - 4*f + 1/30*f**6 - 1/3*f**3 + 1/10*f**5 + 1 + 0*f**2. Let d(w) be the first derivative of q(w). Factor d(o).
o*(o - 1)*(o + 1)*(o + 2)
Let v(y) be the third derivative of -y**10/1587600 + y**8/105840 - y**6/7560 - 2*y**5/15 - 5*y**2. Let j(u) be the third derivative of v(u). Factor j(g).
-2*(g - 1)**2*(g + 1)**2/21
Let i(b) be the third derivative of b**5/20 + 11*b**4/8 - 16*b**2 - 3. Factor i(k).
3*k*(k + 11)
Let t(v) be the second derivative of 0 - 22/9*v**3 + 121/3*v**2 - v + 1/18*v**4. Factor t(k).
2*(k - 11)**2/3
Let u(a) = 28*a**3 - 61*a**2 - 16*a - 13. Let n = -81 + 55. Let l(i) = -13*i**2 + 9*i**3 - 2*i**3 - 2*i**2 - 4*i - 3. Let m(s) = n*l(s) + 6*u(s). Factor m(q).
-2*q*(q - 2)*(7*q + 2)
Let a(v) be the third derivative of -v**6/120 + v**5/10 - 11*v**4/24 + v**3 + 208*v**2. Factor a(c).
-(c - 3)*(c - 2)*(c - 1)
Find d, given that 60*d**2 + 4*d**3 - 300*d - 2*d**3 - 5*d**3 = 0.
0, 10
Let y = -112646/15 - -7510. Suppose -14/15*i**2 + 0 + 2/15*i**3 + y*i - 2/5*i**5 + 14/15*i**4 = 0. Calculate i.
-1, 0, 1/3, 1, 2
Let d(p) be the second derivative of p**5/10 + 23*p**4/6 - p**3/3 - 23*p**2 + 150*p. Solve d(c) = 0.
-23, -1, 1
Let x(q) be the second derivative of 0 + 27*q + 0*q**4 + 0*q**2 - 4/15*q**3 - 1/75*q**6 + 3/50*q**5. Factor x(y).
-2*y*(y - 2)**2*(y + 1)/5
Let c(y) = -5*y**3 + 19*y**2 + 34*y + 30. Let w(s) = -4*s**3 + 18*s**2 + 35*s + 31. Let i(n) = 5*c(n) - 6*w(n). Factor i(x).
-(x + 2)**2*(x + 9)
Let h be 44/36 - (-6 + 7). Let q(d) be the first derivative of 2/9*d**3 - 1/3*d**2 - 1/18*d**4 + h*d - 4. Solve q(p) = 0 for p.
1
Let o(h) be the first derivative of 2*h**6/9 + 56*h**5/15 + 25*h**4/3 + 16*h**3/3 - 66. Suppose o(d) = 0. What is d?
-12, -1, 0
Let s(l) be the third derivative of -3*l**6/80 + l**5/2 - 3*l**4/4 + 43*l**2 + 2*l. Factor s(r).
-3*r*(r - 6)*(3*r - 2)/2
Let y(t) = t**5 + t**4 + 2*t**2 - t + 2. Let b(a) = 8*a**5 - 36*a**4 + 48*a**3 + 240*a**2 + 136*a + 8. Let r(j) = b(j) - 4*y(j). What is i in r(i) = 0?
-1, 0, 5, 7
Let j(g) be the first derivative of -2/3*g - 5/6*g**2 - 2 - 1/12*g**4 - 4/9*g**3. Factor j(i).
-(i + 1)**2*(i + 2)/3
Suppose -6*f + 14 + 10 = 0. Determine j so that -4*j**3 + 3*j**3 + f*j**3 - 6*j**2 = 0.
0, 2
Let p(z) be the third derivative of 0*z**4 + 1/525*z**7 - 3*z**2 + 0*z - 1/150*z**6 + 0 + 1/150*z**5 + 0*z**3. Let p(o) = 0. Calculate o.
0, 1
Suppose -11 = -13*n + 15. Suppose 0 = -k - 0*b + 4*b + 3, n*b = 0. Factor 4/5*i + 8/5*i**k - 2*i**2 - 2/5*i**4 + 0.
-2*i*(i - 2)*(i - 1)**2/5
Let z(d) be the third derivative of 1/96*d**5 + 1/960*d**6 + 1/64*d**4 - 3/16*d**3 + 0*d + 0 + 11*d**2. Factor z(p).
(p - 1)*(p + 3)**2/8
Let l(h) = 3*h**2 - 4*h - 7. Let p(r) = -19*r**2 + 25*r + 44. Let b(w) = -39*l(w) - 6*p(w). Solve b(k) = 0.
-1, 3
Let h be 1*(-2)/(-4)*-2. Let z(c) = -4*c**3 + c. Let d be z(h). Solve 3*s**4 + 3 + 7*s + 3*s + 0 + 12*s**d + 2*s + 18*s**2 = 0.
-1
Let v(c) be the third derivative of c**9/241920 + c**8/80640 - c**7/20160 - c**6/2880 - c**5/2 - 14*c**2. Let y(q) be the third derivative of v(q). Factor y(z).
(z - 1)*(z + 1)**2/4
Let i(p) = -9*p - 2. Let s be i(-2). Let o = s + -14. Factor -2*x + 0*x**3 + 2*x**3 + o - 2*x**3 + 2*x**3 - 2*x**2.
2*(x - 1)**2*(x + 1)
Let y(t) = -5*t**2 - 14*t - 11. Let n(v) = 13 - v**2 - 2*v - v - 15 + 0*v**2. Let l(p) = -11*n(p) + 2*y(p). Determine k, given that l(k) = 0.
-5, 0
Let o(a) = 3*a**4 - 4*a**3 + 18*a**2 + 28*a + 19. Let f(d) = 7*d**4 - 9*d**3 + 36*d**2 + 55*d + 39. Let p(c) = 4*f(c) - 9*o(c). Let p(u) = 0. Calculate u.
-3, -1, 5
Let g(i) = -i + 16. Let c be g(4). Solve 4*a**3 - 4*a**2 + 36*a**2 + 32*a - c*a**2 + 16 = 0 for a.
-2, -1
Let k(f) be the first derivative of 2/9*f**3 + 0*f - 1/18*f**4 - 2/9*f**2 + 5. Factor k(x).
-2*x*(x - 2)*(x - 1)/9
Let c(q) be the second derivative of q**4/6 + q**3 + 3*q**2 - 8*q. Let k(g) = -10*g**2 - 30*g - 31. Let y = -20 - -18. Let d(f) = y*k(f) - 11*c(f). Factor d(w).
-2*(w + 1)*(w + 2)
Let q = -1234 - -1241. Let p(o) be the third derivative of -7*o**2 + 1/12*o**5 + 0*o - 1/42*o**q + 0*o**3 + 0*o**6 + 0 + 0*o**4. Solve p(w) = 0 for w.
-1, 0, 1
Find s, given that 2*s**3 + 5*s**3 - 8*s**3 + 280*s - 3*s**3 + 87*s**2 + 45*s**2 = 0.
-2, 0, 35
Let n(a) = a**2 - 8*a - 8. Let j be n(10). Let p = j + -10. Let z + 6 - 2 - 1 + 3*z**p - 7*z = 0. What is z?
1
Suppose 5*z + 4*x - 16 = 0, 0*x - 11 = -3*z - x. Suppose -z*m + 12 = -m. Find f such that -4*f**2 + 2*f**2 - f + 5*f**m - 3*f**4 + 2*f - f**5 = 0.
-1, 0, 1
Let x(l) be the first derivative of 3*l**4 + 93*l**3 + 333*l**2/2 + 66*l + 175. Find y, given that x(y) = 0.
-22, -1, -1/4
Let x(p) be the second derivative of -125*p**5/12 - 125*p**4/18 + 50*p**3/9 + 20*p**2/3 - 5*p - 28. Factor x(g).
-5*(5*g - 2)*(5*g + 2)**2/3
Let f(r) be the first derivative of r**6/30 + 48*r**5/25 + 311*r**4/10 + 368*r**3/5 + 529*r**2/10 + 7. Let f(k) = 0. What is k?
-23, -1, 0
Let d(h) be the second derivative of -h**4/54 - 314*h**3/27 - 24649*h**2/9 + 3*h + 3. What is k in d(k) = 0?
-157
Let t(d) be the third derivative of d**9/105840 - d**8/23520 + d**7/17640 + 13*d**4/24 - 21*d**2. Let o(f) be the second derivative of t(f). Factor o(v).
v**2*(v - 1)**2/7
Let d(l) be the third derivative of -l**6/540 - l**5/270 + l**4/108 + l**3/27 + 163*l**2. Factor d(t).
-2*(t - 1)*(t + 1)**2/9
Let z = 243 - 2671/11. Let a(y) be the first derivative of -4 + 1/11*y**4 + z*y - 2/11*y**2 + 0*y**3 - 2/55*y**5. Let a(r) = 0. Calculate r.
-1, 1
What is n in -21*n**3 + 84*n + 32 - 5/2*n**4 + 2*n**2 = 0?
-8, -2, -2/5, 2
Let y(d) be the first derivative of d**3/2 - 186*d**2 + 23064*d - 244. Factor y(c).
3*(c - 124)**2/2
Let 3249/4*z + 1/4*z**3 - 57/2*z**2 + 0 = 0. Calculate z.
0, 57
Let o(k) be the first derivative of -12*k**5/5 - 29*k**4 - 84*k**3 - 102*k**2 - 56*k + 127. Find f, given that o(f) = 0.
-7, -1, -2/3
Suppose 2*r - 4*b - 1 - 13 = 0, -r - 2*b + 3 = 0. Let m(x) be the third derivative of 0*x**3 - x**2 + 0 + 1/8*x**4 + 0*x + 1/20*x**r. Factor m(g).
3*g*(g + 1)
Let w be -3 - -18*(-7)/(-14). Let t(k) be the third derivative of -1/40*k**5 + 0*k - 1/160*k**w + 0*k**3 + 0 - 1/32*k**4 + 8*k**2. Fa