 -1/25*w**5 + 0 + 8/15*w**3 + 1/150*w**6 + 6*w + 0*w**4 - 5*w**2. Determine a so that n(a) = 0.
-1, 2
Let r(d) be the second derivative of -d**6/120 + 3*d**5/40 - d**4/4 - 5*d**3/6 - 2*d. Let t(x) be the second derivative of r(x). Factor t(s).
-3*(s - 2)*(s - 1)
Let g(f) be the second derivative of -1/9*f**3 - 3*f - 1/72*f**4 + 0 - 1/3*f**2. Suppose g(o) = 0. Calculate o.
-2
Let a(m) be the third derivative of 0*m**3 - 1/330*m**5 + 1/1155*m**7 + 0*m**6 - 3*m**2 + 0*m**4 + 0 + 0*m. Determine h so that a(h) = 0.
-1, 0, 1
Let l(h) be the third derivative of -6*h**7/35 + 34*h**6/5 - 1012*h**5/15 - 272*h**4 - 384*h**3 - 9*h**2. Let l(g) = 0. What is g?
-2/3, 12
Factor 0*b + 2/7*b**2 - 2/7*b**4 + 1/7*b**5 - 1/7*b**3 + 0.
b**2*(b - 2)*(b - 1)*(b + 1)/7
Let n = 14 + 4. Let h = n + -12. Factor p**2 - h*p**2 + 4*p**2 - 2 - 3*p + 0.
-(p + 1)*(p + 2)
Suppose 0 = -2*a + 2*f + 18, 0 = 5*a - 2*f - 11 - 19. Suppose -3*k**a - 25*k**2 - 2*k**4 + 0*k**3 - 5*k**3 + 25*k**3 + 10*k = 0. What is k?
0, 1, 2
Let y(w) be the third derivative of 1/12*w**5 - 5/8*w**4 + 0*w + 5/3*w**3 + 0 - 16*w**2. Factor y(m).
5*(m - 2)*(m - 1)
Let g be (-4)/(-4)*(0 - -2). Let a(s) be the first derivative of 4 + 0*s + 1/5*s**6 - 1/5*s**g + 0*s**3 - 16/25*s**5 + 3/5*s**4. Factor a(o).
2*o*(o - 1)**3*(3*o + 1)/5
Let b = -9 - -9. Let s be -32 + 36 + (-2 - 1) + 1. Solve -1/3*a + b + 1/6*a**s = 0 for a.
0, 2
Let j(n) be the second derivative of -n**4/18 + 10*n**3/9 - n - 1. Factor j(r).
-2*r*(r - 10)/3
Let i = -89 - -93. Factor 6 - 4*c - 2 - 22 - 6 + i*c**2.
4*(c - 3)*(c + 2)
What is z in -6/5*z**2 - 6/5*z**3 - 12/5 + 2/5*z**4 + 22/5*z = 0?
-2, 1, 3
Let f = 1097 - 2173/2. Let d = 72 - 48. Factor -d*g**3 - 3/2 - 12*g**2 + f*g.
-3*(g + 1)*(4*g - 1)**2/2
Let n(i) = 6*i + 54. Let t be n(-18). Let a be t/(-63)*(-7)/(-2). Suppose 0*g**4 + 3/2*g**5 + 0*g**2 + 0 + 0*g**a + 0*g = 0. What is g?
0
Suppose 0 = -7*f + 2*f. Let q(v) be the first derivative of 2/27*v**3 + f*v + 7 - 1/9*v**2. Factor q(x).
2*x*(x - 1)/9
What is h in 140 + 20 - 409 - 280 - 15*h - h**2 - 31*h = 0?
-23
Solve -29 - 1/2*h**2 + 233/4*h = 0 for h.
1/2, 116
Let z(c) be the second derivative of -3*c**6/10 - 31*c**5/5 - 92*c**4/3 - 136*c**3/3 + 40*c**2 - 275*c. Determine l so that z(l) = 0.
-10, -2, 2/9
Let b(z) be the third derivative of 0 + 1/24*z**4 + 0*z + 1/240*z**5 - 14*z**2 + 1/6*z**3. What is w in b(w) = 0?
-2
Let g(v) be the third derivative of v**6/180 - 31*v**5/30 + 961*v**4/12 - 29791*v**3/9 + 5*v**2 - 1. Factor g(p).
2*(p - 31)**3/3
Suppose 3*y - 4*g - 1 - 36 = 0, 0 = 2*y - 5*g - 27. Let w(d) be the third derivative of -y*d**2 + 0 + 1/120*d**5 + 0*d**3 + 0*d - 1/24*d**4. Factor w(s).
s*(s - 2)/2
Let u(r) = -r**2 - 8*r + 15. Let f be u(-11). Let s = f + 21. Factor 2*o**4 + 53*o**3 - 53*o**s + 2*o**5.
2*o**4*(o + 1)
Let g(q) be the third derivative of -q**7/70 - 19*q**6/20 - 37*q**5/20 - 194*q**2 + 2. Factor g(n).
-3*n**2*(n + 1)*(n + 37)
Let c = -4573 - -9171/2. Factor -5/2*u**5 + 0 - c*u**3 + 0*u - 5*u**2 - 10*u**4.
-5*u**2*(u + 1)**2*(u + 2)/2
Factor -14*g**4 + 73*g**5 - 2*g**3 + 72*g**5 - 210*g**5 + 14*g**2 + 67*g**5.
2*g**2*(g - 7)*(g - 1)*(g + 1)
Let u(i) be the second derivative of 8*i + 0 - 2/9*i**3 - i**2 + 1/18*i**4. Factor u(g).
2*(g - 3)*(g + 1)/3
Let n = -2/481 - -485/962. Let s be 1 + -2 - (-3)/2. Solve -n + 10*j**2 - s*j = 0.
-1/5, 1/4
Let y be (-115)/(-69)*9/30. Solve y*m**2 + 1/2 + m = 0.
-1
Find t, given that 24*t + 25*t - 2*t**2 - 8 + 1 - 9 - 37*t = 0.
2, 4
Let j(d) be the third derivative of 1/45*d**5 + 0 + 10*d**2 + 0*d + 1/180*d**6 + 0*d**4 + 0*d**3. Factor j(o).
2*o**2*(o + 2)/3
Let o(p) be the second derivative of -10*p**2 + 0 + 1/4*p**5 + 15/2*p**3 - 21*p - 5/2*p**4. Solve o(q) = 0.
1, 4
Suppose -4*j - 23 = 29. Let t = 17 + j. Solve 3*y**2 + 5*y**4 + 1 + 0*y + 3*y**2 - t*y**4 + 4*y**3 + 4*y = 0.
-1
Let -4*g + 11/3*g**3 - 2/3*g**2 + 1/3*g**5 + 8/3 - 2*g**4 = 0. Calculate g.
-1, 1, 2
Let k be (12/(-24))/(15/(-45)). Factor -k*v - 9/4*v**2 + 3*v**3 + 3/4 + 3*v**4.
3*(v + 1)**2*(2*v - 1)**2/4
Factor 1/3*h**2 + 2/3*h - 35/3.
(h - 5)*(h + 7)/3
Let d(m) = -4*m**4 - m**3 + m**2 + m - 3. Let q be 1*-3*12/(-18). Let v(k) = 21*k**4 + 6*k**3 - 4*k**2 - 6*k + 16. Let o(x) = q*v(x) + 11*d(x). Factor o(h).
-(h - 1)**2*(h + 1)*(2*h + 1)
Let g(a) be the third derivative of -a**6/540 - 2*a**5/135 + a**4/36 - 7*a**3/6 + 23*a**2. Let m(o) be the first derivative of g(o). Factor m(q).
-2*(q + 3)*(3*q - 1)/9
Suppose 0*v - 1/4 + 1/4*v**2 = 0. What is v?
-1, 1
Let t(j) = 13*j**2 - 22*j + 44. Let f(y) = 11*y**2 - 26*y + 45. Let d(n) = -7*f(n) + 6*t(n). Factor d(q).
(q - 1)*(q + 51)
Find s such that 2*s**2 + 12*s**2 - 6*s + 1121*s**3 - 1131*s**3 + 2*s**4 = 0.
0, 1, 3
Let v(c) be the first derivative of -c**6/60 + c**5/20 - c**3/6 + c**2/4 + 3*c + 1. Let s(h) be the first derivative of v(h). Factor s(u).
-(u - 1)**3*(u + 1)/2
Let n be (5/175)/(1/(-87)). Let v = -11/5 - n. Factor 0*r**3 + 0*r + 2/7 + v*r**4 - 4/7*r**2.
2*(r - 1)**2*(r + 1)**2/7
Let l(m) be the second derivative of -m**6/480 + m**5/48 - 5*m**2 + 34*m. Let x(t) be the first derivative of l(t). Determine q, given that x(q) = 0.
0, 5
Let n = 7277 + -36377/5. Determine d, given that 0*d**4 + 6/5*d + 2/5*d**5 + 4/5 - 4/5*d**2 - n*d**3 = 0.
-1, 1, 2
Suppose 2*r = 3*j + 1, 5*r + 3 = 5*j + 8. Factor r*g**2 + 39*g**3 - g**2 - 37*g**3 - 3*g**2 - 4*g.
2*g*(g - 2)*(g + 1)
Let z(u) = u**2 + 10*u + 21. Let a be z(-2). Let h be ((-2)/a - (0 - 1))/3. What is k in -h*k + 0*k**2 + 1/5*k**3 + 0 = 0?
-1, 0, 1
Let w be (-1647)/366*(-4)/9. Factor 0*z - 7/5*z**4 + 0 - z**3 + 2/5*z**w.
-z**2*(z + 1)*(7*z - 2)/5
Suppose 4 = -3*t + o, t - 26*o + 25*o = -4. Determine x, given that t*x + 1/2*x**3 + 3/2*x**2 - 2 = 0.
-2, 1
Let b = 27 + -20. Let c(g) = -3*g**2 - 15*g + 20. Let p(s) = 9*s**2 + 45*s - 61. Let d(o) = b*c(o) + 2*p(o). Solve d(t) = 0.
-6, 1
Let r(g) be the second derivative of 5/3*g**2 + 5/12*g**5 + 35/18*g**3 + 5/4*g**4 + 0 - 11*g + 1/18*g**6. Factor r(b).
5*(b + 1)**3*(b + 2)/3
Suppose -2/9*k**2 - 2*k + 20/9 = 0. What is k?
-10, 1
Let s(t) be the third derivative of t**5/540 - 11*t**4/36 - 383*t**2. Factor s(b).
b*(b - 66)/9
Let t = 12470 + -12468. Suppose 5/6*c + c**4 - 2/3*c**3 - 1/6*c**5 + 0 - c**t = 0. Calculate c.
-1, 0, 1, 5
Let j(d) be the second derivative of -d**7/14 + 3*d**5/5 + d**4/2 - 3*d**3/2 - 3*d**2 + 49*d. Determine m so that j(m) = 0.
-1, 1, 2
Let c(g) be the second derivative of -1/5*g**6 - 3/10*g**5 - 1/6*g**4 + 0 + 0*g**3 - 7*g + 0*g**2 - 1/21*g**7. Factor c(t).
-2*t**2*(t + 1)**3
Let w = -767 - -2303/3. Solve -c**2 + 1/3*c + c**4 + 1/3*c**3 - w*c**5 + 0 = 0.
-1, 0, 1/2, 1
Factor -25/4*r + 5/4*r**2 - 15/2.
5*(r - 6)*(r + 1)/4
Suppose 51*x - 70*x = 0. Suppose -s + 3*s - 3*p = 23, 5*s - 25 = p. Factor x*i + 0*i**2 + 0 - 2/9*i**5 + 0*i**3 + 2/9*i**s.
-2*i**4*(i - 1)/9
Factor 1/2*c**4 - 11/2 + 16*c + 4*c**3 - 15*c**2.
(c - 1)**3*(c + 11)/2
Suppose 0 = -4*y + 7*y - 12. Suppose -y = -0*v - 2*v. Factor 6 + p**5 - 4 - 3*p + v*p**2 - 1 + 2*p**3 - 3*p**4.
(p - 1)**4*(p + 1)
Let t = -142 + 145. Suppose t*h + 11 = 3*g + 32, -4*g = h + 18. Factor 0*z - 2/15*z**5 + 0 - 8/15*z**4 - 8/15*z**3 + 0*z**h.
-2*z**3*(z + 2)**2/15
Suppose -5*p + 0*m = m - 5, -2*p + m + 9 = 0. Suppose 2*w - d + p = -3*d, 5*d + 5 = 5*w. Factor w - 1/2*x**3 + 7/4*x**2 + 1/2*x - 7/4*x**4.
-x*(x - 1)*(x + 1)*(7*x + 2)/4
Suppose b = 4*f - 16, 2*f + 2 = b - 3*b. Suppose -i - 1 = -f. Find j such that -3*j - 4*j - 15 + j - i*j**2 + 11 = 0.
-2, -1
Let l(f) be the second derivative of f**6/105 - 53*f**5/70 + 285*f**4/14 - 361*f**3/3 - 27436*f**2/7 + 300*f. Factor l(m).
2*(m - 19)**3*(m + 4)/7
Let i(u) be the third derivative of 0*u + 1/105*u**5 + 1/21*u**4 - 8/21*u**3 - 1/420*u**6 + 20*u**2 + 0. Factor i(w).
-2*(w - 2)**2*(w + 2)/7
Suppose 181 = 5*w + 161. Let v(x) be the first derivative of -1/2*x**w - 2*x**3 + 0*x**2 - 3 + 8*x. Factor v(p).
-2*(p - 1)*(p + 2)**2
Let v(r) be the third derivative of -r**6/180 - 8*r**5/15 - 47*r**4/36 - 5*r**2 + 19. Solve v(m) = 0 for m.
-47, -1, 0
Let x(t) be the first derivative of 3*t**5/5 + 39*t**4/4 + 54*t**3 + 138*t**2 + 168*t - 767. Factor x(z).
3*(z + 2)**3*(z + 7)
Let k = -36 - -38. Factor 5*t + 2*t**2 + 4*t**2 + t**2 - 2*t**k.
5*t*(t + 1)
Factor -20*p**3 - 16*