e third derivative of u(k). Factor a(y).
y*(3*y + 1)*(3*y + 2)/3
Let b(u) = 5*u**5 - 4*u**3 + u + 1. Let v(p) = -p**5 - p**4 + p**2 - p - 1. Suppose 8 = -6*r + 2*r. Let f(n) = r*v(n) - 2*b(n). What is o in f(o) = 0?
-1, 0, 1/4, 1
Let c(q) be the third derivative of q**7/3780 - q**6/1620 - q**5/270 - q**3/6 - 5*q**2. Let j(w) be the first derivative of c(w). Factor j(p).
2*p*(p - 2)*(p + 1)/9
Suppose 6 = 5*b - 5*a + 1, 25 = 5*b + 5*a. Factor 2/9*m**4 + 2/9*m**5 + 0*m + 0*m**2 + 0 - 4/9*m**b.
2*m**3*(m - 1)*(m + 2)/9
Let p(r) be the first derivative of -r**3/3 + r + 11. Factor p(m).
-(m - 1)*(m + 1)
Let b(s) = s**3 - s**2 + s - 1. Let i = 26 + -25. Let g(c) = 4*c + 0*c**2 - c**2 + 4*c**3 - 3 + 0*c. Let v(k) = i*g(k) - 3*b(k). Factor v(d).
d*(d + 1)**2
Factor -1/4*i**2 - 3/4*i + 0.
-i*(i + 3)/4
Let h(g) be the second derivative of 0 + 1/600*g**6 + 0*g**2 + 0*g**4 + 3*g - 1/6*g**3 + 1/200*g**5. Let d(a) be the second derivative of h(a). Factor d(t).
3*t*(t + 1)/5
Suppose 6 + s**2 - 6*s - 4*s**2 - 9 = 0. Calculate s.
-1
Let w(u) be the second derivative of u**7/84 - u**6/24 + u**5/40 + u**4/12 - u**3/6 + u**2/8 + 3*u. What is f in w(f) = 0?
-1, 1/2, 1
Suppose 3*g + 0*g = -24. Let k be g/(-126) + 8/36. Factor -4/7*j**2 + 6/7*j**3 + 0 + 0*j + 0*j**4 - k*j**5.
-2*j**2*(j - 1)**2*(j + 2)/7
Suppose 6*m - 3*m = -2*x + 65, -4 = -x. Suppose -2*v = -3*q + m, -5*v - 28 = -4*q - v. Factor 2/5 - b**q - 18/5*b**4 - 22/5*b**3 - 8/5*b**2 + 3/5*b.
-(b + 1)**4*(5*b - 2)/5
Suppose -b = -3*b. Suppose b = -5*f - 3*z + 9, -2*f - 2*f + z = -14. Factor 0 - 3*a**2 + 0 - 15*a**f + 0 + 3*a - 9*a**4.
-3*a*(a + 1)**2*(3*a - 1)
Let t(l) be the first derivative of -1/3*l**2 - 1 + 4/3*l + 1/6*l**4 - 4/9*l**3. Factor t(w).
2*(w - 2)*(w - 1)*(w + 1)/3
Let u = 14 - 10. Let y be -1*2*u/(-16). Determine x so that -1/2*x**3 - y + 1/2*x**2 + 1/2*x = 0.
-1, 1
Suppose 12 = -5*p + 27. Find d such that 2*d**2 + 11 - d - p + 9*d = 0.
-2
Let d(y) = -4*y**2 + 0*y + 2 + 0*y**2 + y**3 - 8 + 2*y. Let f be d(4). Factor -3*t**2 + 3 - 2*t + t**f - 3.
-2*t*(t + 1)
Let y(c) be the first derivative of -c**8/2100 + c**6/450 - 4*c**3/3 - 7. Let u(o) be the third derivative of y(o). Solve u(z) = 0.
-1, 0, 1
Let d(j) be the first derivative of -2*j**5/25 - 3*j**4/10 + 8*j**3/15 - 56. Factor d(k).
-2*k**2*(k - 1)*(k + 4)/5
Suppose 8 = h + h. Suppose 5*c - h = 6. Suppose 2/5*m**c + 0 + 2/5*m = 0. What is m?
-1, 0
Suppose 0 = 5*f - 0 - 10. Let p be (84/16)/7 - -1. Solve -1/2 + 7/2*c**3 - 7/4*c - p*c**5 - 1/2*c**4 + c**f = 0.
-1, -2/7, 1
Let g(s) be the first derivative of s**7/420 + s**6/60 + s**5/20 + s**4/12 - 2*s**3/3 + 2. Let b(d) be the third derivative of g(d). Solve b(k) = 0 for k.
-1
Let o(u) = -2*u**2 - 4*u + 1. Let m(f) = 5 + 0 + f - 2*f**2 - 3 - 5*f. Let v(p) = -3*m(p) + 4*o(p). Determine w, given that v(w) = 0.
-1
Factor 131*b**2 - 133*b**2 + 0 + 8.
-2*(b - 2)*(b + 2)
Let l be (-18)/(-4)*(-1)/(-9)*3. Factor 0*j + l - 3/2*j**2.
-3*(j - 1)*(j + 1)/2
Let c(a) be the first derivative of 2*a**5/15 + a**4/2 + 2*a**3/3 + a**2/3 + 3. What is p in c(p) = 0?
-1, 0
Let g(m) = -m**2 - m - 4. Let a(u) = -9*u**2 - 9*u - 33. Suppose -4*j = -7*j - 99. Let y(b) = j*g(b) + 4*a(b). What is q in y(q) = 0?
-1, 0
Let a(m) be the third derivative of -m**6/228 + 2*m**5/95 - m**4/57 - 3*m**2. Factor a(u).
-2*u*(u - 2)*(5*u - 2)/19
Let f(v) = -3*v**2 + 4*v. Let d = 3 + -8. Let p(g) = -g**2 + 2*g. Let h(o) = d*p(o) + 2*f(o). Factor h(a).
-a*(a + 2)
Let y(f) be the third derivative of 1/300*f**5 - 1/1680*f**8 + 0 + 0*f + 0*f**3 - 1/1050*f**7 + 5*f**2 + 0*f**4 + 1/600*f**6. Factor y(t).
-t**2*(t - 1)*(t + 1)**2/5
Let b be (-375)/(-450) + (1 - 1/3). Determine u, given that -b*u**2 + 0 - u = 0.
-2/3, 0
Suppose 0 = -2*h + 4. Factor 3 - h + 4 + 2*u - 4 + u**2.
(u + 1)**2
Let o(z) be the first derivative of 0*z + 0*z**3 - 1/48*z**4 + 0*z**5 + 1/240*z**6 + z**2 + 2. Let i(p) be the second derivative of o(p). Factor i(x).
x*(x - 1)*(x + 1)/2
Let d(t) = -t**3 - 11*t**2 + 13*t + 16. Let r be d(-12). Factor -4*w**5 - 3*w**5 + 8*w**5 + 9*w**3 - 6*w**r.
w**3*(w - 3)**2
Let x be -3 - -10 - (2 - -2). Let -10*t**2 - 6 - 13*t**3 - 12*t + 3 - x*t**4 + t**3 - 8*t**2 = 0. Calculate t.
-1
Let w(z) be the third derivative of -z**6/660 + z**4/132 + 29*z**2. Factor w(c).
-2*c*(c - 1)*(c + 1)/11
Let k(p) be the third derivative of -p**8/448 - p**7/168 - p**6/480 + p**5/240 - 3*p**2. Factor k(z).
-z**2*(z + 1)**2*(3*z - 1)/4
Let r be (62/(-30) + 2)*-3. Let c = -263/10 - -53/2. Factor r*s**2 - c*s**3 + 0 + 0*s.
-s**2*(s - 1)/5
Let l(c) be the first derivative of -2*c**5/3 - c**4/3 + 4. Suppose l(b) = 0. What is b?
-2/5, 0
Let y(o) = o**2 - o - 5. Let d(k) = -2*k**2 + 2*k + 12. Let w(s) = -5*d(s) - 12*y(s). Let w(x) = 0. Calculate x.
0, 1
Let z(n) be the second derivative of 8/33*n**3 + 49/165*n**6 - 6*n + 0*n**2 + 0 - 26/33*n**4 + 7/11*n**5. Determine q so that z(q) = 0.
-2, 0, 2/7
Let z(l) be the third derivative of -10*l**2 - 7/20*l**5 + 0 + 0*l + 1/10*l**6 + 1/4*l**4 + 1/2*l**3. Factor z(m).
3*(m - 1)**2*(4*m + 1)
Let o(j) be the first derivative of -j**6/24 + 3*j**5/20 - j**4/8 - j**3/6 + 3*j**2/8 - j/4 - 17. Factor o(g).
-(g - 1)**4*(g + 1)/4
Solve 10/3*o**2 + 34/3*o + 4 = 0 for o.
-3, -2/5
Let u = 35 - 51. Let g = -63/4 - u. Solve 5/2*h**2 + 5/4*h**4 - g*h**5 - 5/4*h + 1/4 - 5/2*h**3 = 0.
1
Let h(b) be the second derivative of 1/3*b**3 + 0*b**2 - 1/6*b**4 - 6*b + 0. Solve h(p) = 0.
0, 1
Let y = 9 - 9. Suppose 2/7 - 2/7*h**2 + y*h = 0. What is h?
-1, 1
Let w(o) be the first derivative of -2*o**5/5 + o**4 - 2*o**2 + 2*o - 8. Factor w(p).
-2*(p - 1)**3*(p + 1)
Let w(v) = v. Let m be w(0). Let d = m + 2. Factor -o + d*o + o + o**2.
o*(o + 2)
Factor 20/3 + 25/3*m + 5/3*m**2.
5*(m + 1)*(m + 4)/3
Suppose 5/3*x + 2 - 1/3*x**2 = 0. Calculate x.
-1, 6
Let 5/2*u**4 + 0 + 0*u - 1/2*u**5 - 4*u**3 + 2*u**2 = 0. Calculate u.
0, 1, 2
Factor 0*t**4 - 2/7*t - 2/7*t**5 + 0 + 0*t**2 + 4/7*t**3.
-2*t*(t - 1)**2*(t + 1)**2/7
Suppose -a = -2*t - 2*t + 13, 3*a = -5*t + 12. Suppose t*v + v = 0. Factor -1/4*k**4 + 0 + 0*k**2 + 1/4*k**3 + v*k.
-k**3*(k - 1)/4
Let c be (-12)/(-8) + -2 + 1. Find t, given that 0*t**2 - c*t**4 + 1/2*t**5 + 0*t + 0*t**3 + 0 = 0.
0, 1
Let p(w) = -w**3 - 3*w**2 - 5*w - 2. Let c be p(-2). Let z(j) be the first derivative of -1/3*j**6 + 0*j + 3 + 4/3*j**3 + 0*j**c + j**2 - 4/5*j**5. Factor z(i).
-2*i*(i - 1)*(i + 1)**3
Let 9/5*i**3 - 3/5*i**5 + 3/5*i**4 - 6/5*i + 0 - 3/5*i**2 = 0. Calculate i.
-1, 0, 1, 2
Let t(y) be the second derivative of 0*y**2 + 0 - 1/21*y**3 + 1/105*y**6 - 3/70*y**5 + 1/14*y**4 - y. Let t(k) = 0. What is k?
0, 1
Let g(n) be the first derivative of -n**6/60 + n**5/30 - n**2 - 3. Let b(o) be the second derivative of g(o). Find r such that b(r) = 0.
0, 1
Factor -16/9 - 2/9*w**3 - 8/3*w - 4/3*w**2.
-2*(w + 2)**3/9
Let t(h) be the first derivative of h**4/7 - 2*h**2/7 + 14. Determine r, given that t(r) = 0.
-1, 0, 1
Let t be (-172)/(-22) - 2/(-11). Let r = 11 - t. Factor 6*b + r*b**2 + 1/2*b**3 + 4.
(b + 2)**3/2
Let j be 2/(-15) - 147/(-90). Factor 0 - j*w**2 + 0*w + 6*w**3.
3*w**2*(4*w - 1)/2
Let t be (-130)/(-117) - 2/(-3). Let y(i) be the first derivative of -t*i**3 - 5/4*i**4 - 1 + 1/6*i**2 + 2/3*i. Factor y(l).
-(l + 1)*(3*l - 1)*(5*l + 2)/3
Let m(n) be the third derivative of 0*n - 4/105*n**7 - 8/3*n**3 - 4*n**2 + 1/3*n**5 + 1/168*n**8 + 0 + 1/60*n**6 - 1/3*n**4. Solve m(l) = 0 for l.
-1, 2
Suppose 18*c - 17*c - 3 = 0. Determine q, given that 0*q - 1/2*q**c + 0 + 0*q**2 = 0.
0
Let t(v) = -v**2 + 5*v - 5. Let x be t(5). Let g be (-40)/6*18/x. Suppose -g*f**2 + 2 - 6 + 7*f**2 + 5*f**3 + 16*f = 0. What is f?
2/5, 1, 2
Let q = 92/77 + 1/11. Factor 13/7*o + 24/7*o**2 + q*o**3 + 2/7.
(o + 2)*(3*o + 1)**2/7
Let u(h) = -h**2 - 3. Let k be u(-3). Let p be (10/(-8))/(3/k). Determine o, given that 0*o**5 - o**5 - 2*o**3 + 3*o**p = 0.
-1, 0, 1
Let q be 7/9 - (-6)/(-9). Let l(y) be the first derivative of 2 - 1/18*y**4 - 2/27*y**3 + 2/9*y + q*y**2. Factor l(k).
-2*(k - 1)*(k + 1)**2/9
Let j(l) be the third derivative of -l**8/2240 - l**7/3360 + l**6/480 + l**5/480 - l**3/3 - 3*l**2. Let z(k) be the first derivative of j(k). Factor z(r).
-r*(r - 1)*(r + 1)*(3*r + 1)/4
Let m(n) = 33*n**2 - 24*n - 3. Let c(h) = 34*h**2 - 25*h - 4. Le