Let a = 8 + -5. Factor a*t**2 + 0*t**2 - 5*t + 5*t.
3*t**2
Let h(q) be the third derivative of -5*q**8/672 - 11*q**7/84 - 17*q**6/24 - 23*q**5/12 - 145*q**4/48 - 35*q**3/12 + 19*q**2. Factor h(y).
-5*(y + 1)**4*(y + 7)/2
Let d(k) = -k**2. Let l(r) = 8*r**2 - 3*r + 2. Let t(y) = 28*d(y) + 4*l(y). Factor t(c).
4*(c - 2)*(c - 1)
Let i(v) be the third derivative of 3*v**8/112 - v**7/10 + v**6/20 + 3*v**5/10 - 5*v**4/8 + v**3/2 - 17*v**2. Factor i(x).
3*(x - 1)**3*(x + 1)*(3*x - 1)
Let h(x) = -x**2 + 53*x + 139. Let r(w) = 2*w**2 - 80*w - 208. Let d(g) = -8*h(g) - 5*r(g). Factor d(i).
-2*(i + 6)**2
Let o(b) = 5*b**2 + 5*b**2 - 2*b + 4 - 5*b. Let p(l) = 7*l**2 - 5*l + 3. Suppose -k + 35 = -6*k. Let m(f) = k*p(f) + 5*o(f). Factor m(h).
(h - 1)*(h + 1)
Let t(f) be the third derivative of -f**5/12 + f**4/3 + 2*f**3/3 - 11*f**2. Factor t(l).
-(l - 2)*(5*l + 2)
Let x = -27 + 29. Factor 0*m**x + 2/3 + m - 1/3*m**3.
-(m - 2)*(m + 1)**2/3
Suppose h - 18 = -3*h - 2*a, -4*a + 22 = h. Let c(x) be the first derivative of -1/21*x**6 - 1/7*x**h - 3/7*x**4 + 0*x + 1 - 8/35*x**5 - 8/21*x**3. Factor c(s).
-2*s*(s + 1)**4/7
Let t(u) be the first derivative of -27/4*u**4 - 2/3*u**2 - 5 + 0*u - 4*u**3. Factor t(c).
-c*(9*c + 2)**2/3
Let s(x) be the first derivative of -1/2*x**2 + 0*x + 3 + 2/3*x**3 - 1/4*x**4. Suppose s(n) = 0. What is n?
0, 1
Let b(k) = 2*k**3 - 2*k**2. Let p(c) = 8*c**3 - 9*c**2. Let d(o) = 9*b(o) - 2*p(o). Factor d(t).
2*t**3
Let h(g) be the third derivative of -g**7/1365 - g**6/156 - 3*g**5/130 - 7*g**4/156 - 2*g**3/39 - 39*g**2. Factor h(n).
-2*(n + 1)**3*(n + 2)/13
Let o(u) be the second derivative of u**4/6 - u**2 + 5*u. Determine w, given that o(w) = 0.
-1, 1
Let b = 155 + -152. Find t such that -4/3*t**b + 0*t + 10/3*t**4 + 0*t**2 + 0 = 0.
0, 2/5
Let u = -1/45 + 16/45. Let l(s) be the first derivative of -1 + 1/3*s**2 + 0*s - 2/9*s**3 - u*s**4. Determine p so that l(p) = 0.
-1, 0, 1/2
Let a = 8 - 20. Let y be (2/(-3))/(2/a). Factor -n**3 - n**3 + y*n**3.
2*n**3
Let i(o) = o**3 + 4*o**2 + 3*o. Let j be i(-2). Solve -3 - 5*c**2 + 6*c - c**2 + 0*c + 3*c**j = 0 for c.
1
Let k(s) be the second derivative of s**8/560 + s**7/280 - s**6/120 - s**5/40 - s**3/6 - 3*s. Let z(v) be the second derivative of k(v). Factor z(l).
3*l*(l - 1)*(l + 1)**2
Let n be -2*(-2)/(2 + 0). Suppose -8 + 4 = -2*i. Solve 0*o**2 + 0*o**i - n*o**2 = 0 for o.
0
Let o = -60 - -64. Let w(l) be the first derivative of 4/15*l**3 + 1/15*l**6 - 1 - 4/25*l**5 - 1/5*l**2 + 0*l**o + 0*l. Factor w(m).
2*m*(m - 1)**3*(m + 1)/5
Let a = -452/3 - -151. Determine h, given that 2/3*h**2 - 1/3*h + a*h**3 - 2/3 = 0.
-2, -1, 1
Suppose -5*g - 28 = -5*m + 12, -2*m - 5*g = 19. Let k(a) = 4*a**2 + 4*a + 3. Let t be k(-2). Factor -6*w**4 - 21*w**2 - w**4 - 2 - t*w - 17*w**m + 2*w**4.
-(w + 1)**3*(5*w + 2)
Let f be -6*(-15)/(-42) - -3. Let r = 19/14 - f. Determine s, given that 0*s**2 + 0*s - 1/2*s**5 + 0 + s**4 - r*s**3 = 0.
0, 1
Let u(p) be the third derivative of -p**8/84 + p**6/15 - p**4/6 - 7*p**2. Find l such that u(l) = 0.
-1, 0, 1
Let q be 12/66 + (-32)/(-66). Factor -2/3*n**5 - 10/3*n**2 + 4/3*n + q*n**4 + 2*n**3 + 0.
-2*n*(n - 1)**3*(n + 2)/3
Suppose -74 = 5*l + 1. Let h = -29/2 - l. Solve -1/2*m**3 + 1/2*m - 1/2*m**2 + h*m**4 + 0 = 0 for m.
-1, 0, 1
Let y = -8 + 13. Factor n**3 - 4*n**3 - n**y - 6*n**4 - 2*n**5.
-3*n**3*(n + 1)**2
Let o(w) = -3*w**3 + 2*w**2 + 2*w + 1. Let n be o(-1). Find p, given that 1/3*p**3 + 0 + 0*p**2 - 1/3*p**n + 0*p = 0.
0, 1
Let i(k) be the third derivative of -k**8/840 + k**7/140 - k**6/60 + k**5/60 + 5*k**3/6 - k**2. Let d(f) be the first derivative of i(f). Factor d(b).
-2*b*(b - 1)**3
Suppose -h + 4*u = 12, 0 = -4*h + 6*h + 3*u - 20. Let s(k) be the second derivative of -7/12*k**3 + 1/4*k**2 - k + 0 + 2/5*k**5 + 1/3*k**h. Solve s(l) = 0.
-1, 1/4
Let r = -6 + 8. Factor 2*n**r - 6*n + 9*n - 5*n**2.
-3*n*(n - 1)
Factor 1/7*a**5 + 0*a**2 + 0*a + 6/7*a**4 + 0 + 9/7*a**3.
a**3*(a + 3)**2/7
Let -100*g**3 + 31*g**3 - 2*g**2 + 36*g**4 + 29*g**2 + 9*g - 3 = 0. Calculate g.
-1/3, 1/4, 1
Let u(d) be the second derivative of -d**5/20 + d**4/12 + d**3/6 + d**2/2 + d. Let l be u(-1). What is y in y**4 + 2*y**4 - l*y**2 - y**4 = 0?
-1, 0, 1
Let s(l) be the first derivative of 2/39*l**3 + 0*l**2 + 2/65*l**5 + 2 + 0*l - 1/13*l**4. Solve s(h) = 0.
0, 1
Let i(x) = 5*x + 3. Let k be i(3). Let o be (-13)/(-3) - k/(-27). Solve -2/7*y**o + 2/7*y**3 + 0*y**2 + 0*y**4 + 0*y + 0 = 0.
-1, 0, 1
Suppose -q = 4*r + 2, 0*q = -r + 5*q - 11. Let x(g) = g**3. Let m(p) = p**4 - 9*p**3 + 6*p**2 - 4*p + 1. Let i(k) = r*m(k) - 5*x(k). Factor i(b).
-(b - 1)**4
Let d(q) be the first derivative of -q**7/735 + q**5/105 - q**3/21 - 3*q**2/2 + 1. Let k(m) be the second derivative of d(m). Determine i so that k(i) = 0.
-1, 1
Let g = 1596/8657 - 2/787. Factor -12/11*y + g*y**2 + 18/11.
2*(y - 3)**2/11
Let j(r) be the third derivative of 2/3*r**3 + 1/120*r**6 + 4*r**2 + 0*r + 0 + 1/3*r**4 + 1/12*r**5. Factor j(q).
(q + 1)*(q + 2)**2
Let k(y) be the first derivative of y**4/4 - 2*y**3/3 - 13*y**2/2 - 10*y + 33. Determine u, given that k(u) = 0.
-2, -1, 5
Suppose 2*g - 4 = 0, -4*g + 0 + 8 = -c. Factor -2/5*p**3 + 1/5*p**2 + 1/5*p**4 + 0 + c*p.
p**2*(p - 1)**2/5
Determine w, given that -3 + 5 + 5 + 3*w + w**2 - 5 = 0.
-2, -1
Let k(r) = r**2 + 3*r + 2. Let h be 3/(-24) + (-15)/8. Let z be k(h). Solve 4/7*i**2 + z + 0*i + 2/7*i**3 = 0.
-2, 0
Suppose -4*t + 2*k = 3*k - 7, -3*t - 2*k + 4 = 0. Factor 0*w - 4/7*w**3 + 2/7*w**t + 2/7*w**4 + 0.
2*w**2*(w - 1)**2/7
Let d(c) be the first derivative of -c**7/490 - c**6/70 - 3*c**5/140 + 3*c**2 - 4. Let m(v) be the second derivative of d(v). Solve m(s) = 0 for s.
-3, -1, 0
Factor 0 + 2/5*c**4 + 0*c - 2/5*c**3 + 0*c**2.
2*c**3*(c - 1)/5
Let i(y) be the second derivative of -4/15*y**5 - 2/9*y**4 - 2*y - 1/18*y**3 + 0 + 0*y**2. Factor i(t).
-t*(4*t + 1)**2/3
Let k be (1/4)/(10/120). Factor 3*o**4 - 6*o**2 - o**3 + 5*o**3 - 2*o**k - 5*o**3.
3*o**2*(o - 2)*(o + 1)
Let j(n) be the third derivative of -1/60*n**6 + 0 + 0*n - 3*n**2 - 1/6*n**4 - 1/10*n**5 + 0*n**3. Factor j(y).
-2*y*(y + 1)*(y + 2)
Let p be (0 - 10) + 3/1. Let r = p + 10. Factor -8*k**r - 6*k**2 - k**4 - k**2 - 16 - 17*k**2 - 32*k.
-(k + 2)**4
Let l(t) be the third derivative of 0*t + 1/30*t**5 + 8*t**2 - 1/3*t**3 + 7/120*t**6 + 0 - 7/24*t**4. Solve l(x) = 0 for x.
-1, -2/7, 1
Suppose q + 0*q = 3. Let m be 4/(6/(6 - q)). Let 0 + 2/3*n - 1/3*n**m = 0. What is n?
0, 2
Let a(w) be the third derivative of 3/10*w**3 + 0*w + 4*w**2 + 1/20*w**4 + 1/300*w**5 + 0. What is s in a(s) = 0?
-3
Let l(m) be the first derivative of -m**6/39 - 2*m**5/65 + m**4/26 + 2*m**3/39 - 6. Determine r so that l(r) = 0.
-1, 0, 1
Let s(v) be the first derivative of -2/9*v**3 + 0*v + 0*v**2 + 1/12*v**4 - 6. Factor s(y).
y**2*(y - 2)/3
Suppose -4*w + 5*f = -41, -19 = -0*w - w + 3*f. Find g, given that 8*g + 4*g**3 + 2/3*g**w + 8/3 + 26/3*g**2 = 0.
-2, -1
Let h be ((-27)/(-12))/(9/24). Let u(d) = -2*d**2 + 3*d - 1. Let k(z) = 9*z**2 - 12*z + 5. Let p(n) = h*k(n) + 26*u(n). Determine w so that p(w) = 0.
-2, -1
Let x(y) = -y**4 - 5*y**3 - 28*y**2 - 20*y - 4. Let o(g) = g**4 + 4*g**3 + 29*g**2 + 21*g + 5. Let z(s) = 4*o(s) + 5*x(s). Factor z(k).
-k*(k + 1)*(k + 4)**2
Let g(n) = -6*n**2 - 29*n - 29. Let a(f) = -9*f**2 - 44*f - 44. Let b(t) = -5*a(t) + 8*g(t). What is c in b(c) = 0?
-2
Let h(i) = -3*i**2 + 2*i + 2. Let l be h(2). Let y be ((-2)/l)/(5/585). Factor 33*u**2 + 252*u**3 + 8 - y*u**2 + 30*u**2 + 98*u**4 + 194*u**2 + 72*u.
2*(u + 1)**2*(7*u + 2)**2
Let w(k) be the third derivative of -k**6/30 + k**5/15 + k**4/6 - 2*k**3/3 + 10*k**2. Factor w(d).
-4*(d - 1)**2*(d + 1)
Let k(q) be the first derivative of 5*q**3/3 + q**2 + 5. Find z, given that k(z) = 0.
-2/5, 0
Let x(v) = v**3 + 10*v**2 + v + 12. Let c be x(-10). Let n = 15 + -6. Factor 7*w**3 + 5*w**4 - w**4 - 2*w**4 + 1 + 5*w + n*w**c.
(w + 1)**3*(2*w + 1)
Let m(c) be the first derivative of 3/4*c**2 - 2 + 1/8*c**4 + 1/2*c**3 + 1/2*c. Factor m(o).
(o + 1)**3/2
Let t = -169/9 + 19. Let z(d) be the first derivative of 0*d + 1 - 2/3*d**2 + t*d**3. Solve z(a) = 0 for a.
0, 2
Let c be (20/(-10))/(130/84). Let y = 22/13 + c. Factor 0*a + y*a**2 - 2/5.
2*(a - 1)*(a + 1)/5
Let v(o) be the secon