)**2/2
Let c(m) = m**2 - 2. Let j be c(0). Let b be (-2)/j - (-1)/(-2). Factor 0 - b*v**3 - 1/2*v + v**2.
-v*(v - 1)**2/2
Let h(j) be the third derivative of j**6/140 + 13*j**5/210 - 5*j**4/42 + 64*j**2. Factor h(f).
2*f*(f + 5)*(3*f - 2)/7
Let r(g) be the third derivative of 0*g**3 + 0*g**6 + 1/1512*g**8 + 2/945*g**7 + 0 - 4*g**2 - 1/108*g**4 - 1/135*g**5 + 0*g. Factor r(b).
2*b*(b - 1)*(b + 1)**3/9
Solve -1/2 - 1/2*x**5 - x**3 + 3/2*x**4 - x**2 + 3/2*x = 0.
-1, 1
Let w(z) = z + 9. Let d be w(-9). Let u(l) be the third derivative of 3*l**2 + 0 + 0*l**3 - 1/36*l**4 + d*l - 1/180*l**5. Factor u(s).
-s*(s + 2)/3
Let y be (4/20*0)/(3 - 2). Factor -1/2 + 0*b**3 + b**2 - 1/2*b**4 + y*b.
-(b - 1)**2*(b + 1)**2/2
Let p(f) be the first derivative of 0*f - 2/27*f**3 + 4 + 1/9*f**2. Factor p(o).
-2*o*(o - 1)/9
Let x(a) be the first derivative of -1/2*a**4 + 0*a**2 + 2/3*a**3 - 3 + 0*a. Solve x(l) = 0 for l.
0, 1
Factor 4/5 - 24/5*h + 21/5*h**2 - h**3.
-(h - 2)**2*(5*h - 1)/5
Let d(y) be the first derivative of -y**7/4200 - y**6/900 + y**5/600 + y**4/60 - 2*y**3/3 - 3. Let o(k) be the third derivative of d(k). Factor o(c).
-(c - 1)*(c + 1)*(c + 2)/5
Let h be (-3 + (-3)/(-1))/1. Let b = 0 + 2. Determine n so that 1/4*n**b + h*n - 1/4 = 0.
-1, 1
Let q(b) = -b - 2. Let r be q(-4). Factor i**r + i**3 - 2 + 1 + 2*i**2 - 2*i**2 - i.
(i - 1)*(i + 1)**2
Let y = 141/22 - 54/11. Determine a, given that 3 - 9/2*a + y*a**2 = 0.
1, 2
Let r(s) be the third derivative of -1/15*s**4 + 1/150*s**6 - 1/50*s**5 + 5*s**2 + 1/525*s**7 + 4/15*s**3 + 0 + 0*s. Find w such that r(w) = 0.
-2, 1
Solve 1/2*t**3 + 1/4*t**2 + 0*t + 0 + 1/4*t**4 = 0 for t.
-1, 0
Suppose -3*d + 19 = 4. Factor -4*x**4 + d*x**4 - 2*x**4 - 7*x**3 + 4*x**3 + 3*x - x**2 + 2.
-(x - 1)*(x + 1)**2*(x + 2)
Suppose -3*n + 14 = -v + 2*v, 0 = n - 4*v + 17. Let c(b) = -b + 2. Let h be c(0). Factor w**3 + w + 0 + n - w**2 - h*w**3 - 2.
-(w - 1)*(w + 1)**2
Let y(c) be the first derivative of -c**6/27 + 2*c**5/45 + c**4/9 - 4*c**3/27 - c**2/9 + 2*c/9 - 7. Suppose y(s) = 0. Calculate s.
-1, 1
Let g = 27 + -22. Let u(j) = 9*j**2. Let p(h) = -h**2 + 1. Let o(k) = -3*k**2 + 5. Let z(b) = o(b) - 5*p(b). Let y(f) = g*u(f) - 21*z(f). What is m in y(m) = 0?
0
Let c be (8 - 10) + (-10)/(-2). Factor 0 - 2/5*n**4 + 0*n**2 + 0*n - 2/5*n**c.
-2*n**3*(n + 1)/5
Let i(u) = 3*u**4 - 8*u**3 + 3*u**2. Let z(g) = g**4 - 4*g**3 + g**2. Let d(t) = 3*i(t) - 7*z(t). Solve d(c) = 0 for c.
-1, 0
Let a(d) = d + 1. Let w be a(2). Suppose -w*n + 12 = -n. Factor 24*c**3 - c**4 - 12*c**2 + 2*c + n*c**5 - 11*c**4 - 8*c**4.
2*c*(c - 1)**3*(3*c - 1)
Find y, given that 12*y**2 - 2*y**3 - 2*y**3 - 8*y + 1106 - 1106 = 0.
0, 1, 2
Factor -11*c**2 - 12 + 4*c**3 + 5*c + 14 + 3*c - 3*c.
(c - 2)*(c - 1)*(4*c + 1)
Let x(k) be the third derivative of -1/300*k**6 - 1/150*k**5 + 1/1680*k**8 + 1/120*k**4 + 1/30*k**3 + 1/1050*k**7 + 0*k + 0 - 3*k**2. Factor x(v).
(v - 1)**2*(v + 1)**3/5
Let j(o) be the first derivative of o**5/15 + o**4/12 - 2. Determine s, given that j(s) = 0.
-1, 0
Let y(i) be the first derivative of -12*i**4 + 21/5*i**5 + 11*i**3 + 4 - 3*i**2 + 0*i. Factor y(m).
3*m*(m - 1)**2*(7*m - 2)
Let c(x) = -x**3 - 4*x**2 - 3*x. Let o(u) = u**2 - 5*u + 4. Let b be o(3). Let w(i) = -i**2 - i. Let h(l) = b*w(l) + c(l). Factor h(t).
-t*(t + 1)**2
Suppose -i - 5*x = -0*x - 27, i = 4*x - 18. Let l(k) be the first derivative of 8/15*k**3 - 2/5*k + 3/5*k**i + 3. Factor l(g).
2*(g + 1)*(4*g - 1)/5
Let b(v) be the second derivative of v**5/50 + v**4/15 + v**3/15 - 9*v. Factor b(f).
2*f*(f + 1)**2/5
Let i(c) be the third derivative of 0*c**4 + 0*c**3 + 0 + 1/30*c**6 + 0*c + 1/105*c**7 - c**2 + 1/30*c**5. Factor i(h).
2*h**2*(h + 1)**2
Let g(k) be the second derivative of k**6/60 + k**5/5 + k**4 + 8*k**3/3 + 4*k**2 - k. Find i such that g(i) = 0.
-2
Let m(x) = 4*x**4 + x**2 + 3*x + 4. Let j(h) = -h**4 - h**2 - h - 1. Let t(i) = -3*j(i) - m(i). Find l such that t(l) = 0.
-1, 1
Find c such that 0*c - 2/11*c**4 + 2/11*c**2 + 0 + 2/11*c**3 - 2/11*c**5 = 0.
-1, 0, 1
Let l(d) be the third derivative of -d**8/28 + d**7/14 + 7*d**6/40 - d**5/10 - 37*d**2. Determine h so that l(h) = 0.
-1, 0, 1/4, 2
Let p(s) = -14*s**5 - 6*s**4 + 17*s**3 - 11*s**2 - 3*s + 17. Let i(v) = 5*v**5 + 2*v**4 - 6*v**3 + 4*v**2 + v - 6. Let r(u) = 17*i(u) + 6*p(u). Factor r(b).
b*(b - 1)**3*(b + 1)
Let r(u) be the third derivative of 1/180*u**6 + 3*u**2 + 0*u**5 + 0 + 0*u + 0*u**3 + 0*u**4. Suppose r(y) = 0. Calculate y.
0
Let b = 2 + -2. What is m in 5*m + b*m - 6*m + 4*m**2 = 0?
0, 1/4
Let y(i) be the first derivative of 0*i + 1/2*i**2 + 0*i**4 + 1/20*i**5 - 1/2*i**3 - 1. Let r(m) be the second derivative of y(m). Find u, given that r(u) = 0.
-1, 1
Factor -4*l + 4*l + 5*l**4 - 4*l**2 - 5*l**5 + 5*l**3 - l**2.
-5*l**2*(l - 1)**2*(l + 1)
Let t be (-1)/(-2) + 161/(-14). Let f = 13 + t. Factor f*o**2 + 4/3 + 10/3*o.
2*(o + 1)*(3*o + 2)/3
Let q(r) = r**3 - 5*r. Let f be q(-2). Determine p, given that -2/5*p**4 + 0*p + 2/5*p**f + 0 - 2/5*p**3 + 2/5*p**5 = 0.
-1, 0, 1
Suppose 9 + 1 = 5*i - 5*x, -5*x + 18 = 2*i. Let s be (-14)/(-9) - i/18. Determine z so that -16/3*z**2 + 4/3*z**4 - 14/3*z - 4/3 + 2/3*z**5 - s*z**3 = 0.
-1, 2
Let m be 13/130*(8/11)/2. Let l(u) be the first derivative of 2/11*u**2 + 0*u**3 - m*u**5 - 1/11*u**4 + 2/11*u + 3. Factor l(h).
-2*(h - 1)*(h + 1)**3/11
Let f = 486509/9 + -54319. Let b = -262 - f. Factor -4/9*g + 2/9*g**4 + b*g**3 - 2/9 + 0*g**2.
2*(g - 1)*(g + 1)**3/9
Let b(i) = i**2 - i**2 + 16*i**3 - 24*i - 2*i**2 - 6. Let r(f) = -5*f**3 + f**2 + 8*f + 2. Let k = 2 - 5. Let o(a) = k*b(a) - 8*r(a). Factor o(d).
-2*(d - 1)*(d + 1)*(4*d + 1)
Let y(x) be the third derivative of 4*x**2 - 7/120*x**5 + 0*x - 1/24*x**4 + 0 - 1/60*x**6 + 1/12*x**3. Factor y(g).
-(g + 1)**2*(4*g - 1)/2
Let k(w) = w - 4. Let x be k(9). Suppose 10 = -3*u - 4*d - 0*d, -x*u + d + 14 = 0. Factor -2/3*z**4 + 0 - 2/3*z - 2*z**u - 2*z**3.
-2*z*(z + 1)**3/3
Let d be (-1127)/182 - -6 - 7/(-14). Factor -2/13*n**2 + 6/13*n - d.
-2*(n - 2)*(n - 1)/13
Let y be 24/10 - 4/10. What is d in 4*d - d**2 + 2*d**y - d - 4*d = 0?
0, 1
Let f(z) be the first derivative of 3 + 1/2*z**2 + 1/3*z**3 + 0*z. Factor f(g).
g*(g + 1)
Let s(o) be the first derivative of -o**4/8 + 7*o**3/2 - 147*o**2/4 + 343*o/2 + 13. Find z such that s(z) = 0.
7
Let p(s) be the first derivative of -5*s**6/6 - s**5 + 5*s**4 + 20*s**3/3 - 6. Suppose p(z) = 0. Calculate z.
-2, -1, 0, 2
Let z = -7/81 + 563/891. Factor -2/11 + z*c - 4/11*c**2 - 4/11*c**3 + 6/11*c**4 - 2/11*c**5.
-2*(c - 1)**4*(c + 1)/11
Let p(b) be the first derivative of 3*b**5/25 + 3*b**4/10 - 3*b**2/5 - 3*b/5 - 8. Factor p(f).
3*(f - 1)*(f + 1)**3/5
Let c = -629 + 2519/4. Determine h so that 3/4*h + 0 + c*h**2 = 0.
-1, 0
Let d = 1343/35 + -179/5. Determine p so that -d*p**3 - 2/7*p + 8/7*p**4 + 0 + 12/7*p**2 = 0.
0, 1/4, 1
Let l(k) be the second derivative of 0*k**4 + 0 + 1/14*k**7 + 11/90*k**6 + 1/30*k**5 + 0*k**2 + 0*k**3 - 2*k. Factor l(y).
y**3*(y + 1)*(9*y + 2)/3
Let s(p) = -3*p**3 - 16*p**2 - 13*p - 5. Let x(i) = -5*i**3 - 24*i**2 - 19*i - 7. Let a(z) = 7*s(z) - 5*x(z). Factor a(k).
4*k*(k + 1)**2
Let k(i) be the first derivative of 98*i**3/57 + 42*i**2/19 + 18*i/19 + 14. Factor k(o).
2*(7*o + 3)**2/19
Let s(k) be the first derivative of k**7/2940 - k**6/280 + k**5/84 - k**4/56 - 4*k**3/3 + 1. Let i(m) be the third derivative of s(m). Factor i(l).
(l - 3)*(l - 1)*(2*l - 1)/7
Let y = -10 + 15. Suppose 0 = -y*u + 56 + 29. Find j, given that -7*j**4 + 14*j**5 + 5*j**2 - u*j**4 + 6*j**3 - j**2 = 0.
-2/7, 0, 1
Let n(p) be the third derivative of -p**6/1080 + p**4/72 - p**3/2 - 2*p**2. Let b(r) be the first derivative of n(r). Suppose b(l) = 0. Calculate l.
-1, 1
Let k(h) be the first derivative of 0*h**2 + 0*h + 0*h**4 - 1 + 0*h**3 + 2/5*h**5. Factor k(d).
2*d**4
Let j(a) = -a**5 + a**4 + a**3 + a + 1. Let z = -2 - -1. Let y(b) = 7*b**5 - 4*b**4 - 5*b**3 - 6*b - 6. Let r(m) = z*y(m) - 6*j(m). Suppose r(w) = 0. What is w?
-1, 0
Factor -r**2 - 5*r**2 + 8*r**2 + 2*r**2.
4*r**2
Let b(k) be the second derivative of 0*k**2 + 1/24*k**3 + k + 1/96*k**4 + 0. Factor b(m).
m*(m + 2)/8
Let h(f) be the first derivative of -16/5*f**5 - 31/6*f**4 + 1 + 4/3*f + 5*f**2 + 16/9*f**6 + 44/9*f**3. Determine 