et w(j) be the third derivative of -j**6/660 - j**5/330 + j**4/132 + j**3/33 + 15*j**2. Factor w(f).
-2*(f - 1)*(f + 1)**2/11
Let y(n) be the third derivative of 0*n - 1/18*n**3 - n**2 + 1/180*n**5 - 1/72*n**4 + 1/360*n**6 + 0. Determine t so that y(t) = 0.
-1, 1
Let t = 4024 - 19754/5. Let r = t - 73. Factor 0*w + r - 1/5*w**2.
-(w - 1)*(w + 1)/5
Let p(x) = -9*x + 4. Let u be p(2). Let c = u - -43/3. Factor -c*s**3 + 0 - 2/3*s**4 + 0*s - 1/3*s**5 + 0*s**2.
-s**3*(s + 1)**2/3
Let r be 3 + (-6)/2 - -2. Find t, given that 4*t**3 - t + t - 6*t**5 - r*t + 4*t**5 = 0.
-1, 0, 1
Let h(j) be the second derivative of -j**5/20 + j**3/2 + j**2 - 30*j. Solve h(l) = 0.
-1, 2
Suppose 0 = 4*w - 16 - 0. Suppose w*t - 3 = 3*t + k, -2*k = -2. Factor 2 + 2 - t*s + 2*s**2 - 2*s.
2*(s - 2)*(s - 1)
Suppose 2*p - 3*u + 11 = 0, -5*u = -21 - 4. Let l(c) be the first derivative of 1/15*c**6 + 0*c + 2/25*c**5 + 0*c**4 - 1 + 0*c**3 + 0*c**p. Factor l(n).
2*n**4*(n + 1)/5
Let v(z) be the third derivative of -1/35*z**7 + 0*z**4 + 0*z + 2*z**2 + 0*z**3 + 1/15*z**5 + 1/60*z**6 + 0. Suppose v(u) = 0. Calculate u.
-2/3, 0, 1
Suppose -5*t = 2*t. Suppose 0 = -t*j - 6*j. Factor 1/6*b**2 + 1/6*b**3 + j - 1/6*b**4 - 1/6*b.
-b*(b - 1)**2*(b + 1)/6
Factor -2*h - 14 + 6 + 2*h**2 + 4.
2*(h - 2)*(h + 1)
Let k(m) = -6*m**4 - 2*m**3 + 8*m**2 - 6. Let x(o) = 31*o**4 + 11*o**3 - 40*o**2 + 31. Let a(u) = -11*k(u) - 2*x(u). Suppose a(i) = 0. Calculate i.
-1, 1
Let k be 10/3*6/45. Factor -2/3*w**3 - k*w**4 + 0*w + 0 - 2/9*w**2.
-2*w**2*(w + 1)*(2*w + 1)/9
Suppose -r + 14 = -0*r. Let f be 8/r*21/6. Determine a so that 0*a + 0 - 2/7*a**3 + 2/7*a**f = 0.
0, 1
Let -19 + 18 + 5*r**2 + 2*r - 6*r**2 = 0. Calculate r.
1
Let h be 5/2 - 2/(-4). Suppose h*x - 2 = 2*x. Factor -38/7*i**3 - 2/7*i + 30/7*i**x + 2*i**4 - 4/7.
2*(i - 1)**3*(7*i + 2)/7
Let u(s) be the third derivative of 4*s**7/735 + 11*s**6/420 + s**5/21 + s**4/28 - 22*s**2. Factor u(v).
2*v*(v + 1)**2*(4*v + 3)/7
Let w(l) = -l + 1. Let g(u) = -25*u**3 + 5*u**2 + 17*u + 3. Let z(s) = -g(s) - w(s). Factor z(v).
(v - 1)*(5*v + 2)**2
Let s(l) be the second derivative of l**5/4 - 5*l**4/4 + 5*l**3/2 - 5*l**2/2 + 6*l. Let s(k) = 0. What is k?
1
Let s be (1 + (-24)/21)*(-18 - -16). Factor 2/7*y**3 + 2/7 - 2/7*y - s*y**2.
2*(y - 1)**2*(y + 1)/7
Factor 9*y**4 - 5*y**3 + 2*y**4 + 3*y**4 - 19*y**4.
-5*y**3*(y + 1)
Find w, given that 1/5*w**3 - 1/5*w + 1/5*w**4 - 1/5*w**2 + 0 = 0.
-1, 0, 1
Let a(m) be the second derivative of -m + 0 + 1/24*m**4 + 0*m**2 - 1/20*m**5 + 1/12*m**3. Factor a(z).
-z*(z - 1)*(2*z + 1)/2
Suppose 2*n - 3*n = -2. Determine o so that -o**4 + 4*o**3 - 2*o**2 + 4 - o**n + 0*o**3 + 0 - 4*o = 0.
-1, 1, 2
Let z(q) = 4*q**5 - 25*q**4 + 12*q**3 + 31*q**2 - 5*q. Let i(f) = 6*f**5 - 38*f**4 + 18*f**3 + 46*f**2 - 8*f. Let n(u) = 5*i(u) - 8*z(u). Factor n(k).
-2*k**2*(k - 3)**2*(k + 1)
Let p(l) be the third derivative of l**10/5040 + l**9/7560 - l**8/1680 - l**4/24 - l**2. Let j(o) be the second derivative of p(o). Solve j(s) = 0 for s.
-1, 0, 2/3
Factor 0 + 4/5*w**4 + 4/5*w**2 + 0*w + 8/5*w**3.
4*w**2*(w + 1)**2/5
Factor 1/7*a**4 + 0*a + 0*a**2 + 2/7*a**3 + 0.
a**3*(a + 2)/7
Let j be (-3)/(-2)*-2 - (-70)/21. Let q(y) be the first derivative of j*y**3 - y**2 - 2 + y. Solve q(s) = 0.
1
Let f(q) be the first derivative of q**5/40 - q**3/4 - q**2/2 - q + 3. Let i(u) be the first derivative of f(u). Determine o, given that i(o) = 0.
-1, 2
Let f(g) be the second derivative of -g**6/10 + 3*g**5/20 + g**4 - 2*g**3 - 36*g. Determine u, given that f(u) = 0.
-2, 0, 1, 2
Suppose -3*y = 2*y. Suppose y = -4*v + 15 - 3. Factor 0 - 2 + 3 + v*t + t**3 + 3*t**2.
(t + 1)**3
Let t be 2/3*(22 + 2). Let g = t + -13. Factor 2/3*o**2 + 8/9*o + 2/9*o**4 - 8/9 - 8/9*o**g.
2*(o - 2)**2*(o - 1)*(o + 1)/9
Let t(i) be the third derivative of -i**5/30 - i**4/6 + i**3 + 19*i**2. Let t(a) = 0. Calculate a.
-3, 1
Let y = -47466531 + 107511695423/2265. Let x = y - -2/453. Factor -x*j**2 - 8/5*j - 2/5.
-2*(j + 1)*(3*j + 1)/5
Let q(g) be the second derivative of 0 + 0*g**5 + 0*g**3 - 1/3*g**2 + 1/9*g**4 - 4*g - 1/45*g**6. What is y in q(y) = 0?
-1, 1
Factor 16*x**2 - 3*x**5 + 7*x + 4*x**5 + 2 + 6*x**4 + 14*x**3 + 2*x.
(x + 1)**4*(x + 2)
Let q(n) = -n**2 + n + 1. Let f = 13 - 9. Let c(z) = 4*z**3 - 10*z**2 + 4*z + 6. Let r be (10 + -11)*(-2)/(2 + -4). Let j(a) = f*q(a) + r*c(a). Factor j(s).
-2*(s - 1)**2*(2*s + 1)
Let r(p) be the second derivative of -2*p**6/135 - 11*p**5/90 - p**4/3 - 4*p**3/27 + 8*p**2/9 + 6*p. Find z, given that r(z) = 0.
-2, 1/2
Let t(q) be the third derivative of 1/9*q**3 + 0*q - 1/90*q**5 + 1/180*q**6 - 1/36*q**4 - 3*q**2 + 0. Let t(l) = 0. What is l?
-1, 1
Suppose -32 = d - 2*d. Let r = -23 + d. Suppose -2*k**4 - k**4 - 3*k + 0*k - r*k**2 - 9*k**3 = 0. What is k?
-1, 0
Solve -1/3*c + 1/3*c**2 - 2/3 = 0 for c.
-1, 2
Factor 8*n**2 + 1 + 5 + n**3 - 3*n**3 - 10*n - 2.
-2*(n - 2)*(n - 1)**2
Let s = 57 - 53. Let o(d) be the first derivative of -3/4*d**4 - 2*d**3 - 3/2*d**2 + 0*d + s. Suppose o(m) = 0. Calculate m.
-1, 0
Let i(j) = -j - 3. Let c be i(-6). Let t(a) be the first derivative of 0*a - 1/9*a**c - 1 + 0*a**2. Factor t(z).
-z**2/3
Determine j so that 0*j**3 + 4/9*j - 8/9*j**2 - 4/9*j**5 + 8/9*j**4 + 0 = 0.
-1, 0, 1
Factor 0 - 16/3*m**4 + 0*m - 2/3*m**3 - 10/3*m**5 + 4/3*m**2.
-2*m**2*(m + 1)**2*(5*m - 2)/3
Let z = -6 + 8. Suppose -z = 5*i - 12. Factor 3*r**2 - r**4 - r**4 - r**i.
-2*r**2*(r - 1)*(r + 1)
Let t(l) be the third derivative of -l**7/5040 - l**6/720 + l**4/8 - 6*l**2. Let s(b) be the second derivative of t(b). Determine i so that s(i) = 0.
-2, 0
Suppose -147*s**4 + 12 + 0 + 135*s**2 + 84*s**3 - 78*s - 6*s = 0. What is s?
-1, 2/7, 1
Let h(y) be the second derivative of -y**4/4 + 5*y**3/2 + 21*y**2 + 65*y - 2. What is j in h(j) = 0?
-2, 7
Let r(g) be the first derivative of 1/360*g**6 + 0*g + 0*g**2 + 1/3*g**3 - 2 + 1/120*g**5 + 0*g**4. Let h(i) be the third derivative of r(i). Factor h(m).
m*(m + 1)
Suppose 5*j - 10 = 2*w, 0 = -6*w + 2*j + 25 - 3. Factor -5/4*y**3 - 1/4*y**w + y**4 + 0*y + 0 + 1/2*y**2.
-y**2*(y - 2)*(y - 1)**2/4
Suppose 3*t = 4*p, 4*t = 2*p - 3*p. Let n(z) = -z**2 + 5*z + 6. Let o be n(6). Factor t + 4/3*y**4 + 2/3*y**3 + 0*y**2 + 2/3*y**5 + o*y.
2*y**3*(y + 1)**2/3
Let y(h) be the second derivative of -h**9/1296 + h**8/560 - h**7/1260 + h**3/6 + 5*h. Let q(s) be the second derivative of y(s). Find j such that q(j) = 0.
0, 2/7, 1
Let -18/11*c**3 + 2/11*c**2 - 8/11*c**5 + 2/11*c + 2*c**4 + 0 = 0. Calculate c.
-1/4, 0, 1
Let s be 1*(84/8)/7. Solve 2*d**2 - 1/2*d**5 + 0*d**3 - s*d**4 + 0 + 0*d = 0 for d.
-2, 0, 1
Let n(d) be the first derivative of d**3/3 - d + 2. Let a be n(-1). Factor a*q**2 + 6*q + 2 - q - 6*q**2 - q**2.
-(q - 1)*(7*q + 2)
Suppose -5 = -3*y + 16. Factor -v + 4 + 2*v - y*v + 0*v**2 + 2*v**2.
2*(v - 2)*(v - 1)
Suppose n = -n. Let g be (4/(-7))/(1/(-7)). Factor -1/2*b**g + 1/2*b**2 - 1/4*b**5 + 1/4*b + 0 + n*b**3.
-b*(b - 1)*(b + 1)**3/4
Let i(b) be the second derivative of -5*b**7/126 - b**6/9 + b**5/4 - 15*b. Factor i(k).
-5*k**3*(k - 1)*(k + 3)/3
Let g(j) be the third derivative of j**9/3024 - j**8/840 + j**7/840 + 2*j**3/3 + j**2. Let m(w) be the first derivative of g(w). Factor m(r).
r**3*(r - 1)**2
Let n(h) be the third derivative of h**8/24 + 4*h**7/35 + h**6/20 - h**5/15 + 29*h**2. Factor n(a).
2*a**2*(a + 1)**2*(7*a - 2)
Let s(u) be the second derivative of u**4/3 + 14*u**3/3 - 15*u. Determine z so that s(z) = 0.
-7, 0
Let r(z) = z**3 - 14*z**2 + z - 11. Let l be r(14). Suppose -4*v + 2 = n, -2*v - l*n - 3 = -9. Factor -14/5*j**2 + v - 2/5*j**5 - 4/5*j - 2*j**4 - 18/5*j**3.
-2*j*(j + 1)**3*(j + 2)/5
Let r be 3 + (-2 + 1 - 3). Let g(f) = 2*f**2 - f - 1. Let x be g(r). Find j, given that 0*j + 1/3*j**3 + 4/3*j**5 + 0*j**x + 0 - 5/3*j**4 = 0.
0, 1/4, 1
Suppose -5*k - 10 = -l, 29 = 8*l - 3*l - 4*k. Let t(p) = -26*p**2 + 32*p - 14. Let g(u) = -17*u**2 + 21*u - 9. Let m(f) = l*t(f) - 8*g(f). Factor m(v).
2*(v - 1)*(3*v - 1)
Let s = -11 + -13. Let u be 2/5 + s/(-15). Factor 4*z + 1 + z**2 + 0*z - u*z.
(z + 1)**2
Suppose 0*l**3 - 2*l + 8*l**2 - 2*l**3 - 4*l**2 = 0. Calculate l.
0, 1
Let n(t) = -2*t**4 + 7*t**3 + 23*t**2 + 7*t + 3. Let x(f) = -f**4 - f**3 + f**2 - f. Let s(a) = n(a) - 5*x(a). Factor s(j).
