Let i(m) be the first derivative of m**8/7560 - m**6/810 + m**4/108 + 2*m**3/3 + 1. Let l(g) be the third derivative of i(g). Factor l(n).
2*(n - 1)**2*(n + 1)**2/9
Suppose -2*l + 12 = l. Let a(k) = k**2 + 4*k. Let y be a(-4). Factor -4*b**5 + 2*b**3 - 3*b**l + 1 + y*b**4 - 8*b**2 + 2*b + 10*b**4.
-(b - 1)**3*(b + 1)*(4*b + 1)
Suppose -7*w + 12 = -9. Let n(s) be the first derivative of s**2 - 1/2*s**4 - 1 + 2/3*s**w - 2/5*s**5 + 0*s. Factor n(v).
-2*v*(v - 1)*(v + 1)**2
Let v(w) = -w**2 - 9*w + 12. Let k be v(-10). Let z(r) be the first derivative of 2/5*r**5 + 0*r - 1/2*r**4 + r**k + 2 - 2/3*r**3. Solve z(f) = 0 for f.
-1, 0, 1
Let k(v) be the third derivative of v**8/26880 + v**7/1120 + 3*v**6/320 + v**5/60 + 5*v**2. Let n(m) be the third derivative of k(m). Factor n(h).
3*(h + 3)**2/4
Let q = -11 - -87/7. Factor q*v**4 + 0*v**2 + 0 - 4/7*v**5 - 6/7*v**3 + 0*v.
-2*v**3*(v - 1)*(2*v - 3)/7
Let l(j) be the third derivative of -j**7/1575 - j**6/300 - j**5/150 - j**4/180 - 3*j**2. Factor l(x).
-2*x*(x + 1)**3/15
Let g(r) be the third derivative of -r**8/504 + 2*r**7/315 - r**6/180 + 5*r**2. Factor g(t).
-2*t**3*(t - 1)**2/3
Let 3/2 - 3/4*c**2 + 3/4*c = 0. What is c?
-1, 2
Let n = 13 - 9. Suppose -6*d = -5*d - n. Factor 4/7*v**3 - 2/7*v + 0*v**d + 0*v**2 + 0 - 2/7*v**5.
-2*v*(v - 1)**2*(v + 1)**2/7
Suppose -40*c**2 + c**3 + 2*c**3 - 6*c**3 - 12*c + 25*c**2 = 0. Calculate c.
-4, -1, 0
Suppose -5*f - 5*z = 25, 5*f + 25 = 5*z - 0. Let d = 10 + f. Factor 4 + q**2 - d*q + 3*q - 3.
(q - 1)**2
Factor 3 - 3/5*r**2 - 12/5*r.
-3*(r - 1)*(r + 5)/5
Factor 27/2 - 9/2*r**2 - 39*r.
-3*(r + 9)*(3*r - 1)/2
Factor -10/7*a**2 - 12/7 - 34/7*a.
-2*(a + 3)*(5*a + 2)/7
Solve -3/4*q**4 + 3/4*q + 0 + 3/4*q**2 - 9/4*q**3 + 3/2*q**5 = 0.
-1, -1/2, 0, 1
Let u = 3 - 1. Factor 0*a**2 - 1 - 9*a - a**u + 11*a.
-(a - 1)**2
Suppose 4*u = 7*u - 6. Let 5*m - 9*m**3 + 10*m - 14*m**u + 6 + 2*m**2 = 0. Calculate m.
-2, -1/3, 1
Let z(v) be the third derivative of -2*v**2 + 1/70*v**7 + 0*v + 1/90*v**5 + 0*v**4 + 1/40*v**6 + 0 + 0*v**3. Let z(n) = 0. Calculate n.
-2/3, -1/3, 0
Let x(g) be the first derivative of -g**4/4 + g**2/2 + 9. Solve x(d) = 0.
-1, 0, 1
Let u(y) be the second derivative of y**7/210 - y**6/30 + y**5/20 - 4*y**2 - 3*y. Let r(q) be the first derivative of u(q). Find k such that r(k) = 0.
0, 1, 3
Factor 2/3*p**4 - 2/3*p**5 + 4/3*p**3 + 0*p**2 + 0*p + 0.
-2*p**3*(p - 2)*(p + 1)/3
Suppose 0 = -2*a + 4. Suppose a*i = -0*i + 4. Find z such that -z**3 + i*z**5 + 5*z**3 - 3*z**3 + 2*z - 5*z**3 = 0.
-1, 0, 1
Factor 3 + 2*s**3 + 0*s - s + 7*s - 1 + 6*s**2.
2*(s + 1)**3
Factor 4 + u - 5*u - 4*u**5 + 4*u**4 - 8*u**2 + 8*u**3 + 0*u**4.
-4*(u - 1)**3*(u + 1)**2
Let o(m) be the third derivative of -m**6/120 + 19*m**5/60 - m**4/4 - 2*m**3 + 6*m**2. Let n(k) = 6*k**2 - 2*k - 4. Let f(j) = -14*n(j) + 4*o(j). Factor f(t).
-4*(t - 1)*(t + 1)*(t + 2)
Let o(t) be the third derivative of 0*t + 6*t**2 - 1/10*t**5 + 1/24*t**4 + 0 + 0*t**3. Factor o(z).
-z*(6*z - 1)
Let f(p) = p + 1. Let b(t) = -t**3 + 2*t**2 - 7*t - 6. Let w(l) = l**3 + 4*l**2 + 2*l - 2. Let u be w(-3). Let q(h) = u*b(h) + 6*f(h). Factor q(o).
-o*(o - 1)**2
Determine w so that 2*w**5 + 10*w + 2*w**3 + 4*w**2 - 7*w**3 + 2*w**4 - 6 - 7*w**3 = 0.
-3, -1, 1
Suppose -4*q + 2*n + 2 = q, 2*q = n. Suppose -6*w = -q*w. Factor -2/5*y**3 + 0*y**2 + w + 2/5*y.
-2*y*(y - 1)*(y + 1)/5
Let f(m) be the second derivative of m**8/8400 - m**7/4200 - m**3/2 + 2*m. Let h(p) be the second derivative of f(p). What is g in h(g) = 0?
0, 1
Let l(s) be the third derivative of s**9/1512 + s**8/840 - s**7/420 - s**6/180 + s**3/3 + 2*s**2. Let h(t) be the first derivative of l(t). Factor h(f).
2*f**2*(f - 1)*(f + 1)**2
Let m be 45/60*2/6. Let f(i) be the first derivative of -i**3 + m*i**4 - i + 3/2*i**2 + 3. Factor f(d).
(d - 1)**3
Let i(h) = -h**2 - h**3 + h**2 - h**2. Let w be i(-2). Factor -1/2*l**3 + 4 - 1/2*l**5 + 2*l**w - 5*l**2 + 2*l.
-(l - 2)**3*(l + 1)**2/2
Suppose -2*h - 2*h - 4*t - 16 = 0, -37 = 4*h - 3*t. Let c be (-8)/28*h/9. Solve -c*p**2 - 2/9 - 4/9*p = 0 for p.
-1
Let b be -1 + (-1)/((-12)/16). Let l(w) = -w - 1. Let m be l(-6). Solve -b*p**m + 1/3*p**3 + 0 + 0*p**4 + 0*p**2 + 0*p = 0.
-1, 0, 1
Factor 3*t**2 + 7*t + t + 3 + 1 + t**2.
4*(t + 1)**2
Suppose 377 + 73 = 5*z. Let n be 20/z - (-10)/36. Factor 1/2*p**5 - n*p**2 + 1/2*p**4 + 0 - 1/2*p**3 + 0*p.
p**2*(p - 1)*(p + 1)**2/2
Let p(x) = -x**5 + x**4 - x**3 + x. Let j(d) = -4*d**5 - 8*d**4 + 11*d**3 - 5*d. Let i(k) = j(k) + 5*p(k). Find y, given that i(y) = 0.
-1, 0, 2/3
Let a = -60 + 62. Let l(z) be the first derivative of -3 + 4/3*z**3 + 0*z + 1/4*z**4 + a*z**2. Factor l(x).
x*(x + 2)**2
Let n = 549 + -3835/7. Let -2/7*d**3 - 16/7*d + 10/7*d**2 + n = 0. What is d?
1, 2
Suppose -k + 8 - 4 = 0. Let t be 0 + (-1 - -1) + 5. Solve -4*p**5 - 4*p**4 + 7*p**t - 6*p**2 + 7*p**k + 3 + 3*p - 6*p**3 = 0 for p.
-1, 1
Let s(a) be the third derivative of a**7/840 + a**6/80 + 13*a**5/240 + a**4/8 + a**3/6 + 2*a**2. Determine r, given that s(r) = 0.
-2, -1
Suppose -u + 6*u - 10 = 0. Let o(x) be the third derivative of -1/3*x**3 + 0*x + 2*x**u + 0 + 1/12*x**4 - 1/120*x**5. Determine w so that o(w) = 0.
2
Solve -18/7*q - 24/7*q**2 + 27/7 + 18/7*q**3 - 3/7*q**4 = 0.
-1, 1, 3
Suppose -3*c + 2*g = 2*c - 27, 4*c = -3*g + 17. Solve -7*z**2 - 2*z**2 - 3*z**c + 8*z**4 - z**5 + 4*z + z**2 = 0.
-1, 0, 1
Let b(z) = z**4 + z**2 - z. Let a(v) = -v + 2 - 2 + 2*v**3 + 2*v. Let d(j) = j**2 - 5*j + 2. Let k be d(5). Let m(x) = k*a(x) + 2*b(x). Factor m(q).
2*q**2*(q + 1)**2
Let h(j) be the first derivative of j**8/560 + j**7/120 + j**6/72 + j**5/120 - j**3/3 - 1. Let l(x) be the third derivative of h(x). Factor l(y).
y*(y + 1)**2*(3*y + 1)
Let m be (2/24)/(21/63). Solve -m + 1/8*g**2 - 1/8*g = 0.
-1, 2
What is p in 3*p - 3/5*p**5 + 36/5*p**3 + 0 - 6/5*p**4 - 42/5*p**2 = 0?
-5, 0, 1
Solve 4/3*d - 4*d**2 + 0 - 2*d**4 + 1/3*d**5 + 13/3*d**3 = 0.
0, 1, 2
Let i(k) be the second derivative of k**6/150 - k**5/20 + k**4/10 - 46*k. Factor i(y).
y**2*(y - 3)*(y - 2)/5
Let c(f) = -4*f - 13. Let g be c(-6). Let j = g + -9. Solve 3*n**3 - j*n**2 - 3/2*n**5 + n**4 - 3/2*n + 1 = 0 for n.
-1, 2/3, 1
Suppose -2 = l + i, -1 = 5*l - 4*i + 18. Let g = l - -8. Factor 0*x + 1/4*x**3 - 1/4*x**g + 0 - 1/4*x**4 + 1/4*x**2.
-x**2*(x - 1)*(x + 1)**2/4
Let x = 49/153 - 5/51. Suppose 8/9*f**3 - x*f**2 - 2/3*f**4 + 0 + 0*f = 0. Calculate f.
0, 1/3, 1
Factor -4*b**3 - 24*b**2 + 5*b**4 + 3*b**4 - 4*b**4.
4*b**2*(b - 3)*(b + 2)
Let j(k) = k**3 + 12*k**2 + 13*k + 14. Let b be j(-11). Let y(c) = -c**2 - 8*c + 2. Let u be y(b). Factor 1/2*f**3 + 1/2 + 3/2*f + 3/2*f**u.
(f + 1)**3/2
Factor -108/7*p + 36/7*p**2 - 4/7*p**3 + 108/7.
-4*(p - 3)**3/7
Let w = 30 - 4. Let a be (3/6)/((-3)/(-264) + 0). Determine m so that -a*m**3 - 14*m - 2 - 4*m**5 - 40*m**2 + 0*m - w*m**4 + 4*m**2 - 2*m**5 = 0.
-1, -1/3
Suppose -o + 7 - 18 = -3*j, 2*j = 10. Factor 0*k**3 + 0 + 0*k**2 - 1/4*k**o + 0*k.
-k**4/4
Let w = -15 - -8. Let z = w - -9. Solve 1/3*d**z + 1/3*d**3 + 0 + 0*d = 0.
-1, 0
Let o(q) = q**3 - q**2 + q + 1. Let x(z) = -26*z**2 + 96*z - 2. Let b(k) = 4*o(k) + 2*x(k). Determine h so that b(h) = 0.
0, 7
Let b(g) be the third derivative of g**7/1365 - g**5/78 + 4*g**3/39 - 42*g**2. Suppose b(s) = 0. What is s?
-2, -1, 1, 2
Let y = 112 + -103. Find c such that -27/2 + y*c - 3/2*c**2 = 0.
3
Let r(q) be the second derivative of q**10/105840 - q**9/52920 - q**8/23520 + q**7/8820 - q**4/12 + 6*q. Let f(a) be the third derivative of r(a). Factor f(h).
2*h**2*(h - 1)**2*(h + 1)/7
Let m(y) be the third derivative of 1/420*y**6 + 0 + 5/84*y**4 + 0*y - y**2 - 2/105*y**5 - 2/21*y**3. Factor m(x).
2*(x - 2)*(x - 1)**2/7
Let q be (-469)/42 - (-2)/(-6). Let x = q + 49/4. Suppose 1 - 5/4*g**3 + 3*g + x*g**2 = 0. Calculate g.
-1, -2/5, 2
Factor -8*q**3 - 10*q**2 - 13*q**3 + 7*q**3 - 2*q - 6*q**4.
-2*q*(q + 1)**2*(3*q + 1)
Determine v so that -245*v**5 + 65*v**4 - 1141*v**4 - 1270*v**2 - 1805*v**3 - 40 - 44*v**4 - 380*v = 0.
-2, -1, -2/7
Let j(x) be the second derivative of -x**6/180 - x**5/90 + x**4/36 + x**3/9 - 3*x**2/2 - x. Let l(u) be the first derivative of j(u). Find m such that l(m) = 0.
-1, 1
Let s be 3/(-9) - 18/(-54). Factor -2/11*r**2 + 8/11 + s*r.
-2*(r - 2)*(r + 2)/11
