/105 + o**6/10 + 2*o**5/5 + 5*o**4/6 + o**3 + 10*o**2. Factor a(u).
2*(u + 1)**3*(u + 3)
Determine o, given that -28/9*o**2 - 40/9*o - 2/3*o**3 - 16/9 = 0.
-2, -2/3
Let x(v) be the second derivative of 3*v**5/20 + v**4/24 - v**3/2 - v**2/4 + 26*v. Factor x(s).
(s - 1)*(s + 1)*(6*s + 1)/2
Factor 0*s**2 + 20*s**4 - 4*s**3 - 4*s**2 + 25*s**5 - 37*s**5.
-4*s**2*(s - 1)**2*(3*s + 1)
Let n(r) = -r**3 - 2*r**2 - 5*r. Let f(g) = 2*g**3 + 5*g**2 + 11*g. Let x(p) = 4*f(p) + 9*n(p). Let x(q) = 0. What is q?
0, 1
Let d = -32 - -32. Let b(k) be the first derivative of 0*k**2 + 2 + d*k - 2/3*k**3. Factor b(f).
-2*f**2
Let i be -3 - 2/((-6)/9). Let j(w) be the first derivative of 0*w + i*w**2 + 0*w**3 - 1/2*w**4 - 2. Solve j(c) = 0.
0
Let l(i) be the first derivative of i**5/5 - 11*i**4/16 + 5*i**3/6 - 3*i**2/8 + 1. Factor l(g).
g*(g - 1)**2*(4*g - 3)/4
Let c(s) be the third derivative of s**5/240 + s**4/96 - s**3/12 + s**2. Solve c(m) = 0 for m.
-2, 1
Let p be 12/3 + -9 + 8. Determine b, given that -4/3*b**2 - 20/3*b**5 - 22/3*b**p + 0 + 0*b - 38/3*b**4 = 0.
-1, -1/2, -2/5, 0
Let s(x) be the third derivative of -x**5/330 - x**4/22 - 3*x**3/11 + 6*x**2. Factor s(f).
-2*(f + 3)**2/11
Let k(s) be the first derivative of 2*s**5/7 + 4*s**4/7 + 2*s**3/21 - 2*s**2/7 - 4. Determine c, given that k(c) = 0.
-1, 0, 2/5
Solve 5*k**2 - 8*k**2 + 2*k**3 + 3*k**3 + 20*k - 17*k**2 = 0.
0, 2
Let t(q) be the third derivative of 2*q**2 - 1/180*q**5 + 1/72*q**4 - 1/360*q**6 + 0*q + 0*q**3 + 1/630*q**7 + 0. Solve t(y) = 0.
-1, 0, 1
Determine c so that 4/7*c + 2/7*c**2 + 0 = 0.
-2, 0
Let -357 - 24*a**2 + 102*a - 18 + 123*a + 3*a**3 - 21*a**2 = 0. Calculate a.
5
Find l, given that 4*l**2 - 2*l**3 - 195*l + 195*l = 0.
0, 2
What is v in 1/2*v + 0*v**2 + 0 - 1/2*v**3 = 0?
-1, 0, 1
Let h(x) = x**3 + 13*x**2 + x + 18. Let a be h(-13). Suppose 0 + a = 3*u - 4*y, 2*u = -y + 7. Factor 2/9*i**4 + 0 + 10/9*i**2 + 4/9*i + 8/9*i**u.
2*i*(i + 1)**2*(i + 2)/9
Let l = 625/6 - 103. Let i = 11/6 - l. Suppose 2/3 - 4/3*x + i*x**2 = 0. Calculate x.
1
Let s(u) be the first derivative of -u**3/6 - 3*u**2/2 - 5*u/2 - 11. Factor s(h).
-(h + 1)*(h + 5)/2
Let t(f) be the third derivative of f**5/12 - 5*f**3/6 - 8*f**2. Factor t(a).
5*(a - 1)*(a + 1)
Factor -3/4*f**2 - f - 1/4.
-(f + 1)*(3*f + 1)/4
Let u(b) be the first derivative of b**6/900 - b**5/100 + b**4/30 - b**3/3 + 2. Let o(g) be the third derivative of u(g). Solve o(t) = 0.
1, 2
Let l(a) be the first derivative of 56*a**5/15 - 11*a**4/3 - 16*a**3/3 + 22*a**2/3 - 8*a/3 + 9. Determine q, given that l(q) = 0.
-1, 2/7, 1/2, 1
Let r(l) be the first derivative of -5*l**6/6 - 2*l**5 + 10*l**3/3 + 5*l**2/2 + 7. Factor r(o).
-5*o*(o - 1)*(o + 1)**3
Let d(z) be the third derivative of z**2 - 3/200*z**6 + 0 + 0*z**3 + 0*z**4 + 0*z + 1/50*z**5. Find u such that d(u) = 0.
0, 2/3
Let k(p) be the third derivative of -p**10/50400 + p**9/20160 - p**5/20 + 5*p**2. Let u(w) be the third derivative of k(w). Factor u(d).
-3*d**3*(d - 1)
Factor 1/4*r**3 - 3/4*r - 1/2 + 0*r**2.
(r - 2)*(r + 1)**2/4
Let s(g) be the second derivative of g**6/720 + g**5/120 + g**4/48 - 2*g**3/3 - g. Let t(z) be the second derivative of s(z). Factor t(n).
(n + 1)**2/2
Let f(o) = -o**2 + 9*o + 10. Let y be f(8). Let j be -2 + (-2)/(-15)*y. Find m, given that j*m**4 + 0*m**2 + 0*m + 0*m**3 + 0 = 0.
0
Let b be 19/5 - (-4)/20. Suppose 2 = 3*o - 3*z + 2*z, -b = -4*o + 2*z. Factor o*k - 1/3*k**4 + 1/3*k**3 + 0*k**2 + 0.
-k**3*(k - 1)/3
Let x(z) be the first derivative of -7*z**5/10 + 2*z**4 - 11*z**3/6 + z**2/2 + 1. Suppose x(q) = 0. Calculate q.
0, 2/7, 1
Let v(j) = -5*j**5 + 13*j**4 - 3*j**2 + 3*j - 3. Let d(b) = -5*b**5 + 12*b**4 - 2*b**2 + 2*b - 2. Let r(u) = 3*d(u) - 2*v(u). Factor r(t).
-5*t**4*(t - 2)
Let j(y) be the second derivative of -y**7/14 - 2*y**6/5 - 3*y**5/5 + y**4/2 + 5*y**3/2 + 3*y**2 + y + 31. Solve j(x) = 0 for x.
-2, -1, 1
Suppose 3*l + 323 - 329 = 0. Factor -15/7*r**l + 3/7*r + 12/7*r**3 + 0.
3*r*(r - 1)*(4*r - 1)/7
Let l(u) be the first derivative of -5/3*u**2 - 4/3*u - 1/6*u**4 - 8/9*u**3 - 3. Suppose l(b) = 0. Calculate b.
-2, -1
Suppose 0*w + 3*w = -b + 12, -20 = -4*b + 2*w. Factor b*y**2 - 3*y + y + 4*y - 4*y**2.
2*y*(y + 1)
Let h = -40/253 + -7070/3289. Let j = h - -193/78. Factor -j*t + 1/3 - 1/6*t**2.
-(t - 1)*(t + 2)/6
Let b(t) be the first derivative of -t**4 + 2*t**2 + 28. Factor b(z).
-4*z*(z - 1)*(z + 1)
Let p be (-1 - (-5 - -7)) + 3/1. Factor 2/7*a**2 - 4/7*a + p.
2*a*(a - 2)/7
Factor -20/7*a**2 - 12/7 - 4*a - 4/7*a**3.
-4*(a + 1)**2*(a + 3)/7
Let b(a) be the first derivative of a**4 - a**3 + 2*a**2 + 5*a - 1. Let x(t) = 2*t**3 - t**2 + 2*t + 3. Let d(l) = 3*b(l) - 5*x(l). Factor d(c).
2*c*(c - 1)**2
Let l = 12 - 12. Let p(u) be the first derivative of l*u - 1/12*u**4 + 1 + 0*u**2 + 0*u**3 + 1/5*u**5. Suppose p(g) = 0. What is g?
0, 1/3
Let f(s) be the second derivative of 7*s**8/240 - s**6/90 - s**3 + 6*s. Let z(g) be the second derivative of f(g). Factor z(p).
p**2*(7*p - 2)*(7*p + 2)
Suppose 2*b - 19 + 1 = -4*f, -4*f + b + 21 = 0. Let s be (-375)/10*(-1)/f. Factor -3/2*q**4 - 21/2*q - 3 - s*q**3 - 27/2*q**2.
-3*(q + 1)**3*(q + 2)/2
Let q = -7 - -4. Let b be -3 - -5 - (-3 - q). Factor 0 + 0*p**4 + 0*p**b - 2/5*p**5 + 0*p + 2/5*p**3.
-2*p**3*(p - 1)*(p + 1)/5
Let m = -5 + 2. Let z(i) = 3*i - i**2 - i - i - 1 + 0. Let s(u) = 2*u**3 + u**2 + 5*u - 3. Let p(v) = m*z(v) + s(v). Factor p(c).
2*c*(c + 1)**2
Let 1/3*q**3 - 4/3 - 4/3*q + 1/3*q**2 = 0. Calculate q.
-2, -1, 2
Suppose s - 5*i + 6 = 0, 2*i + 16 = 6*s - s. Suppose 1 = -4*k + 13. Factor z**2 + 6*z**3 - z**k - s*z**3.
z**2*(z + 1)
Let x(n) be the second derivative of n**7/8820 + n**6/630 + n**5/105 - n**4/4 - 5*n. Let t(j) be the third derivative of x(j). Factor t(m).
2*(m + 2)**2/7
Let z(o) be the first derivative of -1/4*o**5 + o + 1/30*o**6 + 3/4*o**4 - 7/6*o**3 + o**2 - 2. Let t(i) be the first derivative of z(i). Factor t(x).
(x - 2)*(x - 1)**3
Let 17*l**2 - 14*l**2 - l - 5*l + 3 = 0. Calculate l.
1
Let d(w) be the second derivative of w**4/84 - w**3/42 - 3*w**2/7 - 20*w. Solve d(y) = 0.
-2, 3
Let b(z) be the second derivative of z**6/60 - z**5/30 - z**4/12 + z**3/3 + 5*z**2/2 + 5*z. Let t(y) be the first derivative of b(y). Let t(j) = 0. What is j?
-1, 1
Let k(d) be the third derivative of d**5/30 - d**4/6 + 2*d**2. Solve k(j) = 0 for j.
0, 2
Let t(s) = 3*s**2 - 127*s - 82. Let h be t(43). Factor 0 + 3/5*l**2 - 9/5*l**3 - 3/5*l**5 + 0*l + 9/5*l**h.
-3*l**2*(l - 1)**3/5
Let o(z) be the first derivative of z**6/2 - 12*z**5/5 + 9*z**4/2 - 4*z**3 + 3*z**2/2 + 5. Factor o(i).
3*i*(i - 1)**4
Suppose 10 = -5*i, 16 = 3*j + 2*j + 2*i. Let v(t) be the third derivative of 0 + 0*t**3 - 1/60*t**5 + 1/24*t**j + 0*t - t**2. Determine b so that v(b) = 0.
0, 1
Suppose 0 = -4*x - 22 + 22. Factor 0*p + 6/7*p**3 - 2/7*p**5 + x + 0*p**4 - 4/7*p**2.
-2*p**2*(p - 1)**2*(p + 2)/7
Suppose -2 = -3*c + r, -3*c = c + 5*r - 28. Factor c*g**2 + 0*g**4 - 2*g**4 + 0*g**2 - 2*g**3 + 2*g.
-2*g*(g - 1)*(g + 1)**2
Let u = -6 + 4. Let m be 4/10 - u/(-5). Factor -s**3 + s**2 + s**4 + 2*s - s + m*s**3 - 2*s**4.
-s*(s - 1)*(s + 1)**2
Suppose 6*o = 7*o. Suppose -b + 3*j + 10 + 0 = o, -b = -j - 6. Factor 1/2*z**2 + 1/2*z**b + 0*z + z**3 + 0.
z**2*(z + 1)**2/2
Factor 4/7*b**2 - 2*b + 2/7*b**3 + 8/7.
2*(b - 1)**2*(b + 4)/7
Let l(p) be the third derivative of -p**7/210 + p**6/5 - 18*p**5/5 + 36*p**4 - 216*p**3 - 10*p**2. Factor l(o).
-(o - 6)**4
Let n(h) be the second derivative of -h**5/5 - h**4/3 - 2*h. Let n(c) = 0. What is c?
-1, 0
Let s(d) be the first derivative of -25/22*d**4 - 24/11*d + 56/11*d**2 - 10/3*d**3 - 7. Factor s(f).
-2*(f + 3)*(5*f - 2)**2/11
Find n, given that 5*n**3 - 21*n**2 + 12*n**2 - n**4 + 1 + 0*n**4 + 7*n - 3 = 0.
1, 2
Suppose l + 3*z = 5*l + 4, -2*z + 6 = -l. Factor 2/7 + 4/7*o + 2/7*o**l.
2*(o + 1)**2/7
Let k(a) = -a**2 - 10*a + 14. Let q be k(-11). Factor 15*t + 2*t**2 - q*t - 11 - 7 - 4*t**2.
-2*(t - 3)**2
Let b(i) be the third derivative of -3/11*i**3 + 1/44*i**4 + 1/66*i**5 + 0 - 3*i**2 + 1/660*i**6 + 0*i. Factor b(c).
2*(c - 1)*(c + 3)**2/11
Find q such that 0 + 12/7*q - 54/7*q**2 = 0.
0, 2/9
Let k(c) be the first derivative of -2/3*c**3 + 0*c**2 + 5 + 2/5*c**5 - 1/3*c**6 + 1/2*c**4 + 0*c. Solve k(y) = 0 f