 g*k**2.
2*(k - 2)*(k - 1)*(k + 1)/9
Factor 0*s + 0*s**2 - 1/5*s**4 + 0*s**3 + 0.
-s**4/5
Suppose -4*u - 3*l = l - 4, u - 4*l - 26 = 0. Factor -u*p - 4/3 - 8/3*p**2.
-2*(p + 2)*(4*p + 1)/3
Let i(v) = 2*v**3 - 6*v**2 + 2*v - 2. Let k(w) be the third derivative of -w**4/24 + w**2. Let f(t) = -i(t) + 4*k(t). Determine c, given that f(c) = 0.
1
Suppose -4*c + 20 = 3*z, 8*z + 2*c - 52 = 3*z. Let m be (1/3)/(6/z). Factor 2/3*t**3 - m*t**4 + 2/3*t**2 + 0 - 2/3*t.
-2*t*(t - 1)**2*(t + 1)/3
Let t(g) = -4*g**3 - g**2 + 2*g + 2. Let l be t(-1). Suppose 3*d**4 + 0 - 4/3*d - 8/3*d**2 + d**l = 0. Calculate d.
-2/3, 0, 1
Suppose -t - t + 5*p - 9 = 0, 0 = 4*p - 12. Let i**3 + 4*i**2 - 14*i**2 - 8 - 2*i + 18*i + i**t = 0. Calculate i.
1, 2
Suppose 5/3*h**3 + 25/3*h + 20/3*h**2 + 10/3 = 0. What is h?
-2, -1
Determine z, given that 15/7*z - 6/7 - 12/7*z**2 + 3/7*z**3 = 0.
1, 2
Let m(c) be the first derivative of -c**4/34 - 14*c**3/51 - 30. Factor m(l).
-2*l**2*(l + 7)/17
Let m(d) = -d**3 + 7*d**2 + 7*d + 9. Let f be m(8). Factor f + 2*c**4 - 10*c - 5 - 6*c**2 + 2*c**3 + 0*c**2.
2*(c - 2)*(c + 1)**3
Let b(d) be the second derivative of -9*d**5/40 + 7*d**4/8 + 2*d**3 - 15*d**2 + 16*d. Suppose b(i) = 0. What is i?
-5/3, 2
Let u(p) be the first derivative of p**7/560 - p**5/80 + p**3/16 - 5*p**2 + 6. Let i(d) be the second derivative of u(d). Factor i(m).
3*(m - 1)**2*(m + 1)**2/8
Let d(k) = -k**3 - 6*k**2 + 8*k + 8. Let h be d(-7). Let m be -1 - (h + (-32)/10). Factor 2/5 + 6/5*p**2 + 2/5*p**3 + m*p.
2*(p + 1)**3/5
Let r = -11 + 23. Suppose 2*s = -2*s + r. Factor g + 0*g**3 + 2*g - 4*g**3 + 2 - g**4 - g**2 + g**s.
-(g - 1)*(g + 1)**2*(g + 2)
Let o(v) = 2*v**2 - 25*v + 12. Let a be o(12). Factor -2/5*y + a + 4/5*y**4 - 4/5*y**2 + 2/5*y**5 + 0*y**3.
2*y*(y - 1)*(y + 1)**3/5
Suppose v = 3*z - 15, -2*v - 5 = -13*z + 12*z. Determine f, given that v + 1/4*f**2 + 1/4*f = 0.
-1, 0
Let o(w) be the third derivative of -1/2*w**3 + 1/4*w**4 + 5*w**2 + 0*w + 0 - 1/20*w**5. Factor o(t).
-3*(t - 1)**2
Let x(w) = w + 17. Let n(k) = 2*k + 35. Let z(p) = 6*n(p) - 13*x(p). Let d be z(-11). Let d + 2/9*m + 2/9*m**2 = 0. What is m?
-1, 0
Let f(y) be the second derivative of y**7/63 + y**6/45 - y**5/30 - y**4/18 - 24*y. Let f(a) = 0. Calculate a.
-1, 0, 1
Factor -2/3*p**2 - 2*p - 4/3.
-2*(p + 1)*(p + 2)/3
Let a(i) be the first derivative of 2*i**3 - 6 + 0*i - 1/2*i**4 - 2*i**2. What is u in a(u) = 0?
0, 1, 2
Let x be 1 - (-2 - 1)*-1. Let h = x + 5. Factor 5 - h - 4*p - 4 - 2*p**2.
-2*(p + 1)**2
Factor 0 + 0*n + 4/15*n**2 - 2/15*n**3.
-2*n**2*(n - 2)/15
Let h(r) be the first derivative of r**7/945 + r**6/180 + r**5/135 + 2*r**2 + 6. Let a(u) be the second derivative of h(u). Factor a(d).
2*d**2*(d + 1)*(d + 2)/9
Factor 6*w**3 - 2*w**3 - 87*w**2 + 87*w**2 + 2*w**4 - 2*w**5.
-2*w**3*(w - 2)*(w + 1)
Let s(v) be the third derivative of v**8/7560 - v**7/1260 + v**6/810 + v**3/2 + 4*v**2. Let w(t) be the first derivative of s(t). Determine p so that w(p) = 0.
0, 1, 2
Let u(k) be the first derivative of -2*k**3/15 - 6. Determine n, given that u(n) = 0.
0
Let a = -6 + 6. Factor a*f + 0 - 1/2*f**2 + 1/2*f**3.
f**2*(f - 1)/2
Let j(q) be the first derivative of 2 + 1/4*q**2 + 5/12*q**3 + 0*q. Solve j(b) = 0.
-2/5, 0
Suppose 2*t = 11*t. Let r(l) be the second derivative of -l + t*l**3 + 2/135*l**6 + 0 + 1/18*l**5 + 0*l**2 + 1/27*l**4. Factor r(u).
2*u**2*(u + 2)*(2*u + 1)/9
Let s be (-1)/3 + (-7966)/42. Let c be 1/((-25)/s) - 4. Factor 12/5*m - 2/5*m**2 - c.
-2*(m - 3)**2/5
Let j(f) be the third derivative of -1/10*f**5 + 0*f**3 + 0*f + 0*f**4 - 11/40*f**6 + 3*f**2 + 0. Factor j(q).
-3*q**2*(11*q + 2)
Let c be 12*((-10)/4 + 3). Factor 1 + 0*x + c*x**2 - 2*x - x - 4.
3*(x - 1)*(2*x + 1)
Let v(n) be the second derivative of -n**5/40 + 5*n**4/24 - n**3/4 - 9*n**2/4 + 7*n. Factor v(x).
-(x - 3)**2*(x + 1)/2
Let v(g) = -6*g**3 - 30*g**2 - 58*g - 24. Let t(j) = -2*j**3 - 10*j**2 - 19*j - 8. Let r(p) = -20*t(p) + 6*v(p). What is c in r(c) = 0?
-2, -1
Let a(g) be the second derivative of g**6/165 + 2*g**5/55 + g**4/11 + 4*g**3/33 + g**2/11 - 7*g. Let a(q) = 0. Calculate q.
-1
Let r(j) be the third derivative of 1/36*j**4 + 0*j + 0 - 3*j**2 - 2/27*j**3 - 1/270*j**5. What is a in r(a) = 0?
1, 2
What is w in 6/7*w**3 + 3/7*w**4 + 9/7 - 12/7*w**2 - 6/7*w = 0?
-3, -1, 1
Let f(h) = -3*h + 1. Let n(o) = -o**2 - 3*o - 3. Let v be n(-2). Let q be f(v). Factor 0 - 1/4*y**3 + 0*y**q + 0*y + 1/4*y**5 + 0*y**2.
y**3*(y - 1)*(y + 1)/4
Let x be (-4)/(-8)*0 - -7. Let l be (x/14)/(1 - -1). Factor f**2 + l - 5/4*f.
(f - 1)*(4*f - 1)/4
Let l(i) be the second derivative of 0*i**2 + 0 - 1/30*i**5 - 1/27*i**3 - i - 1/135*i**6 - 1/18*i**4. Factor l(y).
-2*y*(y + 1)**3/9
Let n(c) = 14*c**2 + 18*c + 12. Let i(z) be the third derivative of -3*z**5/20 - z**4/2 - 4*z**3/3 + 2*z**2. Let l(r) = -8*i(r) - 5*n(r). Solve l(m) = 0.
-2, -1
Suppose -x - 3*x - g + 6 = 0, -g - 2 = 0. Factor -2 - 3*l**3 + 0 + x + 6*l**2.
-3*l**2*(l - 2)
Let k(u) be the second derivative of 2/15*u**4 - 4*u - 1/5*u**2 + 0 - 1/5*u**3. Suppose k(s) = 0. Calculate s.
-1/4, 1
Let x(k) = -2*k**2 - 9*k - 11. Let o(b) = -b**2 - 4*b - 5. Let w(q) = -5*o(q) + 2*x(q). Let j be w(-2). Suppose -5*d + j*d + d**2 + 3*d = 0. Calculate d.
-1, 0
Let l = 19/20 + -93/140. Factor -4/7*m**2 + 2/7*m**3 + l*m + 0.
2*m*(m - 1)**2/7
Let a(i) be the first derivative of i**6/480 + i**5/80 + 5*i**3/3 - 5. Let z(k) be the third derivative of a(k). Determine h, given that z(h) = 0.
-2, 0
Find v, given that -20/3*v**3 + 0*v - 40/3*v**4 + 0*v**2 + 25/3*v**5 + 0 = 0.
-2/5, 0, 2
Suppose -3 + 6 = a - t, 0 = -a + 5*t - 9. Factor -6 + 9*x**2 + a*x**2 - 2*x**2 + 9*x + 2*x**2.
3*(x + 1)*(5*x - 2)
Let x(g) be the second derivative of -1/42*g**7 + 0 - 1/12*g**4 + 0*g**2 - g + 0*g**3 - 3/20*g**5 - 1/10*g**6. Factor x(b).
-b**2*(b + 1)**3
Suppose 3 = -0*c + c - 2*r, -4*r + 1 = 5*c. Let s be (4/(-6) + 1)/c. Factor -1/3*q**3 + 0 - 2/3*q**2 - s*q.
-q*(q + 1)**2/3
Let o = 2235/2 - 1117. Let 1/2 + 0*a - o*a**2 = 0. What is a?
-1, 1
Solve 4*i**4 + 2*i**5 + 2*i**5 - 6*i**5 + 0*i**4 = 0 for i.
0, 2
Let o(a) be the first derivative of a**5/20 - a**4/2 + 2*a**3 - 4*a**2 + 4*a + 6. Let o(u) = 0. Calculate u.
2
Let w(i) be the third derivative of -i**9/302400 - i**8/33600 - i**7/12600 + i**5/60 - i**2. Let m(c) be the third derivative of w(c). Factor m(z).
-z*(z + 1)*(z + 2)/5
Let m(q) be the second derivative of q**4/30 + 4*q**3/15 + 3*q**2/5 + 11*q. Factor m(z).
2*(z + 1)*(z + 3)/5
Let r(n) be the second derivative of n**7/16380 - n**6/2340 + n**5/780 + n**4/3 + 2*n. Let f(u) be the third derivative of r(u). Solve f(k) = 0.
1
Let m(f) be the third derivative of -f**5/12 + 5*f**4/24 - 4*f**2. Let m(i) = 0. Calculate i.
0, 1
Let g(f) be the second derivative of -1/84*f**4 - 1/6*f**3 + 0*f**5 + 0*f**2 + 0 + 1/1260*f**6 - f. Let j(b) be the second derivative of g(b). Factor j(z).
2*(z - 1)*(z + 1)/7
Let j(w) be the second derivative of w**6/20 - 7*w**5/40 + w**4/8 + w**3/4 - w**2/2 - 2*w. Factor j(o).
(o - 1)**3*(3*o + 2)/2
Let i(d) be the third derivative of d**7/840 - d**6/180 - d**5/40 - 5*d**3/6 + 3*d**2. Let x(r) be the first derivative of i(r). Find w such that x(w) = 0.
-1, 0, 3
Let q(d) = -7 - 4*d**3 - 13*d + 3*d + 0*d**2 + 2*d**2 - 4*d**4. Let i(u) = -3*u**4 - 3*u**3 + u**2 - 9*u - 6. Let c(y) = -5*i(y) + 4*q(y). Factor c(o).
-(o - 2)*(o + 1)**3
Let m = -3 - -6. Let z(h) be the third derivative of -2*h**2 + 0*h**5 - 1/12*h**4 + 0 + 1/60*h**6 + 1/6*h**m - 1/210*h**7 + 0*h. Factor z(l).
-(l - 1)**3*(l + 1)
Let t(h) be the third derivative of 0 + 0*h**3 + 0*h + 1/60*h**6 - 1/12*h**4 + 0*h**5 - 5*h**2. Factor t(l).
2*l*(l - 1)*(l + 1)
Suppose 4*w - 4 = 8. Let z(t) be the third derivative of 0*t + 0 - 1/60*t**6 - 1/30*t**7 + 7/60*t**5 + t**2 + 0*t**w + 1/12*t**4. Factor z(b).
-b*(b - 1)*(b + 1)*(7*b + 2)
Factor 3/5*a**3 - 363/5 + 429/5*a - 69/5*a**2.
3*(a - 11)**2*(a - 1)/5
Let c(f) be the second derivative of f**6/40 - f**5/20 + f**2 + 2*f. Let r(x) be the first derivative of c(x). Determine i, given that r(i) = 0.
0, 1
Suppose 0 = -2*l - 5*h + 5, 0 = 7*l - 3*l + 4*h - 4. Factor -3/5*m**2 + 0*m - 12/5*m**3 - 9/5*m**4 + l.
-3*m**2*(m + 1)*(3*m + 1)/5
Factor -5/2*j + 5/3 + 5/6*j**2.
5*(j - 2)*(j - 1)/6
Suppose -