given that 4*v**2 - 2*v - 2*v**2 - 3 - x = 0.
-1, 2
Suppose 4*h - 5*i - 13 = 8, 3*h + 3*i = 9. Factor -1/5*b**2 - 2/5*b**3 + 0*b - 1/5*b**h + 0.
-b**2*(b + 1)**2/5
Factor 10*t**2 - 18*t**2 - t + 9*t**2 + 7*t + 8.
(t + 2)*(t + 4)
Let z(m) = -2*m - 11. Let h be z(-8). Let i(w) = -w**3 + 6*w**2 + w - 4. Let k be i(6). Determine j so that j**3 + j**3 - 2*j**4 + 2*j**2 - k*j**h + 0*j**3 = 0.
-1, 0, 1
Suppose -4*v - 4*b = 4, 0 = -2*v - 3*v - b + 11. Factor -2/5*s - 6/5*s**2 + 0 - 2/5*s**4 - 6/5*s**v.
-2*s*(s + 1)**3/5
Let u = -152 - -457/3. Factor -u*t**3 - 2/3 + 1/3*t + 2/3*t**2.
-(t - 2)*(t - 1)*(t + 1)/3
Let l(n) be the second derivative of 0*n**2 + 0 + 2/5*n**3 + 7*n + 3/25*n**5 + 2/3*n**4. Suppose l(m) = 0. What is m?
-3, -1/3, 0
Suppose 0 = -0*n + 2*n. Let w be (-4)/4*(-3 - n). Factor -4*m**3 + 0*m**w + m**3.
-3*m**3
Factor -7*q**2 - 13*q**3 - q**4 - 3*q**3 - 3*q**4 - 5*q**2.
-4*q**2*(q + 1)*(q + 3)
Let v = 35 + -31. Let g(s) be the third derivative of -1/150*s**5 + 0 - 4/15*s**3 - s**2 + 0*s + 1/15*s**v. Factor g(c).
-2*(c - 2)**2/5
Let y(d) = 5*d**3 - 11*d**2 + 19*d - 9. Let l(o) = 55*o**3 - 120*o**2 + 210*o - 100. Let p(i) = -4*l(i) + 45*y(i). Factor p(m).
5*(m - 1)**3
Let z(a) = -a**3 + 8*a**2 - 12*a + 3. Let v be z(6). Factor 0 + 0*n - 1/3*n**v + 0*n**2.
-n**3/3
Suppose -2 = -b, 5*o - 5*b + 80 = -0*b. Let g = o - -18. Factor -2/7*i**g + 0 - 16/7*i**2 - 10/7*i**3 - 8/7*i.
-2*i*(i + 1)*(i + 2)**2/7
Find p such that 0*p**3 + 2 + 4*p**2 + 16/3*p - 2/3*p**4 = 0.
-1, 3
Let y(s) = s. Let j be y(5). Determine w, given that 5 + 3 - 2*w**2 + 3*w - 4 - j*w = 0.
-2, 1
Factor -2/7*r**4 + 48/7*r - 18/7 + 16/7*r**3 - 44/7*r**2.
-2*(r - 3)**2*(r - 1)**2/7
Let q = 5/21 + 1/21. Determine o so that q*o**2 + 0 + 2/7*o = 0.
-1, 0
Let t = 59/40 + -11/8. Let u(p) be the first derivative of t*p**5 - 3/16*p**4 + 0*p + 4 + 0*p**3 + 1/8*p**2. Factor u(n).
n*(n - 1)**2*(2*n + 1)/4
Let p(n) = -4*n - 1. Let u be p(-1). Find m, given that -4*m**3 + m**2 + 4*m**u + m**3 + m**2 + m = 0.
-1, 0
Let w(n) be the first derivative of -n**8/2520 + n**7/630 - n**6/540 + n**3 + 7. Let f(o) be the third derivative of w(o). Factor f(d).
-2*d**2*(d - 1)**2/3
Factor 6*o - 2*o - o**2 - 1 - 3.
-(o - 2)**2
Let p(q) = q**2 - 4*q + 2. Let t be p(5). Suppose 2 = d + t, 4*d + 26 = 2*g. Find x such that 4*x + 5*x**2 + 7*x**2 - g*x**4 - 9*x**4 - 9*x**5 + 5*x**3 = 0.
-1, -2/3, 0, 1
Let y(t) = -3*t**4 + t**2 + 4*t - 2. Let g = 15 - 12. Let a(b) = 4*b**4 - 5*b + 3. Let h(r) = g*y(r) + 2*a(r). Factor h(q).
-q*(q - 2)*(q + 1)**2
Let q(u) be the third derivative of -3*u**2 + 0 - 1/84*u**4 + 1/210*u**5 - 1/1260*u**6 + 0*u + 2/3*u**3. Let z(m) be the first derivative of q(m). Factor z(p).
-2*(p - 1)**2/7
Let o(l) be the first derivative of l**4/6 + 2*l**3/3 + 2*l**2/3 - 1. Determine u, given that o(u) = 0.
-2, -1, 0
Let s(o) be the second derivative of o**7/5040 + o**6/1440 - o**5/120 - 5*o**4/12 + 5*o. Let q(z) be the third derivative of s(z). Factor q(r).
(r - 1)*(r + 2)/2
Let j(v) be the second derivative of 1/30*v**4 + 0 + 0*v**2 + 3*v - 1/15*v**3. Factor j(b).
2*b*(b - 1)/5
Suppose -7 = -3*b + 8. Suppose -c = b*v - v - 13, -c - 2 = -v. Factor -v*p**4 - 9*p**3 + p**4 + 11*p**3.
-2*p**3*(p - 1)
Let n(l) be the first derivative of 49*l**6/24 + 49*l**5/10 + 45*l**4/16 - 2*l**3/3 - l**2/2 + 1. Suppose n(w) = 0. What is w?
-1, -2/7, 0, 2/7
Let t(k) = k + 7. Let j be t(-5). Let l be (-1)/(j/8) + 4. Find i such that 1/5*i**3 + 0*i**2 - 1/5*i**4 + l + 0*i = 0.
0, 1
Let c = -3 + 7. Factor -4*g**3 - 3*g**4 + 11*g**3 + 3*g**2 - 3*g**5 - c*g**3 + 0*g**4.
-3*g**2*(g - 1)*(g + 1)**2
Let i(o) be the second derivative of o**5/50 + o**4/30 - o**3/15 - o**2/5 + 5*o. Factor i(s).
2*(s - 1)*(s + 1)**2/5
Let t(q) be the first derivative of 0*q - 5 + 0*q**2 + 2/21*q**3 - 1/14*q**4. What is l in t(l) = 0?
0, 1
Let n(z) be the second derivative of -z**4/4 - z**3/2 - z. Factor n(j).
-3*j*(j + 1)
Let o be ((-30)/9)/(2/6). Let k = -8 - o. Find t, given that 0 - 1/4*t**k - 1/4*t = 0.
-1, 0
Let i be 0/(4/4*-1). Let p(v) be the third derivative of -3*v**2 - 27/140*v**6 + i - 10/21*v**4 + 0*v - 39/70*v**5 - 4/21*v**3. Factor p(n).
-2*(n + 1)*(9*n + 2)**2/7
Suppose 0 = -w - 4*w + 15. Find g, given that 69*g**w - 2 - 7*g**4 + 5*g + 8*g - 46*g**3 - 27*g**2 = 0.
2/7, 1
Let m(n) be the third derivative of -4*n**7/735 + n**6/84 + n**5/70 - 5*n**4/84 + n**3/21 - 26*n**2. Solve m(v) = 0.
-1, 1/4, 1
Let m(l) = 2*l**2 + 6*l - 3. Let z(h) = h**2 + 3*h - 1. Let y(i) = 3*m(i) - 5*z(i). Let p be y(-4). Factor p + 2/5*n - 1/5*n**2.
-n*(n - 2)/5
Let -14*c - 9*c**3 + 6*c + 11*c + 6*c**2 + 0*c**3 = 0. What is c?
-1/3, 0, 1
Let d(a) be the second derivative of a**7/63 + 2*a**6/9 + a**5 + 20*a**4/9 + 25*a**3/9 + 2*a**2 - 33*a. Factor d(z).
2*(z + 1)**4*(z + 6)/3
Suppose 3*c - 16 - 17 = 0. Factor 24*j**3 + 12*j**3 - 3*j**2 + c*j**2.
4*j**2*(9*j + 2)
Let s(x) = -x**2 + 5*x**2 - x + 0*x**3 - 3 + x**3. Let u be s(-4). Factor -3 + 0*h**3 + 2*h + 2*h**2 - 2*h**3 + u.
-2*(h - 1)**2*(h + 1)
Let z be (-2 - 8/(-6))/(12/(-9)). Factor 1/2*m - 2*m**4 - 2*m**2 + 3*m**3 + 0 + z*m**5.
m*(m - 1)**4/2
Let p(z) be the third derivative of z**6/1620 + z**5/540 - z**4/54 + z**3/2 + 4*z**2. Let n(w) be the first derivative of p(w). Let n(g) = 0. Calculate g.
-2, 1
Let x(s) = s**3 - 2*s**2 - 14*s - 2. Let g be x(5). Solve 0 - 4/7*m - 4/7*m**g - 8/7*m**2 = 0.
-1, 0
Let f = 5 - 1. Suppose 7*g - 9 = f*g. Find n, given that -2/3*n**2 + 0 - 2/3*n**g + 0*n = 0.
-1, 0
Let x(y) = y**3 + y. Let b(h) be the first derivative of -3*h**4 - 32*h**3/3 - 3*h**2 - 3. Let d(p) = b(p) - 2*x(p). Factor d(z).
-2*z*(z + 2)*(7*z + 2)
Let n(u) be the third derivative of 5*u**2 + 0*u + 0*u**3 - 1/105*u**6 - 1/210*u**5 + 0*u**4 + 0. Factor n(g).
-2*g**2*(4*g + 1)/7
Let z = 4 + -3. Let y(o) be the second derivative of -o**5/4 - o**4/2 - 7*o**3/6 + 2*o. Let m(c) = c**3 + c**2 + c. Let u(a) = z*y(a) + 6*m(a). Factor u(j).
j*(j - 1)*(j + 1)
Let z be 136/26 + 1*-2. Let o = z - 352/117. Factor -4/3*v**2 + 2/9*v + o.
-2*(2*v - 1)*(3*v + 1)/9
Factor -49/3*i**3 - 28/3*i**2 + 0 - 4/3*i.
-i*(7*i + 2)**2/3
Let n(t) be the third derivative of t**6/30 + 2*t**5/15 + t**4/6 - 6*t**2. Factor n(z).
4*z*(z + 1)**2
Let d(k) be the first derivative of k**6/18 - 4*k**5/15 + k**4/6 + 4*k**3/9 - k**2/2 + 1. Factor d(z).
z*(z - 3)*(z - 1)**2*(z + 1)/3
Let c = 9 + -6. Factor 24*m + 7 + 6 - 1 + 0 + c*m**3 + 15*m**2.
3*(m + 1)*(m + 2)**2
Factor -15*g**3 - 5*g**4 + 5*g**4 + 10*g**2 + 7*g**4 - 2*g**4.
5*g**2*(g - 2)*(g - 1)
Let y = 31 + -27. Let g(u) be the first derivative of 1/3*u**3 + 1/2*u + 1/12*u**6 + 1/4*u**y - 3/4*u**2 - 3/10*u**5 + 2. Solve g(z) = 0.
-1, 1
Let b(r) be the second derivative of -r**5/5 + 4*r**4/3 - 10*r**3/3 + 4*r**2 - 7*r. Factor b(f).
-4*(f - 2)*(f - 1)**2
Let d = 1 - 1. Let o = 19 + -93/5. Factor -2/5*f**2 + o*f - 2/5*f**3 + 2/5*f**4 + d.
2*f*(f - 1)**2*(f + 1)/5
Let h = -123/2 + 385/6. Let f(o) be the first derivative of -h*o**3 - 77/16*o**4 + 0*o - 1/2*o**2 - 1 - 49/20*o**5. Factor f(j).
-j*(j + 1)*(7*j + 2)**2/4
Let w be ((-8)/10)/((-4)/10). Let u be (5/(-2) + 2)*0. Solve 0*x**3 + 1/3*x**4 + u*x**w + 0 + 0*x - x**5 = 0 for x.
0, 1/3
Factor 0 + 4/5*m**2 + 12/5*m.
4*m*(m + 3)/5
Let f be 0 - (5 - 3) - -2. Let m(s) be the third derivative of 0*s + s**2 - 1/20*s**6 - 1/12*s**4 + 0 + f*s**3 + 1/10*s**5 + 1/105*s**7. Factor m(x).
2*x*(x - 1)**3
Let d(g) be the third derivative of g**7/42 + g**6/6 + 5*g**5/12 + 5*g**4/12 - 14*g**2. Suppose d(k) = 0. What is k?
-2, -1, 0
Suppose 7*y - 28 = 3*y. Let f(i) be the second derivative of -11/15*i**6 + 0*i**2 - 1/6*i**4 - 4/21*i**y + 1/3*i**3 + 2*i + 0 - 9/10*i**5. Factor f(x).
-2*x*(x + 1)**3*(4*x - 1)
Factor -14*q - 98 - 1/2*q**2.
-(q + 14)**2/2
Let y(m) be the second derivative of 1/80*m**6 + 1/160*m**5 - 1/24*m**3 + 1/336*m**7 + 0*m**2 + 0 - 1/32*m**4 + 2*m. Let y(h) = 0. What is h?
-2, -1, 0, 1
Let n be (20/(-24) - -1)*4. Factor 0*s**2 - n*s**3 + 0 + 2/3*s.
-2*s*(s - 1)*(s + 1)/3
Suppose 46*a**5 - 48*a**5 + 6*a**4 + 2*a - 2*a**4 - 4*a**2 = 0. Calculate a.
-1, 0, 1
Let m(s) = s**2 - 15*s + 16. Let q be m(14). Let o(d) be the first derivative of 0*d + 0*d**q + 2 - 2/3*d**3. Solve o(k) = 0 for k.
0
Let d(h) be the third derivative of 0*h**4 - h**2 - 1/240