
Suppose -3*r = 5*a - 27, -a + 3*a - 4*r + 10 = 0. Factor 1/5*h**a + 2/5 - 3/5*h + 0*h**2.
(h - 1)**2*(h + 2)/5
Let a be 5/3 - (-9)/27. Let z be a/4*12/27. Suppose -2/3*s**2 + 0 + 2/3*s**3 - z*s**4 + 2/9*s = 0. Calculate s.
0, 1
Let g(m) = 4*m**2 - 6*m + 2. Let u(c) = 4*c**2 - 5*c + 1. Let d(o) = 5*g(o) - 6*u(o). Factor d(n).
-4*(n - 1)*(n + 1)
Let r(y) be the second derivative of -1/6*y**4 + 1/25*y**5 + y + 0 + 4/15*y**3 - 1/5*y**2. Factor r(c).
2*(c - 1)**2*(2*c - 1)/5
Let n = 27 - 26. Let h be 36/18*(n - 0). Factor -2/9 + 2/9*l**h + 0*l.
2*(l - 1)*(l + 1)/9
Let t be ((-4)/2160)/(0 - (1 - 0)). Let l(o) be the third derivative of -1/945*o**7 - 1/108*o**4 + 0*o + 1/270*o**5 + t*o**6 + 0 + 3*o**2 + 0*o**3. Factor l(a).
-2*a*(a - 1)**2*(a + 1)/9
Suppose 12 - 4*c + 1/3*c**2 = 0. Calculate c.
6
Let q(r) be the first derivative of -r**4/60 + r**3/30 + r**2/5 + r - 5. Let v(t) be the first derivative of q(t). Factor v(f).
-(f - 2)*(f + 1)/5
Determine z so that 1/5*z**2 + 1/5 - 2/5*z = 0.
1
Factor -3*v - 2*v**3 - 4*v**2 - v**3 + 4*v**3 + 2*v**4.
v*(v + 1)**2*(2*v - 3)
Let j(a) be the second derivative of -1/90*a**5 + 1/9*a**3 - 2/9*a**2 + 0*a**4 - 9*a + 0. Factor j(y).
-2*(y - 1)**2*(y + 2)/9
Let d = 27 - 187/7. Let -d - 4/7*t + 0*t**2 + 4/7*t**3 + 2/7*t**4 = 0. What is t?
-1, 1
Let t(d) = 16*d**4 + d**3 - 26*d**2 - 11*d - 5. Let o(g) = g**4 + g**3 + g**2 + g + 1. Let v(p) = 5*o(p) + t(p). Factor v(c).
3*c*(c - 1)*(c + 1)*(7*c + 2)
Let w(o) = 12*o**2 + 3*o + 9. Let v(t) = 3*t**2 + t + 2. Let r(l) = -9*v(l) + 2*w(l). Factor r(j).
-3*j*(j + 1)
Let a(y) = -y**2 - 4*y. Let c be a(-3). Suppose -c*v**2 + 3*v + v + v - 2*v = 0. What is v?
0, 1
Let s = 8 + -5. Suppose -5*d + 18 = s. Factor 1/3*y**2 - 1/3*y + 0 - 1/3*y**4 + 1/3*y**d.
-y*(y - 1)**2*(y + 1)/3
Let p(w) be the first derivative of 2*w**6/21 - 6*w**5/35 - w**4/14 + 2*w**3/7 - w**2/7 + 7. Suppose p(b) = 0. What is b?
-1, 0, 1/2, 1
Factor 0 - 2/3*c**3 + 8/3*c**2 - 8/3*c.
-2*c*(c - 2)**2/3
Let l(t) = -10*t**2 - 26*t - 22. Let o(a) = -19*a**2 - 51*a - 43. Let w(u) = -11*l(u) + 6*o(u). Find g such that w(g) = 0.
-4, -1
Let j(b) = b**5 - b**4 + b**3 - b**2 - b + 1. Let n(g) = -6*g**5 + 9*g**4 - 9*g**3 + 3*g**2 + 10*g - 7. Let r(f) = 5*j(f) + n(f). Factor r(w).
-(w - 2)*(w - 1)**3*(w + 1)
Let -q**2 - 2*q**4 - 5/2*q**3 + 0*q - 1/2*q**5 + 0 = 0. What is q?
-2, -1, 0
Let s(c) be the third derivative of c**6/300 + c**5/50 + c**4/30 + 9*c**2. Suppose s(m) = 0. What is m?
-2, -1, 0
Let o(f) be the first derivative of -f**5/2 - 5*f**4/2 - 5*f**3 - 5*f**2 - 5*f/2 + 1. Find a, given that o(a) = 0.
-1
Let l(i) be the second derivative of 1/6*i**2 - 2*i + 1/36*i**4 + 1/9*i**3 + 0. Solve l(q) = 0 for q.
-1
Let b = -6 - -8. Suppose -b*l + 4 + 4 = 0. Let 2/7*r - 4/7*r**2 + 0 + 4/7*r**l - 2/7*r**5 + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let s = 237/5 - 47. Factor -s + 4/5*q**2 - 2/5*q.
2*(q - 1)*(2*q + 1)/5
Let i(h) be the second derivative of -3*h + 1/30*h**4 - 1/5*h**2 + 1/50*h**5 - 1/15*h**3 + 0. Factor i(d).
2*(d - 1)*(d + 1)**2/5
Let t(k) = 4*k - 4. Let y(a) = -a**3 + a**2 - 17*a + 17. Let n(o) = -9*t(o) - 2*y(o). Find d such that n(d) = 0.
-1, 1
Let s(p) be the second derivative of p**6/50 - 9*p**5/100 + p**4/20 + 3*p**3/10 - 3*p**2/5 + p + 8. Determine n so that s(n) = 0.
-1, 1, 2
Let t be 1*((10 - 1) + 0). Find s such that -3*s + 8*s + 4*s**4 + 6*s**2 - 4*s + t*s**3 = 0.
-1, -1/4, 0
Let a(q) be the third derivative of -q**7/70 + 3*q**6/20 - q**5/4 + 6*q**2. Factor a(j).
-3*j**2*(j - 5)*(j - 1)
Let u(p) = 3*p**3 - 14*p + 11. Let v(q) = q**3 - 5*q + 4. Let x = 25 + -10. Let s = 26 - x. Let j(z) = s*v(z) - 4*u(z). Suppose j(l) = 0. Calculate l.
-1, 0, 1
Let k be (-64)/4*(-1404)/176. Factor -k*z**2 - 16/11 + 338/11*z**3 + 8788/11*z**4 + 280/11*z.
2*(2*z + 1)*(13*z - 2)**3/11
Let w(p) be the first derivative of 0*p - 2/25*p**5 + 0*p**2 - 2/15*p**3 - 7 + 1/5*p**4. Factor w(d).
-2*d**2*(d - 1)**2/5
Let r(g) = 5*g + 21. Let s be r(-3). Suppose 2/3*d**3 + 2*d - 10/3*d**2 + s = 0. What is d?
-1, 3
Let q(y) be the second derivative of -7*y**5/50 + 4*y**4/15 - y**3/15 - 10*y. Factor q(s).
-2*s*(s - 1)*(7*s - 1)/5
Let x(j) be the second derivative of j**6/180 - j**5/60 + j**3/6 + 2*j. Let v(o) be the second derivative of x(o). Determine a so that v(a) = 0.
0, 1
Let u(m) be the second derivative of -m**6/120 - m**5/16 - m**4/6 - m**3/6 + 6*m. Determine j so that u(j) = 0.
-2, -1, 0
Factor -1/6*a**3 + 1/6*a**4 + 5/6*a - 1/3 - 1/2*a**2.
(a - 1)**3*(a + 2)/6
Suppose -4 = -0*n - 2*n. Let z = 1 - -2. Solve 1 + 2*b - n + b**3 + b**2 - z*b = 0 for b.
-1, 1
Let y(u) be the first derivative of -2*u**3/9 - 6*u**2 - 54*u + 26. Factor y(s).
-2*(s + 9)**2/3
Let s(b) be the second derivative of b**7/14 + b**6/10 - 3*b**5/5 - b**4 - 32*b. Factor s(h).
3*h**2*(h - 2)*(h + 1)*(h + 2)
Suppose 31 = 4*y + 5*x, 0 = -3*y + 4*y - 4*x + 8. Let h(d) = d**3 + d**2 + 3. Let a be h(0). Find s, given that 8*s**2 - a*s**2 - s**2 - 2*s**y - 2 = 0.
-1, 1
Let o = 137/572 + -3/52. Factor 0 - 2/11*g**2 + o*g**5 + 2/11*g**4 - 2/11*g**3 + 0*g.
2*g**2*(g - 1)*(g + 1)**2/11
Let n(y) be the third derivative of -1/20*y**5 - 1/120*y**6 + 0*y - 1/8*y**4 - 3*y**2 - 1/6*y**3 + 0. Solve n(d) = 0 for d.
-1
Let o(n) be the third derivative of n**9/35280 - n**8/7840 + n**7/5880 + n**4/8 + n**2. Let l(z) be the second derivative of o(z). Factor l(u).
3*u**2*(u - 1)**2/7
Let s be 84/21*1/15. Let i(c) be the second derivative of 2*c + s*c**6 + 1/3*c**4 + 0*c**3 + 0 + 0*c**2 + 1/2*c**5 + 1/21*c**7. Suppose i(x) = 0. Calculate x.
-2, -1, 0
Suppose 0*r + 4*r - 12 = 0. Suppose r*i - 3*q = 15, 5*i - 3*q - 19 = -0*q. Factor -4*d**2 + 0*d + 3*d**i + 2*d.
-d*(d - 2)
Let 40*t**3 - 9*t**2 - 6*t - 42*t**3 + 2*t + t**4 + 2*t**2 = 0. Calculate t.
-1, 0, 4
Let g(i) be the second derivative of -1/10*i**5 + 2*i + 0 + 1/30*i**6 + 0*i**4 + 0*i**3 + 0*i**2. Solve g(z) = 0 for z.
0, 2
Let i(r) = -10*r**5 + 5*r**4 + 10*r**3 + 5*r**2 - 5. Let z(k) = -k**5 + k**4 + k**3 + k**2 - 1. Let x(g) = i(g) - 5*z(g). Find p, given that x(p) = 0.
-1, 0, 1
Suppose 0 - 1/8*g**2 - 1/8*g = 0. Calculate g.
-1, 0
Let c be (28 - -1)*(-11 + 10). Let u = -29 - c. Factor 0*a**2 + u*a + 0 + 1/2*a**4 + 0*a**3.
a**4/2
Determine h, given that 4/5*h - h**3 - 2*h**2 + 8/5 + 2/5*h**4 + 1/5*h**5 = 0.
-2, -1, 1, 2
Let i = -34/21 + 30/7. Let w(y) be the first derivative of 6/5*y**5 + i*y - 2 - 7/9*y**6 - 26/9*y**3 - 4*y**2 + 19/6*y**4. Determine q, given that w(q) = 0.
-1, 2/7, 1, 2
Let b(w) be the third derivative of -w**6/60 - w**5/15 - w**4/12 + 13*w**2. Factor b(q).
-2*q*(q + 1)**2
Let z = 40 - 38. Let v(t) be the second derivative of -8/27*t**3 + 2*t - 5/54*t**4 + 0 - 1/90*t**5 - 4/9*t**z. Factor v(q).
-2*(q + 1)*(q + 2)**2/9
Let a(v) be the third derivative of 0 - 1/15*v**5 + 0*v**3 - 2*v**2 + 0*v**4 + 0*v - 3/70*v**7 - 1/10*v**6. Factor a(l).
-l**2*(3*l + 2)**2
Let t(y) be the first derivative of -7 - 1/7*y**4 - 6/35*y**5 + 8/7*y**3 + 8/7*y**2 + 0*y. Find o, given that t(o) = 0.
-2, -2/3, 0, 2
Let x be (0 - 1)*(-7 - -7). Let c(d) be the second derivative of 4*d + x*d**2 + 1/24*d**3 + 3/40*d**5 + 1/168*d**7 + 0 + 1/30*d**6 + 1/12*d**4. Factor c(i).
i*(i + 1)**4/4
Let t(p) be the first derivative of p**4/16 + p**3/6 - p**2/2 - 2*p - 16. Factor t(u).
(u - 2)*(u + 2)**2/4
Suppose 0 = -3*c + 3*p, -2*p = p - 9. Let j(a) = -a**3 - 3*a**2 + 3*a - 2. Let k be j(-4). Let c*y + y - 2*y**3 - 3*y**2 + 2*y**k - y**2 = 0. Calculate y.
-2, 0, 1
Let a(s) be the first derivative of s**3/18 - s**2/6 - 4*s/3 + 3. Factor a(m).
(m - 4)*(m + 2)/6
Let d be 468/910 - (-1 + 5/7). Factor d*u**2 - 2/5*u**3 + 6/5*u + 0.
-2*u*(u - 3)*(u + 1)/5
Let s(c) be the first derivative of 3*c**5/5 - 3*c**4/4 - 3*c**3 + 15*c**2/2 - 6*c - 18. Find b such that s(b) = 0.
-2, 1
Let q(n) = 5*n**4 - 5*n**3 - 18*n**2 + 22*n. Let j(t) = 135*t**4 - 135*t**3 - 485*t**2 + 595*t. Let u(x) = 2*j(x) - 55*q(x). Let u(f) = 0. Calculate f.
-2, 0, 1, 2
Suppose -19 = -5*c + 1. Let -12*p**3 - 23*p**2 + 35*p**2 + 0*p**c - 4*p + 4*p**4 = 0. Calculate p.
0, 1
Let z(m) = -m**3 + 6*m**2 + m - 4. Let g(i) = -i**3 - 9*i**2 + 9*i - 4. Let w be g(-10). Let r be z(w). Factor 0 + 0*h**r + 2/7*h - 2/7*h**3.
-2*h*(h - 1)*(h + 1)/7
Let u(c) = c**3 - 13*c**2 + 3*c - 15. Let k be u(13). Suppose -9