ctor o(p).
2*p*(p - 1)*(p + 1)
Let o(s) be the first derivative of 3 + 3/5*s**5 + 0*s - 1/2*s**6 + 3/4*s**4 + 0*s**2 - s**3. Find k such that o(k) = 0.
-1, 0, 1
Let w(h) be the first derivative of h**6/2 - 9*h**4/2 + 8*h**3 - 9*h**2/2 - 28. Let w(b) = 0. Calculate b.
-3, 0, 1
Suppose 2*x - 12 + 2 = 0. Let g(z) = -19*z**2 + z - 5. Let d(m) = -28*m**2 + m - 7. Let p(r) = x*d(r) - 7*g(r). Factor p(w).
-w*(7*w + 2)
Let h(p) be the second derivative of -2*p + 0*p**5 + 0 + p**2 + 0*p**3 + 1/480*p**6 - 1/96*p**4. Let r(f) be the first derivative of h(f). Factor r(y).
y*(y - 1)*(y + 1)/4
Let d(m) = -5*m**3 + 10*m**2 - 45*m + 4. Let o(a) = 6*a**3 - 9*a**2 + 44*a - 5. Let h(q) = -5*d(q) - 4*o(q). Factor h(j).
j*(j - 7)**2
Suppose -8 = a - 3*a. Let b(t) be the first derivative of -1/15*t**3 + 1/10*t**2 + 1/5*t - 1/20*t**a + 2. Determine u so that b(u) = 0.
-1, 1
Factor -3/7 + 27/7*h - 45/7*h**2 - 75/7*h**3.
-3*(h + 1)*(5*h - 1)**2/7
Let k(n) = -n**3 + 1. Let i = -15 + 14. Let z(p) = -156*p**3 + 72*p**2 - 8*p - 6. Let a(u) = i*z(u) - 6*k(u). Factor a(t).
2*t*(9*t - 2)**2
Let s(m) = -m**5 - m**2 + m + 1. Let r(z) = -9*z**5 + 15*z**4 + 5*z**3 - 14*z**2 + 4*z - 1. Let x(b) = -r(b) - s(b). Suppose x(c) = 0. What is c?
-1, 0, 1/2, 1
Let y(m) = 35*m**2 - 95*m - 60. Let p(l) = -2*l**2 - l - 1. Let v(t) = -30*p(t) + y(t). Factor v(a).
5*(a - 1)*(19*a + 6)
Let a(m) be the first derivative of -2/25*m**5 + 0*m**2 + 1/10*m**4 + 3 + 0*m + 0*m**3. Suppose a(x) = 0. Calculate x.
0, 1
Let w = 13/8 - 9/8. Let r(b) be the second derivative of 0*b**2 - 9/8*b**4 - 2*b + 9/10*b**5 + w*b**3 - 1/4*b**6 + 0. Factor r(s).
-3*s*(s - 1)**2*(5*s - 2)/2
Let h = 521 + -2601/5. Factor -h*s**2 + 4/5*s + 8/5.
-4*(s - 2)*(s + 1)/5
Let s(d) be the first derivative of -3 + 2*d + 3/2*d**2 + 1/3*d**3. Find f, given that s(f) = 0.
-2, -1
Let g be (-7 - -1)*(23 - 29). Let c = -33 + g. Solve 2/9*u**c + 4/9 + 8/9*u**2 + 10/9*u = 0 for u.
-2, -1
Let g(a) = -a**2 - 13*a - 8. Let u be g(-12). Let m be (u*2)/(-14 - -24). What is f in 2/5*f**5 + 0 + 2/5*f**4 - 2*f**2 - m*f - 6/5*f**3 = 0?
-1, 0, 2
Factor -4/3 + 0*l + 1/3*l**2.
(l - 2)*(l + 2)/3
Let b(l) be the first derivative of -l**8/672 - l**7/240 - l**6/360 - 2*l**3/3 + 2. Let p(g) be the third derivative of b(g). Factor p(u).
-u**2*(u + 1)*(5*u + 2)/2
Let a(g) be the second derivative of 0 + 0*g**4 + 0*g**3 + 1/150*g**6 - 4*g + 1/100*g**5 + 0*g**2. Suppose a(y) = 0. Calculate y.
-1, 0
Let s(q) = -2*q**2 + 4*q + 2. Suppose 3*u + 0 = 15. Let h(b) = 3*b**2 - 4*b - 2. Let a(i) = u*s(i) + 4*h(i). Suppose a(j) = 0. What is j?
-1
Let k = -123 + 125. Let q(l) be the first derivative of -3 + 0*l + 3/2*l**4 - k*l**3 + l**2 - 2/5*l**5. Factor q(u).
-2*u*(u - 1)**3
Let i(w) be the third derivative of w**5/300 + w**4/40 + w**3/15 - 4*w**2. Determine q so that i(q) = 0.
-2, -1
Suppose 6*t**2 - 3*t**3 - 3*t**4 - 7 + 7 = 0. Calculate t.
-2, 0, 1
Let o(r) = 3*r**2 - 2*r**2 - 7*r + 6*r. Let i be o(-1). Factor i*m**4 - 2*m**2 - m + 3*m - 2*m.
2*m**2*(m - 1)*(m + 1)
Let c = 38 - 38. Let t(f) be the third derivative of -3*f**2 - 1/6*f**4 + 0*f + 1/336*f**8 - 2/105*f**7 + 0*f**3 + c + 1/15*f**5 + 1/40*f**6. Solve t(w) = 0.
-1, 0, 1, 2
Suppose 5*s - 78 = 3*s. Let x = s - 36. Suppose 3/5*i - 3/5*i**2 - 1/5 + 1/5*i**x = 0. What is i?
1
Let h(f) be the second derivative of f**5/70 + f**4/14 - f**3/21 - 3*f**2/7 - 21*f. Factor h(g).
2*(g - 1)*(g + 1)*(g + 3)/7
Let k(c) be the first derivative of c**6/24 - c**4/2 + c**3/2 + 7*c**2/8 - 3*c/2 - 14. Solve k(x) = 0.
-3, -1, 1, 2
Let m = 301/3 + -287/3. Let -2/3*c - 4/3*c**5 - 4/3 + m*c**3 - 2/3*c**4 + 14/3*c**2 = 0. What is c?
-1, 1/2, 2
Let w be (-4 + 44/12)*-9. Let l(j) be the second derivative of 0*j**5 + 0 + 0*j**2 + 1/120*j**6 - 1/48*j**4 + 2*j + 0*j**w. Determine g so that l(g) = 0.
-1, 0, 1
Let y = 38 + -38. Let h(u) be the first derivative of 1/4*u**2 + y*u - 5/6*u**3 + 1/2*u**4 + 3. Factor h(g).
g*(g - 1)*(4*g - 1)/2
What is c in 2*c**2 + 26*c**2 + 12*c - 4 - 4 - 19*c**3 + 7*c**3 - 20*c**4 = 0?
-1, 2/5, 1
Let l = -13 - -15. Factor 4*g + 10*g - 6*g - 2*g**l - 8.
-2*(g - 2)**2
Let v(b) be the third derivative of -b**6/360 + 2*b**2. Factor v(w).
-w**3/3
Let c(t) be the first derivative of -12*t**6/7 + 74*t**5/35 + 37*t**4/14 - 26*t**3/7 - t**2/7 + 4*t/7 - 16. Find v, given that c(v) = 0.
-1, -2/9, 1/4, 1
Let n = 922 - 917. Solve -56/3*t + 44/3*t**2 + 16/3 + 6*t**n - 20*t**4 + 38/3*t**3 = 0.
-1, 2/3, 1, 2
Factor g**4 + 3*g**3 + 3319 - 3319 + g + 3*g**2 + 0*g**3.
g*(g + 1)**3
Let y(r) = -3*r**3 + 3*r + 5. Let h be y(-2). Let o = -19 + h. Let -3/2*i**o + 3 - 3/2*i**3 + 9/2*i**2 + 15/2*i = 0. Calculate i.
-1, 2
Let t(w) = 4*w**2 - 4*w - 6. Let x(b) = b**2 - b. Let g(m) = -t(m) + 3*x(m). Factor g(p).
-(p - 3)*(p + 2)
Let s = 935/7 - 133. Factor -s*o + 4/7*o**2 + 0.
4*o*(o - 1)/7
Suppose -3*y - y = -8. Let p(w) be the first derivative of 1 + 3/2*w**4 + 0*w**y + 6/5*w**5 + 0*w + 1/3*w**6 + 2/3*w**3. Factor p(f).
2*f**2*(f + 1)**3
Let 3/2*w**3 + 0*w - 3/2*w**5 + 0*w**2 + 0 + 0*w**4 = 0. What is w?
-1, 0, 1
Let a be (36/(-27))/(1/(-3)). What is z in 2*z**a - z**4 - z**2 + z**3 + z**3 - 2*z = 0?
-2, -1, 0, 1
Let 0*g - 1/4*g**3 + 0 + 5/4*g**2 = 0. What is g?
0, 5
Factor 2/3*g + 4/15 + 8/15*g**2 + 2/15*g**3.
2*(g + 1)**2*(g + 2)/15
Let y = -11 - -13. Factor 2*w**3 - 4 + 6*w**2 - 7*w**3 + 12*w - 4*w + w**y.
-(w - 2)*(w + 1)*(5*w - 2)
Let j(y) be the second derivative of -y**3 + 0 + y**2 + 1/2*y**4 - y - 1/10*y**5. Factor j(s).
-2*(s - 1)**3
Let r = -394/3 - -132. Determine f, given that r*f**3 - 10/3*f - 2*f**2 + 2/3*f**4 - 4/3 = 0.
-1, 2
Suppose -4*g = 2*i - 24, -g + 16 = 3*i + g. Suppose j - 8 = -i*a, -3*a + 5*j = 8 + 6. Factor -3*q**5 + 3*q**5 - 2*q**5 + a*q**4.
-2*q**4*(q - 1)
Let g(w) = -5*w + 3*w + w**2 - 2*w + 4. Let z be g(4). Let h(n) = 3*n**3 - n + 2. Let u(l) = 6*l**3 + l**2 - 2*l + 4. Let v(b) = z*u(b) - 9*h(b). Factor v(d).
-(d - 1)**2*(3*d + 2)
Let o(s) be the first derivative of 1/280*s**5 + 2/3*s**3 + 0*s + 1/840*s**6 + 0*s**2 + 1 + 0*s**4. Let r(g) be the third derivative of o(g). Factor r(y).
3*y*(y + 1)/7
Let o(h) = 7*h**2 + 2*h + 3. Let q(z) = -6*z**2 - 3*z - 3. Let f(x) = 3*o(x) + 4*q(x). Factor f(i).
-3*(i + 1)**2
Suppose 6 = -5*u - 4, 3*s - 13 = 2*u. Let z be s/1 - (-56)/(-21). Factor 2*r**3 + z*r + 0 + 4/3*r**2 + 4/3*r**4 + 1/3*r**5.
r*(r + 1)**4/3
Determine n, given that -2/7*n - 4/7*n**2 + 4/7 + 2/7*n**3 = 0.
-1, 1, 2
Suppose -7*y = -2*y. Let k(i) be the first derivative of -1/10*i**5 + 1/4*i**4 - 1/6*i**3 + y*i**2 + 2 + 0*i. Determine h, given that k(h) = 0.
0, 1
Let r(m) be the third derivative of 0*m + 5/56*m**8 + 1/6*m**5 - m**2 - 29/105*m**7 + 11/60*m**6 - 1/6*m**4 + 0*m**3 + 0. What is h in r(h) = 0?
-2/5, 0, 1/3, 1
Let v(o) = 3*o**3 + 6*o**2 - 12*o + 9. Let p = 7 + -12. Let l(s) = -6*s**3 - 11*s**2 + 25*s - 18. Let a(t) = p*v(t) - 3*l(t). Factor a(q).
3*(q - 1)**2*(q + 3)
Let n be (3 + -1)*(-1)/(-2). Let m(s) = s + 1. Let u be m(n). Factor -4 + u + 3 - b**2.
-(b - 1)*(b + 1)
Let y = 22 + -13. Suppose -5*q - 3*x + 11 = 0, 2*q - 5*x - 14 = 9. What is t in 0*t**4 + 2*t**q - 3*t**3 - 5*t**4 + y*t**3 = 0?
0, 2
Suppose -4*d + 3*s = -27, 5*d + 0*s - 32 = 2*s. Suppose 3*f + d = 15. Factor 3*h + 1 + 2*h**2 - 5*h**5 - 3*h**4 - 2*h**f + 4*h**5 + 0*h**5.
-(h - 1)*(h + 1)**4
Suppose 0 = g - 5*p + 4*p - 7, 17 = g - 3*p. Let b(w) be the first derivative of -26/3*w**3 + 8*w - 5/2*w**4 - 4*w**g + 3. Suppose b(a) = 0. Calculate a.
-2, -1, 2/5
Let h(d) = -d**3 - 6*d**2 - 6*d - 1. Let j be h(-5). What is w in 0*w**j + 7*w**3 - w**3 - 4*w**2 - 2*w**4 = 0?
0, 1, 2
Let w(z) = z**3 + z**2 - z - 1. Let p(t) = -2*t**3 - t**2 + 2*t + 1. Let q(y) = -p(y) - w(y). Solve q(x) = 0 for x.
-1, 0, 1
Factor -2/3 - 2*f**2 - 2/3*f**3 - 2*f.
-2*(f + 1)**3/3
Let i be 12/(-20) + (-36)/15. Let r(o) = -6*o**3 - 20*o**2 - 10*o - 2. Let z(h) = 7*h**3 + 20*h**2 + 11*h + 2. Let t(d) = i*z(d) - 2*r(d). Factor t(n).
-(n + 1)**2*(9*n + 2)
Factor -4 - 3*k**2 - 9 - 1 + 2 - 12*k.
-3*(k + 2)**2
Factor 7/4*i**3 + 3/2*i**4 + 0 + 0*i + 1/2*i**2.
i**2*(2*i + 1)*(3*i + 2)/4
Let b(t) be the third derivative of t**9/19656 - t**7/1820 + t**6/1170 + t**3/2 + 8*t**2. Let i(f) be the first derivative of b(f). Suppose i(c) = 0. What is c?
-2, 0, 1
Factor 0 + 4/3