2)/3
Factor 0*x + 0 - 2/13*x**3 + 4/13*x**2.
-2*x**2*(x - 2)/13
Factor 0 + 6/5*d**2 - 2/5*d + 2/5*d**4 - 6/5*d**3.
2*d*(d - 1)**3/5
Suppose -a = -6*a + 20. Let f be (-6)/(-35) - a/(-10). Factor -2*l**3 + f - 24/7*l**2 - 6/7*l.
-2*(l + 1)**2*(7*l - 2)/7
Let q(t) be the second derivative of -27*t**2 - 3/10*t**5 - 3/14*t**7 + 3*t - 7/5*t**6 + 0 - 3/2*t**3 + 10*t**4. Find m, given that q(m) = 0.
-3, -2/3, 1
Let x = 21/2 - 10. Let a(w) be the first derivative of w**2 + 4*w - x*w**4 - 1 - 4/3*w**3. Factor a(s).
-2*(s - 1)*(s + 1)*(s + 2)
Let i(b) be the second derivative of b**5/4 - 25*b**4/12 + 20*b**3/3 - 10*b**2 - 32*b. Find a such that i(a) = 0.
1, 2
Let h(z) be the second derivative of z + z**2 - 1/3*z**3 - 1/60*z**6 + 1/30*z**5 + 0 + 1/12*z**4. Let o(f) be the first derivative of h(f). Factor o(g).
-2*(g - 1)**2*(g + 1)
Suppose 0 = -2*p + 8 - 2. Suppose -p + m + 6 - 1 - m**2 = 0. Calculate m.
-1, 2
Let v(r) be the first derivative of -2*r**5/5 + 3*r**4/2 - 4*r**3/3 - 30. Factor v(j).
-2*j**2*(j - 2)*(j - 1)
Let z(c) be the first derivative of 2*c**3/3 + 8*c**2 + 32*c + 4. Factor z(d).
2*(d + 4)**2
Factor 2/5*y + 2/5*y**2 - 2/5*y**3 - 2/5.
-2*(y - 1)**2*(y + 1)/5
Let t(c) = c**2 - c - 2. Let m be t(-2). Let s = m + -2. Factor -2/7*z + 4/7 - 2/7*z**s.
-2*(z - 1)*(z + 2)/7
Let r(p) be the first derivative of -p**3 - 3*p**2 - 3*p - 9. Factor r(u).
-3*(u + 1)**2
Let h(t) = t**3 + 6*t**2. Let l be h(-6). Let v be 4/((-16)/11) - -3. Find r such that 1/4*r**2 + 1/4*r**3 - 1/4*r**4 + l - v*r = 0.
-1, 0, 1
Let s be 6/(-9) - 28/(-24). Let x = 35/22 - 12/11. Find y such that 1/2*y**2 + 0 - x*y + s*y**3 - 1/2*y**4 = 0.
-1, 0, 1
Let j(b) = -2*b - 4. Let t be j(-4). Let s(i) be the first derivative of -2/3*i**3 + 1/4*i**t + 0*i + 1/2*i**2 + 1. Factor s(u).
u*(u - 1)**2
Let i(j) = -j**3 + 9*j**2 - 10*j + 4. Let h(c) = c**2 - c. Let t(y) = 5*h(y) - i(y). Let l be t(3). Factor x + 3*x + l - x**2 + 3*x**2.
2*(x + 1)**2
Let l(f) be the second derivative of -f**4/24 + f**3/12 + 3*f. Factor l(x).
-x*(x - 1)/2
Let x(v) be the second derivative of v**7/2520 - v**3/2 + v. Let j(q) be the second derivative of x(q). Suppose j(p) = 0. What is p?
0
Factor -5 + 15/2*b - 5/2*b**2.
-5*(b - 2)*(b - 1)/2
Let 0*b**3 - 14*b - 5*b**4 + 29*b**2 - 6*b - 9*b**2 + 5*b**3 = 0. Calculate b.
-2, 0, 1, 2
Let p(n) = -3*n**4 - 6*n**3 + 3*n**2 + 8*n - 2. Let g(h) = 6*h**4 + 12*h**3 - 6*h**2 - 17*h + 5. Let i(v) = -2*g(v) - 5*p(v). Factor i(s).
3*s*(s - 1)*(s + 1)*(s + 2)
Let n(a) = -15*a**2 - 5*a + 5. Let b(h) = -8*h**2 - 2*h + 3. Let s(y) = 5*b(y) - 3*n(y). Factor s(u).
5*u*(u + 1)
Let h(g) be the second derivative of g**9/15120 - g**7/1260 + g**5/120 - g**4/3 + 2*g. Let p(t) be the third derivative of h(t). Let p(k) = 0. Calculate k.
-1, 1
Suppose 0 - 30 = -5*g. Let 9*b - g*b**2 + 6*b**3 - 3*b**3 - 6*b = 0. What is b?
0, 1
Let d(c) be the first derivative of c**3 - 12*c**2 + 21*c - 12. Suppose d(b) = 0. Calculate b.
1, 7
Let f(h) = -h**3 + h**2 - 2*h + 1. Let d(a) = -2*a**3 - 2*a**2 - 4*a + 4. Let j(v) = d(v) - 4*f(v). Factor j(g).
2*g*(g - 2)*(g - 1)
Let q = -36 - -24. Let i be (-1 - -4) + 28/q. Suppose -4/3*j - 2/3*j**2 - i = 0. What is j?
-1
Let 3/2*j**2 + 1/2*j + 0 = 0. What is j?
-1/3, 0
Factor 4/9*z + 0 + 2/3*z**2 + 2/9*z**3.
2*z*(z + 1)*(z + 2)/9
Let t(c) = 9*c**2 + 2*c + 1. Let i be t(-1). Let n be 22/i - (-3)/(-4). Factor -4*d**n + 28 - 28 - d.
-d*(4*d + 1)
Let k = -14 - -20. Let y be 8/(-12) - (-46)/k. Factor 3*d**2 + 4*d**4 + y*d**5 - 5*d**5 - 7*d**2 - 2*d.
2*d*(d - 1)*(d + 1)**3
What is t in -4*t**3 - 293*t + 15*t**2 + 37*t + 49*t**2 = 0?
0, 8
Let g be 3/(-2) + 21/14. Let m(q) be the second derivative of -1/2*q**2 - 1/3*q**4 + 2*q + g + 5/6*q**3. Find z such that m(z) = 0.
1/4, 1
Determine m, given that -134*m - 32*m + 27 + 225*m**2 - 125*m**3 + 31*m = 0.
3/5
Let h(q) be the second derivative of q**6/25 + 4*q**5/25 + 7*q**4/30 + 2*q**3/15 + 11*q. Suppose h(k) = 0. Calculate k.
-1, -2/3, 0
Let v(x) be the third derivative of x**5/270 - 7*x**4/54 + 49*x**3/27 - 35*x**2. Let v(b) = 0. Calculate b.
7
Let d(g) be the second derivative of -g**7/70 + g**6/25 - 3*g**5/100 + 8*g. Determine j so that d(j) = 0.
0, 1
Factor y**3 - 56*y**2 + 0 - y + 1 + 55*y**2.
(y - 1)**2*(y + 1)
Let w(j) = -j**3 - 6*j**2 - 2*j - 9. Let z be w(-6). Factor -p**2 + p**z - 34*p + 34*p.
p**2*(p - 1)
Suppose 2*m - 3*b + 5 = -0, 3*m - b = 10. Let r(o) be the second derivative of 1/24*o**4 + 2*o + 0*o**2 - 1/60*o**6 - 1/12*o**3 + 0 + 1/40*o**m. Factor r(k).
-k*(k - 1)**2*(k + 1)/2
Let m(u) = -u**2 + 9*u - 6. Let h be m(8). Factor h*w**4 + w**2 + 0*w**4 - 5*w**2 + 2.
2*(w - 1)**2*(w + 1)**2
Suppose i + 2 = s + 1, -5*i - 3*s = -35. Suppose 3*t - 5 = i. Let 7/4*m**3 - t*m**2 + 3/4*m + 1/2 = 0. What is m?
-2/7, 1
Let z(m) = m**2 + 5*m - 4. Let l be z(-6). Let n = 3 + -1. Solve -2 - n + 4*k + 0 - k**l = 0 for k.
2
Let o(x) be the third derivative of x**8/168 + x**7/105 - x**6/60 - x**5/30 - 10*x**2. Factor o(m).
2*m**2*(m - 1)*(m + 1)**2
Factor 4*o**3 + 3*o**2 + o**2 - 2*o**3 + 2*o**2 - 8.
2*(o - 1)*(o + 2)**2
Let l(p) be the second derivative of -p**4/36 - 2*p**3/9 - 2*p**2/3 + 11*p. Let l(w) = 0. Calculate w.
-2
Let v(g) be the first derivative of 0*g + 2 - 1/6*g**3 + 0*g**2. Factor v(j).
-j**2/2
Let c be (1/3)/(2/12). Factor -2*x**3 - c*x + 0*x**3 - 4*x**2 + 0*x**2.
-2*x*(x + 1)**2
Let g be ((-6)/9 - -2)*27/42. Factor g*t**2 - 4/7 + 2/7*t.
2*(t + 1)*(3*t - 2)/7
Suppose 5*o - 96 = 2*f, -2*o + 4*o - 3*f - 45 = 0. Suppose 4*p = -5*p + o. Determine i, given that 4/5 + 4/5*i + 1/5*i**p = 0.
-2
Suppose y + 3 = -5*q, -y + 4*y + q - 5 = 0. Let z be (2/(-4))/(y/(-16)). Let -j + 3*j + 5*j**z - j**4 - 2*j**2 - 2*j**4 - 2*j**3 = 0. What is j?
-1, 0, 1
Let z = -190 - -194. Let b(o) be the second derivative of 0*o**2 + 0 + 2*o + 0*o**3 + 3/20*o**5 - 1/4*o**z. Find j such that b(j) = 0.
0, 1
Suppose m = 5, -c = c + 5*m - 33. Let t(q) be the third derivative of 1/90*q**5 + 0*q + 0 - q**2 + 1/180*q**6 + 0*q**c + 0*q**3. Factor t(p).
2*p**2*(p + 1)/3
Let n = -8 - -12. Factor n*k**2 - 2*k**3 + 5 + 6 - 2*k - 11.
-2*k*(k - 1)**2
Let x be (2 - (-48)/(-27)) + 12/27. Factor 3*k + 11/3*k**3 - x - 5*k**2 - k**4.
-(k - 1)**3*(3*k - 2)/3
Let j(m) be the second derivative of -m**6/10 - 3*m**5/20 - 3*m. Factor j(x).
-3*x**3*(x + 1)
Suppose -8*v = -15*v. Let 0 + 2/5*n**3 + 0*n + v*n**2 = 0. Calculate n.
0
Let w(f) = 20*f**5 + 34*f**4 - 60*f**3 - 114*f**2 - 54*f. Let b(c) = 4*c**5 + 7*c**4 - 12*c**3 - 23*c**2 - 11*c. Let q(h) = 14*b(h) - 3*w(h). Factor q(j).
-4*j*(j - 2)*(j + 1)**3
Let y(u) be the second derivative of u**4/3 - 2*u**3 + 4*u**2 + 14*u. Factor y(b).
4*(b - 2)*(b - 1)
Let a(h) be the second derivative of h**7/126 + h**6/18 + 7*h**5/60 - h**4/36 - 4*h**3/9 - 2*h**2/3 + 8*h + 2. Solve a(t) = 0.
-2, -1, 1
Suppose -6*c + 7*c = 5*l - 18, 3*l + 6 = -5*c. Determine y, given that 0*y + 0*y**2 - 7/6*y**5 + 0*y**l + 0 + 1/3*y**4 = 0.
0, 2/7
Let s = 5 + -2. Suppose -2*f - 15 = -5*o, s*f + 2*f = 4*o - 12. Factor 1/4*k**3 + 0*k + 1/4*k**2 + f.
k**2*(k + 1)/4
Let y(a) = a**2 - a + 1. Let o be y(0). Suppose -q + o = -2*m + 2, 0 = -5*m + 2*q + 2. Factor 0*j**2 + m - 8/7*j**4 + 0*j - 2/7*j**3.
-2*j**3*(4*j + 1)/7
Let s(k) = 6*k**2 - 6*k + 6. Let n be s(3). Let o = n - 42. Factor 2/7*v**2 + o - 2/7*v**3 + 0*v.
-2*v**2*(v - 1)/7
Let q(d) = -6*d**3 + 16*d**2 - 12*d + 4. Let y(j) = 5*j**3 - 15*j**2 + 13*j - 3. Let f(a) = 3*q(a) + 4*y(a). Factor f(n).
2*n*(n - 4)*(n - 2)
Let d(u) = -4*u - 22. Let r be d(-6). Find o, given that 0*o + 0 + 4/5*o**r + 6/5*o**3 = 0.
-2/3, 0
Let k(x) be the first derivative of 0*x**2 - 1/3*x**3 - 10 + 0*x - 1/4*x**4. Factor k(o).
-o**2*(o + 1)
Let y(x) be the second derivative of 1/12*x**3 + 0*x**2 + 1/6*x**4 + 0 - 8*x. Factor y(u).
u*(4*u + 1)/2
Suppose 0 = z - 3 + 1. Let 5*s**4 - 5*s**5 - 3*s**4 - 2*s**2 + 0*s**2 + 3*s**5 + z*s**3 = 0. Calculate s.
-1, 0, 1
Let q(k) = -k**2 + 5*k + 14. Let s be q(7). Let j(x) be the third derivative of 0*x - 1/72*x**4 + x**2 - 1/180*x**5 + 1/9*x**3 + s. Factor j(l).
-(l - 1)*(l + 2)/3
Let a be (2/14)/(8/28). Find l, given that a*l**2 + 0*l + 0 = 0.
0
Let s(i) be the first derivative of -i**5/60 + i**3/18 + 3*i - 3. Let l(y) be the first derivative of s(y). Factor l(z).
-z*(z - 1)*(z + 1