
Let l(k) be the first derivative of -2/15*k**3 - 5 - 1/10*k**4 + 1/30*k**6 + 1/25*k**5 + 1/5*k + 1/10*k**2. Factor l(d).
(d - 1)**2*(d + 1)**3/5
Let u(z) = -20*z**2 - 50*z + 15. Let r(c) = -3*c**2 - 7*c + 2. Let k(n) = 15*r(n) - 2*u(n). Factor k(t).
-5*t*(t + 1)
Suppose -4*r + 16 = -0. Let w(o) be the second derivative of 0 - 2*o + 0*o**2 - 1/16*o**r + 1/40*o**5 + 1/24*o**3. Find k, given that w(k) = 0.
0, 1/2, 1
Suppose -4*q = -g - 20, 0*g = 2*q + 3*g + 4. Suppose -2*c + 27 = q*f - 7*c, 5*f = -4*c + 3. Determine w, given that -1/2*w**f + 0*w - 1/2*w**4 + 0 + 0*w**2 = 0.
-1, 0
Factor -v**3 + 254*v + v**5 - v**2 - 254*v + v**4.
v**2*(v - 1)*(v + 1)**2
Factor -4*k + 16/3*k**2 - 4/3*k**3 + 0.
-4*k*(k - 3)*(k - 1)/3
Find l such that -1/2*l + 1 - 1/2*l**2 = 0.
-2, 1
Let o = -2 + 0. Let x = o - -2. Factor 2/7*z**3 + 2/7*z**2 + 0 + x*z.
2*z**2*(z + 1)/7
Let g be (-11)/55*-35 - 5. Factor 1/4*c**5 + 0*c**3 - 1/2*c**g - 1/4*c + 0 + 1/2*c**4.
c*(c - 1)*(c + 1)**3/4
Let d(l) = -2*l**2 + 8*l - 11. Let v(i) = 6*i**2 - 24*i + 32. Let o be (-4)/((-10)/4 + 2). Let n(r) = o*d(r) + 3*v(r). Factor n(b).
2*(b - 2)**2
Suppose -6*m + m + 30 = 0. Let c(d) be the first derivative of -1/8*d**4 + 0*d**2 + 3 + 0*d + 0*d**3 + 1/5*d**5 - 1/12*d**m. Factor c(i).
-i**3*(i - 1)**2/2
Determine b so that -8/7 - 40/7*b + 4/7*b**3 - 6*b**2 + 2*b**4 = 0.
-1, -2/7, 2
Let g(c) = -c**3 + 6*c**2 - 6*c + 7. Let z be g(5). Let r be ((-1)/z)/((-5)/120). Determine q so that -2 + r*q**2 - 11*q**2 + 2*q - q = 0.
-2, 1
Let c(k) = -4*k**2 - 32*k. Let o(y) = 5*y**2 + 31*y. Let z(d) = -3*c(d) - 2*o(d). Factor z(n).
2*n*(n + 17)
Let p = -5 - -8. Let h = p - 11/4. Determine t, given that 0 - 1/4*t + h*t**2 = 0.
0, 1
Let a(g) be the first derivative of g**6/10 + 9*g**5/25 + 3*g**4/10 - 1. Factor a(n).
3*n**3*(n + 1)*(n + 2)/5
Let j(h) be the second derivative of -h**5/130 - h**4/26 - 2*h**3/39 - 9*h. Determine k, given that j(k) = 0.
-2, -1, 0
Let u(y) be the first derivative of -y**6/45 + 4*y**5/75 + y**4/15 - 8*y**3/45 - y**2/15 + 4*y/15 - 6. Solve u(k) = 0.
-1, 1, 2
Let f(r) be the first derivative of 4*r**6/33 - 6*r**5/55 - 4*r**4/11 + 4*r**3/11 + 4*r**2/11 - 6*r/11 - 6. Solve f(q) = 0 for q.
-1, 3/4, 1
Factor 4/13*y - 2/13 - 2/13*y**2.
-2*(y - 1)**2/13
Find i, given that -9*i**2 - 5 + 34*i**2 + 5 + 10*i = 0.
-2/5, 0
Let r(d) be the third derivative of -d**5/12 - 5*d**4/24 + 5*d**3/3 - 12*d**2. Factor r(b).
-5*(b - 1)*(b + 2)
Let k(w) be the third derivative of -w**6/360 - w**5/120 + w**4/12 + w**3/3 - w**2. Let g(m) be the first derivative of k(m). Find y such that g(y) = 0.
-2, 1
Let p(m) be the first derivative of m**9/504 - m**8/168 + m**7/420 + m**6/180 - m**3/3 + 2. Let b(k) be the third derivative of p(k). Let b(y) = 0. Calculate y.
-1/3, 0, 1
Find l, given that 0*l - 2/5*l**2 + 0 = 0.
0
Suppose -2*l = -4*k + 2*l - 160, 0 = -2*k - l - 95. Let c = 317/7 + k. Factor 0*v**2 + 0*v**4 + 0 - 2/7*v**5 + 0*v + c*v**3.
-2*v**3*(v - 1)*(v + 1)/7
Suppose 3*p = -2*i, 4*p - 1 = 2*i + 13. Let v = -1 - -5. Factor 0*y**v + y**3 - y + y**p - y**4 + 0*y**2.
-y*(y - 1)**2*(y + 1)
Let g(v) = v**2 - 2*v - 10. Let w be g(5). Factor 8*j**2 + w*j**2 - 4 + 12*j - 5*j**2 - 4.
4*(j + 2)*(2*j - 1)
Factor 2/9*o**4 - 4/3*o**3 - 8/3*o + 26/9*o**2 + 8/9.
2*(o - 2)**2*(o - 1)**2/9
Let v(l) = l**2 - 5*l - 6. Let w be v(6). Let a be 4 - ((-112)/(-30) + (-10)/25). Suppose a*u**3 + 2/3*u**2 + 0*u + w = 0. Calculate u.
-1, 0
Let h be ((-1)/3)/((-2)/18). Suppose -2*b - b - 12 = -5*m, -h*m + 11 = 2*b. Solve -6*n**m + 6*n**2 + 0*n**2 + 0*n**3 - 2*n + 2*n**4 = 0 for n.
0, 1
Let l(v) = v**5 - 3*v**4 + v**2 - v. Let z(i) = -i**4 - i**3 + i**2 - i. Let s(t) = t**2 - 18*t + 4. Let a be s(18). Let y(g) = a*l(g) - 4*z(g). Factor y(u).
4*u**3*(u - 1)**2
Let j(a) = -4*a**2 + 4*a + 34 - 3*a**3 - 31 - a + 2*a**4. Let f(v) = -v**4 + v**3 + v**2 + v + 1. Let t(y) = f(y) + j(y). Factor t(d).
(d - 2)**2*(d + 1)**2
Find s such that -4/5*s**4 - 6/5*s**3 + 0*s**2 + 2/5*s + 0 = 0.
-1, 0, 1/2
Let y(r) be the third derivative of r**5/30 + r**4/6 + r**3/3 - r**2. Factor y(t).
2*(t + 1)**2
Solve 2*d**2 + 0 + 0*d + 2/3*d**4 + 8/3*d**3 = 0 for d.
-3, -1, 0
Let c(t) be the second derivative of 1/63*t**7 + t - 2/45*t**6 + 1/9*t**4 - 1/9*t**3 + 0 + 0*t**2 + 0*t**5. Determine h, given that c(h) = 0.
-1, 0, 1
Solve 3/2*x**3 + 9/4 - 3*x**2 + 3/4*x**4 - 3/2*x = 0.
-3, -1, 1
Suppose -12 + 4 = -4*h. Suppose -3*b**3 - h*b**4 + b**4 + 5*b**3 + 4*b**2 - 5*b**2 = 0. Calculate b.
0, 1
Suppose 4*z + z = -n + 50, -3*n + 4*z = -55. Let t = n - 22. Solve 0 + 0*k**2 + 1/3*k**5 + 0*k - 2/3*k**4 + 0*k**t = 0.
0, 2
Let c be ((-3)/9 - -1)*6. Factor -3*h**c + 3*h**4 + h**2 - h**4.
-h**2*(h - 1)*(h + 1)
Let o(f) be the third derivative of -f**6/120 + f**5/30 - f**4/24 + 4*f**2. Solve o(u) = 0.
0, 1
Let p(q) be the first derivative of -q**6/120 + q**4/8 - 4*q**3/3 - 8. Let i(a) be the third derivative of p(a). Factor i(x).
-3*(x - 1)*(x + 1)
Factor -1/6*m**2 + 2/3 + 0*m.
-(m - 2)*(m + 2)/6
Let m = -21/5 + 22/5. Let k(w) be the second derivative of m*w**5 + 0*w**4 + w - 1/2*w**3 + 1/2*w**2 + 0. Factor k(p).
(p + 1)*(2*p - 1)**2
Let a(c) = -8*c**3 + 172*c**2 - 152*c + 100. Let p(j) = -j**3 + 19*j**2 - 17*j + 11. Let m(f) = -3*a(f) + 28*p(f). Determine r so that m(r) = 0.
1, 2
Let x be 3 - 6/2 - (-7)/3. Let m = 88 + -259/3. Factor -5/3*o + x*o**4 + m*o**3 - 3*o**2 + 2/3.
(o - 1)*(o + 1)**2*(7*o - 2)/3
Let m(r) be the first derivative of 16*r**3 + 34*r**2 - 20*r - 21. Suppose m(q) = 0. Calculate q.
-5/3, 1/4
Let t(l) be the second derivative of -l**5/70 + l**3/7 + 2*l**2/7 - 12*l. Let t(s) = 0. What is s?
-1, 2
Let i(w) be the first derivative of -2*w**5/35 + w**4/2 - 10*w**3/7 + 13*w**2/7 - 8*w/7 - 16. Factor i(y).
-2*(y - 4)*(y - 1)**3/7
Let k(u) = 5*u + 5. Let d be k(7). Let x be 26/d + (-8)/20. Let -3/4*l + x*l**2 + 1/2 = 0. What is l?
1, 2
Let g(v) = 2*v - 12. Let m be g(8). Find d, given that d**m + 3*d**3 - 3*d**2 - 2*d + 4*d**2 - d**5 - 2*d**2 = 0.
-1, 0, 1, 2
Let t(u) = -21*u + 275. Let j be t(13). Suppose 0 + 1/3*m**j + 1/3*m = 0. What is m?
-1, 0
Let n(v) = 11*v**5 + 45*v**4 + 81*v**3 - 119*v**2 - 6*v - 6. Let p(c) = c**5 + c**3 + c**2 - c - 1. Let h(o) = -n(o) + 6*p(o). Let h(r) = 0. Calculate r.
-5, 0, 1
Let d(u) be the second derivative of -7*u**6/20 - 9*u**5/10 - 3*u**4/8 + u**3/2 + 12*u. Factor d(j).
-3*j*(j + 1)**2*(7*j - 2)/2
Let t be (18/36)/(-2 + 3). Factor -1/2*h**4 + 0*h + 0*h**3 + 0 + t*h**2.
-h**2*(h - 1)*(h + 1)/2
Suppose 0 = -5*o - 10, d + o + 2 = -0. Solve d*x + 3/4 - 3/4*x**2 = 0.
-1, 1
Let a = 2 - 5. Let p be -2 + (a/(-12) - -2). Factor -3/4*g**2 - p + g.
-(g - 1)*(3*g - 1)/4
Let -8/5 - 28/5*i**3 - 8/5*i + 6/5*i**4 + 38/5*i**2 = 0. What is i?
-1/3, 1, 2
Let u be (1 + 19/2)*(-100)/(-1400). Factor u*j**2 - 3/4*j**3 + 0*j + 3/4*j**5 - 3/4*j**4 + 0.
3*j**2*(j - 1)**2*(j + 1)/4
Let u = 31 + -32. Let b be (0 - u)*(-5 + 7). Solve 1/5*h**3 - 2/5*h**b - 1/5*h + 2/5 = 0 for h.
-1, 1, 2
Suppose -3*b = -6*b + 18. Factor -n**3 + 17*n - b*n**2 - 2*n**3 - 20*n.
-3*n*(n + 1)**2
Let q(n) = -3*n**5 + 12*n**4 + 21*n**3 + 18*n**2 - 6*n. Let v(w) = 6*w**5 - 25*w**4 - 42*w**3 - 37*w**2 + 13*w. Let j(r) = -13*q(r) - 6*v(r). Factor j(c).
3*c**2*(c - 4)*(c + 1)**2
Let l = -1259/7 - -181. Factor -l*t**3 + 0*t - 2/7*t**4 + 0 - 8/7*t**2.
-2*t**2*(t + 2)**2/7
Let s(z) be the third derivative of 0*z + 1/15*z**5 + 3*z**2 + 0 + 0*z**3 - 1/12*z**4 + 0*z**6 + 1/168*z**8 - 2/105*z**7. Factor s(a).
2*a*(a - 1)**3*(a + 1)
Let b(n) be the second derivative of 4*n**7/63 + n**6/15 - n**5/30 - 30*n. Factor b(s).
2*s**3*(s + 1)*(4*s - 1)/3
Find y, given that 2*y**5 - 16*y**2 - 8*y**4 - 28*y**3 + 3*y**5 - y**5 = 0.
-1, 0, 4
Let x(a) be the second derivative of a + 0 - 1/18*a**3 + 0*a**4 + 0*a**6 + 0*a**2 + 1/30*a**5 - 1/126*a**7. Factor x(i).
-i*(i - 1)**2*(i + 1)**2/3
Find l, given that -l**2 - 12 - 9 - 15 + 3*l + 9*l = 0.
6
Let y(l) = 7*l + 2. Let m be y(-1). Let v be (-2 - m)/(18/12). Find i, given that -3/5*i**4 + 0*i**3 + 3/5*i**v + 0*i + 0 = 0.
-1, 0, 1
Let v(o) be the first derivative of 12*o**5/5 + 9*o**4/4 - 5*o**3 - 9*o**2/2 + 3*o + 10. Factor v(j).
3*(j - 1)*(j + 1)**2*(4*j - 1)
Let u = -2/499 + 1008/2495. Let t(r) be the first derivative of u*r**5 + 0*r + 2*r**3 + r**2 + 3/2*r