et j(u) be the third derivative of -u**4/24 + u**3/6 - 3*u**2. Let z be j(-3). Suppose -4*r + r + z - r + r**2 = 0. What is r?
2
Let p(b) be the second derivative of b**8/3360 - b**4/6 - 2*b. Let x(n) be the third derivative of p(n). Factor x(d).
2*d**3
Factor 0*x - x**3 - x + 6*x - 4*x.
-x*(x - 1)*(x + 1)
Suppose 34*r = 32*r - 112. Let c be 25/20 - (-54)/r. Factor -c*y**2 + 2/7 + 0*y.
-2*(y - 1)*(y + 1)/7
Let w(l) = 1. Let t(a) = -2*a**2 - 12*a - 12. Let j(m) = -t(m) + 6*w(m). Determine n, given that j(n) = 0.
-3
Suppose -4*p - 4 = -0*p. Let r be (-3)/(p - (0 + 0)). Factor 1/3*m + 1/3*m**r + 0 - 2/3*m**2.
m*(m - 1)**2/3
Let n(z) be the third derivative of 1/42*z**4 + 0 + 4*z**2 - 1/21*z**3 + 0*z - 1/210*z**5. Factor n(b).
-2*(b - 1)**2/7
Let s(n) be the third derivative of n**5/60 + n**4/12 + n**3/3 + 2*n**2. Let x be s(-2). Let 1/3*h**x + 0*h + 0 + 1/3*h**3 = 0. Calculate h.
-1, 0
Factor -5*r**4 + 2*r**4 + 4*r**3 + r**4 - 2*r**2.
-2*r**2*(r - 1)**2
Factor s + 4*s**3 - 8*s**2 - 14*s + 7 + 25 - 3*s.
4*(s - 2)**2*(s + 2)
Suppose 0 = -2*g - 3*d + 16, 0*d - 40 = -5*g + 4*d. Let f = -5 + g. What is a in f*a + 2*a**3 - 5*a + 0*a**2 + 4*a**2 - 4 = 0?
-2, -1, 1
Factor -8/11*h + 0 + 10/11*h**2 - 2/11*h**3.
-2*h*(h - 4)*(h - 1)/11
Factor 0 - 1/4*k**3 + 0*k + 3/4*k**2.
-k**2*(k - 3)/4
Let h be (10/6 - 2)*-12. Factor -2*b**h + 0 + b**4 + 0.
-b**4
Let b(h) = -h**2 + 7*h + 2. Let p be b(6). Let y be (-1)/4 - (-42)/p. Factor 4*c**y - 4*c**4 - 3*c + c + 4*c**2 - 2*c**5.
2*c*(c - 1)**3*(c + 1)
Let x(t) be the third derivative of t**6/420 + t**5/105 - t**4/21 - 8*t**3/21 + 2*t**2. Factor x(v).
2*(v - 2)*(v + 2)**2/7
Let l(i) be the first derivative of -4*i**3/3 + 16*i + 8. Factor l(j).
-4*(j - 2)*(j + 2)
Let c(x) be the third derivative of -x**6/120 - x**5/15 + 5*x**4/24 + x**3/3 + 3*x**2. Let s be c(-5). Factor -4*i**s - i**4 + 3*i**2 + 2*i**2.
-i**2*(i - 1)*(i + 1)
Factor -10*b**2 - 12*b**2 + 3*b**3 + 16*b**2.
3*b**2*(b - 2)
Let j(c) = 7*c**3 - c + 1. Let i be j(1). Let x = i - 4. Solve 0*k**3 - 4*k**3 - 14*k**x + 4*k**2 - 4*k**4 + 18*k**4 = 0 for k.
0, 2/7, 1
Let o = -105 + 107. Factor -2/3 - 1/3*q**3 + 2/3*q**o + 1/3*q.
-(q - 2)*(q - 1)*(q + 1)/3
Let i = -3/7 + 19/28. Let w = 25/3 + -97/12. Factor 0 + 1/4*b**4 - 1/4*b**2 + 0*b - w*b**3 + i*b**5.
b**2*(b - 1)*(b + 1)**2/4
What is u in -9/5*u**2 + 12/5 + 3/5*u**4 - 6/5*u**3 + 12/5*u = 0?
-1, 2
Factor 8/3 - 4/3*y + 4/3*y**3 - 8/3*y**2.
4*(y - 2)*(y - 1)*(y + 1)/3
Let r(z) be the second derivative of -1/6*z**3 - 2*z + 1/12*z**4 + 1/20*z**5 - 1/2*z**2 + 0. Factor r(n).
(n - 1)*(n + 1)**2
Let l = 3/61 + 113/183. Suppose -2/9*j**4 + 2/9*j + 0 + l*j**3 - 2/3*j**2 = 0. Calculate j.
0, 1
Let t(q) be the second derivative of -q**5/35 - q**4/21 + 4*q**3/21 - 12*q. Factor t(p).
-4*p*(p - 1)*(p + 2)/7
Suppose 0 = 3*c + 3*i + 3, -5*i = -i + 16. Let l be (1/2)/((-1)/(-6)). Factor 0*s + 2*s**4 - 3*s - s + c*s**l - 3*s**4.
-s*(s - 2)**2*(s + 1)
Let n(b) be the first derivative of -45*b**4/4 - 5*b**3 + 25*b**2/2 - 5*b - 20. Factor n(a).
-5*(a + 1)*(3*a - 1)**2
Factor 1/8*u**3 + 1/4*u**2 + 1/8*u + 0.
u*(u + 1)**2/8
Let a = 44 + -42. Factor 2/3 + 2*n**2 + 2/3*n**3 + a*n.
2*(n + 1)**3/3
Let b = -2/1051 - -21046/13663. Factor 10/13*o + 2/13 + 10/13*o**4 + 20/13*o**2 + b*o**3 + 2/13*o**5.
2*(o + 1)**5/13
Let w = -355 - -355. Factor -3/2*z**4 + 0*z + 3*z**2 - 3/2*z**3 + w.
-3*z**2*(z - 1)*(z + 2)/2
Factor -1/11*h**5 + 7/11*h**2 + 0 + 5/11*h**4 - 9/11*h**3 - 2/11*h.
-h*(h - 2)*(h - 1)**3/11
Let s(g) = 3*g + 1. Let t(i) = 4*i + 1. Let q(x) = 5*s(x) - 4*t(x). Let o(c) = c**2 + 4*c - 5. Let r(b) = -o(b) - 5*q(b). Find v such that r(v) = 0.
0, 1
Determine f, given that -18/5*f**2 - 2/5*f**4 + 14/5*f + 2*f**3 - 4/5 = 0.
1, 2
Let d(y) be the second derivative of -y**4/6 - 13*y**3/3 + 14*y**2 - 32*y - 1. Find f such that d(f) = 0.
-14, 1
Let p = 9 + -1. Let o be (-11)/(-4) + 2/p. Factor 0 + 1 - o + 2*q**2.
2*(q - 1)*(q + 1)
Let k = -135 - -1351/10. Let i(o) be the second derivative of -o**2 + k*o**5 - o - 1/3*o**3 + 0 + 1/6*o**4. Factor i(m).
2*(m - 1)*(m + 1)**2
Solve 2/5*t + 1/5*t**3 + 3/5*t**2 + 0 = 0 for t.
-2, -1, 0
Let u = 0 - -1. Factor -3*c**2 + 5 + 3*c**3 + c - u - 1 - 4*c.
3*(c - 1)**2*(c + 1)
Let g(h) be the second derivative of h**7/42 + h**6/20 + h**5/40 - 18*h. Factor g(n).
n**3*(n + 1)*(2*n + 1)/2
Let w(c) = -3*c - 2. Let y be w(-2). Let k(f) = f**3 - 3*f**2 + f + 1. Let z(s) = -s + 1. Let r(x) = y*z(x) + 2*k(x). Factor r(g).
2*(g - 3)*(g - 1)*(g + 1)
Let t be 3 - (1 - -1) - -2. Suppose -4*b - 3*b + b**2 + t*b - 3*b**2 = 0. Calculate b.
-2, 0
Let m(x) be the third derivative of -x**10/45360 + x**9/11340 - x**8/10080 - x**4/6 + 3*x**2. Let w(f) be the second derivative of m(f). Factor w(i).
-2*i**3*(i - 1)**2/3
Let c(g) be the second derivative of 5*g**7/42 - g**5/2 + 5*g**3/6 - 2*g. Factor c(t).
5*t*(t - 1)**2*(t + 1)**2
Let n(k) be the third derivative of -k**5/48 + k**4/24 + k**3/24 - 6*k**2. Let n(i) = 0. What is i?
-1/5, 1
Suppose 2*w - 30 = 5*w. Let f be ((-12)/10)/(4/w). Let 5*r**3 + 0*r**3 + 3*r**2 - 4*r**f - 4 = 0. What is r?
-2, 1
Suppose 3*q = -2*q + 20. Let w(p) = -p**2 - 1. Let m(d) = 6*d**2 - 2*d + 4. Let t(u) = q*w(u) + m(u). Let t(h) = 0. Calculate h.
0, 1
Factor 9/4*k + 1/4*k**4 + 0 + 3/4*k**2 - 5/4*k**3.
k*(k - 3)**2*(k + 1)/4
Let b be -1*(-1 - -2) + 4. Let l(q) be the second derivative of -1/16*q**4 - 1/80*q**5 + 2*q - 1/8*q**b - 1/8*q**2 + 0. Determine p so that l(p) = 0.
-1
Solve 6/5*x + 0*x**2 + 3/5*x**4 - 3/5 - 6/5*x**3 = 0.
-1, 1
Let 10*i**3 - 3 + 7 - 10*i**2 + i**4 - 3*i**4 - 10*i + 8*i**4 = 0. Calculate i.
-2, -1, 1/3, 1
Let i = -26 - -18. Let x be i/(-5) + (-8)/(-20). Factor -1/5*m + 0 + 0*m**x + 1/5*m**3.
m*(m - 1)*(m + 1)/5
Let v = 7000/3 - 2297. Let g = v + -36. Suppose 0 + 0*f - 1/3*f**3 + g*f**2 = 0. What is f?
0, 1
Let w = -893/54 - -1/27. Let l = 17 + w. Find j, given that 0*j + 0*j**3 - l*j**4 + 1/2*j**2 + 0 = 0.
-1, 0, 1
Let w(s) be the second derivative of 5*s**7/42 - s**6 + s**5/4 + 10*s**4 + 40*s**3/3 + 30*s. Factor w(p).
5*p*(p - 4)**2*(p + 1)**2
Let t(y) be the first derivative of y**3/12 - y**2/4 + 21. Factor t(o).
o*(o - 2)/4
Factor -95*b**3 + 83*b**3 + 3*b**4 + b + 15*b**2 - 7*b.
3*b*(b - 2)*(b - 1)**2
Suppose j + 11 = 3*f, 5*f - j + 0*j = 21. Find z such that 8/3*z - 25/3*z**2 + 8/3*z**f + 38/3*z**3 - 28/3*z**4 - 1/3 = 0.
1/2, 1
Let d(z) = -z - 15. Let f be d(-15). Let h(o) be the third derivative of 0*o + 0*o**5 + f*o**3 - 1/300*o**6 + 0 + 1/60*o**4 + o**2. Factor h(k).
-2*k*(k - 1)*(k + 1)/5
Let a(n) be the second derivative of -n + 0 - 1/18*n**3 + 1/18*n**4 + n**2 - 1/60*n**5. Let h(g) be the first derivative of a(g). Determine c so that h(c) = 0.
1/3, 1
Let g(v) = -v**3 - 1. Suppose 0 = -4*m - 2*j - 16, -2*m = -4*m - 2*j - 10. Let l(x) = -8*x**3 + 7*x**2 + 8*x - 7. Let u(c) = m*g(c) + l(c). Factor u(z).
-(z - 2)*(z + 1)*(5*z - 2)
Let j(z) = z**3 - 5*z**2 - 7*z + 5. Let d be j(6). Let k be 4/6*d/(-2). Factor 0*i + 1/3*i**3 + 1/3*i**4 - 1/3*i**2 - k*i**5 + 0.
-i**2*(i - 1)**2*(i + 1)/3
Let a be 0 - (-8)/(-2) - -2. Let f be (-1)/(a/(18/3)). Find c such that 2*c - 41*c**f + 32*c**2 - 27*c**3 + 52*c**4 - 4 + 21*c**2 - 14*c**5 - 21*c**2 = 0.
-2/7, 1
Let g(s) = -2*s**3 + s + 0*s + 1 + 3*s**3. Let o(r) = 2 - 6*r**3 - 3*r - r + 2 + 6*r**2 + 12*r. Let w(b) = -4*g(b) + o(b). Factor w(j).
-2*j*(j - 1)*(5*j + 2)
Let k be (-1 - -2)/5 - (-207)/90. Factor -1 - 5/2*v**3 + v**2 + k*v.
-(v - 1)*(v + 1)*(5*v - 2)/2
Let k(m) be the third derivative of m**5/240 - m**3/24 - 7*m**2. Factor k(v).
(v - 1)*(v + 1)/4
Suppose 0 = 13*g + 49 - 75. Determine a, given that -3/2 - 21/4*a + 3*a**3 + 15/4*a**g = 0.
-2, -1/4, 1
Let f be 4 + (-3)/(6/8). Suppose f = 2*j - 8 - 2. Find b, given that -18/11*b**2 - 10/11*b**3 + 14/11*b**j + 18/11*b**4 - 4/11*b + 0 = 0.
-1, -2/7, 0, 1
Let w be (-4)/1 - ((-833)/12)/17. Let k(o) be the first derivative of -w*o**3 + 1/4*o + 1 + 0*o**2. Factor k(l).
-(l - 1)*(l + 1)/4
Solve 48*n + 6*n**4 + 63*n**2 + 14*n**4 + 33*n**3 - 14*n**4 + 12 = 0 for n.
-2, -1, -1/2
Let x(y) = -y**3 - y**2 + y. Let j(t) = 12*t**3 - 4*t**2 - 37*t - 12. Let k(l) = 2*j(l) + 18*x(l). What is f in k(f) = 0?
-1, -2/3, 6
Suppose 34 - 2 = 4*j. Suppose 0 = -4*i + 2*v + j, 0 = -i + 4*i + 3*v + 12. Factor 2