1*k**3 + 2/11.
2*(k - 1)**2*(k + 1)**3/11
Let c(a) be the first derivative of -a**6/20 + a**5/6 - a**4/6 - 5*a**2 + 1. Let p(w) be the second derivative of c(w). Factor p(x).
-2*x*(x - 1)*(3*x - 2)
Find o such that -4/13*o**2 - 2/13*o**4 + 6/13*o**3 + 0 + 0*o = 0.
0, 1, 2
Let h(d) be the third derivative of -d**6/30 + d**5/5 + 2*d**4/3 - 41*d**2. Find m such that h(m) = 0.
-1, 0, 4
Let l(i) be the first derivative of i**8/1680 - i**7/420 + i**5/60 - i**4/24 + i**3/3 - 2. Let v(c) be the third derivative of l(c). Factor v(s).
(s - 1)**3*(s + 1)
Let y(x) = -x - 1. Let t(z) be the third derivative of -z**5/60 + z**4/4 + 5*z**3/6 + 2*z**2. Suppose 5*r = -0*r + 25. Let p(c) = r*y(c) + t(c). Factor p(b).
-b*(b - 1)
Let g(i) be the first derivative of 2 + i + 1/40*i**5 + 1/4*i**3 + 1/8*i**4 + 1/4*i**2. Let h(f) be the first derivative of g(f). Suppose h(u) = 0. Calculate u.
-1
Let y(g) = -5*g**4 - 4*g**3 + 7*g + 2. Let n(s) = 26*s**4 + 20*s**3 - 36*s - 10. Let h(w) = -3*n(w) - 16*y(w). Find a, given that h(a) = 0.
-1, 1
Suppose -4*n - 10 - 2 = 0. Let r(x) = 6*x**2 - 3*x. Let t(q) = -7*q**2 + 2*q. Let z(j) = n*t(j) - 4*r(j). Suppose z(h) = 0. What is h?
0, 2
Factor c - 4*c - c**3 + 0 + 1 + 3*c**2.
-(c - 1)**3
Let i(p) be the first derivative of p**6/24 - p**5/20 - p**4/16 + p**3/12 - 4. Factor i(h).
h**2*(h - 1)**2*(h + 1)/4
Factor 3896*o - 4*o**3 + 4*o**4 - 3892*o - 5*o**2 + o**2.
4*o*(o - 1)**2*(o + 1)
Let l(x) be the third derivative of -x**9/4032 + x**7/560 - x**5/160 + x**3/2 - x**2. Let o(w) be the first derivative of l(w). Factor o(v).
-3*v*(v - 1)**2*(v + 1)**2/4
Let v(u) be the second derivative of -u**4/30 - 2*u**3/5 + 9*u. Suppose v(j) = 0. What is j?
-6, 0
Let j(p) be the first derivative of -16/3*p**4 - 8/9*p**3 - 49/9*p**6 - 154/15*p**5 - 8 + 0*p + 0*p**2. Factor j(b).
-2*b**2*(b + 1)*(7*b + 2)**2/3
Suppose -4*x + 3*s - s = 0, 0 = 2*x + 2*s - 12. Let b be -2 + 2 + 1/2. Determine c, given that 2*c**x + 2*c - c**3 - c**5 - 5/2*c**4 + b = 0.
-1, -1/2, 1
Let f(q) be the second derivative of -q**5/20 - q**4/12 + q**3/6 + q**2/2 + 4*q. Factor f(h).
-(h - 1)*(h + 1)**2
Let y = 7201/30 + -240. Let c(z) be the third derivative of 0*z**3 - z**2 + 0 - y*z**5 + 0*z + 0*z**4. Factor c(b).
-2*b**2
Let u(s) = 3*s**2 - s - 1. Let f be u(-1). Determine t, given that f*t**2 + 2*t**3 - 6*t**3 - 5*t**2 - 2*t**4 = 0.
-1, 0
Let j be 7/4*(3 + 105/(-49)). Find a such that -1/2*a**2 - 1 + j*a = 0.
1, 2
Let f(i) be the third derivative of 8*i**2 - 11/12*i**4 + 2/15*i**6 + 0 + 0*i + 1/3*i**5 + 2/3*i**3. Factor f(b).
2*(b + 2)*(2*b - 1)*(4*b - 1)
Solve 15/4*t**2 + 3/4*t**3 + 21/4*t + 9/4 = 0 for t.
-3, -1
Let u(y) be the first derivative of y**3/3 + 2*y**2 + 3*y - 5. Let u(b) = 0. What is b?
-3, -1
Let d(f) be the second derivative of 5/8*f**4 - 1/4*f**3 - 9/40*f**5 + 0 - 3/4*f**2 + 6*f. Factor d(i).
-3*(i - 1)**2*(3*i + 1)/2
Let h = 5/132 - -133/1716. Let m = 17/78 + h. Factor 0 + 4/3*o**3 + m*o - 5/3*o**2.
o*(o - 1)*(4*o - 1)/3
Let p = -5 - -7. Solve -v**2 + v**2 - 2*v**p = 0.
0
Let t(w) = -w**2 + 12*w + 3. Let j be t(12). Suppose -11*n**3 - 17*n**3 + 8*n**j - 162*n + 128*n**2 - 66*n + 72 = 0. What is n?
2/5, 3
Suppose 2*z - 10 = 4*o, -2*o = 2*z - 1 + 9. Let m be (-2)/z - 2/(-1). Factor -3*y**m + 4*y**4 - 4*y**3 - 4*y + 6*y**2 - 3 + 4.
(y - 1)**4
Let b(o) be the second derivative of o**5/70 - o**4/42 + 15*o. Factor b(f).
2*f**2*(f - 1)/7
Let k(z) = z**2. Let o(y) = -3*y**2 - y. Let s(n) = -8*k(n) - 3*o(n). Factor s(m).
m*(m + 3)
Let j(v) be the second derivative of 1/8*v**4 - 1/20*v**5 - 1/6*v**3 - 2*v + 1/8*v**2 + 0 + 1/120*v**6. Factor j(g).
(g - 1)**4/4
Suppose -5*f + 215 = 35. Let b be 4/(-10) - f/(-15). Factor -a**3 + 2*a + 4*a**b + 3*a**3 + 0*a.
2*a*(a + 1)**2
Let d(y) = -7*y**3 - 3*y**2 - 2*y - 2. Let w(r) = r**3 - r - 1. Suppose -5 = 5*t + 5. Let c(i) = t*w(i) + d(i). Suppose c(f) = 0. What is f?
-1/3, 0
Let i be (4/50)/((-18)/(-520)). Let l = i - 10/9. Suppose 4/5*w**2 + 12/5*w**3 - 2/5*w**4 - 2/5 - 6/5*w**5 - l*w = 0. What is w?
-1, -1/3, 1
Let d(b) be the third derivative of b**8/112 + b**7/14 + 7*b**6/40 + 3*b**5/20 - 5*b**2. Factor d(x).
3*x**2*(x + 1)**2*(x + 3)
Let z(h) be the first derivative of 3*h**6/20 + 9*h**5/40 + h**4/12 + 5*h - 1. Let b(r) be the first derivative of z(r). Let b(w) = 0. What is w?
-2/3, -1/3, 0
Let f(y) be the first derivative of -3*y**5/5 + 6*y**4/5 + 9*y**3/5 - 12*y**2/5 - 12*y/5 - 8. Suppose f(i) = 0. Calculate i.
-1, -2/5, 1, 2
Factor 1/5 + 4/5*p + 3/5*p**2.
(p + 1)*(3*p + 1)/5
Let w = -1 - -10. Let b be 29/w - 14/63. Factor 6*v + 3*v - v**b - 3*v - 4 - v**3.
-2*(v - 1)**2*(v + 2)
Let s(k) be the third derivative of k**6/360 + k**5/360 - k**4/72 - k**3/36 + 8*k**2. Factor s(n).
(n - 1)*(n + 1)*(2*n + 1)/6
What is i in -4/13 + 2/13*i**3 + 10/13*i - 8/13*i**2 = 0?
1, 2
Let z(o) = 2*o**4 + 11*o**3 + 3*o**2 - 2. Let q(x) = -3*x**4 - 22*x**3 - 5*x**2 - x + 5. Let i(a) = 4*q(a) + 10*z(a). Factor i(m).
2*m*(m + 1)*(m + 2)*(4*m - 1)
Let b = -551/72 - -63/8. Factor -2/9*z + b*z**3 + 0*z**2 + 0.
2*z*(z - 1)*(z + 1)/9
Let u = -1537/3 - -513. Suppose -2/9*t**3 - 2/3*t - u*t**2 - 2/9 = 0. What is t?
-1
Let z(f) = 2*f + 4*f**3 + 2 - 3*f**3 - 3*f. Let n be z(0). Find g such that g**5 - 3*g**4 - n*g**3 - g**2 - 2*g**5 - g**3 = 0.
-1, 0
Let y = -11309/4 - -2843. Determine u so that 33/4*u - 6*u**2 - 3/2 - y*u**3 = 0.
-1, 2/7, 1/3
Let b be ((-4)/7)/(12/(-42)). Factor 10*w**2 + 5*w**b - 8*w**2 + 11*w**2 + 54*w + 2*w**3 + 54.
2*(w + 3)**3
Suppose 5*j + 5 = -a + 6*a, 2*a + 10 = 5*j. Let p(z) be the second derivative of 2*z + 0 - 1/20*z**a - 1/12*z**4 + 0*z**3 + 0*z**2. Factor p(o).
-o**2*(o + 1)
Let v(b) = -4*b**4 + 15*b**3 - 11*b**2 - 3*b. Let l(c) = -12*c**4 + 44*c**3 - 32*c**2 - 8*c. Let r(d) = -3*l(d) + 8*v(d). Factor r(x).
4*x**2*(x - 2)*(x - 1)
Factor 50*d**3 - 46*d**3 - 6*d + 2*d.
4*d*(d - 1)*(d + 1)
Let p(y) be the third derivative of y**5/20 + 7*y**4/24 + 20*y**2. Factor p(k).
k*(3*k + 7)
Factor 15/4*h**5 + 27/4*h**3 + 0 - 3/2*h + 39/4*h**4 - 3/4*h**2.
3*h*(h + 1)**3*(5*h - 2)/4
Let j(s) be the second derivative of 1/80*s**5 + 0*s**2 + 0 + 0*s**4 - 5*s - 1/24*s**3. Factor j(d).
d*(d - 1)*(d + 1)/4
Let p(n) be the third derivative of 5*n**8/112 + 4*n**7/35 + n**6/40 - n**5/10 + 6*n**2. Determine x, given that p(x) = 0.
-1, 0, 2/5
Let q be 20/(-10) + -6 + 8. Suppose -2 = -3*d - d + k, d = 5*k + 10. Suppose q - 2/7*j**5 + 0*j - 2/7*j**4 + 0*j**2 + d*j**3 = 0. What is j?
-1, 0
Let w(u) be the third derivative of 0*u**3 + 3*u**2 + 0 + 1/240*u**5 + 0*u - 1/480*u**6 + 0*u**4. Let w(a) = 0. Calculate a.
0, 1
Let j(k) be the first derivative of k**6/2 + 6*k**5/5 - 3*k**4/4 - 2*k**3 - 31. Factor j(v).
3*v**2*(v - 1)*(v + 1)*(v + 2)
Suppose 17*i - 24*i + 14 = 0. Determine w so that -3/2*w**i + 0 - 3/2*w + 3/2*w**3 + 3/2*w**4 = 0.
-1, 0, 1
Let v be (3/(-1))/(6/(-18)). Let k be (v/14)/(33/44). Factor 4/7*j**3 + 4/7 - 6/7*j - k*j**2.
2*(j - 2)*(j + 1)*(2*j - 1)/7
Let c(n) be the second derivative of 0*n**2 - n - 1/4*n**4 + 3/20*n**5 + 0*n**3 + 0. Find b, given that c(b) = 0.
0, 1
Let a(d) = d**5 + d**4 + d**3 + d**2 + 1. Let z(h) = 4*h**5 + 10*h**4 + 2*h**3 - 4*h**2 + 5. Let j(l) = -10*a(l) + 2*z(l). Let j(v) = 0. What is v?
-1, 0, 3
Solve 16 - 48*i - 3*i**3 + 3*i**3 + 13*i**2 - 12*i**3 + 31*i**2 = 0.
2/3, 1, 2
Let w(l) = 6*l**3 + l**2 + 2*l + 1. Let q be w(0). Factor 2*m**5 + 15/2*m + 21/2*m**4 + q + 37/2*m**2 + 41/2*m**3.
(m + 1)**3*(m + 2)*(4*m + 1)/2
Let q(i) be the first derivative of -i**8/5040 + i**6/360 + i**5/180 + 4*i**3/3 - 8. Let d(m) be the third derivative of q(m). Find t such that d(t) = 0.
-1, 0, 2
Let j(o) = -9*o**3 + 7*o**2 + 4*o - 2. Let u(x) = x**2 - x. Let d(z) = j(z) - 5*u(z). Factor d(h).
-(h - 1)*(h + 1)*(9*h - 2)
Let z(s) = s**2 + 2*s - 2. Let v be z(2). Factor 2 + 6*q - 3*q**3 + v*q**2 + 4*q**3 + q**3.
2*(q + 1)**3
Let p = 0 + 2. Suppose 0 = -3*a - h - 3*h + 1, -3*a + 13 = -2*h. Factor w**p - w - 3*w**2 + 5*w - 2*w**a.
-2*w*(w - 1)*(w + 2)
Let r(w) = w**5 + 5*w**4 - 3*w**3 - 7*w**2 - 5*w + 5. Let j(l) = l**5 + 6*l**4 - 3*l**3 - 8*l**2 - 6*l + 6. Let a(t) = -5*j(t) + 6*r(t). Factor a(v).
v**2*(v - 2)*(v + 1)**2
Let l(n) be the third derivative of n**5/510 - 5*n**4/204 - n**2 - 43. Factor l(b).
2*b*(b - 5)/17
Let q(g)