2
Let c(u) be the third derivative of u**8/840 - u**7/525 - u**6/300 + u**5/150 - 6*u**2. Factor c(p).
2*p**2*(p - 1)**2*(p + 1)/5
Let n(s) be the second derivative of -s**8/168 - s**7/105 + s**2 + s. Let a(v) be the first derivative of n(v). Factor a(i).
-2*i**4*(i + 1)
Let m = -9 + 11. Determine j so that -3*j**3 + 3*j**m + 3*j**3 + 2*j**3 + j**3 = 0.
-1, 0
Let t(f) be the second derivative of 2*f**7/63 - 7*f**6/30 + 41*f**5/60 - 37*f**4/36 + 5*f**3/6 - f**2/3 - 6*f. Factor t(q).
(q - 2)*(q - 1)**3*(4*q - 1)/3
Let a(n) be the third derivative of 11*n**7/490 + 13*n**6/280 - 9*n**5/140 - 13*n**4/56 - n**3/7 + 3*n**2. Let a(c) = 0. Calculate c.
-1, -2/11, 1
Let w(i) be the third derivative of i**9/241920 - i**7/20160 + i**5/30 - 4*i**2. Let d(r) be the third derivative of w(r). Solve d(x) = 0 for x.
-1, 0, 1
Let y(m) be the first derivative of 2*m**3/15 + 7*m**2/5 + 4*m - 37. Factor y(d).
2*(d + 2)*(d + 5)/5
Let l = -9 + 11. Let -8*b**2 + 6*b**l + 4*b - 2*b + 0*b = 0. Calculate b.
0, 1
Let 2/5*y - 1/5*y**2 + 0 = 0. Calculate y.
0, 2
Let h be (23 - 19) + (-78)/20. Let r(l) be the second derivative of 0 + h*l**5 - l + 0*l**4 - 1/3*l**3 + 1/2*l**2 - 1/30*l**6. Find g, given that r(g) = 0.
-1, 1
Suppose 0 = -l - l. Suppose -5*b + 10 = -l. Factor -3*p - p**b + p + 4*p.
-p*(p - 2)
Let f(w) = 8*w**5 - 27*w**4 - 11*w**3 + 16*w**2 - 8*w + 11. Let o(x) = 4*x**5 - 14*x**4 - 6*x**3 + 8*x**2 - 4*x + 6. Let g(z) = 6*f(z) - 11*o(z). Factor g(s).
4*s*(s - 1)**3*(s + 1)
Let v(c) = -3*c**4 - 5*c**3 - 3*c**2 + c - 2. Let k(a) = -2*a**4 - 4*a**3 - 3*a**2 + a - 1. Let h(g) = -4*k(g) + 3*v(g). Find s such that h(s) = 0.
-1, 1, 2
Let t(r) be the second derivative of 0 - 11*r - 1/5*r**5 + r**4 + 2/3*r**3 - 2/15*r**6 - 4*r**2. Suppose t(x) = 0. What is x?
-2, -1, 1
Let a(u) be the first derivative of 2/27*u**3 + 2/9*u - 1 + 2/9*u**2. Factor a(x).
2*(x + 1)**2/9
Suppose -6/5*p**3 + 0 + 2*p**2 - 4/5*p = 0. Calculate p.
0, 2/3, 1
Let o(z) be the second derivative of 0 - 1/15*z**6 - 1/6*z**4 + 0*z**3 + 0*z**2 - z + 1/5*z**5. Suppose o(c) = 0. Calculate c.
0, 1
Let y(f) be the first derivative of -4*f**5/5 - 5*f**4/2 + 5*f**2 + 4*f + 1. Suppose y(t) = 0. Calculate t.
-2, -1, -1/2, 1
Let j = 1031 - 1031. What is y in -2/7*y**4 + 4/7*y - 10/7*y**2 + 8/7*y**3 + j = 0?
0, 1, 2
Let w be 0 + (-2 - (10 - 4)). Let m be 14/12 - 12/w. Determine v, given that 6*v**2 + m - 8*v = 0.
2/3
Let -3/8*i**2 + 3/8*i**3 + 1/8*i - 1/8*i**4 + 0 = 0. What is i?
0, 1
Let m = 6 - 6. Solve 6*s**2 + m*s**3 + 9*s**3 - 12*s**5 - 3*s**2 = 0.
-1/2, 0, 1
Suppose -2/7*z**2 - 8/7*z - 8/7 = 0. Calculate z.
-2
Solve 0 + 0*k**3 - 2/5*k**4 + 0*k + 2/5*k**2 = 0.
-1, 0, 1
Determine z, given that -22*z**4 + 20*z**3 + 8*z**2 + 5*z**4 - 20*z**4 + 9*z**4 = 0.
-2/7, 0, 1
Let s(t) be the first derivative of 1/16*t**4 - 3 - 1/3*t**3 + 1/2*t**2 + 0*t. Solve s(c) = 0 for c.
0, 2
Let b(h) be the third derivative of 0*h + 3*h**2 + 1/45*h**5 + 0 + 5/72*h**4 + 1/9*h**3 + 1/360*h**6. Factor b(u).
(u + 1)**2*(u + 2)/3
Let g(s) be the first derivative of 3*s**4/4 - 2*s**3/3 + s**2 - s + 3. Let t be g(1). Let 1/2*b + 1/2 - 1/2*b**t - 1/2*b**3 = 0. Calculate b.
-1, 1
Let -3/2*t - 1 - 1/2*t**2 = 0. What is t?
-2, -1
Let d = -470/77 + 44/7. Solve 0 + 2/11*o - d*o**2 = 0.
0, 1
Find c, given that -6*c**2 - 4*c**2 + 60*c**3 - 65*c**3 - 5*c = 0.
-1, 0
Suppose 2*d + 4*h = 12, 5*d - 3*h = h - 12. Factor 4/3*y**3 + 2/3*y**2 + d*y + 0 + 2/3*y**4.
2*y**2*(y + 1)**2/3
Let d be (4/(-8))/(1 + 44/(-40)). Solve -1/5*l + 1/5 + 1/5*l**4 - 1/5*l**d + 2/5*l**3 - 2/5*l**2 = 0.
-1, 1
Suppose -7*d + 12 = -3*d. Let l(o) be the first derivative of -1/6*o**d + 1/4*o**2 + 2 - 1/8*o**4 + 1/2*o. Factor l(f).
-(f - 1)*(f + 1)**2/2
Let c(z) = -z**3 - 13*z**2 - 12*z + 16. Let h be c(-12). Factor -16*l**5 - 50*l**3 + 80*l**4 + 2 + 10*l - h*l**5 + 0*l - 10*l**2.
-2*(l - 1)**3*(4*l + 1)**2
Let r(y) be the second derivative of -y**5/30 - y**4/9 - y**3/9 + 15*y. Determine d so that r(d) = 0.
-1, 0
Let p(i) = i - 1. Let y(m) = -m**2 + m. Let x = -11 - -15. Let j(o) = x*p(o) - 2*y(o). Factor j(s).
2*(s - 1)*(s + 2)
Factor -1 + 4/5*q + 1/5*q**2.
(q - 1)*(q + 5)/5
Let s(g) be the second derivative of g**4/96 - g**3/16 + 2*g. Factor s(h).
h*(h - 3)/8
Suppose 1/3 + 2*b**2 + 1/3*b**4 + 4/3*b + 4/3*b**3 = 0. What is b?
-1
Factor 8/7 + 6/7*u**2 + 16/7*u.
2*(u + 2)*(3*u + 2)/7
Let x(b) = b**2 - 17*b + 16. Let c be x(16). Let w(p) be the first derivative of -1/6*p**4 + 0*p**2 - 2 - 2/9*p**3 + 4/15*p**5 + c*p. Factor w(h).
2*h**2*(h - 1)*(2*h + 1)/3
Let b(y) be the third derivative of -y**8/672 + y**7/105 - y**6/48 + y**5/60 - y**2. Factor b(l).
-l**2*(l - 2)*(l - 1)**2/2
Let u(o) be the third derivative of o**5/45 + 2*o**4/9 + 8*o**3/9 + 9*o**2 + o. Factor u(b).
4*(b + 2)**2/3
Let y(p) be the first derivative of -p**6/10 - 3*p**5/10 - p**4/4 + 3*p - 8. Let s(c) be the first derivative of y(c). Factor s(n).
-3*n**2*(n + 1)**2
Let b = -15 - -19. Let m(d) be the second derivative of 0 + 0*d**2 + 2*d - 1/80*d**5 - 1/42*d**7 + 0*d**b + 0*d**3 + 1/24*d**6. Factor m(w).
-w**3*(w - 1)*(4*w - 1)/4
Let g = 16 + -3. Let h(u) = u**2 - 12*u - 10. Let a be h(g). What is s in 0*s**2 + 0*s + 1/4*s**a + 0 + 1/4*s**4 = 0?
-1, 0
Let q(u) be the second derivative of -u**4/90 - 2*u**3/45 + u**2/5 + 34*u. Let q(g) = 0. Calculate g.
-3, 1
Let s(d) = d**4 + 2*d**3 + 2*d + 1. Let o(t) = t**3 + t**2 + t. Suppose -2*x + 16 = 2*x. Let y(a) = x*o(a) - 2*s(a). Factor y(z).
-2*(z - 1)**2*(z + 1)**2
Let i(g) be the third derivative of -g**5/360 + g**4/144 + g**3/18 + 21*g**2. Find t, given that i(t) = 0.
-1, 2
Let s(c) be the first derivative of -8*c**2 + 4/5*c**5 - 16*c + 2 + 4*c**3 + 4*c**4. Factor s(k).
4*(k - 1)*(k + 1)*(k + 2)**2
Let v(c) be the third derivative of -c**7/6300 - c**6/1800 + c**4/6 - c**2. Let s(d) be the second derivative of v(d). Suppose s(t) = 0. What is t?
-1, 0
Let h(p) = p + 3 + 0*p - p**2 - 2. Let t(g) = -31*g**2 + 9*g + 9. Suppose -5*l - 27 = 2*y, -4*l + 3*l = 4*y + 9. Let i(b) = y*h(b) + t(b). Solve i(j) = 0 for j.
-2/5, 2/3
Let n = -18 + 23. Let a be -1 + (4 - n/2). Factor -3/4*b**3 + 7/4*b - 1/2 - a*b**2.
-(b - 1)*(b + 2)*(3*b - 1)/4
Let t(o) be the first derivative of o**4/24 + o**3/9 - 3. Factor t(y).
y**2*(y + 2)/6
Let p(l) = l**3 + 18*l**2 - 42*l - 36. Let s be p(-20). Determine a so that -2/3 + 5*a**2 + 7/3*a**s + 1/3*a + 19/3*a**3 = 0.
-1, 2/7
Suppose 0 = 3*p - p - 4. Let l(m) be the first derivative of 0*m + 1 - 5/2*m**4 + 14/3*m**3 - 2*m**p. Factor l(j).
-2*j*(j - 1)*(5*j - 2)
Let h = 705 - 702. Solve 0 - 12/5*r**h - 8/5*r**2 + 4/5*r = 0.
-1, 0, 1/3
Find c, given that -10/7*c + 2/7*c**2 + 8/7 = 0.
1, 4
Let c(b) be the second derivative of -7*b**4/72 - b**3/4 - b**2/6 - b. Factor c(w).
-(w + 1)*(7*w + 2)/6
Let k be 1*5/1*1. Let t(f) = -f**3 + 6*f**2 - 6*f + 5. Let r be t(k). Solve 2/9*a**2 + 0 + r*a + 2/9*a**4 + 4/9*a**3 = 0.
-1, 0
Let h(v) be the first derivative of -v**4/6 + 2*v**3 - 8*v**2/3 - 52. Factor h(j).
-2*j*(j - 8)*(j - 1)/3
Let k = 2 + 1. Suppose -k*d - 2*d + 20 = 0. Find w such that 4/5*w**3 + 1/5*w**d + 4/5*w**2 + 0*w + 0 = 0.
-2, 0
Let b(n) be the third derivative of -n**8/30240 - n**7/3780 + n**5/60 - n**2. Let v(g) be the third derivative of b(g). Find x, given that v(x) = 0.
-2, 0
Let k(n) be the third derivative of n**5/30 + n**4/6 + n**3/3 - 7*n**2. Factor k(i).
2*(i + 1)**2
Let j(m) = 424*m**4 - 1582*m**3 + 584*m**2 - 54*m + 26. Let v(l) = -47*l**4 + 176*l**3 - 65*l**2 + 6*l - 3. Let h(z) = 6*j(z) + 52*v(z). Factor h(k).
4*k*(k - 3)*(5*k - 1)**2
Let w(v) be the third derivative of -v**7/70 - v**6/20 + v**5/20 + v**4/4 - 6*v**2. Find p, given that w(p) = 0.
-2, -1, 0, 1
Factor -m**3 - 2 - 3*m + 2*m - 3*m**2 + 2*m + 5.
-(m - 1)*(m + 1)*(m + 3)
Factor 4*z**2 - 2 - 6*z + 1 + 0 - 3.
2*(z - 2)*(2*z + 1)
Suppose -40*s**5 + 6*s**3 + 2*s**3 + 8*s**2 - 36*s**4 + 4*s**3 = 0. Calculate s.
-1, -2/5, 0, 1/2
Let k(u) be the first derivative of -u**6/1980 - u**5/660 - 5*u**3/3 - 2. Let v(i) be the third derivative of k(i). Factor v(y).
-2*y*(y + 1)/11
Suppose -18*p = -21*p. Let s(r) be the third derivative of p*r + 0*r**4 + 0 + 1/120*r**5 - 2*r**2 + 1/240*r**6 + 0*r**3. Factor s(v).
v**2*(v + 1)/2
Let q be -3 + 142*(-1)/(-46). Let j = 35/138 - q. Factor 1/6*r**2 +