/(-20)). Let k be (u/6)/(4/18). Factor -2*l**2 + 4*l**4 - 2*l**4 - 2*l**3 + 5*l**5 - k*l**5.
2*l**2*(l - 1)*(l + 1)**2
Let m(h) be the second derivative of -11*h**5/120 - h**4/24 - h**2/2 + 5*h. Let z(j) be the first derivative of m(j). Suppose z(i) = 0. Calculate i.
-2/11, 0
Let s = 5 - -5. Let a be 0/2 - (-4)/s. Find z, given that -a*z**2 + 6/5*z - 6/5*z**3 + 2/5 = 0.
-1, -1/3, 1
Suppose 4 = z + z + 4*v, -3*z = 3*v - 9. Factor -6*m**3 + 22*m + 8*m**z - 22*m.
2*m**3*(4*m - 3)
Let f be (6/(-7))/((-4)/28). Factor -f*o**2 - 8*o + 0*o - 2 + 0*o.
-2*(o + 1)*(3*o + 1)
Let b(u) be the third derivative of u**6/120 + u**5/25 + 3*u**4/40 + u**3/15 + 2*u**2. Factor b(y).
(y + 1)**2*(5*y + 2)/5
Factor -8*o - 6 - o - 2*o**2 + o.
-2*(o + 1)*(o + 3)
Let x(v) be the second derivative of 0 + 4*v - 1/6*v**4 + v**3 - 2*v**2. Determine r, given that x(r) = 0.
1, 2
Factor 5*u**2 - 8*u - 5*u**2 - 2*u**2.
-2*u*(u + 4)
Let v = 3 + 0. Factor 4 + 0 + 3*u**v - 7 - 7*u + 4*u + 3*u**2.
3*(u - 1)*(u + 1)**2
Let i(u) be the third derivative of u**8/112 - u**7/70 - u**6/40 + u**5/20 + 8*u**2. Factor i(z).
3*z**2*(z - 1)**2*(z + 1)
Factor -2*r**2 + 6/5*r + 2/5*r**4 + 2/5*r**3 + 0.
2*r*(r - 1)**2*(r + 3)/5
Let d(p) = 6*p**2 - 10*p - 2. Let v(x) be the first derivative of 4*x**3 - 10*x**2 - 3*x - 2. Let w(a) = -5*d(a) + 2*v(a). Suppose w(m) = 0. What is m?
-1/3, 2
Let q be (-1 - -1)/2 + -6. Let c(n) = 8*n**3 - 4*n**2 - 5*n + 7. Let w(o) = -7*o**3 + 3*o**2 + 4*o - 6. Let p(d) = q*c(d) - 7*w(d). Factor p(x).
x*(x + 1)*(x + 2)
Factor 1 - 3/2*c**3 - 7/2*c + 4*c**2.
-(c - 1)**2*(3*c - 2)/2
Let q = 21 - 19. Let y(d) be the first derivative of d**4 + 2 + 0*d**q + 0*d + 7/20*d**5 + 1/3*d**3. Factor y(j).
j**2*(j + 2)*(7*j + 2)/4
Let t = -12 - -17. Let d(h) be the first derivative of 0*h + 1/4*h**2 + 1/2*h**3 + 3/8*h**4 - 2 + 1/10*h**t. Determine a so that d(a) = 0.
-1, 0
Let t(u) be the first derivative of -1/3*u + 0*u**2 + 2 + 1/9*u**3. Factor t(c).
(c - 1)*(c + 1)/3
Let s(q) be the first derivative of q**8/224 - q**7/140 - q**6/80 + q**5/40 + 5*q**2/2 - 3. Let d(z) be the second derivative of s(z). Factor d(h).
3*h**2*(h - 1)**2*(h + 1)/2
Factor 12 + 3/2*h**2 + 27/2*h.
3*(h + 1)*(h + 8)/2
Let a(y) = -6*y**2 - 3*y + 12. Let l(h) = h**2 + h. Let w(g) = -a(g) - 3*l(g). Determine v so that w(v) = 0.
-2, 2
Let v be 2/4 - (-34)/(-4). Let g = 10 + v. Suppose -1/4*f**g + 0 + 1/4*f + 1/4*f**4 - 1/4*f**3 = 0. Calculate f.
-1, 0, 1
Suppose -3*t + 4*t = 12. Factor -62 - 12*o**2 - t*o**3 + 62 - 4*o**4 - 4*o.
-4*o*(o + 1)**3
Factor 6*d**4 - 8*d - 3*d**2 - 2*d**4 + 12*d**3 - d**2 - 4*d.
4*d*(d - 1)*(d + 1)*(d + 3)
Let q(w) be the second derivative of -w**8/40320 + w**7/3780 - w**6/864 + w**5/360 + 5*w**4/12 + w. Let n(s) be the third derivative of q(s). Factor n(b).
-(b - 2)*(b - 1)**2/6
Let y(h) be the third derivative of h**8/112 + h**7/70 - h**6/40 - h**5/20 + 5*h**2. Factor y(k).
3*k**2*(k - 1)*(k + 1)**2
Suppose 2*c + 0*c = 8. Factor 14*p**5 - 6*p - 3*p**3 - 6*p**3 - c - 14*p**4 + 28*p**2 + p**3 - 10*p**4.
2*(p - 1)**3*(p + 1)*(7*p + 2)
Let h(y) = -2*y + 12. Let w be h(4). Let c(o) be the first derivative of -1 - 2/27*o**3 + 1/18*o**w + 0*o + 0*o**2. What is q in c(q) = 0?
0, 1
Let m(o) = o**2 + 5*o - 2. Let t(f) = 3*f**2 + 15*f - 7. Let h(v) = -8*m(v) + 3*t(v). Let k be h(-6). Let k + 2*p**2 - 2 - 1 = 0. What is p?
-1, 1
Let v(h) be the first derivative of 0*h**2 - 1/5*h**5 + 4 - 2/3*h**3 + 0*h - 3/4*h**4. Factor v(u).
-u**2*(u + 1)*(u + 2)
Suppose 2/3*j**4 + 2/3*j - 2/9 - 2/9*j**5 - 4/9*j**2 - 4/9*j**3 = 0. What is j?
-1, 1
Let c(g) = g**2 + g - 4. Let p(w) = -w**2 - w + 5. Let l(h) = -3*c(h) - 2*p(h). Find f such that l(f) = 0.
-2, 1
Factor -8/11*v**2 - 12/11*v**3 - 8/11*v**4 + 0 - 2/11*v - 2/11*v**5.
-2*v*(v + 1)**4/11
Let i(t) = -t**3 + 9*t + 12. Let d be i(-2). Determine f, given that 0 + 0*f + 1/4*f**3 + 1/4*f**d = 0.
-1, 0
Determine j, given that 24/5 - 2/5*j**5 - 32/5*j - 2*j**2 + 18/5*j**3 + 2/5*j**4 = 0.
-2, 1, 3
Let l be 56/21 - -1*1. Let v = 4 - l. Suppose 1/3*o**2 + v - 2/3*o = 0. Calculate o.
1
Let u(b) = b + 5. Let r be u(-5). Let i = 1/31 + 28/93. Find t such that -1/3*t**2 + i + r*t = 0.
-1, 1
Let w(q) be the first derivative of -q**3/2 + 3*q/2 + 10. Factor w(r).
-3*(r - 1)*(r + 1)/2
Let t be (-18)/693*-7 + 7/22. Let 0*k**2 + 0 + 1/2*k - t*k**3 = 0. What is k?
-1, 0, 1
Let v = 3 - 0. Factor -72*z**2 + z - 2*z + 13*z + 63*z**v + 147*z**4.
3*z*(z + 1)*(7*z - 2)**2
Let p(u) = 4*u**5 - 4*u**4 + u**3 + 3*u**2 + 3*u - 3. Let l(j) = 3*j**5 - 4*j**4 + 2*j**3 + 2*j**2 + 2*j - 2. Let r(c) = -6*l(c) + 4*p(c). Factor r(v).
-2*v**3*(v - 2)**2
Let h(p) be the second derivative of -p**6/135 - p**5/15 - 4*p**4/27 - 30*p. Factor h(z).
-2*z**2*(z + 2)*(z + 4)/9
Factor 0 + 9/5*y**3 - 3/5*y**2 + 3/5*y**5 - 9/5*y**4 + 0*y.
3*y**2*(y - 1)**3/5
Let m(v) be the second derivative of 2*v**6/15 + v**5/5 - v**4/3 - 2*v**3/3 - 15*v. Find g such that m(g) = 0.
-1, 0, 1
Let l(x) be the third derivative of 0*x**6 + 1/1008*x**8 + 1/630*x**7 + 5*x**2 + 0 + 0*x**5 + 0*x + 0*x**4 + 0*x**3. Factor l(i).
i**4*(i + 1)/3
Let f(b) be the second derivative of -7*b + 0*b**2 + 0 + 0*b**5 - 2/45*b**6 + 0*b**3 + 0*b**4 - 1/63*b**7. Solve f(r) = 0.
-2, 0
Let t be 28 + -23 + ((-36)/10 - 1). Let j be 2/6 - (-14)/30. Factor -2/5*o**2 - j*o - t.
-2*(o + 1)**2/5
Let v(n) be the second derivative of 2*n**2 - 13/15*n**6 + 11/6*n**4 - 4/3*n**7 + 4*n - 13/3*n**3 + 41/10*n**5 + 0. What is h in v(h) = 0?
-1, 1/4, 2/7, 1
Let k(z) = -5*z**2 + 3*z - 2. Let f(b) = -60*b**2 + 35*b - 25. Let a(l) = 2*f(l) - 25*k(l). Factor a(t).
5*t*(t - 1)
Let f(q) be the second derivative of q**5/80 - 3*q**2 - 5*q. Let r(s) be the first derivative of f(s). Factor r(o).
3*o**2/4
Let c(s) be the second derivative of 18/7*s**7 - 18/5*s**6 + s + 10/3*s**4 + 14/3*s**3 - 18/5*s**5 + 0 + 2*s**2. Determine g so that c(g) = 0.
-1/3, 1
Let x(y) = 6*y**2 - 2*y - 8. Let c(l) = 5*l**2 - l - 9. Let b(k) = 4*c(k) - 3*x(k). Let b(a) = 0. What is a?
-3, 2
Let k(f) be the third derivative of -5*f**8/336 - f**7/21 + f**6/6 + f**5/6 - 5*f**4/8 - 40*f**2. Suppose k(g) = 0. Calculate g.
-3, -1, 0, 1
Let o = 0 - 0. Let t = 2 + 1. Let -3*a**2 + 5*a**2 + o*a**3 - 2*a**t = 0. What is a?
0, 1
Let g(o) = -o**3 - 2*o**2 - 2*o - 2. Let h(k) = -2*k + 6. Let r be h(4). Let v be g(r). Factor 1/5*s**4 - 2/5*s**3 + 1/5*s**v + 0 + 0*s.
s**2*(s - 1)**2/5
Let g(k) be the third derivative of 0 + 0*k**3 + 2*k**2 - 1/240*k**6 + 0*k**7 + 0*k**5 + 0*k**4 + 1/672*k**8 + 0*k. Factor g(x).
x**3*(x - 1)*(x + 1)/2
What is c in -7/5*c**2 - 4/5 - 16/5*c = 0?
-2, -2/7
Let i(t) be the third derivative of t**6/360 + t**5/30 + t**4/6 + 7*t**3/6 + 2*t**2. Let l(k) be the first derivative of i(k). Factor l(h).
(h + 2)**2
Let o(v) be the second derivative of 5*v**7/21 + 3*v**6/2 + 4*v**5 + 35*v**4/6 + 5*v**3 + 5*v**2/2 + 17*v. Factor o(a).
5*(a + 1)**4*(2*a + 1)
Let k(b) be the first derivative of -b**3 + 1. Factor k(w).
-3*w**2
Factor 0*u + 11*u + 4*u**2 + 2*u - u.
4*u*(u + 3)
Factor -16/13 - 2/13*m**2 + 18/13*m.
-2*(m - 8)*(m - 1)/13
Factor 2/15*c**3 + 0 + 4/15*c**2 + 2/15*c.
2*c*(c + 1)**2/15
Let m(w) be the third derivative of -1/6*w**3 - 1/210*w**7 + 0 - 1/10*w**5 + 0*w - 1/30*w**6 - 1/6*w**4 - 4*w**2. Determine s, given that m(s) = 0.
-1
Let w(k) = -k**2 + 12*k - 7. Let d be w(5). Find l such that -80*l**4 - 28*l**3 - 6*l**2 - 32*l**5 - 14*l**2 + d*l - 30*l - 38*l**3 = 0.
-1, -1/4, 0
Let n(d) be the third derivative of d**7/105 - d**6/5 + 3*d**5/2 - 25*d**4/6 + 3*d**2. What is p in n(p) = 0?
0, 2, 5
Let r(z) be the second derivative of 0*z**4 + 0 + 1/300*z**5 - 1/200*z**6 - 3*z - z**2 + 0*z**3. Let n(i) be the first derivative of r(i). Factor n(w).
-w**2*(3*w - 1)/5
Let u(h) = h**3 + 8*h**2 - 10*h - 7. Let m be u(-9). Factor m*b**3 - 3*b**3 - 3*b**2 - 3*b**4 + 6*b**3 + b**3.
-3*b**2*(b - 1)**2
Let c(z) be the first derivative of -z**3/6 - z**2/4 + z - 36. Solve c(d) = 0 for d.
-2, 1
Let r(o) be the first derivative of 1/7*o**4 - 1/21*o**6 + 0*o + 3/35*o**5 + 9 - 1/7*o**3 - 1/7*o**2. Let r(x) = 0. Calculate x.
-1, -1/2, 0, 1, 2
Let b be ((-10)/4)/(-5)*0. Suppose 0*w - 3*w + 6 = b. Factor 2*z - w*z - 3*z**5 + z**5 - 2*z + 4*z**3.
-2*z*(z - 1)**2*(z + 1)**2
Let h(s) be the first derivative of -7*s**5