of f**6/240 + 3*f**5/80 + f**4/8 - 11*f**3/6 + 11*f**2. Let g(b) be the first derivative of x(b). Factor g(w).
3*(w + 1)*(w + 2)/2
Let h be 2*(9 + (-70)/20). Let s(m) be the second derivative of -m**3 + 2*m**2 - 1/40*m**5 - h*m + 0 + 1/4*m**4. Suppose s(n) = 0. Calculate n.
2
Let -121/6 - 11/3*a - 1/6*a**2 = 0. Calculate a.
-11
Let r = -597 - -11943/20. Let d(u) be the second derivative of -1/2*u**4 - r*u**5 + 3*u**2 - 2*u + 1/2*u**3 + 0. Factor d(o).
-3*(o - 1)*(o + 1)*(o + 2)
What is j in 16/9*j + 1/9*j**2 - 4 = 0?
-18, 2
Let p(w) be the first derivative of w**5/35 - w**4/7 - 11*w**3/21 - 3*w**2/7 - 15. Suppose p(i) = 0. What is i?
-1, 0, 6
Suppose -3 = -2*z + 9. Let l(h) be the third derivative of 0 + 0*h**3 + 1/100*h**z + 1/50*h**5 + 0*h - 2*h**2 + 1/60*h**4 + 1/525*h**7. Factor l(i).
2*i*(i + 1)**3/5
Let k(o) be the first derivative of -o**6/1440 + o**5/120 - o**4/24 + 4*o**3/3 + 13. Let i(t) be the third derivative of k(t). Factor i(z).
-(z - 2)**2/4
Let f = -43 - -45. Factor 4*a + 8*a - 3*a**2 + a**f - 2*a**2.
-4*a*(a - 3)
Let b(s) be the first derivative of -s**2 + s**3 + 6*s**2 - 5 + 12*s + s**2. Let b(j) = 0. What is j?
-2
Let n(g) = -2*g**3 - 1. Let f(o) = -18*o**3 + 6*o**2 - 44*o - 58. Let x(s) = -f(s) + 10*n(s). Let x(v) = 0. What is v?
-6, -1, 4
Let g(z) be the first derivative of -z**4 - 28*z**3/3 + 2*z**2 + 28*z + 8. Factor g(t).
-4*(t - 1)*(t + 1)*(t + 7)
Let l(p) be the first derivative of p**6/90 + 2*p**5/15 + 20*p**3/3 + 16. Let s(z) be the third derivative of l(z). Let s(q) = 0. What is q?
-4, 0
Let j(q) = -6*q**4 - 5*q**3 + 12*q**2 + 21*q + 5. Let c(m) = -5*m**4 - 4*m**3 + 12*m**2 + 20*m + 4. Let o(u) = -5*c(u) + 4*j(u). Factor o(k).
k*(k - 4)*(k + 2)**2
Let d(k) be the first derivative of 5*k**4/24 - 5*k**3/6 + 5*k**2/4 - 5*k/6 + 18. Find c such that d(c) = 0.
1
Let m(v) be the first derivative of -v**3/4 - 3*v**2/2 - 9*v/4 + 196. Find u such that m(u) = 0.
-3, -1
Let u(d) be the first derivative of -7*d**6/360 + d**5/10 + d**4/6 - 11*d**3 + 7. Let z(b) be the third derivative of u(b). Factor z(y).
-(y - 2)*(7*y + 2)
Let r(i) = -i**3 + 10*i**2 - 16*i + 2. Let k be r(8). Let 4*t - 20*t**k - 28*t + 24*t**2 + 20 = 0. What is t?
1, 5
Let b(t) = -t**3 - t + 1. Let z(o) = 8*o + 0*o**3 + o**3 + 4*o**3 + 5*o**2 - 2 - o. Let u = 14 - 12. Let p(v) = u*z(v) + 6*b(v). Solve p(j) = 0.
-1, -1/2
Let r be ((-2)/(-21))/(6/36). Factor -r*o**2 + 4/7*o**3 + 4/7 - 4/7*o.
4*(o - 1)**2*(o + 1)/7
Factor -c**5 + 8*c**2 - 8*c**4 - 20*c**2 + 28*c**3 - 4*c**2 - 3*c**5.
-4*c**2*(c - 1)**2*(c + 4)
Suppose 23*k - 16*k - 63 = 0. Let o(f) be the second derivative of k*f + 0 + 0*f**2 - 1/30*f**4 - 1/25*f**5 + 1/15*f**3. Factor o(x).
-2*x*(x + 1)*(2*x - 1)/5
Factor 54/5 - 9/5*a - 3/5*a**2.
-3*(a - 3)*(a + 6)/5
Let v(n) be the second derivative of -n**6/840 + n**5/280 - 13*n**3/3 + 34*n. Let g(c) be the second derivative of v(c). Solve g(u) = 0.
0, 1
Let h be 30/(-8) + -2 - (-4 + -2). Find z such that -3/4*z - h*z**3 + 3/4*z**2 + 1/4 = 0.
1
Let h(w) be the second derivative of -12*w + 0 - 5/42*w**7 + 3/4*w**5 - 5/3*w**3 + 5/12*w**4 - 1/6*w**6 + 0*w**2. Find p, given that h(p) = 0.
-2, -1, 0, 1
Solve 0 + 0*n - 2/11*n**3 + 56/11*n**4 - 4/11*n**2 = 0 for n.
-1/4, 0, 2/7
Let d(v) be the third derivative of 0*v - 3/50*v**7 + 1/10*v**4 - 4/15*v**3 - 1/200*v**6 + 31/150*v**5 + 0 + 23*v**2. Let d(g) = 0. Calculate g.
-2/3, 2/7, 1
Let h(r) be the first derivative of 0*r - 3/8*r**2 - 9/8*r**6 + 18/5*r**5 - 33/8*r**4 - 28 + 2*r**3. Suppose h(w) = 0. Calculate w.
0, 1/3, 1
Suppose -4*d + 5 = -11. Suppose 5 = 3*s - t, -d*t + 28 = s + 3*s. Factor -3*o + o + 3*o**3 - 6*o**3 + 5*o**s.
2*o*(o - 1)*(o + 1)
Let n(w) = 3*w**3 + w**2 + 2*w - 11. Let f(k) = -5*k**3 + 5*k + 8*k**3 - 2*k - 12. Let t(m) = -5*f(m) + 6*n(m). Factor t(c).
3*(c - 1)*(c + 1)*(c + 2)
What is l in 4/3*l**2 + l**3 + 0*l**4 - 1/6*l**5 + 1/2*l + 0 = 0?
-1, 0, 3
Let s(l) be the third derivative of l**7/210 + 4*l**6/45 + 8*l**5/15 - 8*l**3/3 - 19*l**2. Let x(w) be the first derivative of s(w). Factor x(m).
4*m*(m + 4)**2
Suppose 33*d = -3*h + 28*d - 30, 2*h - d - 6 = 0. Suppose h + 2/5*y**5 - 6/5*y**4 + 6/5*y**3 + 0*y - 2/5*y**2 = 0. What is y?
0, 1
Let o(m) be the third derivative of -m**7/105 - m**6/10 - 2*m**5/15 + m**4/2 + 5*m**3/3 - 2*m**2 - 3*m. Factor o(u).
-2*(u - 1)*(u + 1)**2*(u + 5)
Suppose -13*x + 228 = -84. Let r be (2 - 1) + -2 - -3. Suppose x*y**2 + 2*y**3 - 6*y**3 + 0*y**3 - 16*y**r - 4*y = 0. What is y?
0, 1
Let f be 20/(-25) - 24/(-5). Determine d so that -4*d**3 - 32 - 29*d**2 - 5*d**5 + d**5 + 41*d**2 - 16*d**f + 16*d + 28*d**2 = 0.
-2, 1
Suppose -f + 2*f - 10 = 0. Let c(k) = k**3 - 10*k**2 - k + 12. Let p be c(f). Suppose 14*h**2 + 4 + p*h**5 + h + 3*h - 4 + 10*h**4 + 18*h**3 = 0. What is h?
-2, -1, 0
Let a(l) be the second derivative of l**4/6 + 239*l**3/3 + 238*l**2 + 109*l. What is y in a(y) = 0?
-238, -1
Factor -27 - 3/2*z**2 + 33/2*z.
-3*(z - 9)*(z - 2)/2
Let w(g) be the first derivative of g**5/90 - g**4/6 + g**3 - 3*g**2 + 15*g - 11. Let u(t) be the first derivative of w(t). Factor u(r).
2*(r - 3)**3/9
Let u be (-6)/9*(-4 - -1). Let y be ((-12)/(-27))/((-280)/(-180)). Factor -y*a**3 - 2/7 + 2/7*a**u + 2/7*a.
-2*(a - 1)**2*(a + 1)/7
Let x(m) be the third derivative of m**8/13440 - m**7/1680 + m**6/480 - 11*m**5/60 + 5*m**2. Let u(j) be the third derivative of x(j). Solve u(b) = 0 for b.
1
Let n(r) be the first derivative of 1/15*r**5 + 0*r**4 + 0*r**2 + 2*r + 9 - 2/9*r**3. Let o(v) be the first derivative of n(v). Factor o(l).
4*l*(l - 1)*(l + 1)/3
Let l(v) = 5*v**2 - 25*v - 50. Let w(i) = -i**2 + i + 1. Let y(k) = -5*l(k) - 20*w(k). Factor y(d).
-5*(d - 23)*(d + 2)
Let w(a) be the first derivative of 28*a**5/5 - 8*a**4 - 8*a**3 + 16*a**2 - 4*a - 89. Factor w(r).
4*(r - 1)**2*(r + 1)*(7*r - 1)
Determine a so that 4/9*a**3 + 2/9*a**5 + 4/9*a**2 + 2/9 - 2/3*a - 2/3*a**4 = 0.
-1, 1
Let n = -8 + 9. Let c be 3 + n + (2 - 4). Let -2*y**c - 3*y + 25*y**5 + 2*y**4 - 26*y**5 + 4*y = 0. What is y?
-1, 0, 1
Let x(q) be the second derivative of q**5/60 - q**4/9 - 11*q**3/18 - q**2 - 46*q. Solve x(l) = 0.
-1, 6
Factor 0*n + 28/15*n**3 + 2/5*n**4 + 0 - 2/3*n**2.
2*n**2*(n + 5)*(3*n - 1)/15
Let k = 3187/19134 + 1/9567. Factor 1/2*n - 1/3 - k*n**2.
-(n - 2)*(n - 1)/6
Let i(z) = -10*z**2 - 15*z + 5. Suppose 4*s + 5 = -23. Let b(l) = 15*l**2 + 23*l - 7. Let n(o) = s*i(o) - 5*b(o). Factor n(p).
-5*p*(p + 2)
Let y be 2/4*56 - -6. Suppose -42*h + y*h + 24 = 0. Determine k so that 1/3*k**2 - 1/3 + 1/3*k - 1/3*k**h = 0.
-1, 1
Let q(m) be the first derivative of m**6/14 + 6*m**5/35 - 3*m**4/28 - 2*m**3/7 + 149. What is r in q(r) = 0?
-2, -1, 0, 1
Factor -93*x**3 - x**5 - 68*x + 0*x**5 + 140*x**2 - 18*x**4 + 40*x**4.
-x*(x - 17)*(x - 2)**2*(x - 1)
Let j(m) be the third derivative of m**6/40 + 3*m**5/10 + 3*m**4/8 - 5*m**3 - 9*m**2 - 1. Determine r so that j(r) = 0.
-5, -2, 1
Suppose 4*l - 14 = -2*f, -5*l + 5*f = f - 11. Let h be (-1)/(-2) - 280/(-80) - 174/45. Solve h*v**4 + 0*v**2 - 2/15 - 4/15*v + 4/15*v**l = 0.
-1, 1
Let i = -233 - -1865/8. Factor 1/2*g + i*g**2 + 3/8.
(g + 1)*(g + 3)/8
Let o(b) = -b**3 - b**2 + b - 2. Let k(m) = m. Let t be k(-2). Let q be o(t). Factor q*p**2 + 32*p**3 + 0*p**2 - p**4 - 30*p**3.
-p**3*(p - 2)
Let u be (70/49)/10*14. Factor 8/13*q**4 + 2/13*q**u + 0 + 10/13*q**3 + 0*q.
2*q**2*(q + 1)*(4*q + 1)/13
Suppose k + 7 = 5*a - 6, -3*k = 2*a + 5. Let q be (-88)/(-12)*((-65)/(-25) + -2) + -4. Let -q + 1/5*z**a + 3/5*z**3 - 3/5*z + 1/5*z**4 = 0. What is z?
-2, -1, 1
Let a = -7 - -10. Suppose 9*c = -2*h + 4*c - 14, -c = -a*h + 13. Determine v, given that -2*v**3 + v**4 + 1 + h*v + 2*v + v**5 - 2*v - 2*v - 2*v**2 = 0.
-1, 1
Let y(w) be the third derivative of w**5/15 - w**4/3 - 244*w**2. Suppose y(o) = 0. Calculate o.
0, 2
Let p(m) = 2*m - 25. Let d be p(14). Determine n, given that n**3 + 3 - 5*n**2 + 2*n - d + 2*n**2 = 0.
0, 1, 2
Determine b, given that 5*b**4 - 2 - 63 + 30*b + 35*b**2 + 25 - 30*b**3 = 0.
-1, 1, 2, 4
Suppose -23*r = -41*r + 21*r. Factor -8/5*j**2 - 2/5*j**3 + r + 0*j.
-2*j**2*(j + 4)/5
Let w(c) be the second derivative of 2*c**6/75 - 6*c**5/25 - 8*c**4/5 - 52*c**3/15 - 18*c**2/5 - c - 161. Factor w(x).
4*(x - 9)*(x + 1)**3/5
Let u be (-651)/(-147) - (1 + (-4)/7