)*(5*u - 2)/5
Suppose 61 - 49 = 6*h. Let t(k) be the second derivative of -2/75*k**6 - 1/10*k**5 + 0 - 4*k + 1/15*k**3 + 1/5*k**h - 1/10*k**4. Factor t(n).
-2*(n + 1)**3*(2*n - 1)/5
Let g(p) be the first derivative of 0*p**3 + 0*p + 0*p**2 + 25 + 1/45*p**6 + 0*p**4 + 2/75*p**5. Factor g(v).
2*v**4*(v + 1)/15
Let a(q) be the second derivative of q**8/63 - 2*q**7/315 - 2*q**6/45 + q**5/45 - 2*q**2 + q. Let b(f) be the first derivative of a(f). Solve b(r) = 0 for r.
-1, 0, 1/4, 1
Determine r so that 48/5 + 2/5*r**4 - 2*r**3 - 4*r**2 + 8*r = 0.
-2, -1, 2, 6
Let s(z) be the first derivative of -32/39*z**3 + 12/13*z**2 + 0*z - 6 - 2/65*z**5 + 7/26*z**4. Factor s(j).
-2*j*(j - 3)*(j - 2)**2/13
Let j(x) be the third derivative of -x**6/840 - x**5/210 + 5*x**4/168 + x**3/7 - 210*x**2. Find f such that j(f) = 0.
-3, -1, 2
Let v(u) be the first derivative of 2/3*u**3 + 1/2*u**6 + 0*u**2 - 22 + 9/4*u**4 + 2*u**5 + 0*u. Factor v(k).
k**2*(k + 1)*(k + 2)*(3*k + 1)
Let d(x) = -x**3 + 3*x**2 - 9*x + 1. Suppose 4*b = b + 6. Let s(w) = w**3 - 2*w**2 + 10*w. Let i(y) = b*s(y) + 3*d(y). Factor i(r).
-(r - 3)*(r - 1)**2
Let d(v) be the second derivative of 24/5*v**5 + 0 - 2/3*v**3 - 2*v**4 - 23*v + 0*v**2 + 6/7*v**7 - 52/15*v**6. Let d(c) = 0. Calculate c.
-1/9, 0, 1
Suppose -56 = 15*y - 19*y. Factor 90*a**2 + 21 - y + 56*a + 27*a**3 + 28*a + 17.
3*(a + 2)*(3*a + 2)**2
Suppose 5*r = -4*r + 18. Factor 14*m**3 - 4*m**4 + r*m**2 + 21*m**3 + 3*m**4 - 34*m**3.
-m**2*(m - 2)*(m + 1)
Let w(z) be the third derivative of -z**7/105 + z**6/30 + 2*z**5/5 + 7*z**4/6 + 5*z**3/3 - 5*z**2 + 5. Determine u so that w(u) = 0.
-1, 5
Let l be -3*(-6)/(-162)*(-12)/17. Let c(j) be the first derivative of 1/17*j**2 - 1/17*j**4 - 2/17*j + l*j**3 + 7 - 2/85*j**5 + 1/51*j**6. Factor c(p).
2*(p - 1)**3*(p + 1)**2/17
Let n(b) = 9*b**2 - 70*b + 241. Suppose -4 = 8*t - 9*t. Let r(l) = -100*l**2 + 770*l - 2650. Let p(m) = t*r(m) + 45*n(m). Factor p(s).
5*(s - 7)**2
Let i(b) = -2*b**3 - 4*b**2 - 2*b + 1. Let m be i(-2). Factor 33*c**2 - m - 11*c + 6*c - 3*c**2.
5*(2*c - 1)*(3*c + 1)
Let l(n) be the third derivative of -1/720*n**6 + 0*n + 0 + 1/60*n**5 + 2/9*n**3 - 17*n**2 - 1/12*n**4. Factor l(t).
-(t - 2)**3/6
Let y(b) be the third derivative of 0*b**6 + 0*b - 6*b**2 + 0 + 0*b**3 - 1/70*b**5 + 1/735*b**7 - 1/42*b**4. Factor y(v).
2*v*(v - 2)*(v + 1)**2/7
Let o(m) = -m**3 + 1. Let i(h) = -11*h**3 + 6. Let s(p) = i(p) - 6*o(p). Let s(a) = 0. What is a?
0
Let 3/2*m + 1/4*m**2 + 5/4 = 0. Calculate m.
-5, -1
Let u(j) be the second derivative of -j**4/14 - j**3/7 + 6*j**2/7 + 3*j + 30. Find m, given that u(m) = 0.
-2, 1
Let f = -1 - -2. Find n such that 2*n**2 - n**5 + 17*n - f + 1 - 16*n - 2*n**4 = 0.
-1, 0, 1
Let y(z) be the first derivative of -3*z**4/5 - 4*z**3/15 + 8*z + 23. Let r(x) be the first derivative of y(x). Factor r(t).
-4*t*(9*t + 2)/5
Let w(l) be the third derivative of l**8/12096 - l**7/3024 - l**6/216 - l**5/30 + 2*l**2. Let z(q) be the third derivative of w(q). Factor z(t).
5*(t - 2)*(t + 1)/3
Let m(y) be the first derivative of 27*y**5/5 + 6*y**4 - 8*y**3 - 16*y**2 + 3*y + 3. Let g(d) be the first derivative of m(d). Factor g(n).
4*(3*n - 2)*(3*n + 2)**2
Let y(j) be the third derivative of -j**8/672 - 19*j**7/420 - 17*j**6/120 + j**5/60 + 35*j**4/48 + 17*j**3/12 - 352*j**2 - 2. Suppose y(q) = 0. Calculate q.
-17, -1, 1
Let p(k) be the first derivative of -8/5*k**5 + 4*k - 4/9*k**6 + 20 + 11/6*k**4 + 16/3*k**3 - 25/3*k**2. Find c such that p(c) = 0.
-3, -2, 1/2, 1
Let j(b) = -b**2 - 10*b + 13. Let k(o) = 2*o**2 + 20*o - 27. Let x(z) = 5*j(z) + 2*k(z). Find f such that x(f) = 0.
-11, 1
Let b(z) = 5*z**2 - z + 2. Let t(x) = 29*x**2 - 5*x + 10. Let p(l) = 34*b(l) - 6*t(l). Factor p(j).
-4*(j - 1)*(j + 2)
Factor 4/3*s**2 + 0 + 2/9*s**3 + 16/9*s.
2*s*(s + 2)*(s + 4)/9
Let w(g) be the first derivative of g**8/1470 + g**7/980 - g**6/1260 - 10*g**3/3 + 4. Let d(s) be the third derivative of w(s). Solve d(j) = 0 for j.
-1, 0, 1/4
Let l(d) = -d + 8. Let x(f) = 3*f - 24. Let y(o) = -17*l(o) - 6*x(o). Let u be y(5). Factor -19 + 6*g**2 - 2*g**u + 0*g + 2*g + 13.
-2*(g - 3)*(g - 1)*(g + 1)
Let q(h) be the first derivative of h**4/8 - h**3/3 - h**2 + 4*h + 90. Suppose q(b) = 0. What is b?
-2, 2
Let b = 50 - 45. Find s such that 5 + 15 + 6*s - 6 - b - 3*s**2 = 0.
-1, 3
Let d(w) be the first derivative of 2*w**3/3 - 9*w**2 - 20*w - 84. Factor d(x).
2*(x - 10)*(x + 1)
Let t(r) be the second derivative of r**4/6 + 14*r**3 + 152*r**2 + 165*r. Let t(a) = 0. What is a?
-38, -4
Let d be ((-264)/(-60) - 12) + 1 + 7. Factor -2/5 + d*y**2 + 0*y.
2*(y - 1)*(y + 1)/5
Let y = 23 - 20. Suppose 0 = -y*n - 2*x + 2, 5*x = x + 4. Let 0 + n*o**2 - 1/2*o + 0*o**4 + o**3 - 1/2*o**5 = 0. Calculate o.
-1, 0, 1
Factor 242/15 - 8/15*u**3 + 178/15*u**2 - 1012/15*u.
-2*(u - 11)**2*(4*u - 1)/15
Let m be 1 - 1 - (2 - 2). Factor -10*z + m*z**2 + z**2 + 9*z + 0*z**2.
z*(z - 1)
Let f(z) = -5*z**3 + 38*z**2 - 20*z - 4. Let p(t) = 37*t**2 - 20*t - 6. Let g(a) = -3*f(a) + 2*p(a). Factor g(u).
5*u*(u - 2)*(3*u - 2)
Let y be 12/24*(-24)/(-90). Suppose 2/15*v - y*v**3 - 2/15*v**2 + 2/15 = 0. Calculate v.
-1, 1
Let -20*p**3 - 34*p**3 + 11*p**3 - 30*p**2 + 1 + 18*p - 7*p**3 - 3 = 0. What is p?
-1, 1/5
Let m(a) be the third derivative of a**8/60480 + a**7/15120 - 7*a**5/30 - 7*a**2. Let y(s) be the third derivative of m(s). Factor y(q).
q*(q + 1)/3
Let m = 493 + -492. Let f(s) be the first derivative of 0*s + 0*s**2 - 1/3*s**3 + 1/5*s**5 + m + 0*s**4. Suppose f(d) = 0. Calculate d.
-1, 0, 1
Let s(d) be the second derivative of d**4/4 - 9*d**3 - 189*d**2/2 + 6*d + 38. Determine p so that s(p) = 0.
-3, 21
Let n = -11 - -14. Factor 4*f**3 + 5*f**2 + 5*f + 5*f**2 + f**n.
5*f*(f + 1)**2
Suppose 3*b + 3*y - 5*y - 46 = 0, 0 = -4*b - 3*y + 50. Let x be 110/b + -2 + -10 + 5. Solve 3/7*i**4 + 3/7*i**5 - 6/7*i**2 + 3/7 + 3/7*i - x*i**3 = 0 for i.
-1, 1
Solve -5*d**5 + 12*d**4 - 37*d**4 + 17*d**4 + 15*d**2 + 25*d**3 + 13*d**4 = 0.
-1, 0, 3
Let o(m) be the third derivative of m**6/30 - m**5/10 - m**4/6 + m**3 - 3*m**2 - 22. Factor o(f).
2*(f - 1)*(f + 1)*(2*f - 3)
Factor 190*q**2 + 150*q + 105 - 185*q**2 + 12 + 28.
5*(q + 1)*(q + 29)
Let f(h) = 13*h + 24. Let d be f(8). Let i = d + -126. Factor 2/3*z**i + 0 - z + 1/3*z**3.
z*(z - 1)*(z + 3)/3
Let i(n) be the second derivative of -n**4/24 + 5*n**3/12 - n**2 + 4*n + 16. Factor i(o).
-(o - 4)*(o - 1)/2
Suppose 2 = 2*q - 5*c - 3, -4 = -3*q + 4*c. Let l(h) be the third derivative of q + 0*h**3 + 2/15*h**5 + 2*h**2 - 1/8*h**4 + 0*h + 1/40*h**6. Factor l(w).
w*(w + 3)*(3*w - 1)
Let y be (-132)/(-90) + ((-48)/10)/6. Factor 2/9*i**3 + 0*i**2 - y*i + 4/9.
2*(i - 1)**2*(i + 2)/9
Let h = 11 - 19. Let v = -5 - h. Solve 3*m**v - m**2 + 3*m + 3*m**2 - 4*m = 0.
-1, 0, 1/3
Let g be (4 + -13)*5/5. Let l(v) = -12*v**2 - 9*v - 6. Let y(x) = -x**2. Let n(j) = g*y(j) + l(j). What is c in n(c) = 0?
-2, -1
Let y be (1/(-10) - 19/(-38))*6. Factor 1/5*z**2 + y*z + 36/5.
(z + 6)**2/5
Let k(o) = -4*o**2 + 70*o - 33. Let i be k(17). Let l(b) be the first derivative of -i - 4/5*b + 2/15*b**3 + 1/5*b**2. Solve l(s) = 0.
-2, 1
Let b = 707/85 - 163/85. Factor -4/5*n**3 - 84/5*n - 72/5 - b*n**2.
-4*(n + 2)*(n + 3)**2/5
Let u(f) = f**2 - 16*f + 17. Let c be u(15). Suppose 10*k - 31 = -11. Determine z so that 4 - 6*z**2 + z**k + 0*z**2 + 2*z + z**2 - c*z**3 = 0.
-2, -1, 1
Let j be ((1 - -2) + -5)/(4/(-6)). Factor 3*i - 8*i - 2*i**2 + j*i + 6*i.
-2*i*(i - 2)
Let f(l) = -l**3 - 8*l**2 + l - 4. Let g = 1 + -6. Let u(t) = -t**3 - 7*t**2 + t - 3. Suppose 5*d + 3 = 33. Let n(o) = d*u(o) + g*f(o). Factor n(z).
-(z - 1)*(z + 1)*(z + 2)
Let u(y) be the third derivative of y**8/112 - 8*y**7/35 + 7*y**6/20 + 4*y**5/5 - 15*y**4/8 + 36*y**2 - 3*y. Let u(d) = 0. Calculate d.
-1, 0, 1, 15
Let b be (-6)/9*(-7 + 4). Factor 2*m**2 - b*m + 45 - 13 - 8*m - 6*m.
2*(m - 4)**2
Let z(c) be the third derivative of -c**5/180 - 5*c**4/72 + c**3/3 - 28*c**2. Let z(h) = 0. What is h?
-6, 1
Let p(i) be the third derivative of i**7/42 + i**6/24 - 3*i**2 - 5*i. Factor p(u).
5*u**3*(u + 1)
Let c = 44 + -70. Let x = -24 - c. Factor -6/11*u**x + 2/11*u**3 - 2/11 + 6/11*u.
2*(u - 1)**3/11
Suppose -5*d + 406 + 519 = 0. Let r = 189 - d. Factor -1/9*g**r + 0 + 1/9*g**2