 - k - 1. Let n be o(0). Let p(r) = n*j(r) + 6*l(r). Find q such that p(q) = 0.
2
Let v be (72/300)/((-2)/(-15)). Factor v*g**2 + 27/5*g - 12/5*g**3 + 6/5.
-3*(g - 2)*(g + 1)*(4*g + 1)/5
Let t be -2 + 0 + 305/150. Let u(v) be the second derivative of 0*v**3 + 1/18*v**4 + 1/63*v**7 - 1/45*v**6 + 0*v**2 + 0 + v - t*v**5. Factor u(o).
2*o**2*(o - 1)**2*(o + 1)/3
Let s(i) = -135*i**2 - 325*i - 80. Let m(r) = 5*r**2 + 12*r + 3. Let n(h) = 55*m(h) + 2*s(h). Determine p, given that n(p) = 0.
-1
Let g(y) be the second derivative of y**8/6720 + y**7/1680 + y**6/1440 + y**3/3 - 2*y. Let w(v) be the second derivative of g(v). Find x, given that w(x) = 0.
-1, 0
Let u be (-3 - (-6)/(-3))/((-3)/3). Let w(h) be the first derivative of 0*h**3 + 0*h + 0*h**2 + 7/9*h**6 - 2 + 1/3*h**4 + 6/5*h**u. Factor w(d).
2*d**3*(d + 1)*(7*d + 2)/3
Let y(c) = c**2 - 5*c + 4. Let d be y(4). Solve -2/5*g**2 + 4/5*g - 2/5*g**3 + d = 0 for g.
-2, 0, 1
Let q(z) be the first derivative of -8 + 0*z + 3/10*z**2 + 1/15*z**3. Let q(s) = 0. What is s?
-3, 0
Let m(y) = -2*y**2 + 14*y - 23. Let z be m(4). Let h(t) be the first derivative of -4/3*t**3 + 0*t - 9/2*t**4 + 0*t**2 - 4*t**5 - z. Factor h(c).
-2*c**2*(2*c + 1)*(5*c + 2)
Let g be 2/7 + 386/(-1400). Let w(y) be the third derivative of -1/60*y**4 - 2/15*y**3 + g*y**6 + 0 + 2/75*y**5 + 0*y - y**2. Factor w(f).
2*(f + 1)**2*(3*f - 2)/5
Let d = 1/43 - -75/473. Suppose 2/11*o**2 + 2/11*o**3 + 0 - d*o**5 - 2/11*o**4 + 0*o = 0. Calculate o.
-1, 0, 1
Let t be 10/55 + 156/110 + -1. What is r in -t*r + 3/5*r**2 + 1/5 - 1/5*r**3 = 0?
1
Let t(q) be the second derivative of q**8/840 + q**7/420 - q**6/180 - q**5/60 + 7*q**3/6 - 7*q. Let j(d) be the second derivative of t(d). Solve j(o) = 0 for o.
-1, 0, 1
Determine j, given that -27*j + 2*j**2 + j**4 + 3*j - 6*j**2 + 18 + j**4 + 8*j**3 = 0.
-3, 1
Let n be (-8)/(-16) + (-3)/6. Let d(h) be the first derivative of -1/9*h**6 + 0*h**3 + n*h**2 + 0*h - 4/45*h**5 + 3 + 1/18*h**4. Find j, given that d(j) = 0.
-1, 0, 1/3
Let k(n) be the third derivative of n**5/150 - n**4/20 + 2*n**3/15 + 25*n**2. Factor k(v).
2*(v - 2)*(v - 1)/5
Let m be (-5)/(-90) - (-4)/9. Find o such that -1/2*o + m*o**3 - 1/2*o**4 + 0 + 1/2*o**2 = 0.
-1, 0, 1
Let c = -2 - -3. Let z(n) be the first derivative of -1/20*n**5 - 1/2*n**2 - 1/2*n**3 - 1/4*n - c - 1/4*n**4. Factor z(v).
-(v + 1)**4/4
Suppose -13*d = -20*d. Factor -8/9*m + 2/9*m**4 + 2/3*m**3 + 0 + d*m**2.
2*m*(m - 1)*(m + 2)**2/9
Let q(a) be the third derivative of a**5/24 - 25*a**4/48 + 4*a**2. Let q(v) = 0. Calculate v.
0, 5
Suppose -1 = 12*q - 37. Let g(o) be the first derivative of -2/25*o**5 - 2/15*o**q + 0*o**2 + 1/5*o**4 + 0*o + 3. Determine t so that g(t) = 0.
0, 1
Let q(u) = -u**2 + 5*u - 1. Let o be q(4). Let r = 53 - 50. Determine s, given that -2*s**2 + s**3 - 3*s**o + s**r + 3*s**3 = 0.
0, 1
Let c be (-12)/(-60) + 2/10. Factor 0*o + c*o**3 - 8/5 + 6/5*o**2.
2*(o - 1)*(o + 2)**2/5
Let l(d) be the second derivative of 0*d**3 + 1/10*d**5 + 1/63*d**7 - 4*d + 0 + 0*d**2 - 1/18*d**4 - 1/15*d**6. Factor l(z).
2*z**2*(z - 1)**3/3
Factor 0 - 1/5*n**4 - 3/5*n + n**2 - 1/5*n**3.
-n*(n - 1)**2*(n + 3)/5
Factor -19 + 0*s**2 + 3*s + 21 + s**2.
(s + 1)*(s + 2)
Let c(d) be the third derivative of -d**6/120 - d**5/20 + 5*d**2. What is u in c(u) = 0?
-3, 0
Let x(s) be the third derivative of s**5/60 - s**3/6 - 6*s**2. Solve x(z) = 0 for z.
-1, 1
Let s(q) be the third derivative of -q**8/10080 + q**7/420 - q**6/40 + q**5/20 - q**2. Let t(a) be the third derivative of s(a). Factor t(b).
-2*(b - 3)**2
Factor -24/7*n**2 - 12/7*n**4 - 8/7*n - 26/7*n**3 - 2/7*n**5 + 0.
-2*n*(n + 1)**2*(n + 2)**2/7
Let s(c) be the second derivative of 3*c**5/140 - c**4/21 - c**3/42 + c**2/7 + 19*c. What is v in s(v) = 0?
-2/3, 1
Factor -10/7 - 8/7*i + 2/7*i**2.
2*(i - 5)*(i + 1)/7
Let q(y) be the first derivative of -2*y**3/9 + y**2/3 + 7. Let q(z) = 0. Calculate z.
0, 1
Suppose -2*k + 4*h = 2*k + 8, -3*k + h - 6 = 0. Let m be k/7 - 69/(-21). Factor w**3 + 5*w**2 - 2*w**5 + w**m - 2*w**4 - 3*w**2.
-2*w**2*(w - 1)*(w + 1)**2
Factor x**5 + 0*x + 5/2*x**3 + 11/4*x**4 + 0 + 3/4*x**2.
x**2*(x + 1)**2*(4*x + 3)/4
Factor 8/7*o + 2/7*o**3 + 0 - 8/7*o**2.
2*o*(o - 2)**2/7
Let u(f) = 3*f**2 - 2*f + 2. Suppose -5*b - 5*x = 5, b - 5*x + 40 = -3*b. Let q(y) = 7*y**2 - 4*y + 5. Let d(g) = b*u(g) + 2*q(g). Factor d(w).
-w*(w - 2)
Let z be ((-30)/(-8) + -3)*4/162. Let f(g) be the second derivative of 0 + 2/9*g**3 + g**2 + z*g**4 - 3*g. Factor f(x).
2*(x + 3)**2/9
Let g(p) be the third derivative of -p**8/2520 + p**7/1575 + p**6/900 - p**5/450 - 3*p**2. Solve g(b) = 0.
-1, 0, 1
Let w(f) = 14*f**2 - 6*f - 44. Let s(i) = -5*i**2 + 2*i + 15. Let o(h) = 8*s(h) + 3*w(h). Factor o(a).
2*(a - 3)*(a + 2)
Solve -3/2 + 6*i - 6*i**2 = 0 for i.
1/2
Let l(r) = -11*r**3 + 3*r**2 + 23*r + 1. Let m(s) = 7*s**3 - 2*s**2 - 15*s - 1. Let y(d) = -5*l(d) - 8*m(d). Factor y(z).
-(z - 3)*(z + 1)**2
Suppose -2*k + 1 + 3 = 0. Let b be ((-2)/4)/((-2)/8). Determine t, given that -2*t**k + 8*t**2 - b*t + 3*t**2 = 0.
0, 2/9
Let p(z) be the first derivative of -8/15*z**3 - 98/25*z**5 + 0*z**2 + 0*z - 14/5*z**4 - 6. Factor p(h).
-2*h**2*(7*h + 2)**2/5
Let z(b) = -b**2 + 6*b + 7. Suppose -4*f + 25 = f. Let t(x) = -x**2 + 5*x + 6. Let h(d) = f*z(d) - 6*t(d). Let h(n) = 0. What is n?
-1, 1
Let h(p) be the third derivative of p**10/604800 - p**8/40320 + p**6/2880 - p**5/10 - 3*p**2. Let x(a) be the third derivative of h(a). Factor x(z).
(z - 1)**2*(z + 1)**2/4
Suppose 3 - 9 - 30*r - 19 - 5*r**2 = 0. What is r?
-5, -1
Let w(x) be the second derivative of 3*x + 1/42*x**7 - 1/3*x**4 + 0*x**2 + 1/6*x**3 + 0 + 3/10*x**5 - 2/15*x**6. Factor w(t).
t*(t - 1)**4
Let k = 10 - 43. Let t = k + 35. Factor -b**t - 5/4*b - 1/2 - 1/4*b**3.
-(b + 1)**2*(b + 2)/4
Determine z so that -24*z + 96 + 3/2*z**2 = 0.
8
Factor -8*a + 0*a**3 + 2*a - 2 + 2*a**3 - 2.
2*(a - 2)*(a + 1)**2
Let k(t) = 4*t**3 - 6*t**2 - 4*t + 4. Let i be k(2). Factor 1/3*q**5 - 4/3*q**i - 5/3*q + 4/3*q**3 + 2/3 + 2/3*q**2.
(q - 2)*(q - 1)**3*(q + 1)/3
Factor 78*x - 507 + 4*x**2 - 9*x**2 + 2*x**2.
-3*(x - 13)**2
Let x be -1*(-2)/(-2) - -3. Let c(s) = 10*s**2 + 3*s + 1. Let g(f) = -4*f + 3*f**2 + 0*f + 2*f + 3*f. Let u(z) = x*c(z) - 7*g(z). Factor u(k).
-(k - 1)*(k + 2)
Let l(q) = -q**3 + 7*q**2 + 8*q + 4. Let i be l(8). Suppose i*h = h. Factor -2/7*s**3 + 0*s + 0 + h*s**2 + 2/7*s**4.
2*s**3*(s - 1)/7
Suppose -2*z - 8/3*z**2 - 2/3*z**3 + 0 = 0. What is z?
-3, -1, 0
Let w(c) be the first derivative of -c**5/20 - c**4/8 + c**3 - 2*c**2 - 8. Let j(h) be the second derivative of w(h). What is o in j(o) = 0?
-2, 1
Let z(g) be the third derivative of -g**5/10 - 5*g**4/21 - 4*g**3/21 + 4*g**2. Let z(n) = 0. Calculate n.
-2/3, -2/7
Let i(d) = -2*d**2 - 24*d + 72. Let u(g) = 3*g**2 + 48*g - 144. Let r(o) = 7*i(o) + 4*u(o). Factor r(v).
-2*(v - 6)**2
Factor 4*c - 8 - 1/2*c**2.
-(c - 4)**2/2
Factor -8 - u - 6*u + 3*u + 8*u**2 - 8*u.
4*(u - 2)*(2*u + 1)
Let w = -8 - -17. Factor -5*c + 7*c + 10*c + w + 3*c**2.
3*(c + 1)*(c + 3)
Let z(l) = -4*l**5 - 2*l**4 + 2*l**3 + 13*l**2 + 7*l - 1. Let t(m) = -4*m**5 - 3*m**4 + 2*m**3 + 12*m**2 + 6*m - 1. Let x(a) = -5*t(a) + 4*z(a). Solve x(h) = 0.
-1, 1/4, 1
Let h = 624 + -622. Factor h*q**2 + 2/7*q**4 - 10/7*q**3 + 0 - 6/7*q.
2*q*(q - 3)*(q - 1)**2/7
Let m(q) = -q**3 + 6*q**2 - 4*q - 1. Let t be m(5). Let l(r) be the second derivative of 0 - 2*r - 1/21*r**t - 3/70*r**5 + 0*r**2 + 0*r**3. Factor l(x).
-2*x**2*(3*x + 2)/7
Solve -3/7*t**3 + 0 - 1/7*t**2 + 0*t = 0 for t.
-1/3, 0
Let i be 2/(-7) - 18/(-21). Suppose -3*p - 6 = 0, 4*v - 4*p + 0 = 28. Suppose -2/7*a + 2/7*a**4 + i*a**3 + 2/7 - 4/7*a**2 - 2/7*a**v = 0. Calculate a.
-1, 1
Let m(s) = -3*s - 2. Let z be m(-2). Let g(i) be the third derivative of 0*i**3 + 0*i - 1/150*i**5 + 1/60*i**z - 2*i**2 + 0. Let g(b) = 0. Calculate b.
0, 1
Determine m, given that 40*m**3 - 8*m**5 + 8*m**2 + 22*m**5 + 70*m**4 - 24*m**4 = 0.
-2, -1, -2/7, 0
Suppose -3*s + 17 = -1. Let r(i) be the first derivative of -2 - 1/20*i**5 - 1/4*i + 1/6*i**3 + 1/8*i**2 - 1/8*i**4 + 1/24*i**s. Factor r(w).
(w - 1)**3*(w + 1)**2/4
Let d(s) be the third derivative of -s**5/30 + s**4/4 - 2*s**2. Determine o so that d(o) = 0.
0, 3
Determine r, given that -70*