(k). Factor o(i).
4*(i - 1)**2
Let x be 17/(-17)*(-1)/32. Let m(y) be the third derivative of x*y**4 + 0 + 0*y**5 - 1/480*y**6 - 1/12*y**3 + y**2 + 0*y. What is l in m(l) = 0?
-2, 1
Let y(n) be the second derivative of 0*n**3 - 1/14*n**7 + 0*n**5 - 3*n - 1/10*n**6 + 0*n**4 + 0*n**2 + 0. Determine i, given that y(i) = 0.
-1, 0
Let k(s) = -6*s**3 - s**2 + 16*s + 7. Let r(p) = -p**3 - p**2 + p + 1. Let n(z) = -5*k(z) + 35*r(z). Factor n(l).
-5*l*(l + 3)**2
Let x(h) be the first derivative of -h**3/8 + 27*h**2/8 - 243*h/8 - 26. Factor x(o).
-3*(o - 9)**2/8
Let a = -138 + 974/7. Find h such that -2/7*h**2 - 8/7 + a*h = 0.
2
Let w = -50279/60 + 838. Let i(q) be the third derivative of 0*q**4 + 0*q**3 - q**2 - w*q**5 + 0*q + 0. What is o in i(o) = 0?
0
Let l(q) be the third derivative of -q**6/660 + q**5/330 + 18*q**2. Factor l(z).
-2*z**2*(z - 1)/11
Let h = 17 + -8. Let k be 3/h*6 - -1. Factor 0 - 2/3*f**2 - 5/3*f**k + 7/3*f**4 + 0*f.
f**2*(f - 1)*(7*f + 2)/3
Let 1/4 - 1/4*y**2 - 1/4*y + 1/4*y**3 = 0. Calculate y.
-1, 1
Let n(f) = f**2 - 7*f + 3. Suppose 3*m - 12 - 9 = 0. Let k be n(m). Find i, given that -2*i**5 - 4*i**k + 2*i**5 + 2*i**4 + 2*i**5 = 0.
-2, 0, 1
Factor 0*u + 10/3*u**3 + 0 + 8/3*u**4 + 2/3*u**5 + 4/3*u**2.
2*u**2*(u + 1)**2*(u + 2)/3
Let o(p) = -p**3 - 8*p**2 + 18*p + 4. Let d(c) = 6*c**3 + 40*c**2 - 91*c - 22. Let t(r) = -6*d(r) - 33*o(r). Factor t(y).
-3*y*(y - 4)**2
Let k(d) be the second derivative of d**4/18 - d**3/9 - 2*d**2/3 + 17*d. Solve k(c) = 0.
-1, 2
Let f = 462 + -1297/3. Let q = 30 - f. Solve q*u**5 + 0*u**2 + 0 + 0*u - 1/3*u**4 + 0*u**3 = 0.
0, 1
Suppose 69 = 5*o + 19. Let w = o - 7. Find t, given that 0 + 0*t - 2/9*t**w + 2/9*t**4 + 0*t**2 = 0.
0, 1
Suppose 4*c = -2*s + 8, 3*s - 5 = 3*c - 2. Find n, given that -14*n**s - 22*n**2 - 3 - 30*n + 11*n**2 - 6 = 0.
-3/5
Let l(s) be the second derivative of s**4/24 + s**3/6 - 3*s**2/4 - 48*s. Factor l(h).
(h - 1)*(h + 3)/2
Let n(h) be the second derivative of 0*h**2 + 0*h**4 + h + 1/120*h**5 + 0 + 1/360*h**6 - 1/2*h**3. Let w(j) be the second derivative of n(j). Solve w(l) = 0.
-1, 0
Suppose 4*u = 8*u - 12. Factor 2/9*i**4 - 2/9*i**2 + 0 - 2/9*i + 2/9*i**u.
2*i*(i - 1)*(i + 1)**2/9
Factor 12*m**3 - 25*m + 16*m**4 + m**5 + 4*m**3 - 8*m**2 + 3*m**5 - 8 + 5*m.
4*(m - 1)*(m + 1)**3*(m + 2)
Let p be (-10)/(-25)*65/8 - 3. Solve p*g**2 - 1/4*g**4 + 0*g**3 + 0 + 0*g = 0 for g.
-1, 0, 1
Let h = 75 - 74. Let c(t) be the first derivative of 0*t**2 + 0*t - h - 1/3*t**3. Factor c(f).
-f**2
Factor -44*r**2 - 49*r**3 - 10*r - 20*r**5 - 42*r**3 - 68*r**4 + 2*r + 7*r**3.
-4*r*(r + 1)**3*(5*r + 2)
Suppose -6*q - 6 = -24. Suppose 2*i + 10 = v, 0*i + 4*i + 24 = 3*v. Let 0*o**4 + 3*o**4 - o**v + 0*o**3 + 4*o**5 - 4*o**q - 2*o**2 = 0. What is o?
-1, -1/2, 0, 1
Let q be 2/(-14) + 39*20/168. Determine u, given that -3*u + q + 1/2*u**2 = 0.
3
Suppose -8 + 4*d + 3*d**2 - 3*d**2 - 4*d**2 - 16*d = 0. Calculate d.
-2, -1
Let t(x) = 5*x**4 + 6*x**3 - 15*x**2 - 4*x + 10. Let p(k) = k**3 + k. Let s(c) = p(c) - t(c). Factor s(o).
-5*(o - 1)**2*(o + 1)*(o + 2)
Let w(p) = -10*p**2 + 8*p + 16. Let d(n) = -72 - 1 + 40*n**2 + 10 - 33*n + n**3. Let s(r) = -2*d(r) - 9*w(r). Factor s(u).
-2*(u - 3)**2*(u + 1)
Let u(b) = -2*b**3 + 2*b**2 + 17*b - 23. Let f(c) = -5*c**3 + 5*c**2 + 35*c - 45. Let l(q) = -3*f(q) + 5*u(q). Factor l(x).
5*(x - 2)*(x - 1)*(x + 2)
Suppose 3*r = -2*f + 46, 6*f + 66 = 3*r + 3*f. Let o be 7/3 - (-12)/r. Let 5/4*l**4 + 3/4*l**o + 0*l + 0 - 1/2*l**2 = 0. What is l?
-1, 0, 2/5
Factor 3*i**2 + 4*i - 2*i + i**2 + 2*i.
4*i*(i + 1)
Suppose l = v + 1, 16 = -4*l + 3*v - 4*v. Let b = 7 + l. Solve 0*g**4 - 6*g**3 - 7*g**b - 3*g**3 - 2*g**2 = 0 for g.
-1, -2/7, 0
Let a = -8 + 10. Solve 6*h**2 - 3*h**3 - a - h + 6*h**3 - 2*h**2 = 0 for h.
-1, 2/3
Let k(r) be the third derivative of -r**10/30240 - r**9/15120 + 5*r**4/24 - 5*r**2. Let a(c) be the second derivative of k(c). Factor a(t).
-t**4*(t + 1)
Let f(j) be the second derivative of j**10/60480 + j**9/30240 - j**8/13440 - j**7/5040 - j**4/12 - 4*j. Let w(h) be the third derivative of f(h). Factor w(n).
n**2*(n - 1)*(n + 1)**2/2
Let r(b) = b**4 - 8*b**2 - 14. Let u(l) = 2*l**4 - 16*l**2 - 29. Let t(g) = -9*r(g) + 4*u(g). Let w(p) be the first derivative of t(p). Factor w(z).
-4*z*(z - 2)*(z + 2)
Suppose 5/8*o - 3/4 - 1/8*o**2 = 0. What is o?
2, 3
Let i be (-14)/63 + (-382)/(-18). Let m be (-14)/i*(-6)/10. Factor -2/5 + 0*c + m*c**2.
2*(c - 1)*(c + 1)/5
Let t = -10 + 10. Let q(b) = b + 25. Let l be q(-23). Factor -2/7*z - 2/7*z**l + t.
-2*z*(z + 1)/7
Let h(a) be the first derivative of -a**6/120 - 4*a**3/3 + 4. Let x(n) be the third derivative of h(n). Find v such that x(v) = 0.
0
Suppose -2*l + 3*v = 3*l - 35, 3*v + 31 = 4*l. Suppose 0*x**l - 1 - x**4 + 2*x**2 + x**2 - x**2 = 0. What is x?
-1, 1
Let k(r) = -r**5 - r**4 - r**2 + 1. Let w(v) = -4*v**5 - 4*v**4 - 5*v**3 - 6*v**2 + 8*v + 1. Let o(a) = 5*k(a) - w(a). Factor o(h).
-(h - 1)**3*(h + 2)**2
Let d(z) be the first derivative of z**3/8 - 9*z**2/16 - 16. Factor d(a).
3*a*(a - 3)/8
Let m = 4 - 8. Let r be (m/6)/((-5)/30). Factor a + 0*a**2 - 2*a**2 - 1 + a**r - 2*a**3 + a**5 + 2.
(a - 1)**2*(a + 1)**3
Suppose -16 = 3*s - 7*s. Let i(x) = -x**3 + 4*x**2 + 2*x - 5. Let o be i(s). Factor a**o - 2*a**5 + 5*a**3 - 4*a**3.
-2*a**3*(a - 1)*(a + 1)
Factor -2/9*z**2 - 4/3*z - 2.
-2*(z + 3)**2/9
Determine r so that 261*r + 250*r - 535*r - 4*r**2 = 0.
-6, 0
Let q(k) be the first derivative of k**3/6 - k**2/4 + 1. Suppose q(y) = 0. What is y?
0, 1
Let l(v) be the first derivative of v**3/3 + 11*v**2/2 + 14*v + 6. Let w be l(-10). Let 0*p + 2/7*p**2 + 0*p**3 - 2/7*p**w + 0 = 0. Calculate p.
-1, 0, 1
Let g(p) = -2*p + 1. Let m(y) = -3*y**2 + 48*y - 114. Let f(z) = -6*g(z) - m(z). Factor f(t).
3*(t - 6)**2
Let g be 0/((-12)/(-4) - 1). Determine b, given that g*b - 2/7*b**2 - 2/7*b**3 + 0 = 0.
-1, 0
Suppose -4 = 3*y - 5*y. Let -60*v**4 - 20*v**y + 0*v**2 + 50*v**5 + 4*v**2 - 86*v**3 + 14*v**3 = 0. Calculate v.
-2/5, 0, 2
Let p be 288 - (-1 - (-3 - 1)). Let j be 76/p*(-5)/(-2). Factor -2/3*z**3 - j*z + 0 + 4/3*z**2.
-2*z*(z - 1)**2/3
Suppose -2*m - 14 = -5*p - m, 5*m + 10 = -5*p. Let w(s) be the second derivative of 0 + 0*s**4 + 0*s**2 + 1/27*s**3 + p*s - 1/90*s**5. Factor w(t).
-2*t*(t - 1)*(t + 1)/9
Let q(m) be the first derivative of 5*m**6/48 - m**5/5 - m**4/8 + 5*m**3/12 - m**2/16 - m/4 - 1. Factor q(j).
(j - 1)**3*(j + 1)*(5*j + 2)/8
Let s(d) = -3*d**3 + 24*d**2 + 3*d. Let q(a) = -3*a**3 + 25*a**2 + 2*a. Let v(h) = -3*q(h) + 2*s(h). Factor v(n).
3*n**2*(n - 9)
Let i(j) be the third derivative of j**6/30 - 4*j**5/15 - j**4/2 + 12*j**3 + 3*j**2. What is v in i(v) = 0?
-2, 3
Let h = -108 - -110. Factor 3*r**3 + 3/5*r**5 - 6/5*r**h - 12/5*r**4 + 0*r + 0.
3*r**2*(r - 2)*(r - 1)**2/5
Let i(a) = -a**2 + 14*a - 15. Let z be i(12). Let q be (0 + 3)/z*21. Factor -q*p**3 + p - 3*p + 16*p**2 - 2*p.
-p*(p - 2)*(7*p - 2)
Let z(m) be the first derivative of 1/10*m**2 - 6 - 17/15*m**3 + 7/10*m**4 + 2/5*m. Factor z(o).
(o - 1)*(2*o - 1)*(7*o + 2)/5
Suppose -5*a - 1 = -26. Determine n so that 0*n + 1/3*n**2 + 1/3*n**a + 0 + n**3 + n**4 = 0.
-1, 0
Let i be 1 + 4 + 0 + -2. Let m(f) = 3*f**4 + 3*f. Let q(r) = -r**5 - r**4 - r**3 + r. Let x(n) = i*q(n) - m(n). Solve x(u) = 0.
-1, 0
Let j(m) = -m + 2. Let o(c) = c - 1. Let w(p) = 4*j(p) + 5*o(p). Let y be w(1). Factor 0 - 2/9*u**5 + 2/9*u + 4/9*u**2 + 0*u**3 - 4/9*u**y.
-2*u*(u - 1)*(u + 1)**3/9
Let x(v) be the second derivative of 4/51*v**3 + 1/170*v**5 + 0 + 0*v**2 + 8*v - 2/51*v**4. Find s such that x(s) = 0.
0, 2
Suppose -3*n + 8*n - 10 = 0. Suppose 2*u - 1 = -4*t + 11, -4*u + 4*t = 0. Factor -3 - v**u + n*v + 0*v - 1 + 3.
-(v - 1)**2
Let p(d) = d**2 + 2*d + 2. Let a(g) = -5*g**2 - 9*g - 9. Let s(b) = -2*a(b) - 11*p(b). Solve s(l) = 0.
-2
Suppose d + y - 7 = 0, d = -d + 4*y - 10. Factor 59*a - d + 3*a**2 - 59*a.
3*(a - 1)*(a + 1)
Solve 32 + 17*o + 0*o + 6*o - 2*o**2 + 7*o = 0.
-1, 16
Let p = 84 + -2519/30. Let n(c) be the second derivative of p*c**4 + 0 + 1/5*c**2 + 2/15*c**3 + c. What is v in n(v) = 0?
-1
Let b be (-44)/(-8) + (-1)/2. Let z(m) be the second derivative of 2*m - 3/10*m**b + 1/15*m**6 + 1/2*m**4 - 1/3*m**3 + 0*m**2 + 0. Let z(q) = 0. What is q?
0, 1
Let w(q) be the