- 6. Let x(v) be the first derivative of s(v). Solve x(g) = 0 for g.
2
Let f be 6 + 0 + -2 - 8/2. Let y(l) be the second derivative of -8/7*l**2 + 4/21*l**3 - l + f - 1/84*l**4. Factor y(d).
-(d - 4)**2/7
Let 0*u**2 - 2/9*u**5 + 4/9*u**3 + 0 + 0*u**4 - 2/9*u = 0. What is u?
-1, 0, 1
Let j(q) be the third derivative of -q**8/168 - q**7/35 - q**6/20 - q**5/30 - 13*q**2. Factor j(n).
-2*n**2*(n + 1)**3
Find v, given that -72 - 123*v**2 - 24*v**2 - 19*v**2 - 28*v**2 + 332*v + 16*v**3 + 14*v**2 = 0.
1/4, 2, 9
Let n(w) be the second derivative of -2*w**6/15 - w**5/5 + w**4/3 + 2*w**3/3 - 3*w - 15. Solve n(q) = 0 for q.
-1, 0, 1
Let s(k) be the first derivative of -k**6/2 + 21*k**5/5 - 33*k**4/4 - 7*k**3 + 18*k**2 - 588. Solve s(v) = 0.
-1, 0, 1, 3, 4
Let k = -1039 + 1039. Let f(a) be the third derivative of 1/54*a**4 + 2/27*a**3 + 0*a + 1/540*a**5 + k + 7*a**2. Factor f(g).
(g + 2)**2/9
Let q be 8/132 + 30/45. Suppose q*r**2 + 0 - 16/11*r - 2/11*r**4 + 4/11*r**3 = 0. Calculate r.
-2, 0, 2
Let z(l) = -6*l**4 + 111*l**3 - 183*l**2 - 15*l. Let c(k) = k**4 - 16*k**3 + 26*k**2 + 2*k. Let q(m) = -15*c(m) - 2*z(m). Suppose q(v) = 0. Calculate v.
0, 2, 4
Suppose 0 = -3*o - 4*n - 195 + 204, 3*o + 5*n - 9 = 0. Factor -1/2*r**o - 1/2 - 3/2*r**2 - 3/2*r.
-(r + 1)**3/2
Let j be (135/25 - 5) + 26/10. Let k be 6/2 + (j + 0)*-1. Factor 3/4*l**2 + 0*l + k - 3/4*l**3.
-3*l**2*(l - 1)/4
Suppose 34*z - 36*z + 6 = 0. Let n(x) be the third derivative of 0 - x**2 + 1/24*x**4 + 0*x**z - 1/60*x**5 + 0*x. Let n(r) = 0. Calculate r.
0, 1
Let m(u) = -2*u**4 - 9*u**3 - 2*u**2 - 6*u - 1. Let x(l) = -l**4 - 4*l**3 - 2*l - 1. Let b(n) = 6*m(n) - 15*x(n). Factor b(w).
3*(w - 1)**2*(w + 1)*(w + 3)
Factor 16/3*q + 2/3*q**2 + 8.
2*(q + 2)*(q + 6)/3
Let h(x) = x**2 - 10*x - 14. Let m be h(12). Factor -7*n - m*n**2 + 19*n - 5*n**3 - 17*n.
-5*n*(n + 1)**2
Suppose 0 = 8*o - o - 105. Suppose -13 + o = n. Factor -4/5 + 6/5*t**3 + 14/5*t - 16/5*t**n.
2*(t - 1)**2*(3*t - 2)/5
Let v(o) be the second derivative of 49*o**6/10 - 1239*o**5/20 + 219*o**4/2 + 178*o**3 + 84*o**2 - 134*o. Determine r so that v(r) = 0.
-2/7, 2, 7
Find c, given that 3*c**2 - 8*c**4 + 0 - 7/2*c**5 + 17/2*c**3 + 0*c = 0.
-3, -2/7, 0, 1
Let a = 10838 + -10834. Suppose 7/12*y**a + 0 - 25/12*y**2 + 1/2*y + y**3 = 0. Calculate y.
-3, 0, 2/7, 1
Let y(w) = -17*w**2 - 290*w + 656. Let v(x) = 6*x**2 + 96*x - 219. Let l(u) = 8*v(u) + 3*y(u). Determine q so that l(q) = 0.
-36, 2
Let m(t) be the first derivative of -t**3/6 - 23*t**2/2 - 529*t/2 + 74. Find x such that m(x) = 0.
-23
Let d be (-2782)/286 - -10 - 105/(-220). Let k = -6 - -11. Suppose 0 + 9/4*x**k - 3/4*x**2 + d*x**4 + 0*x - 9/4*x**3 = 0. Calculate x.
-1, -1/3, 0, 1
Let b = 822 - 578. Let n be 2/11 - b*7/(-770). Factor -9/5 - n*f - 3/5*f**2.
-3*(f + 1)*(f + 3)/5
Factor -2197000/9*d - 35701250/9 - 2/9*d**4 - 16900/3*d**2 - 520/9*d**3.
-2*(d + 65)**4/9
Let s(o) = o**2. Let d(p) = -14*p**2 - 10*p - 1. Suppose y + 4*y - 33 = -2*c, -4*y + 24 = c. Let h(v) = y*s(v) + d(v). Factor h(a).
-(a + 1)*(9*a + 1)
Let y(s) be the third derivative of -s**10/10080 + s**8/1120 - s**6/240 - 19*s**4/24 + 36*s**2. Let p(k) be the second derivative of y(k). Factor p(g).
-3*g*(g - 1)**2*(g + 1)**2
Determine m so that 4*m**2 - 10/3*m - 8 - 2/3*m**3 = 0.
-1, 3, 4
Let f(c) be the second derivative of 0*c**4 + 0*c**5 - 1/60*c**6 - 11*c + 0 + 0*c**2 + 0*c**3. Factor f(g).
-g**4/2
Let n(h) = h**3 - 3*h**2 - 12*h + 12. Let u be n(5). Suppose 0 = 5*t + 4*i - 50, -3*i + 55 = 5*t + 2*i. What is s in -11 + t*s**2 - u*s**2 + 11 = 0?
0
Let w(d) = -d**3 + 30*d**2 + 676*d - 42. Let o be w(45). Factor 4/7*t**o - 2/7*t**4 + 0 - 2/7*t**2 + 0*t.
-2*t**2*(t - 1)**2/7
Let p(i) be the first derivative of -i**2 + 3/5*i**5 + 3/2*i**6 + 0*i + 11 - 23/4*i**4 + 13/3*i**3. Suppose p(v) = 0. What is v?
-2, 0, 1/3, 1
Factor 12/5*o + 2/5*o**2 - 14/5.
2*(o - 1)*(o + 7)/5
Let v be (-1 - (-10)/6)*861/(-156). Let c = v - -23/6. Suppose 0 - c*i**3 - 4/13*i - 6/13*i**2 = 0. What is i?
-2, -1, 0
Let l(b) be the second derivative of 0*b**3 + 0 + 18*b + 1/12*b**4 + 1/60*b**6 + 1/15*b**5 - 1/12*b**2. Factor l(o).
(o + 1)**3*(3*o - 1)/6
Let r be ((-13)/143)/((-6)/22). Suppose -1/3*s**2 - 2/3*s - r = 0. Calculate s.
-1
Let -5/2*b**3 + 3/2*b**2 + 13/2*b - 1/2*b**4 - 5 = 0. Calculate b.
-5, -2, 1
Let u be (-2)/3 - (-22)/33. Let g = 61 + -34. Solve -18*s**3 + 0 + g*s**2 + 10*s**4 + u - 7*s**4 = 0 for s.
0, 3
Let p be 6/8 + (-51)/(-12). Suppose 0 = -8*f + p*f + 6. Find a such that 12*a**3 + 4 + 28*a**f + 22*a + 3*a - 5*a = 0.
-1, -1/3
Let j(t) = t**3 + 29*t**2 - 26*t + 120. Let v be j(-30). Determine u so that 0 - 2/7*u**2 + v*u - 8/7*u**3 = 0.
-1/4, 0
Factor 12 + 3/2*q**2 + 21*q - 15/2*q**3.
-3*(q - 2)*(q + 1)*(5*q + 4)/2
Suppose -f + 4*l + 4 = 0, -l - 8 = -5*l. Let q be 2/(-7) + f/14. Solve 10/7*t**2 + 0 - 8/7*t**3 - q*t + 2/7*t**4 = 0.
0, 1, 2
Let d be -6*-4*(-2 + 545/270). Solve d*z**3 - 16/9*z + 0 - 2/9*z**4 + 8/9*z**2 = 0.
-2, 0, 2
Find x, given that -3*x + 3/4*x**4 - 1 - 1/4*x**3 - 11/4*x**2 + 1/4*x**5 = 0.
-2, -1, 2
Let o(g) be the second derivative of g**7/84 - g**6/5 + 57*g**5/40 - 67*g**4/12 + 13*g**3 - 18*g**2 + 96*g. Factor o(v).
(v - 3)**2*(v - 2)**3/2
Let l(n) be the third derivative of n**6/120 - 13*n**5/60 + 35*n**4/24 + 49*n**3/6 + 44*n**2. Find m, given that l(m) = 0.
-1, 7
Let n = 32616 + -32614. Let -3/7*r**4 + 0 + 1/7*r**n - 4/7*r**3 + 2/7*r = 0. What is r?
-1, 0, 2/3
Let t(b) be the second derivative of -b**5/90 - 5*b**4/54 - 2*b**3/9 - 16*b + 5. Determine a, given that t(a) = 0.
-3, -2, 0
Let x(f) be the third derivative of 0 + 1/30*f**5 + 1/60*f**6 + 0*f + 1/336*f**8 + 1/6*f**3 - 1/70*f**7 + f**2 - 1/8*f**4. Factor x(k).
(k - 1)**4*(k + 1)
Determine r so that 10*r**2 + 8 - r**2 - 3*r**2 - 7*r**2 + 7*r = 0.
-1, 8
Let j(d) = -d + 18. Let g be j(17). Let v(b) = b**2 + 1. Let q be v(g). Determine w, given that 10/7*w**3 - 10/7*w + 2/7 - 8/7*w**4 + 6/7*w**q = 0.
-1, 1/4, 1
Let h(b) be the second derivative of 0 - 5*b - 6/5*b**2 - 1/20*b**4 + 2/5*b**3. Solve h(s) = 0 for s.
2
Let s(k) be the third derivative of 0*k + 1/210*k**6 + 0*k**3 - 16*k**2 + 0*k**5 + 0 - 1/1176*k**8 + 0*k**7 - 1/84*k**4. Factor s(z).
-2*z*(z - 1)**2*(z + 1)**2/7
Let u be ((-2)/17)/(12/(-120)). Let x = 134/85 - u. Factor -2/5*h**3 + x*h - 2/5 + 2/5*h**2.
-2*(h - 1)**2*(h + 1)/5
Let c be ((-2)/17 + (-3312)/3060)*(-5)/2. Determine i, given that -2 - 14*i**c + 10/3*i + 38/3*i**2 = 0.
-3/7, 1/3, 1
Let f(b) be the second derivative of b**7/7560 - b**6/360 - b**4/4 - 19*b. Let q(n) be the third derivative of f(n). Factor q(u).
u*(u - 6)/3
Suppose f + 4*z = -10, 8 = -5*z - 7. Factor -86*h + 3*h**3 + 10*h**f + 91*h - 18*h**3.
-5*h*(h - 1)*(3*h + 1)
Suppose -3/5*c**3 - 48/5 - 72/5*c - 27/5*c**2 = 0. Calculate c.
-4, -1
Let f be -1 + 6/(-3) + 236/24. Let s = 22/3 - f. Suppose 1/4*x**2 + s + 3/4*x = 0. Calculate x.
-2, -1
Suppose -6 = -5*w - t + 9, 4*w = -t + 12. Find k such that w*k**2 - 11*k**2 + 3*k**2 = 0.
0
Let p(k) = k**2 - 368*k + 365. Let v(m) = -12*m**2 + 3681*m - 3648. Let a(t) = 21*p(t) + 2*v(t). Factor a(l).
-3*(l - 1)*(l + 123)
Let w(a) = 2*a. Let m be w(2). Let z(i) = i**3 - 3*i**2 - 2*i - 5. Let y be z(m). Find n such that -7*n**3 - 5*n + 9*n**y - n - 4 = 0.
-1, 2
Let l = 1466 - 1462. Let i(t) = t**3 - 7*t**2 + 5*t + 8. Let w be i(6). Let 2/5*q + 6/5*q**l + 0 - 6/5*q**w - 2/5*q**3 = 0. What is q?
-1, 0, 1/3, 1
Let i(p) be the third derivative of 1/24*p**6 + p**5 + 0*p - 9*p**2 + 75/8*p**4 + 125/3*p**3 + 0. Factor i(l).
5*(l + 2)*(l + 5)**2
Let l(d) = 4*d**2 - 10*d + 4. Let o(n) = -5*n**2 + 12*n - 4. Suppose -70 = -4*q - 58. Let y(t) = q*o(t) + 4*l(t). Factor y(s).
(s - 2)**2
Let w = 67 - 49. Let a(d) = d**2 - 16*d - 36. Let s be a(w). Factor s - 2/3*y**2 + 0*y + y**3 + 0*y**4 - 1/3*y**5.
-y**2*(y - 1)**2*(y + 2)/3
Let w(y) be the second derivative of -5*y**4/12 + 5*y**3 - 25*y**2/2 - 167*y. Let w(j) = 0. What is j?
1, 5
Let l be 3/90*-4*25/(-160). Let u = l - -7/48. Determine r so that 1/2*r**3 - 1/6*r**2 + 0*r + 0 + u*r**4 - 1/2*r**5 = 0.
-1, 0, 1/3, 1
Let z = 1705/63 + -241/9. Solve z*v**3 + 2/7*v**2 - 4/7*v + 0 = 0.
-2, 0, 1
Let y(l) = -l**3 + l**2 - 13*l + 14*l + 11 - 10. Let i(x) = -2 - 11*x - 20*x**2 + 10*x**3 + 4*x**3 - 3. Let t(h) =