etermine j, given that 13 - 15*j**2 - 3 - 2*j**p - 5*j + 2*j**2 = 0.
-1, 2/3
Let s(a) be the first derivative of -a**9/1008 + a**8/280 - a**7/280 - 14*a**3/3 - 7. Let k(i) be the third derivative of s(i). Suppose k(f) = 0. Calculate f.
0, 1
Factor 0 - 3/4*v + 1/4*v**2 + 3/4*v**3 - 1/4*v**4.
-v*(v - 3)*(v - 1)*(v + 1)/4
Suppose -26*h + 13 = -221. Let b(y) be the second derivative of 0*y**3 + 1/28*y**7 - 1/12*y**6 + 0*y**4 + 1/20*y**5 + 0 + 0*y**2 - h*y. What is a in b(a) = 0?
0, 2/3, 1
Factor -1/2*v**4 + 3*v**3 + 0 - 6*v**2 + 4*v.
-v*(v - 2)**3/2
Let j(d) = -37*d + 523. Let x be j(14). Let k(l) be the second derivative of -1/10*l**6 - l**3 - 5/4*l**4 + 0 - 8*l - 3/5*l**x + 0*l**2. Factor k(m).
-3*m*(m + 1)**2*(m + 2)
Let f(z) = -95*z**4 + 250*z**3 - 35*z**2. Let b(s) = -8*s**4 + 21*s**3 - 3*s**2. Let c(x) = 35*b(x) - 3*f(x). Solve c(o) = 0.
0, 3
Let k be 312/(-21) + 6 + 4 + 6. Factor 2/7*f**3 + 10/7*f + k*f**2 + 4/7.
2*(f + 1)**2*(f + 2)/7
Let v(p) be the second derivative of 25*p**7/14 + 23*p**6/2 + 189*p**5/10 + 5*p**4/2 - 23*p**3/2 + 9*p**2/2 - 3*p + 15. Find w, given that v(w) = 0.
-3, -1, 1/5
Let v(z) = z - 14. Let i be v(17). Factor -121 + 109 - 6*d**2 - 9*d**i + 24*d + 3*d**2.
-3*(d - 1)*(d + 2)*(3*d - 2)
Let p(o) = 29*o**2 + 1771*o - 1817. Let t(s) = -5*s**2 - 295*s + 303. Let x(z) = -6*p(z) - 34*t(z). Factor x(u).
-4*(u - 1)*(u + 150)
Let p(x) be the first derivative of 0*x + 4/3*x**3 - 2*x**2 - 1. Let p(a) = 0. What is a?
0, 1
Let q be ((-5)/(-15))/(1/69). Suppose 0 = 5*o - 2 - q. Suppose -5*t**5 - t**3 + 5*t**5 + 2*t**4 - t**o = 0. What is t?
0, 1
Let u be (-1 - 3/(-3)) + 2. Let r = -464 - -467. Determine a so that -2/9*a**r + 4/9 + 8/9*a**u - 10/9*a = 0.
1, 2
Let z(x) = 16*x**3 + x**2 - x. Let o be z(1). Suppose 0 = 13*f - o*f. Suppose f*n**3 - 2/7*n + 4/7*n**2 + 2/7*n**5 - 4/7*n**4 + 0 = 0. What is n?
-1, 0, 1
Let z = 435 - 434. Let h(d) be the first derivative of -2*d**3 + 2*d**4 - 2*d - 4*d**2 + 8/5*d**5 - z. Factor h(s).
2*(s - 1)*(s + 1)*(2*s + 1)**2
Suppose 16/5*z - 44/5*z**2 + 0 = 0. What is z?
0, 4/11
Let n(z) be the first derivative of z**3/2 + 3*z**2/2 - 148. Factor n(h).
3*h*(h + 2)/2
Let x(c) be the second derivative of 3*c**5/40 + 17*c**4/2 - 139*c**3/4 + 105*c**2/2 + 293*c. Factor x(r).
3*(r - 1)**2*(r + 70)/2
Let o(b) = 23*b**2 + 8 - 8*b**2 + 21*b + 0*b + 2*b. Let c(y) = -7*y**2 - 11*y - 4. Let f(q) = -13*c(q) - 6*o(q). Let f(r) = 0. Calculate r.
-4, -1
Suppose 34*v = 17*v + 20*v. Let c(j) be the second derivative of 7*j - 1/4*j**4 + 3/2*j**2 + v + 0*j**3. Let c(m) = 0. Calculate m.
-1, 1
Suppose 0 = 2*t - 8*p + 12*p + 364, -5*t - 3*p = 931. Let j = t - -2076/11. Suppose 2/11*h**2 + j + 8/11*h = 0. What is h?
-2
Let u be (-14)/(-4) - (-13)/(-26). Factor -4*h**u + 1 - 1 - 22*h**2 - 2*h**4 + 20*h**2.
-2*h**2*(h + 1)**2
Let l(z) be the second derivative of z**4/4 - 2*z**3/3 + 2*z**2 - 14*z. Let k be l(1). Suppose 1/3*x + 0 + x**2 - 4/3*x**k = 0. Calculate x.
-1/4, 0, 1
Suppose 26*i = 21*i - 205. Let q = i + 44. Suppose 0*h**2 + 2/7*h**4 + 4/7*h**q + 0*h + 0 = 0. Calculate h.
-2, 0
Suppose -5*j = -2*z + 76 - 28, 6*j + 40 = -2*z. Find w such that -8/3*w**z + 0 - 8/3*w + 10*w**3 - 8*w**2 = 0.
-1/4, 0, 2
Suppose -3*u + x = -5, -x = 3*u - 0*x - 13. Determine n so that -2*n**u - 34*n**4 + 32*n**4 + 2*n**2 + 0*n + 2*n = 0.
-1, 0, 1
Determine x, given that -324 + 81*x**4 - 15*x**3 - 693*x**2 + 32*x - 33*x**5 - 1112*x + 48*x**5 = 0.
-3, -2, -2/5, 3
Let u(x) be the third derivative of -x**8/216 + 4*x**7/315 - x**6/180 - x**5/135 - 2*x**2 + 8. Solve u(z) = 0.
-2/7, 0, 1
Let z(i) = 30*i**4 + 6*i**3 - 21*i**2 - 12*i - 3. Suppose 25*d - 12 = 29*d. Let c(y) = y**4 - y**3 + y**2 - 1. Let j(x) = d*c(x) + z(x). Factor j(g).
3*g*(g - 1)*(3*g + 2)**2
Let w be -2 + 28/(-49) + 15/5. Find n such that 0*n + 0 + w*n**3 + 3/7*n**4 - 3/7*n**5 - 3/7*n**2 = 0.
-1, 0, 1
Let c be 0 + 18 + -7 - 9. Let l(z) be the second derivative of 0*z**c - 1/20*z**5 - 2*z - 1/12*z**4 + 0 + 0*z**3. Determine k so that l(k) = 0.
-1, 0
Let r(l) = -l**5 + l**4 - l**3 - 2. Let j(g) = 5*g**5 + 55*g**4 - 40*g**3 - 60. Let x(q) = j(q) - 30*r(q). Suppose x(h) = 0. What is h?
-1, 0, 2/7
Let j(p) be the first derivative of 0*p**3 + 1/8*p**2 - 1/16*p**4 + 4 + 0*p. Factor j(c).
-c*(c - 1)*(c + 1)/4
Let x(f) be the second derivative of -1/80*f**5 + 0 + 0*f**3 - 7*f - 1/32*f**4 - 1/2*f**2. Let h(n) be the first derivative of x(n). What is y in h(y) = 0?
-1, 0
Let m(j) be the second derivative of -j**4/66 + 86*j**3/33 - 1849*j**2/11 - 54*j. Determine d so that m(d) = 0.
43
Let q = -36 + 39. Factor -4*j**q + 8*j - 2*j**3 - 6*j**4 - 10*j**4 + 14*j**4.
-2*j*(j - 1)*(j + 2)**2
Let l(v) = v**3 - 8*v**2 + 4. Let m be l(8). Let r be (-2)/6*(-1 - 0). Let 1/3*z**2 + r*z - 1/3*z**3 - 1/3*z**m + 0 = 0. What is z?
-1, 0, 1
Let f(m) be the third derivative of -2/9*m**5 - m + 1/3*m**4 + 0*m**3 + 30*m**2 + 1/1512*m**8 + 2/189*m**7 + 13/540*m**6 + 0. Factor f(g).
2*g*(g - 1)**2*(g + 6)**2/9
Factor 66*m - 18 - 144*m**2 - 98*m**3 + 46*m**2 + 47*m**2 + 37*m**2.
-2*(m + 1)*(7*m - 3)**2
Let y = -121/14 + 17/2. Let o = y - -33/7. Factor 0 - o*g - 2/7*g**3 - 16/7*g**2.
-2*g*(g + 4)**2/7
Let v(w) be the second derivative of w**7/21 + 7*w**6/45 - w**5/45 - 10*w**4/27 - 8*w**3/27 - w + 21. Solve v(q) = 0.
-2, -2/3, 0, 1
Let j(y) be the second derivative of -1/10*y**5 - 7*y + 7/12*y**4 + y**2 - 7/6*y**3 + 0. Factor j(f).
-(f - 2)*(f - 1)*(2*f - 1)
Suppose -5*f + 160 + 265 = -4*o, -381 = -4*f - 5*o. Let x be (11 + 1)*(f/(-15) - -6). Factor 2*s - x + 14/5*s**2.
2*(s + 1)*(7*s - 2)/5
Suppose -u = 26*a - 30*a + 17, u = a - 2. Let -2*z + 3/5*z**2 - 4/5*z**4 + 3/5 + 12/5*z**u = 0. What is z?
-1, 1/2, 3
Let s(g) be the first derivative of g**3/2 + 39*g**2/4 + 45*g - 39. Determine k so that s(k) = 0.
-10, -3
Factor -3*f**3 + 7 + 9*f**4 - 7 + 0 - 3*f**5 - 3*f**4.
-3*f**3*(f - 1)**2
Let q(i) be the second derivative of 3*i**3/2 + 2*i. Let l be q(1). Factor l*s**3 - 2*s**4 - 7*s - 5*s - s**4.
-3*s*(s - 2)**2*(s + 1)
Let u(f) be the third derivative of f**5/30 - 4*f**3/3 + 2*f**2 + 13*f. Determine k so that u(k) = 0.
-2, 2
Let i(b) be the first derivative of -2*b**3 - 1/12*b**6 - b**2 + 3 + 0*b - 3/5*b**5 - 13/8*b**4. What is m in i(m) = 0?
-2, -1, 0
Let r(o) be the third derivative of 1/40*o**5 + 0*o**3 - 10*o**2 + 0*o + 0*o**4 + 0 + 1/280*o**7 + 3/160*o**6. Suppose r(y) = 0. What is y?
-2, -1, 0
Let b be (-36)/(2/((-8)/3)). Let q be 44/b + (-3)/12. Factor 2/3*r**2 - 2/3*r**3 + 2/3*r - q.
-2*(r - 1)**2*(r + 1)/3
Suppose 0 = -5*g - 17 - 3. Let s be 384/(-16)*g/9. Factor -8/3*b**3 + 8*b**2 + 1/3*b**4 + 16/3 - s*b.
(b - 2)**4/3
Let u(y) be the third derivative of y**8/2688 - y**7/168 + 29*y**6/960 - y**5/15 + y**4/16 - 40*y**2. Factor u(l).
l*(l - 6)*(l - 2)*(l - 1)**2/8
Let d(f) be the first derivative of f**7/280 + f**6/360 - f**5/60 + 23*f**3/3 - 26. Let p(a) be the third derivative of d(a). Factor p(c).
c*(c + 1)*(3*c - 2)
Suppose 4*l + 3*a = 5, 2*l + a + a = 2. Solve -27*p**2 + 8 + 13*p**2 + 12*p**l = 0.
-2, 2
Let a(h) be the first derivative of -2*h**3/3 + h**2 + 4*h + 196. Let a(k) = 0. What is k?
-1, 2
Let x(r) be the second derivative of 3/8*r**3 - 3/4*r**2 - 1/16*r**4 + 0 + 15*r. Factor x(q).
-3*(q - 2)*(q - 1)/4
Factor 7*g**3 - 135*g**2 - 79*g**4 - 8 + 117*g**2 + 78*g**4 + 20*g.
-(g - 2)**3*(g - 1)
Let d(q) be the first derivative of q**5/15 - q**4/10 - 9*q**2/2 + 30. Let s(w) be the second derivative of d(w). Factor s(z).
4*z*(5*z - 3)/5
Let d be (-3)/((-135)/125) - 144/(-648). Suppose 4/5 - 6/5*m - 2/5*m**4 - 2/5*m**2 + 6/5*m**d = 0. What is m?
-1, 1, 2
Suppose -18*h**2 + 11/2*h**4 + 0 - 12*h**3 - 1/2*h**5 + 0*h = 0. Calculate h.
-1, 0, 6
Let i(o) be the second derivative of -169*o**4/18 - 208*o**3/3 - 192*o**2 - 6*o + 10. Find u, given that i(u) = 0.
-24/13
Let b be (-2 - 33/(-21)) + (-17)/(-7). Factor 4 + 2*s**b + s + 2*s**3 + 6 - 12 - 3*s**3.
-(s - 2)*(s - 1)*(s + 1)
Let g(p) be the second derivative of p**4/84 + 4*p**3/21 - 10*p**2/7 + 21*p + 3. Factor g(t).
(t - 2)*(t + 10)/7
Let k(d) = -11*d**4 + 80*d**3 - 134*d**2 + 80*d - 19. Let u(x) = -155*x**4 + 1120*x**3 - 1875*x**2 + 1120*x - 265. Let q(t) = 55*k(t) - 4*u(t). Factor q(l).
5*(l - 3)*(l - 1)**2*(3*l - 1)
Let l = 19/15 + -7/6. Factor 3/5*k + l*