067/5. Let p = x + 349. Find d, given that -3/7*d**2 + p*d - 6/7 = 0.
1, 2
Find k, given that -6*k**3 + 6*k - 48/5 + 3/5*k**4 + 9*k**2 = 0.
-1, 1, 2, 8
Let j(y) be the third derivative of -13*y**6/8 + 29*y**5/20 + 4*y**4 + 2*y**3 + 4*y**2 - 5. Let j(r) = 0. Calculate r.
-2/5, -2/13, 1
Let i(b) = -8425*b**2 + 220*b + 45. Let h(c) = -383*c**2 + 10*c + 2. Let o(f) = -45*h(f) + 2*i(f). Find m, given that o(m) = 0.
0, 2/77
Let z be (-24)/(-312) - (-76)/26. Factor 9/4*l**5 + 1 + 6*l + 67/4*l**z + 57/4*l**2 + 39/4*l**4.
(l + 1)**3*(3*l + 2)**2/4
Suppose 0*z = -4*p + 3*z + 65, 2*p = -z + 45. Let x = 4 - 2. Factor p - 2*s - 20 - x*s**2.
-2*s*(s + 1)
Let w(a) be the second derivative of 4/17*a**2 + 5/102*a**4 + 8/51*a**3 + 0 + 1/170*a**5 - 12*a. Suppose w(t) = 0. What is t?
-2, -1
Let g(f) be the second derivative of -f**4/120 - 2*f**3/3 - 20*f**2 - 34*f. Solve g(m) = 0.
-20
Let c(s) be the first derivative of s**5/240 - s**4/96 - 13*s**2/2 + 15. Let t(x) be the second derivative of c(x). What is w in t(w) = 0?
0, 1
Let n(c) be the second derivative of c**5/60 - 89*c**4/12 + 7921*c**3/6 - 704969*c**2/6 - 112*c + 1. Suppose n(a) = 0. Calculate a.
89
Factor -92/3*p + 2/3*p**2 - 94/3.
2*(p - 47)*(p + 1)/3
Let w(f) be the first derivative of -1/3*f**2 + 1/6*f**4 + 0*f + 7/15*f**5 - 7/9*f**3 - 16. Let w(v) = 0. What is v?
-1, -2/7, 0, 1
Let m(d) be the third derivative of 1/210*d**5 + 1/42*d**4 - 2*d**2 + 0*d + 1/21*d**3 + 0. Determine t so that m(t) = 0.
-1
Let u(l) be the first derivative of 2*l**5/95 - 16*l**3/57 + 32*l/19 - 42. Factor u(g).
2*(g - 2)**2*(g + 2)**2/19
Let w = -16/959 - -11588/4795. Factor -w - 3/5*v**2 + 3*v.
-3*(v - 4)*(v - 1)/5
Let h(b) be the first derivative of -1/18*b**4 + 0*b**2 + 12 + 0*b - 2/9*b**3. Solve h(a) = 0.
-3, 0
Let j(f) = 2*f**4 + 6*f**3 - 11*f**2 + 3*f + 3. Let q(g) = 4*g**4 + 10*g**3 - 21*g**2 + 5*g + 5. Let r(b) = 5*j(b) - 3*q(b). Factor r(i).
-2*i**2*(i - 2)*(i + 2)
Let i(v) be the first derivative of -8/5*v**2 + 64/5*v + 1/15*v**3 + 23. Let i(h) = 0. What is h?
8
Let r be (-19)/(-9) + (-215)/129. Let m(k) be the first derivative of k**2 + r*k**3 - 7 - 4/3*k. Factor m(f).
2*(f + 2)*(2*f - 1)/3
Let h = 1753/7 - 250. Let n = h + -1/7. Factor -n*a**2 + 2/7*a**3 + 2/7 - 2/7*a.
2*(a - 1)**2*(a + 1)/7
Suppose -3*s - z = -255, 3*z + 3 = 4*z. Suppose -81*y = -s*y + 12. Factor -8/7*n**2 + 16/7*n + 10/7*n**y - 2/7*n**5 - 12/7*n**3 + 0.
-2*n*(n - 2)**3*(n + 1)/7
Let d(n) = 5*n**2 + 9*n - 20. Let p(k) = -k**2 + k - 1. Let y(r) = -d(r) - 6*p(r). Factor y(z).
(z - 13)*(z - 2)
Let q(u) = 2*u**4 - u**3 + 3. Let x(h) = -5*h**4 + 2*h**3 - 6*h**2 - 9. Let c(n) = 6*q(n) + 2*x(n). What is y in c(y) = 0?
-2, 0, 3
Let j(c) be the second derivative of c**7/2940 + c**3/6 + 5*c. Let r(m) be the second derivative of j(m). What is k in r(k) = 0?
0
Suppose -6*w**2 + w - 2*w**2 + 10*w**2 - 5*w - 2*w - 36 = 0. What is w?
-3, 6
Let h(n) = -23*n - 2. Let k be h(1). Let p = -18 - k. Suppose 12 - 6*g**2 - g**2 + 4*g + 2*g**2 - 4*g**3 - p*g**2 = 0. Calculate g.
-3, -1, 1
Suppose 8*t - 5*t = 0. Suppose 6 = 2*q + 2*c, 3*q - 3*c - 4 - 5 = 0. Factor 0 + 0*i**2 - 1/4*i**q + t*i + 1/4*i**5 + 0*i**4.
i**3*(i - 1)*(i + 1)/4
Let f(v) = 27*v**4 - 37*v**3 - 6*v**2 + 12*v + 3. Let j(l) = -l**3. Let x = 36 + -35. Let r(i) = x*f(i) - j(i). Let r(z) = 0. What is z?
-1/3, 1
Let r(s) = -4*s**3 - 4*s**2 + 3*s. Let u be r(-4). Determine l so that -31*l**3 - 149 - u*l**2 + 4*l**3 - 43 - 336*l - 3*l**4 - 12*l**3 = 0.
-4, -1
Let d(t) be the third derivative of -t**8/3024 - 2*t**7/315 - 7*t**6/216 + t**5/45 + t**4/6 - 280*t**2. Find u such that d(u) = 0.
-6, -1, 0, 1
Let l(n) be the first derivative of n**9/25704 + n**8/14280 + 14*n**3/3 + 1. Let i(h) be the third derivative of l(h). Factor i(t).
2*t**4*(t + 1)/17
Suppose 6*f - 10 = -4. Let i be (-18)/((-5)/3 - f). Factor 9/2*c - 3/4*c**2 - i.
-3*(c - 3)**2/4
Let -134/9*j**2 - 260/9*j**3 - 14*j**4 + 8/9 + 8/9*j = 0. Calculate j.
-1, -2/7, 2/9
Let f(u) be the second derivative of u**7/14 + u**6/5 - 3*u**5/20 - u**4/2 + 122*u. Factor f(c).
3*c**2*(c - 1)*(c + 1)*(c + 2)
Let u(r) be the third derivative of 0 - 26*r**2 + 0*r + 2/3*r**3 + 1/2*r**4 - 1/3*r**5 - 1/10*r**6 + 8/105*r**7. Factor u(a).
4*(a - 1)**2*(a + 1)*(4*a + 1)
Let y(o) be the first derivative of 8*o**7/315 - o**6/90 + 8*o**2 - 13. Let i(q) be the second derivative of y(q). Factor i(w).
4*w**3*(4*w - 1)/3
Let 11/5*z + 3*z**2 - 13/5*z**4 - 11/5*z**3 - 2/5 = 0. Calculate z.
-1, 2/13, 1
Let y(s) be the first derivative of -s**4/12 - 17*s**3/9 - 21*s**2/2 + 27*s - 265. Factor y(n).
-(n - 1)*(n + 9)**2/3
Let s(i) = -3*i**2 - 14*i + 31. Let c(u) = 5*u**2 + 10*u - 30. Let f(d) = -6*c(d) - 5*s(d). Factor f(y).
-5*(y + 1)*(3*y - 5)
Let l = -1071 - -9641/9. Factor l*y**2 - 2/9*y - 4/9.
2*(y - 2)*(y + 1)/9
Factor 465/2*k**2 - 51*k + 0 - 27/2*k**3.
-3*k*(k - 17)*(9*k - 2)/2
Let q = 26 - 24. Factor -3 + 9 - 5*b**2 - q - 8*b.
-(b + 2)*(5*b - 2)
Let j(d) be the second derivative of d**6/180 - 7*d**5/60 - 67*d**4/72 - 22*d**3/9 - 3*d**2 - d + 24. Factor j(o).
(o - 18)*(o + 1)**2*(o + 2)/6
Let i = 48 - 100. Let h be (-44)/i - (-2)/13. Factor -10*z**3 + 11*z**2 - 3 + h + 10*z - 9*z.
-(z - 1)*(2*z - 1)*(5*z + 2)
Let u(i) be the second derivative of i**6/24 - i**5/12 - 5*i**4/12 + 45*i**2/2 - 18*i. Let z(p) be the first derivative of u(p). Solve z(x) = 0 for x.
-1, 0, 2
Let a(s) be the first derivative of 3/2*s**2 - 4/5*s**5 - 1/2*s**4 + 0*s - 1/6*s**6 - 7 + 4/3*s**3. Factor a(z).
-z*(z - 1)*(z + 1)**2*(z + 3)
Let g be (6/12)/(2/8). Suppose -6*p + 6*p**g + 4*p**3 - 2*p**2 - 2*p = 0. Calculate p.
-2, 0, 1
Let o(y) be the second derivative of 0*y**3 - 5/48*y**4 - 1/80*y**5 + 0 - 13*y + 0*y**2. Solve o(g) = 0 for g.
-5, 0
Determine x, given that 0*x + 0 + 10/9*x**2 - 8/9*x**4 - 38/9*x**3 = 0.
-5, 0, 1/4
Let d = 69 + -64. Let s be (-4)/(-10)*d + 0. Factor 1/4*p**s - 1/4 - 1/4*p**3 + 1/4*p.
-(p - 1)**2*(p + 1)/4
Let s(a) = 5*a**4 - 9*a**3 - 50*a**2 - 128*a - 92. Let v(g) = -14*g**4 + 26*g**3 + 151*g**2 + 383*g + 275. Let z(b) = 11*s(b) + 4*v(b). Solve z(n) = 0 for n.
-2, 11
Suppose 26*k + 48 = 152. Factor 1/2*m**2 + m - 1/2*m**k - m**3 + 0.
-m*(m - 1)*(m + 1)*(m + 2)/2
Let f be (3/(-20))/(25/100)*(-10)/9. Let w be (-2 - -2)/(-1 + 3). Factor 0*m + w*m**2 + 0 + f*m**3.
2*m**3/3
Let k = -14/207 - -256/3105. Let j = 397/540 + k. Determine x so that -1/4*x**3 - j*x**2 - 1/4 - 3/4*x = 0.
-1
Let n(s) = 6*s - 8. Let i be n(2). What is k in 11*k**2 + i*k - 13*k**2 - 13 - 8*k**4 + 22*k**2 - 4*k**3 + 1 = 0?
-3/2, -1, 1
Suppose -41*a = -5*l - 44*a + 22, 0 = l - 2*a + 6. Let b(k) be the second derivative of -1/12*k**4 + 0*k**3 + 0 - 3*k + 0*k**l. Factor b(d).
-d**2
Suppose -5*q + 19 = y, -19 = -15*y + 11*y - q. Let z(i) = 6*i**2 - i - 1. Let l be z(-1). Factor -h**4 + 3 + 0*h**y + h**4 - l*h**2 + 3*h**4.
3*(h - 1)**2*(h + 1)**2
Let l(k) = 2*k**3 + 8*k**2 - 25*k - 4. Let h be l(-6). Determine u, given that -1 + 3/2*u**3 - 5/2*u + 2*u**h = 0.
-2, -1/3, 1
Let w = -25 + 45. Let y be w/5 - (-24 + 1). Determine r so that -12*r - 12 - y*r**4 + 25*r**3 + 37*r**2 - 4*r**2 - 7*r**3 = 0.
-2/3, 1
Let f = -3815/2 + 1909. Factor -3/2*d**3 + f*d + 3/2*d**2 - 3/2.
-3*(d - 1)**2*(d + 1)/2
Let y(v) be the second derivative of -v**6/165 - 4*v**5/55 + 501*v. Factor y(g).
-2*g**3*(g + 8)/11
Let l(n) = -7*n**2 + 8*n - 3. Let v(c) be the second derivative of c**4/2 - 7*c**3/6 + c**2 + 8*c. Let s(g) = -5*l(g) - 6*v(g). Let s(u) = 0. What is u?
-1, 3
Suppose 12 = 3*q - q. Let m(f) = f**3 - 7*f**2 + 5*f + 6. Let x be m(q). Factor -v**3 + 4*v**3 + x*v**3 + 5*v**4 + 3*v**5 + v**4.
3*v**3*(v + 1)**2
Let c(j) be the second derivative of -j**5/130 + j**4/39 + 4*j**3/39 - 8*j**2/13 - j - 79. Factor c(p).
-2*(p - 2)**2*(p + 2)/13
Let r(f) be the third derivative of -f**6/60 - 37*f**5/30 + 77*f**4/12 - 13*f**3 + 217*f**2. Factor r(i).
-2*(i - 1)**2*(i + 39)
Let u be (-35808)/(-1280) - 28 - (-2)/16. Factor 3/5 + 1/2*w + u*w**2.
(w + 2)*(w + 3)/10
Let w = 15 - 11. Suppose 4*j + 36 = w*x, -5*x + 9 = 4*j - 0*j. Solve 2*a**x + 7*a**5 - 6*a**5 = 0 for a.
0
Factor 380*x + 14 - 754*x + x**2 + 383*x.
(x + 2)*(x + 7)
Determine y, given that -4*y**5 + 128 + 7*y + 111*y**2 - 129*y + 44*y**3 - 7*y**2 - 3*y**4 - 13*y**4 - 134*y = 0.
-4, 1, 2
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