- 11/6. Find p, given that -p + b + 1/2*p**2 = 0.
1
Let n = -1/44 + 5/132. Let j(m) be the second derivative of 0*m**2 - m + 0 + 0*m**3 - n*m**4. Factor j(s).
-2*s**2/11
Let b(t) be the second derivative of -t**8/5040 + t**7/1260 - t**6/1080 + t**3/2 - 2*t. Let w(a) be the second derivative of b(a). Factor w(m).
-m**2*(m - 1)**2/3
Let w(t) be the first derivative of 1/50*t**6 - 1/5*t**3 + 0*t**5 - t - 3/20*t**4 + 1 + 0*t**2. Let d(s) be the first derivative of w(s). Solve d(f) = 0.
-1, 0, 2
Factor -16/3*t**2 - 196/3 + 112/3*t.
-4*(2*t - 7)**2/3
Let y(b) = -b**2 - 5*b - 2. Let i be y(-2). Let t be (-1 - (-4)/i)/(-2). Solve 0*u - 1/5*u**2 + 1/5*u**4 + 0 + t*u**3 = 0 for u.
-1, 0, 1
Let a(w) be the third derivative of w**7/70 - 13*w**6/160 + 3*w**5/16 - 7*w**4/32 + w**3/8 - 49*w**2. Find r, given that a(r) = 0.
1/4, 1
Let o(x) = 56*x**5 - 264*x**4 + 415*x**3 - 239*x**2 + 32. Let q(c) = 28*c**5 - 132*c**4 + 208*c**3 - 120*c**2 + 16. Let t(g) = -4*o(g) + 9*q(g). Factor t(a).
4*(a - 2)*(a - 1)**3*(7*a + 2)
Let a = 5 - 2. Find p, given that -3*p**3 + 3*p**a + 3*p**5 - 3*p**3 + 3*p**4 - 3*p**2 = 0.
-1, 0, 1
Factor 1/2*h**3 - 3/2*h - 1 + 0*h**2.
(h - 2)*(h + 1)**2/2
Let m(l) be the second derivative of l**6/75 - 3*l**5/100 + l**4/60 + 8*l. Determine b so that m(b) = 0.
0, 1/2, 1
Let a = 46 + -44. Factor -1/3*z**3 - 5/3*z + 2/3 + 4/3*z**a.
-(z - 2)*(z - 1)**2/3
Let r = -7 + 29/4. Let s(l) be the first derivative of 1/3*l**3 - 1/2*l - 2 - 1/12*l**6 - 1/10*l**5 - 1/4*l**2 + r*l**4. Factor s(h).
-(h - 1)**2*(h + 1)**3/2
Let a(l) = -2*l**2 - 27*l - 13. Let b be a(-13). Let -1/2*v + 1/2*v**3 + 1/2*v**4 + b - 1/2*v**2 = 0. What is v?
-1, 0, 1
Let q(u) be the first derivative of -u**4/9 - 11*u**3/27 - 5*u**2/18 + 2*u/9 + 20. Factor q(l).
-(l + 1)*(l + 2)*(4*l - 1)/9
Let b be (56/(-210))/((-112)/50 - -2). Factor -4/9*q - 2/3*q**3 + 0 + b*q**2 + 2/9*q**5 - 2/9*q**4.
2*q*(q - 1)**3*(q + 2)/9
Let t(v) be the third derivative of -v**6/30 + 3*v**2. Factor t(p).
-4*p**3
Let m = 31 + -29. Factor -1/3*r**m - 1/3 + 2/3*r.
-(r - 1)**2/3
Let y(v) be the first derivative of -3 + 8/3*v**3 + 4*v + 1/2*v**4 + 5*v**2. Let y(t) = 0. Calculate t.
-2, -1
Let o(b) be the first derivative of -2/3*b**3 - 11/15*b**5 + 1/3*b + 7/6*b**4 - 1/6*b**2 + 1/6*b**6 + 3. Let o(d) = 0. What is d?
-1/3, 1
Let u(q) = 16*q - 3. Let m be u(3). Let w be 10/m - (-26)/45. Factor 3/5*v**3 - 1/5*v - w*v**2 + 2/5.
(v - 1)**2*(3*v + 2)/5
Suppose -2*y + 6*a + 55 = a, -2*a - 6 = 0. Let r = y + -39/2. Factor r*s - 1/2*s**2 + 0.
-s*(s - 1)/2
Let i = -1/356 - -719/2492. Factor 0 + 0*t + 4/7*t**2 + 8/7*t**4 - 10/7*t**3 - i*t**5.
-2*t**2*(t - 2)*(t - 1)**2/7
Let i(d) be the first derivative of 4/7*d - 3/7*d**2 + 3 + 1/14*d**4 + 0*d**3. Suppose i(v) = 0. Calculate v.
-2, 1
Let f(u) be the third derivative of u**7/672 + u**6/480 - u**5/40 + u**4/24 + u**3/2 - 2*u**2. Let a(i) be the first derivative of f(i). Solve a(n) = 0.
-2, 2/5, 1
Let j(d) be the first derivative of d**4 - 16*d**3/5 + 18*d**2/5 - 8*d/5 + 10. Factor j(l).
4*(l - 1)**2*(5*l - 2)/5
Let g = -47 + 49. Let h(r) be the first derivative of -2/21*r**3 - 1/7*r**g + 2 + 0*r. Solve h(k) = 0.
-1, 0
Let z = 941/4275 + 1/475. Factor -14/9*i**2 + z*i**5 + 2*i**3 + 4/9*i + 0 - 10/9*i**4.
2*i*(i - 2)*(i - 1)**3/9
Let p(g) be the third derivative of -g**6/80 + g**5/20 + g**4/4 - 2*g**3 + 3*g**2. Let p(b) = 0. What is b?
-2, 2
Factor 64 + 1/4*y**4 + 24*y**2 + 4*y**3 + 64*y.
(y + 4)**4/4
Find s, given that -3803 + 100*s**3 - 60*s**4 + 3803 + 8*s + 60*s**2 - 108*s**5 = 0.
-1, -1/3, -2/9, 0, 1
Suppose -5*t = -2*d - 28, 0 = -d - 0*d + 3*t - 14. Let m = d + 17. Factor 1/3*i**m + 1/3*i + 0 - 2/3*i**2.
i*(i - 1)**2/3
Let k(t) = -4*t - 73. Let u be k(-19). Factor -1/2 - 3/2*x**2 - 3/2*x - 1/2*x**u.
-(x + 1)**3/2
Let x = -25 - -29. Let j(w) be the third derivative of -1/105*w**7 + 0 - 1/12*w**x + 0*w - 1/3*w**3 - 2*w**2 - 1/168*w**8 + 1/15*w**5 + 1/30*w**6. Factor j(d).
-2*(d - 1)**2*(d + 1)**3
Let i be ((-21)/(-18))/7 + (-2)/(-4). Find a, given that 0*a**2 + 1/3*a**4 - 2/3*a**3 + i*a - 1/3 = 0.
-1, 1
Let a(o) be the third derivative of 0*o + 0 - 1/2*o**3 + 3*o**2 - 1/20*o**5 - 1/4*o**4. Factor a(m).
-3*(m + 1)**2
Let f be 5/6 + 8/(-16). Let r be 6 + -10 - 26/(-6). Factor 2/3*c + f*c**2 + r.
(c + 1)**2/3
Let m(f) be the first derivative of f**6/12 + f**5/10 - f**4/6 - 3*f**2/2 - 3. Let n(h) be the second derivative of m(h). Factor n(d).
2*d*(d + 1)*(5*d - 2)
Let u(n) = -n**2 + 5*n + 8. Let x be u(6). Suppose 1/3 + 0*r - 1/3*r**x = 0. What is r?
-1, 1
Let r(i) = -6*i**5 - 10*i**4 + 2*i**3 - 6*i - 10. Let d(v) = 2*v**5 + 3*v**4 - v**3 + 2*v + 3. Let u(k) = -10*d(k) - 3*r(k). Find t, given that u(t) = 0.
-1, 0, 1
Let n(u) be the second derivative of -u**6/90 + u**5/30 + u**4/9 - u**3/9 - u**2/2 - 39*u. Factor n(l).
-(l - 3)*(l - 1)*(l + 1)**2/3
Suppose 0*f**4 + 0*f + 6/11*f**3 + 0 - 2/11*f**5 - 4/11*f**2 = 0. Calculate f.
-2, 0, 1
Let m(d) = -5*d**4 - 3*d**3 + 9*d**2 - 7*d. Let f(u) = 9*u**4 + 6*u**3 - 17*u**2 + 13*u. Let y(o) = 6*f(o) + 11*m(o). Determine s, given that y(s) = 0.
0, 1
Let x = -36 - -109/3. Suppose x - 1/3*v**2 + 0*v = 0. What is v?
-1, 1
Factor 5/2*w**2 + 0 - 5/6*w**4 + 0*w**3 - 5/3*w.
-5*w*(w - 1)**2*(w + 2)/6
Let b(z) = z - 1. Let f(x) = -x**2 - 5*x + 8. Let d(h) = -4*b(h) - f(h). Let s be d(-3). Factor 3*q + 2 + s*q**2 - 2*q**2 + q**2.
(q + 1)*(q + 2)
Suppose 4/19*g**3 - 2/19*g**5 - 2/19*g + 4/19*g**2 - 2/19*g**4 - 2/19 = 0. Calculate g.
-1, 1
Let x be (33/22)/(3/4). Suppose -x*n + 2 = -2. Determine l, given that -1/2*l**3 - 1/2*l**4 + 1/2*l**n + 0*l + 0 + 1/2*l**5 = 0.
-1, 0, 1
Let o(z) be the third derivative of -z**8/112 - z**7/35 + z**5/10 + z**4/8 + 5*z**2. Find q such that o(q) = 0.
-1, 0, 1
Let x(m) be the third derivative of 0 + 0*m**4 + 0*m**3 - 1/168*m**8 + 0*m**7 + 0*m + 0*m**5 + 1/60*m**6 - 10*m**2. Factor x(n).
-2*n**3*(n - 1)*(n + 1)
Let t(q) = 6*q - 18. Let a be t(3). Factor 14/5*j**2 + 4/5*j + a.
2*j*(7*j + 2)/5
Let u(x) = 8*x**3 - 4*x**2 - 8*x. Let w(t) = -t**4 + 9*t**3 - 5*t**2 - 9*t. Let y(g) = 6*u(g) - 4*w(g). Find z, given that y(z) = 0.
-3, -1, 0, 1
Suppose -d + 2*u - 6 + 2 = 0, 0 = -2*d + 2*u. Suppose -7/2*n**d + 3/2*n**3 - 5/2*n**5 + 7/2*n**2 + n + 0 = 0. What is n?
-1, -2/5, 0, 1
Let k be (-23)/4 + -9 + 15. Factor 0*a - k + 1/4*a**2.
(a - 1)*(a + 1)/4
Let b(a) = a**3 + a**2 - a + 4. Let x be b(0). Factor 8*t - x*t**2 + 0 + 3 - 7.
-4*(t - 1)**2
Let c = -4 - -7. Let k(a) be the third derivative of 0*a - 1/36*a**4 + 2/27*a**3 + 1/540*a**6 + c*a**2 + 0*a**5 + 0. Factor k(t).
2*(t - 1)**2*(t + 2)/9
Let l(r) be the second derivative of -r**5/60 + r**4/18 + r**3/18 - r**2/3 - 2*r. Factor l(o).
-(o - 2)*(o - 1)*(o + 1)/3
Let b(i) be the third derivative of -5*i**2 + 1/360*i**6 + 0 + 0*i**5 + 0*i**3 - 1/72*i**4 + 0*i. Factor b(q).
q*(q - 1)*(q + 1)/3
Solve 3 + 3 - 9*m + 405*m**2 - 402*m**2 = 0 for m.
1, 2
Let x(l) be the third derivative of l**7/210 - l**6/60 - l**5/60 + l**4/12 + 9*l**2. Factor x(q).
q*(q - 2)*(q - 1)*(q + 1)
Factor -8/3*x + 4/3 - 7/3*x**3 - 19/3*x**2.
-(x + 1)*(x + 2)*(7*x - 2)/3
Solve 16/3*u**2 - 2/3 - 5/3*u - 3*u**3 = 0 for u.
-2/9, 1
Factor 135*p - 9*p**2 - 675 + 1/5*p**3.
(p - 15)**3/5
Let c(g) = -8*g**4 - 11*g**3 + g**2 + 3*g - 3. Let j(r) = -23*r**4 - 32*r**3 + 4*r**2 + 8*r - 8. Let y(t) = -8*c(t) + 3*j(t). Solve y(h) = 0.
-2, 0, 2/5
Let a = 9 - 5. Let r be (-2)/4 + 18/a. Let -2 + 8*b + 16*b**3 + r*b - 24*b**2 + 0 = 0. Calculate b.
1/2
Factor 5/3 - 35/6*n**3 + 40/3*n**2 - 55/6*n.
-5*(n - 1)**2*(7*n - 2)/6
Factor -23/2*j**2 - 121/2 - 143/2*j - 1/2*j**3.
-(j + 1)*(j + 11)**2/2
Let w(u) = 3*u**2 - 11*u + 5. Let c(y) = 4*y**2 - 12*y + 6. Let d(b) = 5*c(b) - 6*w(b). Factor d(s).
2*s*(s + 3)
Suppose -3*x + 26 = 10*x. Let f(y) be the first derivative of -5/2*y**x + 2*y + 3 - 1/4*y**4 + 4/3*y**3. Suppose f(m) = 0. Calculate m.
1, 2
Let z(j) be the first derivative of 2*j**4/33 + 4*j**3/11 + 9*j**2/11 - 2*j + 3. Let h(c) be the first derivative of z(c). Find u, given that h(u) = 0.
-3/2
Let i(b) = 3*b**4 - b**3 + b**2 - b - 2. Let x(k) = -10*k**4 + 4*k**3 - 4*k**2 + 3*k + 7. Let s(g) = -7*i(g) - 2*x(g). Find n, given that s(n) = 0.
-1, 0, 1
Let 0 + 1/2*q**2 + 2*q = 0. What is q?
-4, 0
Let a(i) be the third derivative o