2)**2/6
Let h be ((-1)/18)/(3/(-9)). Let k(z) be the second derivative of -4*z - 1/9*z**3 + h*z**2 + 0 + 1/36*z**4. Solve k(l) = 0 for l.
1
Let u(a) be the second derivative of 0 + 1/45*a**4 + 1/45*a**3 - 5*a + 0*a**2 + 1/150*a**5. Factor u(k).
2*k*(k + 1)**2/15
Let x be (-10)/(-5) + (1 - 1*-9). Let p be (-8)/x + 8/9. Factor 0 - p*a**3 + 0*a - 2/9*a**2.
-2*a**2*(a + 1)/9
Let s(q) be the third derivative of -q**9/30240 - q**8/13440 + 11*q**4/12 - 23*q**2. Let z(a) be the second derivative of s(a). Factor z(n).
-n**3*(n + 1)/2
Let y(p) be the third derivative of 4*p**2 + 0 - 7/156*p**4 + 2/39*p**3 + 0*p + 1/78*p**5. Factor y(d).
2*(d - 1)*(5*d - 2)/13
Suppose -c - 4*a - 17 = 0, -2 = c - 5*a - 30. Solve 61 - 3*f**4 + 2*f**5 - 2*f**c - 61 = 0.
-1/2, 0, 2
Let m = 26880/13 + -403096/195. Find t, given that -2/3*t - 2/15*t**2 - m = 0.
-4, -1
Let j(u) be the second derivative of 85*u**4/2 + 53*u**3/2 - 9*u**2 - 9*u - 37. Factor j(c).
3*(5*c + 2)*(34*c - 3)
Suppose 14*n - 8*n - 30 = 0. Factor -d - 4*d**2 + n - 29 - 27*d.
-4*(d + 1)*(d + 6)
Let r(h) be the third derivative of h**6/3780 + h**5/180 + 5*h**4/126 - 11*h**3/2 + 45*h**2. Let d(b) be the first derivative of r(b). Factor d(j).
2*(j + 2)*(j + 5)/21
Let n(x) = x**2 - 3*x + 1. Let y be n(-6). Suppose -57*z**2 + 92*z**2 + 5*z**3 + 25*z - 10 - y*z**2 = 0. Calculate z.
1, 2
Factor 100*v - v**2 + 685 - 392 - 392.
-(v - 99)*(v - 1)
Suppose 4*m = o - 300, 4*o = m - 0*m + 1155. Factor -40*b**3 + 5*b**4 + 80*b**2 - 288*b + o*b.
5*b**2*(b - 4)**2
Let m(r) be the second derivative of 49*r**7/120 - 49*r**6/40 + 63*r**5/40 - 9*r**4/8 - 7*r**3/6 + 4*r. Let c(l) be the second derivative of m(l). Factor c(i).
(7*i - 3)**3
Let w(h) be the second derivative of -7*h**5/8 - 13*h**4/6 - 19*h**3/12 - h**2/2 + 66*h. Determine u, given that w(u) = 0.
-1, -2/7, -1/5
Let c(g) be the second derivative of 0 - 5/12*g**4 - 5/6*g**2 + 1/12*g**5 + 8*g + 5/6*g**3. Solve c(j) = 0 for j.
1
Suppose 0 = 3*t - 2*p - 24 + 8, -2*p - 28 = -5*t. Find h such that -9*h**4 + 15*h**2 + 14*h - 22*h - 2 + t*h**3 + 8*h**2 - 14 = 0.
-1, 4/3
Let p(u) = u**3 - u**2 + 1. Let z(g) = -g**4 + 8*g**3 - 4*g**2 - 31*g - 19. Let f(l) = -2*p(l) + 2*z(l). Factor f(h).
-2*(h - 5)*(h - 4)*(h + 1)**2
Determine g, given that 0*g + 4/7*g**5 - 4/7*g**3 + 8/7*g**4 - 8/7*g**2 + 0 = 0.
-2, -1, 0, 1
Let n(s) be the first derivative of 1/6*s**2 + 4/9*s**3 - 1/6*s**4 - 2/3*s + 1/18*s**6 - 2/15*s**5 + 33. Suppose n(k) = 0. What is k?
-1, 1, 2
Let p(g) be the first derivative of -2/5*g**3 + 2*g + 30 + 14/5*g**2. Let p(r) = 0. What is r?
-1/3, 5
Suppose 5*w - 5 = -19*h + 24*h, -2*h + 3*w = 5. Find a such that 3/7 - 3/7*a**h + 0*a = 0.
-1, 1
Let j be ((-972)/(-24))/((-8)/6 - -2). Determine o so that -j*o**2 - 27*o - 3 = 0.
-2/9
Let b(j) = -j**3 - j + 1. Let t(u) = 16*u**3 - 134*u**2 + 278*u - 94. Let w(s) = 6*b(s) + t(s). Solve w(l) = 0.
2/5, 2, 11
Let h be (5 + 1)*(7/2 + -3). Let -2*k**4 + 59*k - 8*k**h + 6*k**4 - 59*k + 4*k**2 = 0. Calculate k.
0, 1
Let m be ((-4)/28)/((-264)/924). Find a such that -m*a**2 + 1/4*a**4 + 0*a**3 + 1/4 + 0*a = 0.
-1, 1
Let z(d) be the second derivative of d**4/36 - 17*d**3/9 + 289*d**2/6 - 2*d - 3. Let z(b) = 0. Calculate b.
17
Let r = -27 + 76. Let 6 - 9 - r*j - 11*j - 17 - 25*j**2 = 0. What is j?
-2, -2/5
Let r(u) be the first derivative of u**4/3 + 16*u**3/3 - 26*u**2/3 - 81. Factor r(p).
4*p*(p - 1)*(p + 13)/3
Let b(c) = 19*c**4 - 64*c**3 + 15*c**2 - 5*c + 5. Let y(z) = -z**4 - 2*z**3 + z**2 + z - 1. Let u(m) = -b(m) - 5*y(m). Factor u(s).
-2*s**2*(s - 5)*(7*s - 2)
Suppose -7 = 15*c - 16*c. Suppose -c*f + 15 = 1. Factor 0 + 1/3*o**3 - 2/3*o - 1/3*o**f.
o*(o - 2)*(o + 1)/3
Let x(y) be the third derivative of y**8/112 + y**7/35 + y**6/40 + 2*y**2 + 12*y. Let x(q) = 0. Calculate q.
-1, 0
Let x(b) = -12*b**4 - 26*b**3 - 28*b**2 + 10*b - 8. Let g(m) = -8*m**4 - 18*m**3 - 18*m**2 + 7*m - 5. Let z(u) = 8*g(u) - 5*x(u). Factor z(d).
-2*d*(d + 1)*(d + 3)*(2*d - 1)
What is l in -5*l**2 - 1 + 8*l**2 - 5*l**3 + 221*l - 445*l + 225*l + 2*l**4 = 0?
-1/2, 1
Let y = -4779 - -62129/13. Solve y*w**3 + 0 + 0*w + 0*w**2 = 0.
0
Let r = -101 + 335. Let h = r - 2104/9. Suppose h*j + 2/9 - 2/9*j**2 - 2/9*j**3 = 0. Calculate j.
-1, 1
Let y = -2048 - -2048. Find k such that 0 - 8/5*k**4 + 0*k**2 + 4/5*k**3 + 4/5*k**5 + y*k = 0.
0, 1
Let a = -20 - -22. Let -2*w**5 - 3*w**4 + 4*w**a + w + w + w**4 - 2*w**4 = 0. Calculate w.
-1, 0, 1
Let l(n) be the second derivative of n**7/420 + n**6/120 + 15*n**2/2 - 9*n. Let g(v) be the first derivative of l(v). Factor g(f).
f**3*(f + 2)/2
Let i = 49/1110 + -2/185. Let c(v) be the second derivative of 0 - 1/20*v**5 - i*v**6 + 0*v**2 + 1/12*v**4 - v + 1/6*v**3. Factor c(k).
-k*(k - 1)*(k + 1)**2
Let v be (-48)/(-15)*(2 + 3). Let d(g) = g**2 - 15*g - 14. Let a be d(v). What is n in 6 + 5*n**a - 11*n**2 - 3*n**2 - 3*n = 0?
-1, 2/3
Let u(o) = 5*o**4 - 37*o**3 + 75*o**2 - 69*o + 18. Let x(l) = -110*l**4 + 815*l**3 - 1650*l**2 + 1520*l - 395. Let n(w) = -45*u(w) - 2*x(w). Factor n(p).
-5*(p - 4)*(p - 1)**3
Let l(c) be the third derivative of c**8/23520 + c**7/980 + c**6/168 - 5*c**5/84 - 7*c**4/6 + 3*c**2. Let u(m) be the second derivative of l(m). Factor u(v).
2*(v - 1)*(v + 5)**2/7
Let h(s) be the first derivative of -3*s**4/16 + 59*s**3/4 - 2697*s**2/8 + 2523*s/4 + 402. Factor h(a).
-3*(a - 29)**2*(a - 1)/4
Let t(h) be the second derivative of -1/10*h**3 - 1/20*h**4 - 12*h + 0 - 1/100*h**5 - 1/10*h**2. What is x in t(x) = 0?
-1
Suppose 0 = 10*p - 10 - 40. Let z be ((-8 + p)/(-6))/2. Factor -1/4*k**3 + 0*k**2 + z*k + 0.
-k*(k - 1)*(k + 1)/4
Suppose 3*q - 4 = -1. Let n = -6 + 10. Factor -2*o**2 - 11*o**4 + 8*o**4 + 2 - q + 4*o**n.
(o - 1)**2*(o + 1)**2
Factor 2/11*f**4 - 6/11 - 12/11*f**3 - 28/11*f**2 - 2*f + 2/11*f**5.
2*(f - 3)*(f + 1)**4/11
Let r(d) be the first derivative of -d**6/720 + d**4/12 - 2*d**3/3 + 1. Let t(y) be the third derivative of r(y). Factor t(i).
-(i - 2)*(i + 2)/2
Suppose -5*y - d = -0*y - 800, 5*d = 2*y - 347. Factor -157*k**2 + 3*k + y*k**2 - 3*k - 4*k.
4*k*(k - 1)
Factor 12 - 5/2*r**3 + 61/2*r + 16*r**2.
-(r - 8)*(r + 1)*(5*r + 3)/2
Solve -128/3*o + 172/3*o**3 - 16/3 - 44*o**2 + 104/3*o**4 = 0.
-2, -1/2, -2/13, 1
Suppose -q + 31 = -15. Factor 3*w - 43*w**2 + q*w**2 - 3 + 3.
3*w*(w + 1)
Suppose 0*b = b + 3*w - 29, 5*b - w - 65 = 0. Let l = b + -10. Factor 2*v - 5/2*v**3 - 3*v**2 - 1/2*v**l + 4.
-(v - 1)*(v + 2)**3/2
Let x(j) be the second derivative of -j**5/110 - 2*j**4/11 - 15*j**3/11 - 50*j**2/11 - 28*j + 2. Find i such that x(i) = 0.
-5, -2
Let u be (-3)/(-2) - (-4)/8. Suppose -u*z = -v - 35, -6*z = -5*z - 5*v - 22. Let 72*f - z*f**2 - 12*f**3 - 29*f**3 - 43*f**2 - 9*f**3 - 16 = 0. What is f?
-2, 2/5
Let y(a) be the first derivative of -2*a**3/3 - 61*a**2 - 120*a - 504. Find f, given that y(f) = 0.
-60, -1
Let t be (-43 + 41)/((-12)/1). Let 1/6*r**5 + 0 + t*r**2 + 1/2*r**3 + 0*r + 1/2*r**4 = 0. What is r?
-1, 0
Let y = -34 + 36. Suppose 0 = u + y*u - 12. Determine s, given that 4*s**4 - s**3 - 5*s**u + 2*s**4 + 2*s**3 - s**5 - s**2 = 0.
-1, 0, 1
Suppose 5*l = 7 + 23. Let x be (3/3)/((-7)/(-14)). Find r such that -2*r**2 - l + 0*r**2 - r**x - 9*r = 0.
-2, -1
Let s(d) be the third derivative of 0*d**3 - 25*d**2 + 1/42*d**4 + 0*d + 1/210*d**5 - 1/49*d**7 + 0 - 4/105*d**6. Solve s(g) = 0.
-1, -2/5, 0, 1/3
Let a = 22017/1610 - -9/230. Let 18/7*u + 0 + 128/7*u**3 + a*u**2 = 0. Calculate u.
-3/8, 0
Let r(y) = 385*y**3 - 25*y**2 - 1360*y + 190. Let t(n) = 97*n**3 - 6*n**2 - 340*n + 48. Let m(p) = 4*r(p) - 15*t(p). Find u, given that m(u) = 0.
-2, 2/17, 2
Let u(m) be the second derivative of -m**5/90 - 2*m**4/9 - 20*m**3/27 - 8*m - 26. Factor u(p).
-2*p*(p + 2)*(p + 10)/9
Let -3*n**5 + 4*n**3 + 38 - 3*n**2 + 21*n + 30*n**4 - 22*n**3 + 16 - 81*n**2 = 0. Calculate n.
-1, 1, 2, 9
Let m(p) = -110*p**3 + 202*p**2 - 51*p - 34. Let t(c) = -54*c**3 + 101*c**2 - 26*c - 16. Let q(b) = 6*m(b) - 13*t(b). Factor q(h).
(h - 2)*(2*h - 1)*(21*h + 2)
Suppose -4*w - 5*w = -2*w. Suppose 1 = 3*p - 8, -r + 3*p - 6 = w. Find q such that 1/2*q**r + 0 + q**2 + 1/2*q = 0.
-1, 0
Let l(u) be the third derivative of -u**9/11340 - u**8/5040 + u**7/1890 + u**6/540 + u**4/4 - 14*u**2. Let d(i) be the second derivative of l(i). Factor d(y).