 3*f. Let p be (4 - 0 - m) + (-4)/(-10). Factor l**3 + p*l**2 + 2/5 + 9/5*l.
(l + 1)**2*(5*l + 2)/5
Let s(d) be the third derivative of d**8/10080 - 3*d**5/20 - 2*d**2. Let z(w) be the third derivative of s(w). Factor z(b).
2*b**2
Let h(v) = -4*v**3 + 68*v**2 + 160*v + 8. Let w(u) = 3*u**3 - 45*u**2 - 107*u - 5. Let a(p) = -5*h(p) - 8*w(p). Suppose a(g) = 0. What is g?
-2, 0, 7
Let x = 48 + -45. Factor -24*k + x*k**2 - 5*k**2 - 72 + 0*k**2.
-2*(k + 6)**2
Factor -192*y + 0 - 3/4*y**4 - 15*y**3 - 96*y**2.
-3*y*(y + 4)*(y + 8)**2/4
Let m be (-132)/(3/1)*1/(-2). Find v, given that 2*v - 12*v**2 + m*v**2 - 7*v**2 - v**4 = 0.
-1, 0, 2
Let q(p) be the first derivative of 2*p**5/55 + p**4/11 - 2*p**3/33 - 2*p**2/11 - 19. Factor q(a).
2*a*(a - 1)*(a + 1)*(a + 2)/11
Let k(f) be the third derivative of -f**6/60 + 7*f**5/60 - f**4/8 + 19*f**2. Factor k(m).
-m*(m - 3)*(2*m - 1)
Determine h, given that 1/5*h**4 - 54/5*h**3 + 781/5*h**2 + 676/5 - 1404/5*h = 0.
1, 26
Let l(t) be the second derivative of -t**5/20 - t**4/12 + 2*t**3 - 94*t. Factor l(f).
-f*(f - 3)*(f + 4)
Let t(s) = 5*s + 235. Let k be t(-47). Let p(o) be the first derivative of -3 - 1/45*o**6 + 4/75*o**5 - 4/45*o**3 + k*o + 1/15*o**2 + 0*o**4. Factor p(b).
-2*b*(b - 1)**3*(b + 1)/15
Let i(o) = -4*o**2 + 2*o - 24. Let x(t) = -2*t**2 - 3. Let y(u) = -i(u) + 4*x(u). Factor y(l).
-2*(l + 2)*(2*l - 3)
Let o = -43 - -42. Let h be (-1)/(-3) - 0*o/(-2). Solve 1/3 - 2/3*z + h*z**2 = 0 for z.
1
Let f be ((-6)/4 + 0)/(9/(-42)). Let t be (1/(-5))/((f - 3) + -5). Factor 2/5*g**2 + 1/5*g**3 + t*g + 0.
g*(g + 1)**2/5
Solve -32/3 + 0*f + 16/3*f**2 - 2/3*f**4 + 0*f**3 = 0.
-2, 2
Suppose 24*r - 26*r + 8 = 0. Factor -66*s**2 - 71*s - 78*s**2 - 121*s - 3*s**r - 36*s**3.
-3*s*(s + 4)**3
Let v(o) be the second derivative of o**4/48 + o**3/4 + o**2 - 48*o. Find i, given that v(i) = 0.
-4, -2
Solve 230 - 4*i**2 - 220*i + 5*i**2 + 2190 - 4*i**2 + 8*i**2 = 0 for i.
22
Let c(n) be the second derivative of -n**6/165 + n**5/110 + 21*n**4/22 + 81*n**3/11 + 270*n**2/11 - 74*n + 2. Factor c(f).
-2*(f - 10)*(f + 3)**3/11
Let p(i) = -i**4 + i**3 - i**2 - i + 1. Let u(v) = -23*v**4 + 63*v**3 + 12*v**2 - 53*v + 18. Let o(x) = -3*p(x) + u(x). Determine y, given that o(y) = 0.
-1, 1/2, 3
Let p be 5*(-6)/20*(-95)/285. Solve -1/2*g**2 + p + 0*g = 0.
-1, 1
Let f(s) be the first derivative of 36*s**5/35 + 33*s**4/14 + 40*s**3/21 + 4*s**2/7 + 42. Factor f(c).
2*c*(2*c + 1)*(3*c + 2)**2/7
Let k(c) = 8*c**4 + 61*c**3 - 59*c**2 - 5. Let l(g) = 4*g**4 + 30*g**3 - 30*g**2 - 2. Let d(j) = 2*k(j) - 5*l(j). Factor d(w).
-4*w**2*(w - 1)*(w + 8)
Suppose -12 = 4*y - 5*v, 7*y + 5*v + 4 = 19*y. Suppose -28/11*t - 48/11*t**y - 10/11*t**4 - 6/11 - 36/11*t**3 = 0. Calculate t.
-1, -3/5
Let l be 5 + 5/(-25)*149. Let y = 126/5 + l. Factor -6/5*o**2 - 4/5*o + y.
-2*(o + 1)*(3*o - 1)/5
Suppose 3*l = 3*c - 15, 0 = 5*c - l - 3*l - 28. What is k in -5*k**2 - 2*k - 2*k**2 + c*k**2 - 2*k**2 = 0?
-2, 0
Factor 1/4*n**3 - 1/4*n**5 + 1/4*n**4 + 0 - 1/4*n**2 + 0*n.
-n**2*(n - 1)**2*(n + 1)/4
Let o(k) be the first derivative of 5*k**4/4 + 5*k**3 - 45*k**2/2 + 25*k + 84. Factor o(q).
5*(q - 1)**2*(q + 5)
Let k(j) be the third derivative of -j**5/270 - 77*j**4/108 - 76*j**3/27 - 21*j**2 + 2. Factor k(q).
-2*(q + 1)*(q + 76)/9
Factor 2*n**3 - 56/3*n + 4*n**2 - 2/3*n**4 + 16.
-2*(n - 2)**3*(n + 3)/3
Let d(h) be the first derivative of -2*h**3/3 - 238*h**2 - 28322*h - 920. Factor d(g).
-2*(g + 119)**2
Let r be 1 + 6/(-8) - 176/1216. Find f, given that 8/19*f - r - 12/19*f**2 + 8/19*f**3 - 2/19*f**4 = 0.
1
Factor -334 + 19*n**3 + 54 + 692*n - 14*n**3 + 8*n**3 + 15*n**3 + 1000*n**2.
4*(n + 1)*(n + 35)*(7*n - 2)
Let b be 2/8 - (8 + (-165)/12). Let m(v) be the first derivative of 8/3*v**3 - 12*v**4 - 6 + 0*v**2 + 0*v + 18*v**5 - 25/3*v**b. Factor m(c).
-2*c**2*(c - 1)*(5*c - 2)**2
Let n(d) be the third derivative of -d**7/525 + d**6/150 + d**5/50 - d**4/15 - 4*d**3/15 - 127*d**2. Solve n(f) = 0.
-1, 2
Let q(s) be the second derivative of -3*s**5/80 + s**4/4 - 3*s**3/8 + 53*s - 2. Factor q(x).
-3*x*(x - 3)*(x - 1)/4
Let s(v) be the second derivative of v**6/210 - 2*v**4/21 + 8*v**2/7 - 62*v. Factor s(z).
(z - 2)**2*(z + 2)**2/7
Let t(u) be the second derivative of 0*u**2 - 2*u**3 + 11*u - 3 + 2*u**4 + 1/10*u**6 - 3/4*u**5. Factor t(r).
3*r*(r - 2)**2*(r - 1)
Let i(p) be the second derivative of -p**7/12600 + p**6/900 - 2*p**4 + 38*p. Let n(a) be the third derivative of i(a). Factor n(l).
-l*(l - 4)/5
Determine b, given that 2*b - 5*b**2 + 4*b**3 - 27*b**4 + 8*b**4 + 10*b**4 + 8*b**4 = 0.
0, 1, 2
Let c = 40 - 38. Let z be (c + -6)*4/(-104). Let -2/13*f**3 + z*f + 2/13 - 2/13*f**2 = 0. Calculate f.
-1, 1
Suppose -3*r - 22 = -4*h, -2*r + 6*h - 24 = h. Let s be (-35)/(-14) + r/4. Factor -q - q**s + q + 1.
-(q - 1)*(q + 1)
Let g(m) be the second derivative of 0 + 1/2*m**4 - 5/2*m**2 - 1/20*m**5 - 2*m**3 + 4*m. Let q(f) be the first derivative of g(f). Let q(b) = 0. Calculate b.
2
Let c(i) be the second derivative of 2/15*i**6 + 0 + 0*i**2 - 4/5*i**5 + 4/3*i**4 + 0*i**3 + 4*i. Find p, given that c(p) = 0.
0, 2
Let m be (-6 - (16 + -22))/1. Find l such that m - 8/9*l**3 - 2/9*l**2 + 0*l = 0.
-1/4, 0
Let r(c) be the first derivative of -2*c**3/9 + 4*c**2/3 - 2*c + 72. Factor r(k).
-2*(k - 3)*(k - 1)/3
Let a(c) be the third derivative of 0*c + 5/336*c**8 - 14*c**2 + 0*c**5 + 0*c**4 + 0*c**7 + 0 + 0*c**3 - 1/24*c**6. Find x such that a(x) = 0.
-1, 0, 1
Factor -10/9*b**3 + 2/9*b**4 + 4/3*b**2 + 8/9*b - 16/9.
2*(b - 2)**3*(b + 1)/9
Factor 1/2*i**2 + 3/2*i + 1.
(i + 1)*(i + 2)/2
Let b = -19 + 22. Let i = -1 + b. Factor -19*l**3 + 7*l**2 - 3*l**i - 1 + 20*l + 15*l**3 + 13.
-4*(l - 3)*(l + 1)**2
Let v = 3/4967 - -4955/19868. What is m in 1/2*m**3 - 1/4*m + 1/2*m**2 - 1/4 - 1/4*m**5 - v*m**4 = 0?
-1, 1
Let q(j) be the second derivative of j**6/75 + 2*j**5/25 - 14*j**4/15 + 32*j**3/15 + 84*j. Factor q(m).
2*m*(m - 2)**2*(m + 8)/5
Determine p so that 2/3*p**3 + 2/3*p**5 + 28/3*p**2 + 16/3 - 8/3*p**4 - 40/3*p = 0.
-2, 1, 2
Let f(u) = -u**2 + 13*u + 4. Let t be f(13). Suppose 3*a = t*a - 2. Find s such that 48*s + 48*s**a + 29*s**4 - 5*s**4 + 3*s**5 + 48*s**2 + 72*s**3 = 0.
-2, 0
Let k(n) = -17*n**3 - 6*n**2 + n + 14. Let w(i) = 6*i**3 + 2*i**2 - 5. Let x(z) = -3*k(z) - 8*w(z). Let x(p) = 0. What is p?
-1, -2/3, 1
Let g(r) be the first derivative of -r**4/14 - 2*r**3/7 + 4*r**2/7 + 24*r/7 - 311. Factor g(m).
-2*(m - 2)*(m + 2)*(m + 3)/7
Solve 12/5 - 16/5*q + 7/5*q**2 - 1/5*q**3 = 0.
2, 3
Let g(n) be the third derivative of -n**7/945 - n**6/60 - n**5/10 - n**4/4 + 116*n**2. Factor g(c).
-2*c*(c + 3)**3/9
Let i(b) be the third derivative of 1/70*b**8 + 27/100*b**6 - 14*b**2 - 1/5*b**4 + 0 + 4/25*b**5 + 0*b + 0*b**3 + 19/175*b**7. Suppose i(c) = 0. Calculate c.
-2, -1, 0, 1/4
Suppose -5*y = 2*b - 14, 2*b - 8 + 12 = 4*y. Let 16/7*w**y + 16/7*w**4 - 4/7*w - 4/7*w**5 - 24/7*w**3 + 0 = 0. What is w?
0, 1
Let n = 29243 + -29241. Find f, given that 6 + 15/2*f + 3/2*f**n = 0.
-4, -1
Let w be (-4)/2200*-2*1020/8. Let m = w + 3/22. Factor -m*v**2 + 0 + 3/5*v.
-3*v*(v - 1)/5
Suppose 0 = 472*h - 487*h. Let y(l) be the first derivative of 0*l**3 - 4/5*l**5 + 0*l + h*l**2 - 2*l**4 - 7. Factor y(a).
-4*a**3*(a + 2)
Let t be 13 + (-1648)/140 + (124/20 - 6). Factor -46/7*r**2 + 20/7*r + t*r**3 + 16/7.
2*(r - 4)*(r - 1)*(5*r + 2)/7
Let f = 467/13620 - 4/227. Let p(u) be the second derivative of 2*u + 0*u**2 + 1/15*u**3 + 0 - f*u**4. Determine m so that p(m) = 0.
0, 2
Let k(c) = -15*c + 6. Let j be k(0). Suppose 8*p = 13*p - 4*u + j, -p + 4*u - 14 = 0. Factor -1/6*t - 1/6*t**p + 0.
-t*(t + 1)/6
Let j = 15/4 + -97/28. Suppose -30*k - 23*k + 159 = 0. Factor 0 + 2/7*z**2 - j*z**k + 0*z.
-2*z**2*(z - 1)/7
Let c be (-2346)/6732 - (-2)/11 - (-22)/60. Factor -c*x + 1/5*x**2 - 2/5.
(x - 2)*(x + 1)/5
Let s(o) be the third derivative of -1/8*o**4 + 1/2*o**3 - 1/4*o**5 + 0 - 3/40*o**6 + 0*o - 18*o**2. Suppose s(t) = 0. Calculate t.
-1, 1/3
Let n = -26 - -28. Let 6*u + 5*u**2 - 18*u**3 - 3*u**n - 3*u**4 + 21*u**5 - 5*u**2 - 15*u**5 = 0. Calculate u.
-1, 0, 1/2, 2
Let f(r) be the second derivative of -r**7/5040 + r**6/1080 - r**5/720 - 3*r**3/2 - 7*r. Let a(p) be the second derivative of f(p). Suppose a(z) = 0. What is z?
0