*9/1260 + r**8/210 + r**7/90 + r**6/90 - r**4/12 - 2*r**2. Let s(x) be the second derivative of n(x). Factor s(j).
4*j*(j + 1)**2*(3*j + 2)
Let l(c) be the third derivative of -c**8/6720 - c**7/420 + c**5/30 + 18*c**2. Let x(d) be the third derivative of l(d). Suppose x(r) = 0. Calculate r.
-4, 0
Factor 13 - 2 - 5*n**2 - 12*n - 17*n**2 + 38*n**2 - 15*n**2.
(n - 11)*(n - 1)
Let n = 189 - 562/3. Let h(f) be the second derivative of 3*f**2 + 1/6*f**4 + 1/10*f**5 + 0 + 5*f - n*f**3. What is r in h(r) = 0?
-3, 1
Suppose -3*v = -2*b - 31, 5*v - b - 33 - 7 = 0. Let p(c) be the first derivative of v + 0*c - 4/3*c**3 - 4*c**2. Find a, given that p(a) = 0.
-2, 0
Let l = -6899/30 - -230. Let g(x) be the third derivative of 0*x + 5*x**2 + 0 - l*x**5 + 0*x**3 - 1/12*x**4. Suppose g(h) = 0. Calculate h.
-1, 0
Factor 71/3*n - 86/3*n**2 - 2 + 7*n**3.
(n - 3)*(n - 1)*(21*n - 2)/3
Let v(p) = -373*p + 746. Let g be v(2). Determine k, given that 10/11*k**2 - 4/11*k + g - 6/11*k**3 - 2/11*k**4 + 2/11*k**5 = 0.
-2, 0, 1
Let m be (3 - (1 + 4))*2 + 10. Let g(y) be the second derivative of 1/15*y**m + 9*y + 4/3*y**3 + y**4 + 2/5*y**5 + 0 + y**2. Solve g(x) = 0 for x.
-1
Suppose -65 = -0*n - 5*n. Suppose 4*b - n = -1. What is c in 4*c - 6*c**2 + c**4 - 2*c**3 - 2*c**b - 11*c**4 + 16*c**2 = 0?
-1, -2/5, 0, 1
Let j(g) be the third derivative of -g**5/60 + 19*g**4/24 - 131*g**2. Let j(o) = 0. Calculate o.
0, 19
Let k be (-1)/((-8)/(-10) - 1). Suppose -5*r + k - 15 = -5*s, 2*r + 19 = 5*s. Factor 12*x**2 + 4*x - 13*x**r + 2*x**2 + 23*x**3.
2*x*(x + 1)*(5*x + 2)
Let n(m) = m + 3. Let l be n(-1). Let 4*k**2 - 8*k**l - 1 - 2*k + 4 + 2*k**3 + k**4 = 0. What is k?
-3, -1, 1
Let m(d) = 44*d**3 - 533*d**2 + 691*d - 232. Let p(r) = -21*r**3 + 267*r**2 - 346*r + 116. Let f(k) = -6*m(k) - 13*p(k). Solve f(y) = 0.
2/3, 29
Let l = -3 + 8. Suppose 0 = -5*n + l - 0. Suppose -t**4 + 0*t**4 - 2*t**2 + n + 2*t**4 + 0 = 0. What is t?
-1, 1
Let g be (-60)/(-7) + (-4)/7. Suppose -g*v + 15 = -3*v. What is w in 3*w**4 - 3*w**4 + 0*w**5 - 3*w**4 + v*w**5 = 0?
0, 1
Let f(u) be the third derivative of u**8/560 + u**7/175 + u**6/200 - 283*u**2. Solve f(n) = 0.
-1, 0
Factor 1/6*m**4 - 2*m**2 - 1/3*m**3 - 7/3*m - 5/6.
(m - 5)*(m + 1)**3/6
Let t be (-589)/57 + 19 + (-35)/5. Let -1/6*a**4 + a**3 - 1/2 + t*a - 2*a**2 = 0. What is a?
1, 3
Let p(w) be the third derivative of -w**10/40320 + 3*w**8/8960 - w**7/1680 + 5*w**4/8 - 15*w**2. Let s(m) be the second derivative of p(m). Factor s(v).
-3*v**2*(v - 1)**2*(v + 2)/4
Let x be (3*-2)/3*-5. Let r(f) = 3*f**2 - 9*f - 2. Let v(w) = -3 + 2 - w**2 + 19*w - 23*w + 2*w**2. Let g(l) = x*v(l) - 4*r(l). Factor g(c).
-2*(c + 1)**2
Let w(s) be the second derivative of s**8/1344 + s**7/252 + s**6/144 - 11*s**4/6 - 14*s. Let f(l) be the third derivative of w(l). Determine r so that f(r) = 0.
-1, 0
Let x(l) = -l**3 - 12*l**2 - 20*l + 4. Let z be x(-10). Factor -8/11*k**2 + 0*k**3 + 2/11*k**z + 0 + 0*k.
2*k**2*(k - 2)*(k + 2)/11
Suppose -2*l = -7*l. Factor -5*a + 3*a - 2*a**2 + 3*a + l*a + a**3.
a*(a - 1)**2
Let c(i) be the second derivative of i**4 - 9/4*i**3 + 0*i**2 + i + 0 + 3/40*i**5. Factor c(r).
3*r*(r - 1)*(r + 9)/2
Let -4/7*n**4 - 12/7*n**5 + 20/7*n**3 + 4/7*n**2 - 8/7*n + 0 = 0. What is n?
-1, 0, 2/3, 1
Let d be ((-14)/420)/(93/(-620)). Factor 2/9*z - 4/3 + 4/3*z**2 - d*z**3.
-2*(z - 6)*(z - 1)*(z + 1)/9
Determine o, given that 3/5*o**3 + 1449/5*o + 1323/5 + 129/5*o**2 = 0.
-21, -1
Let w(k) be the third derivative of -25/24*k**4 - 1/3*k**5 - 5/3*k**3 - 1/24*k**6 + 12*k**2 + 0*k + 0. Factor w(g).
-5*(g + 1)**2*(g + 2)
Determine c so that 8*c**3 - 4/3*c + 1/3*c**4 - 28 + 21*c**2 = 0.
-21, -2, 1
Let v(y) = y**4 - 5*y**3 + 1. Let w(a) = 5*a**4 - 32*a**3 + 35*a**2 + 12*a - 32. Let f(x) = -4*v(x) + w(x). Suppose f(b) = 0. Calculate b.
-1, 1, 6
Let g(v) be the third derivative of 0 + 0*v - 1/44*v**4 - 1/330*v**5 - 32*v**2 - 2/33*v**3. Factor g(l).
-2*(l + 1)*(l + 2)/11
Suppose 0 = -3*v + 9, -46 + 71 = 5*z + 5*v. Factor 6/5*c**z - 12/5*c**3 - 3/5*c**5 - 1/5*c + 2*c**4 + 0.
-c*(c - 1)**3*(3*c - 1)/5
Factor -76/15*x + 722/15 + 2/15*x**2.
2*(x - 19)**2/15
Let g(x) = -13*x**3 + 84*x**2 - 92*x - 7. Let y(w) = -6*w**3 + 42*w**2 - 45*w - 3. Let d(l) = -3*g(l) + 7*y(l). Factor d(v).
-3*v*(v - 13)*(v - 1)
Let g(z) be the first derivative of z**7/315 - z**5/45 + z**3/9 - 5*z**2 - 6. Let w(f) be the second derivative of g(f). Factor w(l).
2*(l - 1)**2*(l + 1)**2/3
Let q(j) = 3*j**3 - 2*j**2 - 13*j. Let v(r) = 10*r**3 - 2*r**2 - 40*r. Let i(t) = -14*q(t) + 4*v(t). Factor i(y).
-2*y*(y - 11)*(y + 1)
Let v be (-5)/(-720)*-14 + (-4)/(-32). Let p(k) be the second derivative of -v*k**4 + 0 + 1/9*k**3 - 2*k + 0*k**2. Factor p(b).
-b*(b - 2)/3
Let m(w) = w. Let j be m(2). Suppose j*u + 10 = 7*u. Solve p**5 + 17*p + 15*p**3 + 6*p**4 - p**3 + u + 16*p**2 - 8*p = 0 for p.
-2, -1
Let u(y) be the second derivative of 3*y**5/40 + 7*y**4/72 - y**3/18 - 770*y. Factor u(n).
n*(n + 1)*(9*n - 2)/6
Let b be (2/4)/((-3)/(-4)). Let o = -28964/3 + 9658. Let -b*w**4 - 6*w**2 - 4/3 - o*w**3 - 14/3*w = 0. Calculate w.
-2, -1
Let b(g) be the second derivative of -g**6/6 + 3*g**5/4 + 5*g**4/6 - 10*g**3 + 20*g**2 - 624*g. Solve b(q) = 0 for q.
-2, 1, 2
Factor 0*t**3 + 0 - t**2 + 1/3*t**4 + 2/3*t.
t*(t - 1)**2*(t + 2)/3
Solve -88/5 - 2/5*n**2 - 6*n = 0.
-11, -4
Let i(r) be the first derivative of -21 - 3/2*r - 1/12*r**3 + 5/8*r**2. Determine t, given that i(t) = 0.
2, 3
Let l(c) be the first derivative of c**7/14 - c**6/5 - 3*c**5/20 + c**4/2 + 11*c - 3. Let x(b) be the first derivative of l(b). Factor x(i).
3*i**2*(i - 2)*(i - 1)*(i + 1)
Let o(w) = -w**3 - w**2 + 4*w + 1. Let d(l) = 9*l**3 - 221*l**2 + 2624*l - 2424. Let m(z) = d(z) + 4*o(z). Factor m(c).
5*(c - 22)**2*(c - 1)
Factor 2/19*p**2 - 344/19 - 18*p.
2*(p - 172)*(p + 1)/19
Let r(k) be the third derivative of k**8/112 - 17*k**7/210 + 11*k**6/40 - 23*k**5/60 + 2*k**3/3 - 24*k**2. Suppose r(b) = 0. What is b?
-1/3, 1, 2
Suppose 0 - 21/2*f**3 + 5/2*f - 8*f**2 = 0. What is f?
-1, 0, 5/21
Let b(o) be the first derivative of 3/4*o**4 + 5 + 0*o - 3/2*o**2 + 0*o**3. Solve b(h) = 0 for h.
-1, 0, 1
Suppose 4*f = -2*t - 4, t + 3*t - 5*f - 44 = 0. Find x, given that -5 + 8 + 0 + 3*x**4 + t*x**2 + 12*x**2 - 12*x - 12*x**3 = 0.
1
Let u(c) be the third derivative of -c**6/480 - 7*c**5/240 + c**4/12 - 41*c**2 - 7*c. Factor u(w).
-w*(w - 1)*(w + 8)/4
Let s(d) be the second derivative of -d**4/6 - 4*d**3/3 - 4*d**2 - 6*d - 12. Factor s(a).
-2*(a + 2)**2
Factor -32/7*r + 24/7 - 6/7*r**2 + 12/7*r**3 + 2/7*r**4.
2*(r - 1)**2*(r + 2)*(r + 6)/7
Let b(c) be the second derivative of 0 + 11*c + 0*c**3 + 3/2*c**2 - 1/4*c**4. Factor b(r).
-3*(r - 1)*(r + 1)
Let w(n) be the first derivative of -n**6/900 - n**5/100 - 4*n**3 + 9. Let f(t) be the third derivative of w(t). Solve f(y) = 0.
-3, 0
Let m be (-4004)/330 + 12 - (-96)/45. Factor -4/3 - 4/9*r**m - 16/9*r.
-4*(r + 1)*(r + 3)/9
Let r(m) be the third derivative of m**5/420 + 61*m**4/168 + 10*m**3/7 + m**2 + 7*m. Factor r(z).
(z + 1)*(z + 60)/7
Let o(p) be the third derivative of 3/175*p**7 + 3/5*p**3 + 0*p + 5*p**2 + 0 - 1/10*p**6 - 1/840*p**8 + 23/75*p**5 - 11/20*p**4. Let o(r) = 0. Calculate r.
1, 3
Let j(q) be the third derivative of -q**8/504 - 16*q**7/315 - 16*q**6/45 - 378*q**2. Factor j(a).
-2*a**3*(a + 8)**2/3
Let z(i) be the second derivative of -5*i**4/4 - 11*i**3 - 12*i**2 - 4*i + 2. Factor z(k).
-3*(k + 4)*(5*k + 2)
Factor -5*b + 58*b**3 - 10*b + 3*b**5 + 18*b**4 - 46*b**3 - 18*b**2.
3*b*(b - 1)*(b + 1)**2*(b + 5)
Let h = -66 + 183. Solve -l**2 + h*l**3 + 1 + 0 + l - 118*l**3 = 0.
-1, 1
Let q be (-100)/360 - 2/(-4). Let d be (-3)/6*-1 - 5/18. Suppose d*w**2 + q*w + 0 = 0. What is w?
-1, 0
Let l(f) be the first derivative of f**7/420 + f**6/36 + 2*f**5/15 + f**4/3 - 10*f**3/3 - 9. Let d(v) be the third derivative of l(v). Factor d(t).
2*(t + 1)*(t + 2)**2
Let d = -13907 - -13909. Let -1/4*j**3 + 3/4 + 5/4*j**d - 7/4*j = 0. What is j?
1, 3
Let t(n) be the third derivative of n**7/105 - 6*n**6/35 + 2*n**5/21 + 172*n**2. Factor t(h).
2*h**2*(h - 10)*(7*h - 2)/7
Suppose 3*a**4 + 33*a**2 + 30*a**2 - 495*a + 24 - 24*a**3 + 429*a = 0. Calculate a.
1, 2, 4
Let a(y) be the first derivative of -y**3/21 - 3*y**2/7 + 135*y