 the third derivative of h**8/16800 + h**7/2100 + h**6/600 + h**5/300 - h**4/8 - h**2. Let i(y) be the second derivative of p(y). Factor i(c).
2*(c + 1)**3/5
Factor -4*r**2 + 13*r - 7*r + 6*r - 12*r**3 + 4*r**4.
4*r*(r - 3)*(r - 1)*(r + 1)
Solve 0*g**2 + 1 + 6*g**2 - g**3 - 7*g**2 + g = 0 for g.
-1, 1
Factor -56*y - 66*y**2 - 8 + 112*y**3 - 28*y**4 + 0 - 4*y**4.
-2*(y - 2)**2*(4*y + 1)**2
Factor 1/2*w**3 + 5/2*w + 1 + 2*w**2.
(w + 1)**2*(w + 2)/2
Factor -2/21*l**2 + 0 + 4/21*l.
-2*l*(l - 2)/21
Let o = -8/3 + 17/6. Let y(d) be the second derivative of -1/12*d**4 + o*d**3 - 3*d + 0*d**2 + 0. Suppose y(m) = 0. Calculate m.
0, 1
Let k = -133/4 + 963/28. Suppose -2/7*o**2 + 10/7*o**4 - k - 16/7*o + 2*o**3 + 2/7*o**5 = 0. Calculate o.
-2, -1, 1
Let v(p) be the third derivative of p**6/180 + p**5/30 + 19*p**2. Factor v(s).
2*s**2*(s + 3)/3
Determine b, given that 0 - 50/3*b**3 + 20*b**2 - 16/3*b = 0.
0, 2/5, 4/5
Let b(j) = -2*j**3 + 16*j**2 + 9*j - 2. Let z(k) = -k**3 + 11*k**2 + 6*k - 1. Let n(s) = -5*b(s) + 7*z(s). Factor n(l).
3*(l - 1)**2*(l + 1)
Determine i, given that -27/8 + 27*i + 64*i**3 - 72*i**2 = 0.
3/8
Let w(o) be the third derivative of -o**5/12 + 5*o**4/12 - 5*o**3/6 + 35*o**2. Factor w(q).
-5*(q - 1)**2
Let b(z) be the first derivative of -7/60*z**6 - 3/2*z**2 - 1/4*z**4 + 2/3*z**3 - 2/5*z**5 + 0*z - 1. Let h(k) be the second derivative of b(k). Factor h(s).
-2*(s + 1)**2*(7*s - 2)
Let a(j) be the first derivative of j**4/16 + j**3/2 + 9*j**2/8 - 4. Factor a(s).
s*(s + 3)**2/4
Let f(y) be the second derivative of 1/10*y**5 + 1/105*y**7 + y + 0*y**3 + 1/15*y**4 + 4/75*y**6 + 0*y**2 + 0. Factor f(j).
2*j**2*(j + 1)**2*(j + 2)/5
Factor 3/4*x + 3/2 - 3/4*x**2.
-3*(x - 2)*(x + 1)/4
Factor -2/3*n + n**2 + 0 - 1/3*n**3.
-n*(n - 2)*(n - 1)/3
Let c = 8896/19 + -468. Factor c + 2/19*z**2 + 6/19*z.
2*(z + 1)*(z + 2)/19
Let u be (-50)/(-12) + 2/(-12). Factor -f**5 + f**4 - f**3 + f**u + 2*f**3 - f**2 - f**4.
-f**2*(f - 1)**2*(f + 1)
Let x(v) be the first derivative of v**6/9 + 16*v**5/45 + v**4/3 - v**2/9 + 11. Find p, given that x(p) = 0.
-1, 0, 1/3
Factor -1/5*y**2 + 0 - 3/5*y.
-y*(y + 3)/5
Let s(k) = 2*k**2 - 2*k - 2. Let q be s(2). Let x(v) = v**3 - 3*v**2 + v + 2. Let f be x(3). Solve d**2 + q - f + 2 = 0.
-1, 1
Let v = 1333/18 - 74. Let l(x) be the second derivative of 0 + 0*x**2 - 1/60*x**5 - 1/90*x**6 + 1/36*x**4 + v*x**3 - x. Determine n so that l(n) = 0.
-1, 0, 1
Let k(s) = -s**3 - s. Let n(u) = 15*u**4 - 51*u**3 + 51*u**2 + 3*u - 12. Let a(f) = 3*k(f) + n(f). Find x such that a(x) = 0.
-2/5, 1, 2
Let c(a) be the third derivative of -3*a**2 + 0 + 1/21*a**4 - 11/420*a**6 - 2/49*a**7 + 0*a + 2/35*a**5 + 25/1176*a**8 + 0*a**3. Solve c(x) = 0 for x.
-2/5, 0, 1
Let -2*m**3 - 16*m**2 + 3*m + m - 4*m = 0. Calculate m.
-8, 0
Let p(u) be the second derivative of u**7/840 - u**5/120 + u**3 - 7*u. Let b(n) be the second derivative of p(n). Find t, given that b(t) = 0.
-1, 0, 1
Let h(l) be the first derivative of l**4/6 + l**3/3 + 3*l - 4. Let g(v) be the first derivative of h(v). Determine q so that g(q) = 0.
-1, 0
Let w(z) be the second derivative of 2*z**6/15 + 2*z**5/5 - z**4 - 8*z**3/3 + 8*z**2 - 12*z. What is n in w(n) = 0?
-2, 1
Let i(k) be the first derivative of -k**8/5880 + k**7/1470 + k**6/1260 - k**5/210 - k**3 - 1. Let t(h) be the third derivative of i(h). Factor t(r).
-2*r*(r - 2)*(r - 1)*(r + 1)/7
Solve 10/3*u - 5*u**5 + 5/3*u**3 - 35/3*u**4 + 0 + 35/3*u**2 = 0 for u.
-2, -1, -1/3, 0, 1
Let r = 145/298 + 2/149. What is q in 1 + r*q**3 + 0*q**2 - 3/2*q = 0?
-2, 1
Let h(w) be the third derivative of -w**7/280 + w**6/240 + w**5/60 - w**4/48 - w**3/24 - w**2 - 2. Suppose h(d) = 0. Calculate d.
-1, -1/3, 1
Let j be 24/(3*(-1)/(-4)). Factor 36*m**4 - 45*m**3 - 6*m + 59*m**2 - 3*m**4 - 9*m**5 - j*m**2.
-3*m*(m - 1)**3*(3*m - 2)
Let s(k) be the first derivative of -25*k**4/18 - 80*k**3/27 - 16*k**2/9 - 22. Factor s(l).
-2*l*(5*l + 4)**2/9
Let i(c) be the third derivative of -1/60*c**5 - 5*c**2 + 0*c + 0 - 3/2*c**3 + 1/4*c**4. Factor i(x).
-(x - 3)**2
Let r(g) be the third derivative of g**6/480 + g**5/80 + g**4/32 - g**3/2 - 4*g**2. Let f(j) be the first derivative of r(j). Factor f(u).
3*(u + 1)**2/4
Suppose -g = 2*g - 9. Suppose -g*u + 14 = -4*c, -5*c + 4 = 5*u - 2*c. Let -4*v - 12*v**u + 7*v**5 - 40*v**4 + 7*v**4 + 2*v**3 - 4*v + 44*v**3 = 0. What is v?
-2/7, 0, 1, 2
Factor 16/3 + 40/3*l + 4*l**2 - 6*l**3.
-2*(l - 2)*(3*l + 2)**2/3
Let r(z) be the third derivative of -z**7/1680 - z**6/960 + 11*z**2. Factor r(h).
-h**3*(h + 1)/8
Find x such that 1 - 60*x + 80*x - 16 - 5*x**2 = 0.
1, 3
Let z = -17 - -17. Factor -2/3*d**5 + 0*d**3 + z + 4/3*d**2 - 4/3*d**4 + 2/3*d.
-2*d*(d - 1)*(d + 1)**3/3
Let w(p) be the first derivative of -36*p**5 - 6*p**4 + 112*p**3/3 - 20*p**2 + 4*p - 8. Find z, given that w(z) = 0.
-1, 1/5, 1/3
Solve -44/3*f**3 - 64/3*f**2 + 0 + 16/3*f + 12*f**4 = 0 for f.
-1, 0, 2/9, 2
Let u(b) = b**4 - 16*b**3 + 20*b**2 - 11*b + 3. Let q(w) = -3*w**4 + 32*w**3 - 40*w**2 + 21*w - 5. Let l(p) = 3*q(p) + 5*u(p). Suppose l(r) = 0. What is r?
0, 1, 2
Let f(r) = r**2 + 41*r - 248. Let b(p) = p**2 + 83*p - 494. Let t(j) = 3*b(j) - 5*f(j). Factor t(a).
-2*(a - 11)**2
Let y be 4 + 0 - (0 - (-110)/35). Solve y*d**3 + 0 - 2/7*d - 4/7*d**2 = 0.
-1/3, 0, 1
Suppose 0 = 2*v + 4, p + 4*v - 3*v + 2 = 0. Find w such that p*w + 0 - 2/11*w**2 = 0.
0
Let a(b) = 9*b**3 - 3*b**2 - 6*b + 6. Let t(v) = v**2 - 1 + 7*v + 3*v**2 - 6 + 0*v**2 - 10*v**3. Let k(p) = 7*a(p) + 6*t(p). Solve k(j) = 0 for j.
-1, 0
Let j = -23034/5 + 23527/5. Let q = j + -96. Factor q*x**4 - 1/5*x + 0 - 3*x**3 + 7/5*x**2 - 4/5*x**5.
-x*(x - 1)**3*(4*x - 1)/5
Let d be 3*(-4)/12*2/(-3). Find r such that 2*r**2 + 2/3 - d*r**3 - 2*r = 0.
1
Let x be (28/(-35))/(7/((-21)/6)). Factor 0 - x*g**2 + 2/5*g**3 + 0*g.
2*g**2*(g - 1)/5
Let b(o) be the first derivative of o**4/2 - 2*o**3/3 - o**2 + 2*o - 3. Determine n, given that b(n) = 0.
-1, 1
Suppose -2/7*w**2 + 10/7*w + 12/7 = 0. Calculate w.
-1, 6
Let v(g) be the second derivative of -g**6/135 - g**5/90 + 2*g**4/27 + 4*g**3/27 + 47*g. Factor v(s).
-2*s*(s - 2)*(s + 1)*(s + 2)/9
Let x be (27/(-24) + 0)*(-4 + 3). Factor 3/8*b**2 - 1/2 + x*b**3 - b.
(b - 1)*(3*b + 2)**2/8
Let b(f) = 105*f**3 - 25*f**2 - 65*f + 65. Let o(w) = -8*w**3 + 2*w**2 + 5*w - 5. Let c(p) = -3*b(p) - 40*o(p). Factor c(g).
5*(g - 1)**2*(g + 1)
Let 6/5*w - 2/5*w**2 - 4/5 = 0. Calculate w.
1, 2
Let w(f) = f**3 - f**2 + f. Let s(i) = -17*i**3 - 9*i**2 + 9*i. Let n(m) = -2*s(m) + 14*w(m). Determine t, given that n(t) = 0.
-1/3, 0, 1/4
Let p be (-32)/(-4) - 4/(-2). Suppose -2*x + p = -0*x. Factor -b**3 + 2*b**x - 2*b**3 + b**3.
2*b**3*(b - 1)*(b + 1)
Let q(o) be the second derivative of 0*o**4 + 0*o**5 + 1/360*o**6 + 0 + 0*o**3 - 2*o + o**2. Let k(d) be the first derivative of q(d). Factor k(u).
u**3/3
Let q(c) = 1 + 8 - 3*c + 7 - 20 + 2*c**3. Let d(w) = -w**3 - w**2 + 1. Let z(u) = u**3 + 5*u**2 - 7*u. Let h be z(-6). Let n(o) = h*d(o) + 2*q(o). Factor n(i).
-2*(i + 1)**3
Let v(r) be the third derivative of r**5/30 + r**4/8 + r**3/6 + 3*r**2. Let v(h) = 0. What is h?
-1, -1/2
Let n(p) = 17*p**4 + 25*p**3 - 21*p**2 - 11*p + 5. Let x(t) = 9*t**4 + 13*t**3 - 11*t**2 - 5*t + 3. Let l(m) = 6*n(m) - 10*x(m). Determine f so that l(f) = 0.
-2, -2/3, 0, 1
Let h(k) be the first derivative of k**4/12 + k**3 + 5*k**2/2 - 25*k/3 - 36. Determine p so that h(p) = 0.
-5, 1
Let q(v) be the first derivative of -v**5/60 - v**4/12 - v**3/6 - v**2/2 - 2. Let a(z) be the second derivative of q(z). Factor a(d).
-(d + 1)**2
Suppose 10 = 4*w - 3*g, -5*g + 9 = 2*w - 9. Find l, given that 1/3*l**w + 0*l**2 + 0 + 0*l + 1/3*l**3 = 0.
-1, 0
Factor 2/5*l**3 + 0 - 2/5*l**2 + 0*l.
2*l**2*(l - 1)/5
Let i(c) = c**2 - 4*c + 2*c - c**2 + c**3. Let s be i(2). Factor 0*w**2 - s*w + 0*w**3 - 2*w**2 + w**3 + 5*w.
w*(w - 1)**2
Let c(u) be the third derivative of 1/240*u**5 + 2/3*u**3 - 8*u**2 + 1/12*u**4 + 0 + 0*u. Factor c(k).
(k + 4)**2/4
Let b(z) be the first derivative of -z**3/6 + z**2/2 - z/2 - 6. Find q such that b(q) = 0.
1
Let k(x) be the third derivative of -x**9/36960 + x**8/9240 - x**7/6930 + x**5/30 - x**2. Let p(h) be the third derivative of k(h). Factor p(w).
-2*w*(3*w - 2)**2/11
Let q(x) = -6*x**5 -