- 4. Factor y(v).
2*(v + 1)**2*(4*v - 7)/15
Let h(a) be the second derivative of 4*a**6/15 + 27*a**5/5 + 75*a**4/2 + 473*a**3/6 - 363*a**2/2 + 970*a. Find r, given that h(r) = 0.
-11/2, -3, 1/2
Suppose -400/3 - 1/3*w**2 - 40/3*w = 0. Calculate w.
-20
Let s(z) be the third derivative of z**8/112 + z**7/70 - 27*z**6/40 - 77*z**5/20 - 37*z**4/4 - 12*z**3 + 656*z**2. Factor s(w).
3*(w - 6)*(w + 1)**3*(w + 4)
Find u such that -2*u**2 + 0*u**2 - 51 - 2*u**2 + 32*u - 13 = 0.
4
Let x be (-138)/(-135) + (-7 - 366/(-54)). Let i = 4 - 0. Solve 0*y + x*y**3 - 6/5*y**i + 2/5*y**5 + 0 + 0*y**2 = 0 for y.
0, 1, 2
Let g(n) be the first derivative of 0*n + 3*n**4 - 3 - 4/5*n**5 + 2*n**2 - 4*n**3. Factor g(f).
-4*f*(f - 1)**3
Suppose -127 + 532 = 5*c. Let k = 84 - c. Solve 0*h**k + 0*h - 3/5*h**5 - 12/5*h**2 + 9/5*h**4 + 0 = 0.
-1, 0, 2
Let o(m) be the second derivative of -m**6/180 - m**5/60 + 4*m**3/3 - 9*m. Let d(k) be the second derivative of o(k). What is p in d(p) = 0?
-1, 0
Let j be (-18 - -12) + 3*-66. Let u = 215 + j. Factor -u*a + 1 + 121/4*a**2.
(11*a - 2)**2/4
Let u(p) be the third derivative of -p**6/780 - p**5/39 - 8*p**4/39 - 32*p**3/39 + 5*p**2. Suppose u(i) = 0. Calculate i.
-4, -2
Let u(m) be the third derivative of m**6/120 - m**5/15 - 17*m**4/8 - 15*m**3 - 20*m**2. Factor u(l).
(l - 10)*(l + 3)**2
Let z = -382 - -382. Let k(t) be the third derivative of -1/360*t**6 + 0*t + 0 + 4*t**2 + 0*t**4 + z*t**3 - 1/630*t**7 + 1/1008*t**8 + 1/180*t**5. Factor k(v).
v**2*(v - 1)**2*(v + 1)/3
Let i(q) be the second derivative of -q**6/6 - 3*q**5/4 + 5*q**4/12 + 5*q**3/2 - 6*q + 3. Find z such that i(z) = 0.
-3, -1, 0, 1
Let a(v) be the first derivative of -v**2/2 + 4*v - 5. Let p be a(0). Factor 2*d**3 + 3*d**2 + 4*d**4 - p*d**3 - 4*d**3 - d**4.
3*d**2*(d - 1)**2
Let p(x) be the second derivative of x**7/42 + x**6/10 + x**5/20 - x**4/4 - x**3/3 - x - 54. Factor p(z).
z*(z - 1)*(z + 1)**2*(z + 2)
Let a be (7/(-756))/(10/(-4)). Let f(u) be the third derivative of 1/36*u**4 - 6*u**2 + 0 + 2/27*u**3 + a*u**5 + 0*u. Factor f(z).
2*(z + 1)*(z + 2)/9
Suppose 3*p - 2*p - 15 = -5*k, 0 = -3*k - p + 9. Factor y - y**4 + 3*y**k + 2 + 14*y**2 - 2 - 17*y**2.
-y*(y - 1)**3
Let c(s) = 3*s**4 - s**2 + s. Let r(y) = 7*y**4 + 3*y**3 - 6*y**2 + 2*y. Let b(p) = 2*c(p) - r(p). Solve b(a) = 0.
-4, 0, 1
Let m(n) be the second derivative of -1/45*n**6 - 2/15*n**5 - 5/18*n**4 + 7*n + 0*n**2 - 2/9*n**3 + 0. Let m(z) = 0. Calculate z.
-2, -1, 0
Let q(s) = 3*s**2 - 15*s - 9. Let r be q(7). Find j such that 31 + r + 76*j - 198*j - j**3 - 15*j**2 + 74*j = 0.
-8, 1
Suppose 4 = 47*r - 46*r. Solve 4 - 64*n**2 + 56*n**3 + 4*n**4 + r + 4 + 8*n - 16*n**4 = 0 for n.
-1/3, 1, 3
Factor 0 + 88/3*o**3 - 16/3*o**4 + 47/3*o**2 + 2*o.
-o*(o - 6)*(4*o + 1)**2/3
Let w(b) = -b. Let s(x) = -18*x - 9. Let h(j) = -j**2 - 37*j - 17. Let l(q) = 3*h(q) - 7*s(q). Let i(o) = l(o) + 6*w(o). Factor i(v).
-3*(v - 4)*(v + 1)
Factor -1/3*m**2 + 239/3*m + 80.
-(m - 240)*(m + 1)/3
Let i(b) be the third derivative of -b**6/120 + b**4/8 + b**3/3 + 13*b**2. Let n(g) be the first derivative of i(g). Solve n(v) = 0.
-1, 1
Let y(c) be the second derivative of -c**5/130 + 4*c**4/39 - 17*c**3/39 + 10*c**2/13 + 7*c - 17. Find d, given that y(d) = 0.
1, 2, 5
Suppose 0 = -0*f - 5*f + 2*q - 6363, -2*f + 4*q = 2558. Let n = 7649/6 + f. Factor 9/2*s**2 + 13/6*s + 7/6*s**4 + n*s**3 + 1/3.
(s + 1)**3*(7*s + 2)/6
Let y(t) = 18*t**3 - 17*t**2 - 7*t. Suppose -72 = 3*z + 9*z. Let a(x) = -19*x**3 + 16*x**2 + 6*x. Let u(g) = z*y(g) - 7*a(g). Suppose u(o) = 0. What is o?
0, 2/5
Let v(i) be the second derivative of -i**7/168 + i**6/40 - i**5/40 + 37*i. Let v(u) = 0. What is u?
0, 1, 2
Let h = -7 + 10. Factor 17 + 11 - 28 + 4*k**h + 36 + 44*k**2 + 76*k.
4*(k + 1)**2*(k + 9)
Factor -11*h + 21 + 15*h - 69 + 2*h**2.
2*(h - 4)*(h + 6)
Factor 5/2*p**3 + 0 + 3/2*p + 7/2*p**2 + 1/2*p**4.
p*(p + 1)**2*(p + 3)/2
Suppose -6*y + 5*y + 3*d - 4 = 0, 2*y + 4 = 5*d. Let t be 252/y + 2 + -2. Suppose -3 - 9/2*a + 27/2*a**4 - 75/2*a**3 + t*a**2 = 0. Calculate a.
-2/9, 1
Let k(a) be the third derivative of 0*a**3 - 1/21*a**7 + 0*a + 1/15*a**5 - 18*a**2 + 0 + 1/84*a**8 + 0*a**4 + 1/60*a**6. Determine h so that k(h) = 0.
-1/2, 0, 1, 2
Let i be ((-23)/46)/(-2 - 7751/(-3872)). Let n = -276 - i. Factor -n*v - 8/7*v**3 + 2/7*v**4 + 10/7*v**2 + 0.
2*v*(v - 2)*(v - 1)**2/7
Let a(x) = 39*x**2 + 111*x + 86. Let q(w) = -2*w**2 - 3*w + 1. Let p(v) = a(v) - 5*q(v). Factor p(r).
(7*r + 9)**2
Let g = -923 - -923. Factor 0*a - 3/7*a**4 + g*a**2 + 0 + 0*a**3.
-3*a**4/7
Let z be (-492)/(-205)*(-30)/(-8). Let s(f) be the first derivative of 0*f + 2/57*f**3 - z + 2/19*f**2. Factor s(o).
2*o*(o + 2)/19
Let o(k) be the third derivative of k**5/70 + 67*k**4/14 + 4489*k**3/7 + 12*k**2 + k. Factor o(x).
6*(x + 67)**2/7
Let z(k) be the second derivative of -k**4/54 - 61*k**3/27 - 58*k**2/3 - 1055*k. Factor z(s).
-2*(s + 3)*(s + 58)/9
Let x be (525/(-250))/((-4)/10) - 5. Find l, given that 0 + x*l**2 - 1/2*l = 0.
0, 2
Suppose 0 = -3*t + 15 - 0. Let p(f) = -9*f**2 - 12*f - 9. Let y(d) = 4*d**2 + d + 4*d**2 + 8 + 10*d + 0 + 0*d**2. Let h(w) = t*p(w) + 6*y(w). Factor h(o).
3*(o + 1)**2
Let h be (-250)/350*7/(-3). Determine z so that -25/3*z**3 - 35/3*z**2 - h*z**4 - 5*z + 0 = 0.
-3, -1, 0
Suppose -252 + 352 = 122*k - 388. Solve 7/4*v**2 - 5/4*v**3 + 1/4*v**k - 3/4*v + 0 = 0.
0, 1, 3
Let h(k) = 38*k + 116. Let i be h(-3). Let m(d) be the first derivative of -4*d + 3/2*d**4 + 4/3*d**3 + 6 - 3*d**i. Let m(t) = 0. Calculate t.
-1, -2/3, 1
Let p be (-84)/18 + 4 + (-170)/(-12). Let w(a) be the second derivative of 0 - 1/4*a**4 - a - 3*a**3 - p*a**2. Solve w(b) = 0 for b.
-3
Let x(d) be the first derivative of -d**5/80 - 5*d**4/96 - d**3/12 + 6*d**2 - 7. Let n(o) be the second derivative of x(o). Suppose n(f) = 0. Calculate f.
-1, -2/3
Let s(x) = -24*x**3 + 4*x**2 + 24*x + 8. Let g(t) = 45*t**3 - 7*t**2 - 48*t - 16. Let z(l) = 6*g(l) + 11*s(l). Suppose z(m) = 0. What is m?
-2, -1/3, 2
Suppose 105 = 15*a - 0*a. Let j(o) be the third derivative of 0*o**3 - 7*o**2 + 0 + 0*o**4 + 1/945*o**a - 1/270*o**6 + 0*o + 1/270*o**5. Factor j(b).
2*b**2*(b - 1)**2/9
Let s = -76 - -22. Let h = -52 - s. Factor -2/3*v**h - 2/3*v**3 + 2/3*v**4 + 2/3*v**5 + 0*v + 0.
2*v**2*(v - 1)*(v + 1)**2/3
Let t(q) be the first derivative of 7 + 8/3*q**3 + 0*q + 1/90*q**6 + 0*q**2 - 1/10*q**5 - 2/3*q**4. Let z(g) be the third derivative of t(g). Solve z(n) = 0.
-1, 4
Suppose -2 = -11*o + 13*o. Let z be 1 - o - (84/(-30))/7. Factor z*p**3 + 4/5 + 4/5*p - 4*p**2.
4*(p - 1)**2*(3*p + 1)/5
Let t be 0 + 158/56 + (-47)/188. Let t*w + 0 - 12/7*w**2 + 2/7*w**3 = 0. Calculate w.
0, 3
Let t(m) = -m. Suppose 0 = 10*o - 5*o + 5. Let y(n) = 3*n**3 + 12*n**2 + 16*n + 6. Let s(g) = o*y(g) - t(g). Factor s(x).
-3*(x + 1)**2*(x + 2)
Let m(q) be the first derivative of -q**6/3 - 14*q**5/5 + 3*q**4 + 208*q**3/3 + 32*q**2 - 768*q + 518. Suppose m(b) = 0. Calculate b.
-4, 2, 3
Let 12*k**4 + 9*k - 10*k - 9*k - 129*k**3 - 41*k + 195*k**2 - 27 = 0. What is k?
-1/4, 1, 9
Let -121/6*h + 0 - 1/6*h**2 = 0. What is h?
-121, 0
Suppose 2*g - 26 + 6 = -4*i, 2*g - 4*i + 12 = 0. Let z(m) be the third derivative of 1/40*m**6 + g*m**3 + 0*m**4 + m**2 + 0*m + 0 - 3/20*m**5. Factor z(j).
3*(j - 2)**2*(j + 1)
Let x(q) = 2*q**4 - 14*q**3 - 24*q**2 - 2*q + 2. Let i(z) = 4*z**4 - 14*z**3 - 24*z**2 - 3*z + 3. Let g(o) = -2*i(o) + 3*x(o). Suppose g(w) = 0. Calculate w.
-4, -3, 0
Let q be 14 - 9 - 1/(15/66). Determine d so that -3/5*d**4 + q*d**2 + 6/5*d**3 + 0 - 6/5*d**5 + 0*d = 0.
-1, -1/2, 0, 1
Let a(d) be the first derivative of 2*d**5/5 + 9*d**4 + 218*d**3/3 + 252*d**2 + 392*d + 51. Let a(w) = 0. Calculate w.
-7, -2
Let t(b) be the first derivative of -b**6/6 + 13*b**5/15 + 17*b**4/12 - 37*b**3/9 + 5*b**2/3 + 20. Let t(h) = 0. What is h?
-2, 0, 1/3, 1, 5
Suppose 5*z = -2*d + 16, 2*z = 4 - 0. Factor 0*r**2 - 2*r**2 + r**2 + 3 - r**d - 2 + r.
-(r - 1)*(r + 1)**2
Suppose f + t + t = 0, 3*f = 2*t + 8. Find d, given that -29*d**3 - 12 + 5*d**2 + 4*d**f + 26*d**3 = 0.
-1, 2
Let c(b) be the third derivative of 0*b**3 + 0*b - 14*b**2 + 1/12*b**4 + 0 + 1/120*b**5. Let c(a) = 0. Calculate a.
-4, 0
Let j(g) be the first derivative of g**6/9 + 24*g**5/5 + 54*g**4 + 40. Fact