 q*x**4 - 3/8*x**5 + 9/4*x**3 - 21/4*x**2 + 33/8*x - 9/8.
-3*(x - 1)**4*(x + 3)/8
Let z(t) be the second derivative of -t**5/120 + t**4/12 - t**3/3 + 5*t**2 + 12*t. Let r(w) be the first derivative of z(w). Find c such that r(c) = 0.
2
Find n, given that 338/5 + 28/5*n**2 + 1/5*n**3 + 221/5*n = 0.
-13, -2
Let o(x) be the second derivative of x**4/108 - 5*x**3/18 - 8*x**2/9 + 77*x. Solve o(w) = 0.
-1, 16
Let q(o) be the second derivative of 1/90*o**5 - 1/54*o**4 - 1/27*o**3 + 1/135*o**6 + 0 - o + 0*o**2. Factor q(f).
2*f*(f - 1)*(f + 1)**2/9
Let t(h) be the third derivative of -h**7/630 + h**6/180 + h**5/180 - h**4/36 - 69*h**2. Factor t(l).
-l*(l - 2)*(l - 1)*(l + 1)/3
Let n(k) = k**2 - 8*k + 8. Let i be n(8). Let s be (-8 + 1)*((-198)/(-42) + -5). Factor 0*t**2 - 21 - t**s - i*t + 5.
-(t + 4)**2
Let r(m) = 7*m**2 - 28*m - 30. Let v(g) = -6*g**2 + 28*g + 30. Let q(d) = 4*r(d) + 5*v(d). Let q(s) = 0. Calculate s.
-1, 15
Suppose 39*r - 2209 - 3424 = -17. Factor r + 12*q**2 - 2/3*q**3 - 72*q.
-2*(q - 6)**3/3
Let t be (0 - (-4)/(-10)) + (-1056)/(-240). Let m(l) be the first derivative of 9/4*l**t + 0*l + 0*l**2 - 2*l**3 - 4 - 3/5*l**5. Suppose m(a) = 0. What is a?
0, 1, 2
Let i(a) = 12*a**5 - 305*a**4 + 49*a**3 + 942*a**2 - 910*a + 194. Let s(c) = -c**5 - 2*c**3 - c**2 - 2. Let v(m) = -i(m) + 3*s(m). Solve v(g) = 0 for g.
-2, 1/3, 1, 20
Let l(s) be the third derivative of -6*s**2 + 0*s**3 + 0*s**5 + 0 + 1/360*s**6 + 1/3024*s**8 - 2/945*s**7 + 0*s**4 + 0*s. Suppose l(g) = 0. What is g?
0, 1, 3
Let v be ((-36)/(-30))/(16/10). Let f(h) be the second derivative of 0 + 3/2*h**3 - v*h**4 + h - 3/2*h**2 + 3/20*h**5. Factor f(l).
3*(l - 1)**3
Let d(i) be the third derivative of -7*i**5/30 - 23*i**4/18 - 8*i**3/9 - 333*i**2. Factor d(t).
-2*(t + 2)*(21*t + 4)/3
Let s = 1844 + -1842. Solve 3/2*a**4 + 11/4*a**3 - 9/4*a**5 - a - a**s + 0 = 0 for a.
-2/3, 0, 1
Let s be (-8)/(15120/(-1863)) - (-4)/(-14). Factor 3/10*c**2 + s*c + 1/5.
(c + 2)*(3*c + 1)/10
Suppose 96*w - 30 = 86*w. Let l(d) be the first derivative of 2/39*d**w - 2/65*d**5 + 0*d - 7 - 1/26*d**4 + 1/13*d**2. Solve l(y) = 0 for y.
-1, 0, 1
Let w(c) = c**3 - 28*c**2 + 27*c + 3. Let x be w(27). Let q(o) be the first derivative of 1/16*o**4 - 1/6*o**x + 0*o - 3/8*o**2 - 11. Factor q(j).
j*(j - 3)*(j + 1)/4
Suppose 6*h + 14 = 5*h + 4*p, -21 = -h - 3*p. Factor -2*c - 9*c + 4*c - 8*c**2 + h*c**3 - c.
2*c*(c - 2)*(3*c + 2)
Let q(m) be the first derivative of m**4/30 - 8*m**3/45 + m**2/5 - 61. Find c, given that q(c) = 0.
0, 1, 3
Let g(j) be the second derivative of -2*j + 2/15*j**5 + 0*j**3 - 1/9*j**4 + 7/90*j**6 + 0 - 5/126*j**7 + 0*j**2. Suppose g(l) = 0. Calculate l.
-1, 0, 2/5, 2
Factor -10*a**2 - 34*a - 29*a**2 + 24 - 49*a + 17*a.
-3*(a + 2)*(13*a - 4)
Let q = -753 + 755. Suppose -f = -4*j - 5, 2*j = -0*j + 2*f - 10. Factor -1/5*k**q - 2/5*k + j + 1/5*k**3.
k*(k - 2)*(k + 1)/5
Let w = 825 - 3299/4. Let b(c) = -c**3 - 2*c**2 + 4*c + 3. Let s be b(-3). Factor 0*x + 1/4*x**4 + s*x**2 + 0 - w*x**3.
x**3*(x - 1)/4
Let l = -87 - -191. Suppose -5*k + 3*k = l. Let w(i) = -i**2 + i. Let a(p) = -8*p**2 + 10*p. Let j(z) = k*w(z) + 6*a(z). Suppose j(n) = 0. What is n?
-2, 0
Let w(s) be the third derivative of 9/14*s**3 - 1/140*s**5 + 24*s**2 + 0*s + 0*s**4 + 0. Suppose w(v) = 0. Calculate v.
-3, 3
Suppose -9*c = -5*c - 144. Suppose 33*h = c*h - 3. Determine k, given that -h - 1/4*k**3 + 1/4*k**2 + k = 0.
-2, 1, 2
Let g(v) be the second derivative of 2*v**7/105 - 4*v**5/15 + v**2 - 30*v. Let z(a) be the first derivative of g(a). Suppose z(y) = 0. What is y?
-2, 0, 2
Let h = -2721 - -2724. Determine k, given that 24/7*k**2 + 4/7*k**4 + 16/7*k + 16/7*k**h + 4/7 = 0.
-1
Let w(g) be the third derivative of -1/2*g**3 + 0 + 3/20*g**5 - 1/4*g**4 - 9*g**2 + 0*g. Factor w(r).
3*(r - 1)*(3*r + 1)
Let i(b) be the second derivative of 1/12*b**4 + 1/24*b**3 - 1/80*b**5 + 0 - 5*b - 1/2*b**2. Factor i(h).
-(h - 4)*(h - 1)*(h + 1)/4
Let j be (-6)/(-10) - 78/780. Let t(i) be the second derivative of -1/10*i**6 + 0 + 9/20*i**5 - j*i**4 - 2*i + 0*i**3 + 0*i**2. Suppose t(x) = 0. What is x?
0, 1, 2
Let u(n) be the second derivative of -n**4/48 - 19*n**3/8 - 55*n**2/4 - 198*n - 1. Find q such that u(q) = 0.
-55, -2
Let g = -12 + 14. Let v(h) = -h**3 + 3*h**2 - 2. Let o be v(g). Suppose 2*r - r**2 + 2*r - r - 2*r**o = 0. What is r?
0, 1
Suppose f = h + 4*f - 14, 0 = -4*h + 5*f - 12. Solve 6 + 118*r**h - 162*r + 26 + 34*r**2 - 36*r**3 - 14*r = 0 for r.
2/9, 2
Let q(k) be the third derivative of -1/12*k**5 + 10/3*k**3 + 5/8*k**4 + 0 + 0*k + 30*k**2. Factor q(v).
-5*(v - 4)*(v + 1)
Let g(z) = z - 5. Let a = 1 - -8. Let b be g(a). Factor -v**b + 2*v**3 + 0*v**3 - v**4.
-2*v**3*(v - 1)
Factor -12*k**2 + 17*k + 6 + 0*k**2 + 3*k**3 + 5*k**2 + 21*k**2.
(k + 1)*(k + 3)*(3*k + 2)
Let z(m) = 3*m**2 + 13*m + 29. Let h(j) = -2*j**2 - 7*j - 15. Let r(s) = -5*h(s) - 3*z(s). What is o in r(o) = 0?
-2, 6
Let q(r) be the second derivative of -2/3*r**4 + 0*r**2 + 0*r**3 + r + 0 + 1/5*r**5. Factor q(z).
4*z**2*(z - 2)
Let j(h) be the second derivative of h**4/60 + 122*h**3/15 + 7442*h**2/5 - 727*h + 1. Suppose j(z) = 0. Calculate z.
-122
Let d(j) be the second derivative of j**5/25 - j**4/3 + 4*j**3/5 + 377*j. Factor d(x).
4*x*(x - 3)*(x - 2)/5
Let l = 1330 - 1328. Factor -3/2*y**l + 0 + 3/2*y + 3/2*y**4 - 3/2*y**3.
3*y*(y - 1)**2*(y + 1)/2
Suppose 3*y - 6 = 5*y. Let z be (-3 - y) + -3 - -8. Factor 4*x**3 - 16*x - 16*x**4 + 19*x**5 + 1 + 40*x**2 - 15*x**z - 33.
4*(x - 2)**3*(x + 1)**2
Let t(b) = b**3 - 4*b**2 - 19*b + 55. Let w be t(6). Let c(m) be the second derivative of -w*m + 0 + 0*m**2 - 1/6*m**3 + 1/12*m**4. What is r in c(r) = 0?
0, 1
Let q(a) be the first derivative of -2*a**5/15 - 5*a**4/3 - 56*a**3/9 - 2*a**2 + 30*a - 15. Determine b, given that q(b) = 0.
-5, -3, 1
Factor 0 + 2/3*x**5 + 0*x + 16/3*x**3 - 8/3*x**2 - 10/3*x**4.
2*x**2*(x - 2)**2*(x - 1)/3
Let p(d) be the first derivative of d**5/60 - d**4/8 + d**3/3 + 3*d**2 - 34. Let l(w) be the second derivative of p(w). Solve l(g) = 0 for g.
1, 2
Suppose -1199 = 10*b - 1229. Solve 4/3 - 4*g - 4/3*g**b + 4*g**2 = 0 for g.
1
Suppose l - 32 = -q + 22, 54 = l - 2*q. Let t be (1/(-2))/((-9)/l). Let 2*z - z**4 - 7*z**t + 0*z + 4*z**3 + z**5 + z**2 + 0*z = 0. Calculate z.
-1, 0, 1, 2
Suppose -7*s + 12 = -3*s, 2 = 2*l + 4*s. Let n(m) = -m**2 - 7*m - 3. Let t be n(l). Factor 4*c**2 + 3*c + c**2 - t*c**2 + 2*c**3 - 7*c.
2*c*(c - 2)*(c + 1)
Let l(h) be the third derivative of h**8/1512 - h**7/135 + 11*h**6/540 - h**5/54 - 85*h**2. Factor l(k).
2*k**2*(k - 5)*(k - 1)**2/9
Let a(r) = r**4 + r**2 - r + 1. Let o(m) be the first derivative of 4*m**5/5 - m**2 + 2*m + 7. Let t(k) = 4*a(k) - 2*o(k). Determine j, given that t(j) = 0.
-1, 0, 1
Suppose 3*y - 25 = -2*y. Factor -8*p**4 + 2*p**3 + 0*p + 14/3*p**y + 4/3*p**2 + 0.
2*p**2*(p - 1)**2*(7*p + 2)/3
Factor -294*a + 184/5*a**2 + 180 - 6/5*a**3.
-2*(a - 15)**2*(3*a - 2)/5
Let a(q) = -q**3 + 29*q**2 + 4*q + 24. Let h be a(29). Let g = h - 136. Solve 3/4*l - 3/4*l**3 + 0 + 9/8*l**g - 9/8*l**2 = 0.
-1, 0, 2/3, 1
Let c(x) be the third derivative of -x**9/15120 + x**7/1050 + 8*x**3/3 - 26*x**2. Let k(n) be the first derivative of c(n). Determine l so that k(l) = 0.
-2, 0, 2
Factor 192/7*q**2 + 21 + 48*q.
3*(8*q + 7)**2/7
Let l be -49 - -45 - 364/(-90). Let h(n) be the first derivative of -3 + 0*n + 1/18*n**4 - 1/9*n**2 + 2/27*n**3 - l*n**5. Factor h(a).
-2*a*(a - 1)**2*(a + 1)/9
Let f(i) = -36*i**2 - 40*i + 32. Let m(w) = -12*w**2 - 13*w + 10. Let l(y) = -3*f(y) + 8*m(y). Factor l(g).
4*(g + 2)*(3*g - 2)
Let t(i) be the second derivative of 1/15*i**4 + 1/150*i**5 + 0 - 3/2*i**2 - 2*i + 4/15*i**3. Let f(k) be the first derivative of t(k). Factor f(o).
2*(o + 2)**2/5
Factor 53/4*w + 11/2 + 7/4*w**3 - 1/4*w**4 + 39/4*w**2.
-(w - 11)*(w + 1)**2*(w + 2)/4
Determine y so that -26 + 54*y - 72*y**2 + 21*y**4 + 67*y + 25*y - 22 - 48*y**3 + 46*y = 0.
-2, 2/7, 2
Let r(c) be the third derivative of -c**6/90 + c**5/45 + c**4/3 - 84*c**2 - 2*c. Factor r(v).
-4*v*(v - 3)*(v + 2)/3
Let w be 1/((-552)/(-1239) + (-9)/21). Let x = w - 57. Solve -8/3*j - 26/3*j**x + 8/3 - 10/3*j**3 = 0 for j.
-2, -1, 2/5
Let y(w) = -w**3 - 4*w**2 - 4*w - 1. Let l be y(-3). Let v(a) be the first der