irst derivative of 5*o**4 + o**5 + 25/3*o**3 + 5*o**2 + 0*o + 21. Factor d(f).
5*f*(f + 1)**2*(f + 2)
Let k(g) be the third derivative of -9*g**8/2240 + 11*g**7/840 + g**6/15 - g**5/10 - g**4/2 + 2*g**2. Let v(b) be the second derivative of k(b). Factor v(m).
-3*(m - 2)*(m + 1)*(9*m - 2)
Let k(z) be the first derivative of -12 - 2/7*z**6 + 16/7*z**5 - 72/7*z**2 + 32/7*z - 51/7*z**4 + 248/21*z**3. Find x, given that k(x) = 0.
2/3, 1, 2
Let n(i) be the third derivative of -i**6/600 - i**5/50 - i**4/10 - 7*i**3/6 - 3*i**2. Let c(z) be the first derivative of n(z). Suppose c(x) = 0. Calculate x.
-2
Let j(d) be the first derivative of -d**6/27 + 2*d**5/15 + d**4/6 - 14*d**3/27 - 2*d**2/3 + 34. Suppose j(p) = 0. Calculate p.
-1, 0, 2, 3
Let o(m) be the third derivative of m**5/270 - 23*m**4/27 + 2116*m**3/27 + 144*m**2. Factor o(u).
2*(u - 46)**2/9
Factor -139*f + 27*f - 113*f - 20*f**2 - 55.
-5*(f + 11)*(4*f + 1)
Let n(f) = f**5 + 9*f**4 - f**3 - 29*f**2 + 26. Let q(c) = c**5 + 19*c**4 - c**3 - 59*c**2 + 51. Let v(s) = -11*n(s) + 6*q(s). Solve v(z) = 0.
-1, 1, 2
Let h(m) = 15*m**3 + 150*m**2 - 340*m + 165. Let y(v) = -17*v**3 - 148*v**2 + 341*v - 164. Let t(s) = -6*h(s) - 5*y(s). Determine j so that t(j) = 0.
-34, 1
Let l(n) be the third derivative of -n**6/1260 + n**5/420 + n**4/42 + n**3 - 20*n**2. Let q(j) be the first derivative of l(j). Factor q(o).
-2*(o - 2)*(o + 1)/7
Let s(k) be the first derivative of k**3 - 27*k**2/2 - 30*k - 268. Factor s(m).
3*(m - 10)*(m + 1)
Let i(u) be the second derivative of -u**5/10 - 85*u**4/12 - 154*u**3 - 441*u**2/2 - 36*u. Determine b, given that i(b) = 0.
-21, -1/2
Let d = -433 - -440. Let f(r) be the first derivative of -3*r - d - 1/4*r**4 + 5/2*r**2 - 1/3*r**3. Factor f(i).
-(i - 1)**2*(i + 3)
What is s in -2/3*s - 4*s**2 + 4 + 2/3*s**3 = 0?
-1, 1, 6
Determine n so that -36*n - 17*n + 51*n**3 + 18*n**4 - 18*n**2 - 3*n**5 + 5*n = 0.
-2, -1, 0, 1, 8
Let g(c) be the third derivative of c**6/120 - 7*c**5/30 + 2*c**2 - 9. Factor g(t).
t**2*(t - 14)
Let t(p) be the first derivative of 5*p**4/4 + 15*p**3 - 340*p**2 - 1078. Find c, given that t(c) = 0.
-17, 0, 8
Suppose -15*x = -20 - 40. Factor -2*y - 5*y**3 - 4*y**x + 13*y**3 + y - 7*y + 4*y**2.
-4*y*(y - 2)*(y - 1)*(y + 1)
Let r(s) be the third derivative of -5*s**8/336 - s**7/7 - s**6/3 + s**5/6 + 15*s**4/8 + 10*s**3/3 + 26*s**2. Factor r(k).
-5*(k - 1)*(k + 1)**3*(k + 4)
Find c, given that -637/8*c + 127/4 + 5/8*c**2 = 0.
2/5, 127
Suppose 37*y - 36*y - 2*d = -8, -3*y = -4*d + 16. What is t in -t + y - 3/2*t**2 = 0?
-2/3, 0
Let v(p) be the second derivative of -p**5/48 - 5*p**4/32 - 5*p**3/12 - 2*p**2 - 25*p. Let b(n) be the first derivative of v(n). Factor b(l).
-5*(l + 1)*(l + 2)/4
Let g(d) = d**2 - 44*d + 470. Let y be g(18). Let c(s) be the first derivative of -2 + 5/3*s**3 + 0*s - 5*s**y. Let c(f) = 0. Calculate f.
0, 2
Let j(s) be the third derivative of -s**6/780 + 61*s**5/390 + 125*s**4/156 + 21*s**3/13 + 33*s**2 - 2*s. Factor j(f).
-2*(f - 63)*(f + 1)**2/13
Let a(i) = 2*i + 2. Let r(w) = w**4 - 32*w**3 + 222*w**2 + 542*w + 287. Let t(u) = -2*a(u) - 2*r(u). Factor t(v).
-2*(v - 17)**2*(v + 1)**2
Let a be ((-13)/3)/((-1)/3). Suppose -76*p + 86*p = 80. What is f in -3*f + 6*f**3 + 2 + 6*f**2 - 3*f**4 + p - 3*f**5 - a = 0?
-1, 1
Let v(o) be the first derivative of -4*o**3/3 + 236*o**2 + 476*o - 387. Factor v(i).
-4*(i - 119)*(i + 1)
Let n(u) be the first derivative of u**6/36 - u**5/6 - u**4/24 + 17*u**3/18 + u**2 - 232. Suppose n(h) = 0. What is h?
-1, 0, 3, 4
Let p(o) be the first derivative of -o**4/14 + 4*o**3/7 + 51*o**2/7 + 88*o/7 + 11. Factor p(i).
-2*(i - 11)*(i + 1)*(i + 4)/7
What is v in -12/7*v**3 + 18/7*v**2 + 0 + 2/7*v**4 - 8/7*v = 0?
0, 1, 4
Let w(k) be the second derivative of k**6/1800 + k**5/200 + k**3/6 - 6*k**2 + 8*k - 1. Let t(s) be the second derivative of w(s). What is i in t(i) = 0?
-3, 0
Let -2/3*z**3 + 8/9 + 2/9*z**4 + 2/3*z - 10/9*z**2 = 0. Calculate z.
-1, 1, 4
Let y(a) = -4*a**3 + 4*a**2 - 7*a + 5. Let m(f) = 3*f**3 - 3*f**2 + 8*f - 4. Let r(t) = 5*m(t) + 4*y(t). Factor r(h).
-h*(h - 4)*(h + 3)
Let n be ((-5406)/170 + 33)/((-42)/(-10) + -1). Factor -1/2 + 1/8*w**2 - n*w.
(w - 4)*(w + 1)/8
Factor -25/9*q**2 + 22/9*q + 7/9 - 4/9*q**3.
-(q - 1)*(q + 7)*(4*q + 1)/9
Let y(w) be the first derivative of -1/14*w**2 - 5/21*w**3 - 4 + 1/28*w**4 + 5/7*w. Let y(b) = 0. What is b?
-1, 1, 5
Let l = -2024 + 2024. Let 1/11*z**4 + l + 2/11*z - 3/11*z**2 + 0*z**3 = 0. Calculate z.
-2, 0, 1
Let t(o) be the second derivative of -o**4/12 + 11*o**3/6 + 13*o**2 + 100*o. Factor t(x).
-(x - 13)*(x + 2)
Factor 0 + 1/2*r + 1/4*r**3 - 11/12*r**2.
r*(r - 3)*(3*r - 2)/12
Let u be (-2)/76*-4*7/7. Let j = 13/57 + u. Find t such that j*t**2 + 1/3 + 2/3*t = 0.
-1
Let h(k) be the second derivative of 13*k**9/10584 + k**8/2940 - 3*k**3 + 26*k. Let i(p) be the second derivative of h(p). Let i(v) = 0. What is v?
-2/13, 0
Let h(w) = w**3 + 11*w**2 + 14. Let a be h(-11). Suppose a*j + 5*j - 95 = 0. Factor 4/3*l**3 + 0 + 0*l**4 + 0*l**2 - 2/3*l**j - 2/3*l.
-2*l*(l - 1)**2*(l + 1)**2/3
Let c = -16835 - -84187/5. Determine l, given that -12/5*l**2 - 4/5*l**4 + 0 - c*l**3 - 4/5*l = 0.
-1, 0
Suppose -1458 + 1/2*t**3 - 109/2*t**2 + 1512*t = 0. What is t?
1, 54
Factor 45*u + 675/4*u**2 + 3.
3*(15*u + 2)**2/4
Suppose 5*n = 3*n + 10. Let a be n - -8*(-1 + 3/4). Factor -9/2*v + a + 3/2*v**2.
3*(v - 2)*(v - 1)/2
Let q(p) be the first derivative of -22*p**2 + 16/3*p**3 + 12 + 24*p + p**4. Suppose q(t) = 0. Calculate t.
-6, 1
Let x(c) be the second derivative of -c**7/21 + c**5/2 - 4*c**3/3 - 6*c + 21. Suppose x(r) = 0. What is r?
-2, -1, 0, 1, 2
Suppose -2*k - 35 = -1. Let t = k - -19. Determine z so that -27*z + 35*z - t - 2*z**2 - 4 = 0.
1, 3
Let 0*x + 0 + 10/19*x**3 - 8/19*x**2 - 2/19*x**4 = 0. What is x?
0, 1, 4
Let y(d) be the third derivative of 1/15*d**5 - 1/30*d**6 + 0*d + 0 - 2/3*d**3 + 10*d**2 + 1/6*d**4. Suppose y(h) = 0. Calculate h.
-1, 1
Let k(u) be the first derivative of u**4/12 - 11*u**3 + 1089*u**2/2 - 11979*u + 44. Factor k(d).
(d - 33)**3/3
Let g(k) = -26*k**3 + 44*k**2 + 64*k + 62. Let a(i) = 9*i**3 - 15*i**2 - 21*i - 21. Let n(q) = 17*a(q) + 6*g(q). Factor n(d).
-3*(d - 5)*(d + 1)**2
Factor -33/2*x**2 - 5*x**3 + 0 - 1/2*x**4 - 18*x.
-x*(x + 3)**2*(x + 4)/2
Let s(h) be the third derivative of h**7/525 - h**6/100 - 7*h**5/75 + h**4/5 + 8*h**3/3 + 117*h**2. Suppose s(f) = 0. What is f?
-2, 2, 5
Let n(x) be the first derivative of 0*x - 2*x**2 + 8/3*x**3 - x**4 - 5. Factor n(l).
-4*l*(l - 1)**2
Let y be (-900)/1485*(16/20 + 2/(-1)). Factor y*u - 2/11*u**2 + 0 - 8/11*u**3 + 2/11*u**4.
2*u*(u - 4)*(u - 1)*(u + 1)/11
Let z(y) be the second derivative of 2*y - 3/4*y**5 + 5/2*y**3 - 45/2*y**2 + 1/24*y**6 + 175/48*y**4 - 1. Determine u so that z(u) = 0.
-1, 1, 6
Factor -40 + 2/3*r**2 + 118/3*r.
2*(r - 1)*(r + 60)/3
Suppose -y - 5*u = 3, -3*y + 9 = 2*y + u. Factor 20*b**3 + 2*b**2 + 5*b**4 - 21*b**2 + 0*b**y - 6*b**2.
5*b**2*(b - 1)*(b + 5)
Let t(o) = -3 + 8*o - 9*o + 3 + 1. Let b(q) = -2*q**2 - 22*q + 16. Let c(v) = -2*b(v) + 36*t(v). Let c(n) = 0. Calculate n.
-1
Suppose 3*s = -4*x - 4, x = 3*s - 66 + 80. Solve 1/4 - 1/4*c**x + 0*c = 0.
-1, 1
Factor 2*j**4 - 2*j**3 + 8*j**2 + 2*j - 13*j**2 - j**2 + 4.
2*(j - 2)*(j - 1)*(j + 1)**2
Let t be -3*(-10)/6 + 2 + -2. Factor -g**3 - 210*g**2 + t*g**5 + 215*g**2 - 4*g**3 - 5*g**4.
5*g**2*(g - 1)**2*(g + 1)
Let u be (-14 - 82/(-6))/(44/(-33)). Let t = 7 - 5. Factor -1/2*k - 1/4 - u*k**t.
-(k + 1)**2/4
Suppose -9 = -2*k - 5*j + 22, -2*k - 14 = -4*j. Factor -6*m + 12*m**2 - 10 - 2*m**4 - 2*m + 8*m**k + 0*m**3 + 0*m**3.
-2*(m - 5)*(m - 1)*(m + 1)**2
Let k = 44 + -38. Let i(x) be the second derivative of 0 + 1/3*x**4 + 2*x**2 - 1/21*x**7 + 3*x - 4/15*x**k + 5/3*x**3 - 2/5*x**5. Factor i(u).
-2*(u - 1)*(u + 1)**3*(u + 2)
Let d(f) = 4*f**2 + f + 5. Let h be d(0). Suppose 12 = 4*z + 3*x, -3*x + 5 = -h*z - 7. Let z*w - 3/8 + 3/8*w**2 = 0. Calculate w.
-1, 1
Suppose -32*c**2 + 4*c**4 - 10*c**3 - 23*c - 32*c + 37*c = 0. Calculate c.
-1, 0, 9/2
Factor 50489 + z**2 - 218*z - 168*z - 13240.
(z - 193)**2
Suppose -3*y + 23 = 2*l, -4*l + 17 = -y + 6. Let a(d) be the second derivative of 0 + 5*d + 2*d**3 + 3/20*d**y + d**4 + 0*d**2. Let a(r