rd derivative of x**8/112 - 3*x**6/20 + 2*x**5/5 - 3*x**4/8 + 10*x**2 + 6*x. Factor c(p).
3*p*(p - 1)**3*(p + 3)
Let h be (1 + (-22)/12)/((-10404)/324 - -31). Factor -15/4*c + h*c**3 - 9/4 - 3/4*c**2.
3*(c - 3)*(c + 1)**2/4
Let o(f) = -4*f**3 + 152*f**2 + 284*f. Let w(s) = 2*s**3 - s**2 - s. Let c(m) = o(m) + 4*w(m). Factor c(h).
4*h*(h + 2)*(h + 35)
Let v be 0 - 55/(-264)*4. Let i(n) be the second derivative of -v*n**3 - 8*n - 3/20*n**5 + 1/2*n**2 + 0 + 7/12*n**4. Factor i(r).
-(r - 1)**2*(3*r - 1)
Factor 2/7*v**3 + 0 - 46/7*v**2 + 44/7*v.
2*v*(v - 22)*(v - 1)/7
Let h = -148 - -144. Let z(f) = -219*f - 108. Let r be z(h). Solve -512*y**4 - 81/8 + r*y**3 - 432*y**2 + 108*y = 0.
3/8
Factor 10*a**4 - 129*a**3 - 2*a**2 + 141*a**3 - 8*a**2 - a**5 - 11*a.
-a*(a - 11)*(a - 1)*(a + 1)**2
Let i(h) = -h**2 + 11*h - 8. Let n be (-2)/5 + 1028/20. Let f(z) = -7*z**2 + 88*z - 65. Let o(k) = n*i(k) - 6*f(k). Solve o(g) = 0.
2/3, 3
Solve 21/5*j**2 - 12/5*j - 36/5 - 3/5*j**3 = 0 for j.
-1, 2, 6
Find g, given that -6728/3 - 232/3*g - 2/3*g**2 = 0.
-58
Let j(t) be the second derivative of 4/3*t**3 + 1/3*t**4 + 1/30*t**6 + 0 - 4*t - 7/30*t**5 - t**2. Let w(r) be the first derivative of j(r). Factor w(l).
2*(l - 2)**2*(2*l + 1)
Suppose -3*m - 11 = -d, 41*d - 3*m = 36*d + 19. Find v such that 5/2*v**3 + 1/2*v - 4*v**d + 1 = 0.
-2/5, 1
Let q = -12395/7 - -1772. Factor -6/7*w**2 - q*w + 3/7*w**3 + 0.
3*w*(w - 3)*(w + 1)/7
Let k = -211/540 - -2/5. Let c(i) be the third derivative of 0*i - k*i**4 - 4*i**2 + 0 - 1/270*i**5 + 2/27*i**3. Solve c(z) = 0 for z.
-2, 1
Factor 14/3 - 2*w**2 - 1/3*w**3 + 3*w.
-(w - 2)*(w + 1)*(w + 7)/3
Let r(f) be the first derivative of 3*f**6/2 - 12*f**5 - 27*f**4/4 + 14*f**3 - 73. Find p, given that r(p) = 0.
-1, 0, 2/3, 7
Let r(g) = 8*g**3 - 56*g**2 - 188*g - 130. Let s(a) = -7*a**3 + 54*a**2 + 187*a + 130. Let z(u) = -2*r(u) - 3*s(u). Suppose z(y) = 0. Calculate y.
-2, -1, 13
Let m = -1914/43 + 11785/258. Find v such that -2/3*v - 7/2*v**3 + 0 + 1/3*v**4 - 10/3*v**2 + m*v**5 = 0.
-1, -2/7, 0, 2
Let a = -1474/9 - -164. Let d = 1/138 + 91/138. Suppose -8/9*h + d*h**2 + a = 0. Calculate h.
1/3, 1
Let v(o) = -18*o**2 - 1500*o + 93750. Let s(l) = -11*l**2 - 1000*l + 62500. Let y(x) = 8*s(x) - 5*v(x). Factor y(n).
2*(n - 125)**2
Let w be (-15)/18*(-24)/60. Let k(q) be the second derivative of w*q**2 - 1/90*q**6 + 0 + 1/60*q**5 + 1/12*q**4 - 5/18*q**3 + 7*q. Factor k(p).
-(p - 1)**3*(p + 2)/3
Let r(d) = 6 + 4*d**2 - 2*d - 2*d - 3. Let b(a) = -12*a**2 + 12*a - 8. Let i(f) = -3*f**2 + 10*f. Let x be i(2). Let m(c) = x*r(c) + 3*b(c). Factor m(o).
-4*o*(o - 1)
Let u(a) be the third derivative of -a**10/37800 + a**9/3780 - a**8/1680 - a**5/3 + 21*a**2. Let r(y) be the third derivative of u(y). Factor r(b).
-4*b**2*(b - 3)*(b - 1)
Let i(p) be the second derivative of -p**5/120 + p**4/8 + 7*p**3/12 - 5*p**2/2 - 29*p. Let j(b) be the first derivative of i(b). Factor j(k).
-(k - 7)*(k + 1)/2
Let v(k) = -5*k**3 + 3*k**2 - 10*k - 12. Let w(h) = -11*h**3 + 6*h**2 - 21*h - 24. Let s(p) = 13*v(p) - 6*w(p). Let s(u) = 0. Calculate u.
-3, -2, 2
Let q(a) be the first derivative of -a**3/3 + a**2/2 - a - 16. Let m(f) = -4*f**3 - 32*f**2 - 28*f + 60. Let x(c) = -m(c) + 4*q(c). Factor x(s).
4*(s - 1)*(s + 4)**2
Factor -2/3*u**4 - 16*u**2 + 32/3*u + 0 + 6*u**3.
-2*u*(u - 4)**2*(u - 1)/3
Let l(t) be the second derivative of 3*t**5/20 - 7*t**3/2 + 9*t**2 - 4*t - 1. Factor l(m).
3*(m - 2)*(m - 1)*(m + 3)
Let g = -226 + 216. Let q be 1 - ((-5)/g + -1). Let 0*s + q*s**2 - 3/2 = 0. What is s?
-1, 1
Let a = -21 + 17. Let y(u) = 48*u**3 - 67*u**2 + 22*u - 3. Let l(w) = 48*w**3 - 68*w**2 + 23*w - 3. Let s(r) = a*y(r) + 5*l(r). Factor s(z).
3*(z - 1)*(4*z - 1)**2
Let a(x) be the first derivative of 1/40*x**6 + 2*x + 0*x**2 + 0*x**5 + 1/4*x**3 + 6 - 3/16*x**4. Let n(k) be the first derivative of a(k). Solve n(l) = 0.
-2, 0, 1
Let w(o) = o - 1. Let p(x) = 2*x + 16. Let f be p(-7). Let z(d) = 21*d - 54*d + d**f + 22*d + 10. Let h(u) = 18*w(u) + 2*z(u). Let h(c) = 0. Calculate c.
1
Let l(y) = -y**4 - y**2. Let q(v) = v**4 - 5*v**3 + 121*v**2 - 195*v + 90. Let s(m) = 6*l(m) + q(m). Solve s(x) = 0.
-6, 1, 3
Let s(u) be the first derivative of u**3/2 - 9*u**2/2 + 27*u/2 + 74. Find y, given that s(y) = 0.
3
Let j = 1661/2 + -11623/14. Factor 3/7*y**3 - y + 2/7*y**2 + j.
(y - 1)*(y + 2)*(3*y - 1)/7
Let a(j) be the second derivative of -3*j**6/10 - 87*j**5/20 + 5*j**4/2 - 81*j. Suppose a(w) = 0. Calculate w.
-10, 0, 1/3
Let k = 3/5891 - -5885/11782. Let s be (0 + -1)/(-1) - -2. Factor 0 - k*b**s + b + 1/2*b**2.
-b*(b - 2)*(b + 1)/2
Factor 228 + 25*o**2 + 157 + 390*o + 36*o**2 - 56*o**2.
5*(o + 1)*(o + 77)
Factor 5*k + 50 - 24*k - 20*k - 47 + k**2 + 71.
(k - 37)*(k - 2)
Let b(z) = z**3 - 2*z - 1. Let x(j) = 7*j**3 - 4*j**2 - 17*j - 2. Let g(i) = -40*b(i) + 5*x(i). Factor g(a).
-5*(a - 1)*(a + 2)*(a + 3)
Let y = -659 + 661. Let i(r) be the first derivative of 6 - 1/6*r**y + 1/9*r**3 + 0*r. Factor i(c).
c*(c - 1)/3
Let b = 0 + 8. Suppose -4*d + 0*d + 4*j - 4 = 0, -4*d + 5*j - b = 0. Solve 3*g**d + 3*g + 4*g - g**2 - 3*g**4 - 7*g + g**5 = 0 for g.
0, 1
Solve 192/5*y - 3/5*y**4 + 36/5*y**3 + 0 - 144/5*y**2 = 0.
0, 4
What is j in -6*j**2 + 3*j + 13*j**5 - 36*j**5 + 6*j**4 + 20*j**5 = 0?
-1, 0, 1
Factor -3/7*s + 3/7*s**3 + 0 + 0*s**2.
3*s*(s - 1)*(s + 1)/7
Let i(v) be the first derivative of v**6/2160 - v**5/120 + 5*v**4/144 + 2*v**3/3 - 11. Let t(z) be the third derivative of i(z). Find n, given that t(n) = 0.
1, 5
Factor 3/7*t**2 + 8/7*t - 2/7*t**3 + 4/7 - 1/7*t**4.
-(t - 2)*(t + 1)**2*(t + 2)/7
Let y be 0*(-1)/2*(-2)/1. Let o(a) be the third derivative of y + 1/60*a**5 + 2*a**2 + 0*a - 1/96*a**4 + 0*a**3. Factor o(n).
n*(4*n - 1)/4
Let y = -30819 - -215735/7. Factor 18/7*s + y*s**2 + 16/7.
2*(s + 1)*(s + 8)/7
Let s(j) = 2*j**3 + 172*j**2 - 2*j - 170. Let b be s(-86). Factor 2/3*f**b - 4 + 10/3*f.
2*(f - 1)*(f + 6)/3
Let v(r) be the third derivative of r**7/105 - r**6/120 - r**5/12 - r**4/12 + 6*r**2 - 1. Determine w so that v(w) = 0.
-1, -1/2, 0, 2
Let q(i) be the first derivative of -58*i**6/3 + 48*i**5 + 199*i**4 + 136*i**3 - 16*i**2 - 808. Suppose q(l) = 0. What is l?
-1, 0, 2/29, 4
Let y(w) be the second derivative of -w**4/18 - 112*w**3/9 - 3136*w**2/3 - 192*w. Solve y(b) = 0 for b.
-56
Find c such that 24*c - 10*c**2 + 9 + c**4 - 8/3*c**3 = 0.
-3, -1/3, 3
Let w(z) = -364*z - 8. Let u be w(-4). Solve 81 + u*r**2 - 49 + 1892*r**3 + 368*r - 2219*r**5 - 940*r**4 - 581*r**5 = 0 for r.
-2/5, -2/7, -1/4, 1
Factor 45/2*q - 23 + 1/2*q**2.
(q - 1)*(q + 46)/2
Let f(t) be the first derivative of t**2 - 15 + 2/3*t**3 - 4*t. Factor f(j).
2*(j - 1)*(j + 2)
Let 6*a**2 + 3*a**3 + 0 - 3/2*a**4 + 0*a - 3/4*a**5 = 0. Calculate a.
-2, 0, 2
Let i = -27 + 30. Suppose -19 = -4*w - i. Factor -2*u + 2 - 10*u**2 + 9*u**w - 5*u**3 - u**4 - u**3 + 8*u.
2*(u - 1)**2*(u + 1)*(4*u + 1)
Suppose 30 = 11*d - 5*d. Let p(t) be the third derivative of 0 - 1/18*t**d + 2/9*t**4 + 0*t - 4*t**2 + 1/180*t**6 - 4/9*t**3. Factor p(g).
2*(g - 2)**2*(g - 1)/3
Suppose -11*a + 3*a - 8 = 0. Let g = 1 + a. Factor 4/7*i**3 + 0*i**2 + g + 0*i - 2/7*i**4.
-2*i**3*(i - 2)/7
Let n be (-7)/(-28) - (0 + 61/4). Let q be (-2)/n*(-7 + 13). Factor -4/5*i**3 + 1/5*i**4 + 4/5*i + 3/5*i**2 - q.
(i - 2)**2*(i - 1)*(i + 1)/5
Suppose 12*v - 2*v - 1270 = 0. Let q = -127 + v. Factor -3/2*o**2 + 3/2*o + q.
-3*o*(o - 1)/2
Let f(y) be the first derivative of -y**5/15 - y**4/12 + 2*y**3/3 + 440. Factor f(z).
-z**2*(z - 2)*(z + 3)/3
Let x = -196 - -200. Let o(u) be the first derivative of -1/4*u**x + 1/4*u**3 + 5 + 0*u + 1/8*u**2. Factor o(n).
-n*(n - 1)*(4*n + 1)/4
Factor -3/2*r**2 - 18 - 12*r.
-3*(r + 2)*(r + 6)/2
Let t be -5 + (-7)/((-1666)/2941) + (-1)/(-7). Solve -t*f**3 + 0 + 15/2*f**5 - 5/2*f**2 + 5/2*f**4 + 0*f = 0 for f.
-1, -1/3, 0, 1
Let v be 3561*7/(-105) - -7. Let x = v + 231. Suppose -3/5*i**2 - x*i**4 - 11/5*i**3 + 6/5 + 11/5*i = 0. Calculate i.
-3, -1, -2/3, 1
Let n(m) = m**3 + 18*m**2 - 19*m - 18. Let l be n(-19). Let w be 3/(-18) - l/60. Determine k so that -w + 2/15*k**2 - 2/15*k**3 + 2/15*k = 0.
-1, 1
Let m(t) be the first derivative of 4*t**3/15 - 48*t**2/5 + 69. Solve m(h) = 0 for h.
0, 24
Let z be (10 - 7)*(-10)/(-6). Solve -4*l*