- 1/3*k**4 - 1/30*k**5. Let h(q) be the first derivative of w(q). Factor h(y).
-2*y*(y + 3)**2/3
Let b(l) be the third derivative of 1/6*l**3 + 1/240*l**6 - 1/48*l**4 - 1/60*l**5 + 0*l + 0 - 16*l**2. Determine u, given that b(u) = 0.
-1, 1, 2
Let m(b) be the first derivative of -b**7/7980 - b**6/855 - b**5/228 - b**4/114 - 2*b**3/3 + 12. Let i(p) be the third derivative of m(p). Factor i(w).
-2*(w + 1)**2*(w + 2)/19
Let p(y) be the first derivative of -y**3/5 + 576*y**2/5 - 110592*y/5 + 475. Suppose p(n) = 0. Calculate n.
192
Suppose 258*x - 207*x**2 - 640 - 45*x + 568 + 63*x**3 + 3*x**4 = 0. Calculate x.
-24, 1
Let g be (5/2 - -1) + 362/(-724). Let l(x) be the second derivative of 0*x**g - 3/40*x**5 + 0 + 1/4*x**4 + 0*x**2 - 7*x. Factor l(q).
-3*q**2*(q - 2)/2
Let h(k) = 2*k - 5. Let t(l) = 155*l**3 + 145*l**2 - 20*l + 25. Let f(n) = -5*h(n) - t(n). Factor f(a).
-5*a*(a + 1)*(31*a - 2)
Suppose 2*j - 17*j = -60. Let q(u) be the first derivative of -6 + 8*u + j*u**2 + 2/3*u**3. Find p, given that q(p) = 0.
-2
Let f(z) be the first derivative of -1/2*z**2 - 4/3*z**6 + 0*z - 7/3*z**3 - 9/2*z**4 - 4*z**5 - 22. Factor f(r).
-r*(r + 1)*(2*r + 1)**3
Suppose -4*g = -9 - 11. Let a(w) be the second derivative of 0 + 1/54*w**4 - 2/9*w**2 + 1/9*w**3 + 3*w + 1/135*w**6 - 1/30*w**g. Factor a(i).
2*(i - 2)*(i - 1)**2*(i + 1)/9
Factor -6*y - y**2 + 7*y + 3*y.
-y*(y - 4)
Let 8*b**2 + 16/7*b**4 + 8/7 - 44/7*b**3 - 34/7*b - 2/7*b**5 = 0. What is b?
1, 4
Find c, given that -37/3*c**4 - 32/3*c + 5/3*c**5 + 18*c**3 + 64/3*c**2 + 0 = 0.
-1, 0, 2/5, 4
Let n be (-437)/38*(-500)/1150. Factor -1/2*z**2 + n - 3/2*z.
-(z - 2)*(z + 5)/2
Let s be (-222)/370 + (1 - 364/10). Let y = s + 39. Factor 2/5*f**y + 2/5*f - 4/5*f**2 + 0.
2*f*(f - 1)**2/5
Let f(u) be the second derivative of -u**6/25 + u**5 - 223*u**4/30 + 112*u**3/15 + 64*u**2/5 + 27*u. Determine c, given that f(c) = 0.
-1/3, 1, 8
Let z be -2*(-7 + 6/1). Let d(w) be the third derivative of 3/2*w**4 + 1/40*w**6 - 7*w**z + 3/10*w**5 + 0 + 4*w**3 + 0*w. Suppose d(g) = 0. What is g?
-2
Let j be (-37 - -1)*(-3)/9. Suppose 11 + 13 = j*k. Factor 1/3*o**k - 1/3*o + 0.
o*(o - 1)/3
Let p(a) = -16*a**3 - 40*a**2 - 160*a - 144. Let x(y) = -18*y**3 - 38*y**2 - 160*y - 144. Let k(j) = -7*p(j) + 6*x(j). Factor k(n).
4*(n + 2)**2*(n + 9)
Let q(n) = 3*n**5 + 6*n**4 + 3*n**3 - 2*n + 2. Let w(v) = 20*v**5 + 38*v**4 + 19*v**3 + v**2 - 13*v + 13. Let t(i) = -39*q(i) + 6*w(i). Let t(b) = 0. What is b?
-1, 0, 1, 2
Let s(u) = 2*u + 18. Let k be s(-7). Find n, given that k*n**2 + 28*n - 25*n - n**2 - 6 = 0.
-2, 1
Let -7*l**3 - 9*l**3 + 11*l - l**2 - 2*l + l**4 + 8*l**3 - l = 0. Calculate l.
-1, 0, 1, 8
Let d(k) = 6*k**3 - 6*k**2 - 13*k - 35. Let b(g) = g**3 - g**2 - 2*g - 6. Let m(y) = -34*b(y) + 6*d(y). Factor m(c).
2*(c - 3)*(c + 1)**2
Let l be (1641/39 - 42) + (-14)/(-26). Factor l*r**2 + 14/13*r - 4/13.
2*(r + 2)*(4*r - 1)/13
Let z(d) be the second derivative of -d**4/14 + d**3/21 - 39*d - 2. Factor z(c).
-2*c*(3*c - 1)/7
Let n be ((-3)/21)/(292/(-28) + 9). Let j(y) be the third derivative of 2*y**2 - 1/150*y**5 + 0*y - 3/5*y**3 + n*y**4 + 0. Determine r, given that j(r) = 0.
3
Let q(n) be the second derivative of n**6/96 - n**5/12 + 5*n**4/24 - 22*n**2 - 41*n. Let s(x) be the first derivative of q(x). Factor s(j).
5*j*(j - 2)**2/4
Let h(f) = 4*f**2 + 5*f + 9. Let a = 19 - 18. Let q(b) = b**2 + b + 1. Let l(n) = a*h(n) - 5*q(n). Factor l(i).
-(i - 2)*(i + 2)
Suppose 176 - 41 = 3*b. Let r be (-1 - 6*(-6)/b)*-3. Factor -3/5*o**2 - r*o + 0.
-3*o*(o + 1)/5
Let z = -2348 + 2348. Factor -2/9*w**2 + z + 10/9*w**3 - 14/9*w**4 + 0*w + 2/3*w**5.
2*w**2*(w - 1)**2*(3*w - 1)/9
Factor -34/15*v + 2/5 - 4/5*v**2.
-2*(v + 3)*(6*v - 1)/15
Let i = 818 + -818. Let z(t) be the second derivative of i + 0*t**2 + 1/4*t**4 - t + 1/2*t**3. Factor z(p).
3*p*(p + 1)
Suppose 8*o = j + 3*o - 191, -3*j - 2*o + 539 = 0. Let l = 185 - j. Determine s so that -3/4*s**3 + 9/4*s**2 - 3/4*s**l + 3/2 + 15/4*s = 0.
-1, 2
Let x be (-4)/(-16)*(-128)/(-96). Let 3 + x*n**3 + 7/3*n**2 + 5*n = 0. Calculate n.
-3, -1
Suppose 2*q + 11 = 19. Determine w so that -5*w + 4*w**2 - 54*w**3 + w**2 - 5*w**q + 59*w**3 = 0.
-1, 0, 1
Let n(j) be the third derivative of j**6/1620 + j**5/270 + j**3 + 8*j**2. Let y(m) be the first derivative of n(m). Factor y(g).
2*g*(g + 2)/9
Let s = -66 + 68. Let l(h) be the third derivative of 0 - 1/4*h**5 + 1/8*h**4 + h**3 + 1/20*h**6 + 0*h - 3*h**s. Factor l(b).
3*(b - 2)*(b - 1)*(2*b + 1)
Determine s, given that -6*s**2 + 2 + 0 + 3*s**4 - 1 + 2 = 0.
-1, 1
Let v be 3/75*(-3 - -4). Let s(p) be the first derivative of v*p**5 + 0*p + 3/20*p**4 + 1/10*p**2 + 3 + 1/5*p**3. Suppose s(f) = 0. Calculate f.
-1, 0
Let b(f) be the third derivative of -f**5/15 - f**4/3 - 2*f**3/3 - 2*f**2 + 9*f. Factor b(a).
-4*(a + 1)**2
Let u(x) be the first derivative of -x**4/34 + x**2/17 + 68. Factor u(g).
-2*g*(g - 1)*(g + 1)/17
Suppose -5*b - 22 = -147. Let s be (-5)/b - ((-162)/(-10))/(-3). Suppose -18/5*q**4 + 0 - 4/5*q - 22/5*q**5 + 18/5*q**2 + s*q**3 = 0. Calculate q.
-1, 0, 2/11, 1
Let o(g) be the first derivative of -2/3*g**6 - 6*g**4 + 16/5*g**5 - 16 + 16/3*g**3 - 2*g**2 + 0*g. Let o(s) = 0. What is s?
0, 1
Find l, given that 3/5*l**2 + 42/5*l + 99/5 = 0.
-11, -3
Let q(w) be the first derivative of w**3 + 189*w**2/2 - 192*w - 573. Factor q(b).
3*(b - 1)*(b + 64)
Let u(z) = 2*z**4 + 18*z**3 - 30*z**2 + 22*z. Let w(x) = -5*x**4 - 55*x**3 + 91*x**2 - 65*x. Let i = 2 + -8. Let s(y) = i*w(y) - 17*u(y). Factor s(t).
-4*t*(t - 4)*(t - 1)**2
Let q(c) be the first derivative of c**8/560 - c**6/40 - c**5/20 + 4*c**3/3 + 15. Let h(v) be the third derivative of q(v). Determine i, given that h(i) = 0.
-1, 0, 2
Suppose 26*m = 22*m + 12. Suppose -4*f + 10 = -2*z, 3*f - m = 2*z + 3. Factor z*c - 3/2*c**3 + 0 + 3/2*c**2.
-3*c*(c - 2)*(c + 1)/2
Let u = 641/12 - 191/12. Determine p so that 125/2 + 15/2*p**2 - u*p - 1/2*p**3 = 0.
5
Factor -7/4*t**2 - 47/4*t + 7/2.
-(t + 7)*(7*t - 2)/4
Let q be 1 + (76/(-1026) - (-25)/(-27)). Let u(c) be the first derivative of 3 + 2*c**2 + 4/3*c**3 + q*c. Factor u(i).
4*i*(i + 1)
Let w(m) = m**3 - 2*m**2 - 3*m - 4. Let t be w(-4). Let f be (-11)/(-44) - (-6)/t*1. Determine v so that f*v**2 + 0 - 2/11*v = 0.
0, 1
Let o(i) = 5*i**2 + 98*i + 291. Let n(j) = 20*j**2 + 390*j + 1165. Let s(p) = 6*n(p) - 25*o(p). Factor s(f).
-5*(f + 3)*(f + 19)
Let x(p) = -5*p**3 + 12*p**2 + 3*p + 3. Let s(w) = -16*w**3 + 36*w**2 + 10*w + 10. Let r(j) = 3*s(j) - 10*x(j). Let r(n) = 0. What is n?
0, 6
Let d(t) = 4*t**2 - t + 1. Let j be d(1). Let r be (3/(-15)*j)/((-16)/40). Determine h, given that r + 18*h + 81/2*h**2 = 0.
-2/9
Let v = 322 + -1598/5. Solve -38/5*m + v - 14/5*m**2 = 0 for m.
-3, 2/7
Let t(r) be the first derivative of -2*r**5/15 - 2*r**4/3 + 22*r**3/9 - 2*r**2 + 25. Factor t(h).
-2*h*(h - 1)**2*(h + 6)/3
Suppose 3*a + 30 = 5*v + 6*a, -a = -v - 2. Suppose -v*m + 150 = 18. Find p such that -3*p**3 - 2*p + 6*p**2 - 47*p**4 + 2*p + m*p**4 = 0.
-2, 0, 1
Let n(y) be the second derivative of y**7/14 - y**6/5 - 3*y**5/10 + 2*y**4 - 7*y**3/2 + 3*y**2 + 14*y. Let n(b) = 0. Calculate b.
-2, 1
Let y be (-6)/(-10) + (-15)/25 + 2. Factor -6*g**y + g**2 + 38*g + 11*g - 14*g.
-5*g*(g - 7)
Let t(d) be the first derivative of -3*d**4/28 + 4*d**3/7 - 15*d**2/14 + 6*d/7 + 51. Factor t(h).
-3*(h - 2)*(h - 1)**2/7
Let n = 25 + -19. Let s be 3/3 - ((-10)/n + 0). Factor 0 - 1/3*c**4 - 4*c**2 - 2*c**3 - s*c.
-c*(c + 2)**3/3
Suppose 0 = 8*i - 1 - 15. Let u(r) be the second derivative of 0 + 0*r**3 + 4*r + 0*r**i - 1/6*r**4. Suppose u(o) = 0. Calculate o.
0
Let b be (2/3)/(3/27). Let 15 + b*r**2 + 30*r + 10 - r**2 = 0. What is r?
-5, -1
Let h(d) be the first derivative of -2*d**5/25 - 2*d**4/5 + 2*d**3/3 - 16. Find j, given that h(j) = 0.
-5, 0, 1
Let k = 1735 - 1733. Let l(o) be the second derivative of k*o**2 - 5/12*o**4 - 4*o - 4/3*o**3 + 0. Find g, given that l(g) = 0.
-2, 2/5
Suppose -5*s = -20, 0*w = -w + 4*s - 15. Let p be 16*((-51)/18 + w + 2). Let 4/3 - 5/3*v**2 - p*v = 0. Calculate v.
-2, 2/5
Let d = 13 + -12. Let -d + 3*r**2 - 4*r**2 - 9*r**2 - 3*r**3 - 1 - 9*r = 0. Calculate r.
-2, -1, -1/3
Let z(n) = -2*n**2 + n + 2. Let l(y) = -13*y**2 + 244*y - 2872. Let b(j) = -l(j) + 4*z(