s). Factor d(k).
(k - 2)*(k + 2)
Let x(a) = -47*a**2 + 26*a - 4. Let n(j) = -187*j**2 + 103*j - 16. Let y(q) = -4*n(q) + 18*x(q). Factor y(u).
-2*(7*u - 2)**2
Let m(u) = u + 7. Let s be m(-11). Let d be (-15)/(-3) - s/(-2). Factor 0*c**3 + 2*c**d + c**4 - 2*c**3 - c**2.
c**2*(c - 1)*(c + 1)
Let w(j) be the first derivative of 7/5*j**4 - 4/5*j - 1 + 8/15*j**3 - 7/5*j**2 - 4/25*j**5 - 7/15*j**6. Solve w(u) = 0.
-1, -2/7, 1
Let v(n) be the second derivative of -n**6/10 - 3*n**5/20 + n**4/4 + n**3/2 - 2*n. Factor v(d).
-3*d*(d - 1)*(d + 1)**2
Determine v, given that -5*v**3 + 6*v**3 - 4*v**4 + 3*v**4 = 0.
0, 1
Let l(k) be the first derivative of -k**3 - 6*k**2 - 12*k - 1. Find u, given that l(u) = 0.
-2
Let a(g) be the first derivative of -1/360*g**6 + 0*g**5 - 1 + g**2 + 0*g**3 + 0*g**4 + 0*g. Let r(f) be the second derivative of a(f). Factor r(p).
-p**3/3
Let i(l) = l - 1. Let w be i(3). Solve w*q**2 + 105 - 105 = 0 for q.
0
Let s(u) be the first derivative of u**3/6 - u**2 + 3*u/2 + 14. Factor s(p).
(p - 3)*(p - 1)/2
Suppose -10 + 5 = -f - h, 2*h - 8 = -f. Determine i so that 1/3*i**f - 1/3*i - 2/3 = 0.
-1, 2
Factor -8*r + 32 + 1/2*r**2.
(r - 8)**2/2
Factor 0 + 2/5*u**2 - 6/5*u.
2*u*(u - 3)/5
Let a be (14/(-21)*1)/((-32)/6). Let s(b) be the first derivative of a*b**2 - 1/8*b**4 + 3 + 1/24*b**6 + 1/20*b**5 - 1/6*b**3 + 1/4*b. Factor s(m).
(m - 1)**2*(m + 1)**3/4
Let k = -37 - -39. Let f(x) be the first derivative of -2 - 1/5*x**2 - 4/5*x + 14/25*x**5 - 19/10*x**4 + k*x**3. Factor f(a).
2*(a - 1)**3*(7*a + 2)/5
Let i be (-215)/(-360) - (-6)/(-16). Factor 0 - 2*v**3 - 8/9*v**5 + 2/9*v - 22/9*v**4 - i*v**2.
-2*v*(v + 1)**3*(4*v - 1)/9
Let h be 0 + 2 + -2 + 4. Let y(r) = -3*r**3 - 23*r**2 + 27*r - 1. Let x(g) = 2*g**3 + 12*g**2 - 14*g. Let p(s) = h*y(s) + 7*x(s). Factor p(c).
2*(c - 2)*(c - 1)**2
Let 0*s + 1/2*s**2 + 0 + 7/4*s**4 - 9/4*s**3 = 0. Calculate s.
0, 2/7, 1
Let x(z) be the first derivative of -2/21*z**3 + 1/14*z**4 + 0*z + 0*z**2 + 3. Let x(i) = 0. Calculate i.
0, 1
Let f(k) be the third derivative of -k**5/330 - k**4/44 - 2*k**3/33 + 12*k**2. Factor f(r).
-2*(r + 1)*(r + 2)/11
Determine j, given that 0 + 0*j + 0*j**3 - 4/9*j**5 - 4/9*j**4 + 0*j**2 = 0.
-1, 0
Suppose 142*b = 133*b + 27. Let 0 + 0*s - 4/13*s**5 + 2/13*s**4 + 4/13*s**b - 2/13*s**2 = 0. Calculate s.
-1, 0, 1/2, 1
Let p(m) be the third derivative of -m**6/40 - 3*m**5/20 - 3*m**4/8 - m**3/2 + 11*m**2. Suppose p(y) = 0. Calculate y.
-1
Let t be 5 + -5 + 4 + (-224)/60. Determine q so that 2/3*q**4 - 2/5*q**2 - 14/15*q + 14/15*q**3 - t = 0.
-1, -2/5, 1
Let q(m) be the second derivative of m**6/10 - 3*m**5/50 + 9*m. Suppose q(f) = 0. Calculate f.
0, 2/5
Let p(x) be the third derivative of -x**8/1176 - x**7/735 + x**6/210 + x**5/105 - x**4/84 - x**3/21 - 13*x**2. Determine g so that p(g) = 0.
-1, 1
Factor 2/7*a - 4/7*a**2 - 4/7*a**3 + 2/7*a**4 + 2/7*a**5 + 2/7.
2*(a - 1)**2*(a + 1)**3/7
Let k(w) be the third derivative of w**8/1008 - w**7/315 + w**6/360 + 10*w**2. Factor k(o).
o**3*(o - 1)**2/3
Let u(v) be the second derivative of v**6/105 + 3*v**5/70 - 4*v**3/21 + 18*v. Find f, given that u(f) = 0.
-2, 0, 1
Let i(b) = -10*b**2 + 122*b + 116. Let q(u) = -2*u**2 + 24*u + 23. Let w(x) = -3*i(x) + 16*q(x). Determine v, given that w(v) = 0.
-1, 10
Let s be -4*2*(-4)/48. Let g(z) be the first derivative of s*z**3 + 0*z + 3 + 0*z**2. Find n, given that g(n) = 0.
0
Let o(l) be the first derivative of l**3/9 + 4*l**2/3 + 7*l/3 + 10. Find n, given that o(n) = 0.
-7, -1
Let y(k) be the first derivative of -5*k**5 - 15*k**4/4 + 10*k**3/3 + 37. Factor y(p).
-5*p**2*(p + 1)*(5*p - 2)
Let q(n) be the second derivative of -2*n**7/21 + 4*n**6/15 - 2*n**4/3 + 2*n**3/3 + 11*n + 2. Factor q(i).
-4*i*(i - 1)**3*(i + 1)
Let m be 4/(-26) + (-51)/(-78). Find x, given that 0*x + 0 - m*x**2 - 7/4*x**3 = 0.
-2/7, 0
Suppose -5*z + 3*z + 3*v = 9, 0 = -2*z + 2*v - 6. Suppose -54*t**2 - 108*t - 79 - t**4 + z*t**4 - 2 - 12*t**3 = 0. Calculate t.
-3
Let f(u) be the first derivative of -u**5/25 - u**4/15 + 4*u**3/15 + 6*u - 3. Let b(m) be the first derivative of f(m). What is p in b(p) = 0?
-2, 0, 1
Determine j so that -3*j**3 - j**5 + 3*j**4 + 24*j**2 - 27*j**2 + 6*j**5 - 2*j**5 = 0.
-1, 0, 1
Let s(q) be the third derivative of q**8/84 - 4*q**7/105 - q**6/30 + 2*q**5/15 + 21*q**2. Solve s(r) = 0 for r.
-1, 0, 1, 2
Let a(b) be the first derivative of b**4/12 + 7*b**3/9 + 5*b**2/2 + 3*b - 16. Factor a(g).
(g + 1)*(g + 3)**2/3
Let o(u) be the second derivative of 0 + 3*u - 1/18*u**4 - 1/9*u**3 + 0*u**2. Factor o(r).
-2*r*(r + 1)/3
Let u(l) be the first derivative of l**8/168 - l**6/60 - 2*l**2 + 9. Let j(f) be the second derivative of u(f). Let j(v) = 0. Calculate v.
-1, 0, 1
Let t(w) = -w**2 + 7*w + 11. Let i be t(8). Let x(c) be the second derivative of 1/70*c**5 + 3*c + 0 + 2/7*c**2 + 5/21*c**i + 2/21*c**4. Factor x(k).
2*(k + 1)**2*(k + 2)/7
Let r(t) be the third derivative of t**5/120 + t**4/24 + t**3/12 - 21*t**2. Factor r(h).
(h + 1)**2/2
Let j(n) be the second derivative of -n**6/420 + n**5/210 - 3*n**2/2 - 3*n. Let v(d) be the first derivative of j(d). What is g in v(g) = 0?
0, 1
Let z(g) = -5*g. Let y be z(-2). Suppose 2*o - y = d - 2*d, 5*o - 28 = -4*d. Factor -1/3 + 2/3*p + p**d.
(p + 1)*(3*p - 1)/3
Let m(j) be the first derivative of -j**3/4 - 9*j**2/4 - 6*j + 20. Factor m(i).
-3*(i + 2)*(i + 4)/4
Let f(w) = -6*w**2 + 6*w + 9. Let g(c) be the second derivative of 11*c**4/12 - 2*c**3 - 9*c**2 + 2*c. Let a(y) = -5*f(y) - 3*g(y). Suppose a(x) = 0. What is x?
-1, 3
Let d(w) be the third derivative of -w**7/5040 - w**6/720 - 5*w**4/24 + 4*w**2. Let a(t) be the second derivative of d(t). Suppose a(s) = 0. What is s?
-2, 0
Let t(f) be the second derivative of -3*f**5/100 + f**4/10 - f**3/10 + 38*f. Let t(d) = 0. Calculate d.
0, 1
Suppose -s - 2*t = -t - 9, 0 = -3*s + 2*t + 2. What is l in 2*l**4 + 2*l**2 + l**2 - 6*l**3 + l**s = 0?
0, 1
Let v(y) be the third derivative of 5*y**8/96 + 23*y**7/84 + y**6/8 + 13*y**2. Suppose v(k) = 0. Calculate k.
-3, -2/7, 0
Find a, given that -16*a + 21*a**3 + 16*a**2 + 27*a**3 - 52*a**3 = 0.
0, 2
Let a(c) be the second derivative of c**4/42 + c**3/21 - 3*c. Suppose a(g) = 0. Calculate g.
-1, 0
Suppose 0 + 0*z - 1/4*z**2 = 0. What is z?
0
Suppose -4*z - 4*c - 5 = 3, -5*z - c = -6. Let j be (-4)/z*(-1)/3. Factor j*h**3 + 0 + 2/9*h**2 - 4/9*h.
2*h*(h + 1)*(3*h - 2)/9
Let z(u) = -u**3 + 7*u**2 + 13*u + 11. Let m(o) be the second derivative of -o**5/10 + o**4/2 + 2*o**3 + 6*o**2 - 5*o. Let d(k) = 3*m(k) - 4*z(k). Factor d(t).
-2*(t + 1)*(t + 2)**2
Let y(w) be the first derivative of 3*w**5/35 - 2*w**3/7 + 3*w/7 - 15. Factor y(m).
3*(m - 1)**2*(m + 1)**2/7
Let h = 34 + -34. Let x(f) be the third derivative of 0*f**3 + 3*f**2 + 0*f + 1/36*f**4 - 1/180*f**5 + h. Factor x(s).
-s*(s - 2)/3
Let k(x) = -3*x**4 - 6*x**3 + 4*x**2 + 5*x. Let u(s) = -4*s**4 - 9*s**3 + 6*s**2 + 7*s. Let a(b) = 7*k(b) - 5*u(b). Factor a(o).
-o**2*(o - 2)*(o - 1)
Let g(h) be the second derivative of 0 + 0*h**2 + 0*h**3 + 1/24*h**4 + 3*h. Suppose g(n) = 0. What is n?
0
Let k(w) be the second derivative of 1/6*w**4 + 0 + w + 1/10*w**5 + 0*w**3 + 0*w**2. Suppose k(h) = 0. Calculate h.
-1, 0
Let b(p) = -p**3 - 5*p**2 + 6. Let k(r) = -5*r**3 - 26*r**2 + 31. Let d(c) = -11*b(c) + 2*k(c). Factor d(t).
(t - 1)*(t + 2)**2
Suppose -2*w - w + 12 = 0. Let m be (2/5)/(12/15). Factor m*b - b**w + 0 + b**2 - 1/2*b**5 + 0*b**3.
-b*(b - 1)*(b + 1)**3/2
Let s(o) = -o**3 + o**2 - o. Let t = -18 + 13. Let f(m) = 3*m**3 - 5*m**2 + 5*m. Let r(g) = t*s(g) - f(g). Factor r(y).
2*y**3
Let n(q) be the third derivative of -q**7/1260 - q**6/180 - q**4/12 + q**2. Let y(h) be the second derivative of n(h). Factor y(m).
-2*m*(m + 2)
Let x be 21/(-392)*-20*4/10. Factor x*d**2 + 9/7*d + 6/7.
3*(d + 1)*(d + 2)/7
Suppose 3*y + 10 = 5*y. Let z = 7 - y. Factor -1/4*m**z + 0*m + 0.
-m**2/4
Let j(n) be the first derivative of -n**4/4 - 2*n**3/3 - n**2/2 + 1. Determine w, given that j(w) = 0.
-1, 0
Let w = 55/8 - 479/72. Find s such that w*s**2 + 4/9*s + 2/9 = 0.
-1
Let n be -5*((-21)/15 + 1 + 0). Solve 2/5*m**n - 4/5*m + 0 + 2/5*m**3 = 0 for m.
-2, 0, 1
Suppose 13 - 13 = -3*k. Factor -2/9*w**3 + 0 + 2/9*w + k*w**2.
-2*w*(w - 1)*(w + 1)/9
Let f(w