6*p**3 + 6*p**2 - 4*p - 4. Let x = -42 + 43. Let d(j) = j**3 + j**2 - 1. Let n(y) = x*i(y) - 4*d(y). Factor n(m).
2*m*(m - 1)*(m + 2)
Let x(k) be the second derivative of -10*k**7/21 + 2*k**6/5 + 12*k**5/5 + 4*k**4/3 + 2*k + 10. Find l such that x(l) = 0.
-1, -2/5, 0, 2
Suppose 3 = -2*k + 27. Let w be 3/(69/k - 2). Solve 0*p - w*p**4 + 0*p**3 - 2/5*p**5 + 0*p**2 + 0 = 0.
-2, 0
Suppose -d + 12*v - 11*v = 0, -v - 4 = -2*d. Solve -3/4*i**3 + 1/4*i**d + 0 + i + 0*i**2 = 0.
-1, 0, 2
Let b(i) be the third derivative of 2/33*i**3 + 7*i**2 + 0*i - 1/660*i**6 + 0 - 5/132*i**4 + 2/165*i**5. Factor b(d).
-2*(d - 2)*(d - 1)**2/11
Let z(a) = a**3 + 6*a**2 - 14*a + 18. Let y be z(-8). Factor 49*j - 57*j + 4*j**y - 4 - 8.
4*(j - 3)*(j + 1)
Factor 12*f**2 + 4*f**3 - 108*f + 221*f - 105*f.
4*f*(f + 1)*(f + 2)
Let n(t) be the second derivative of -3*t**5/20 + 9*t**4/2 - 54*t**3 + 324*t**2 - 87*t. Find p, given that n(p) = 0.
6
Suppose -13*f = -12*f - 7. Let l(r) = -6*r**3 + r**2 - 5*r. Let t(k) = 9*k**3 - 2*k**2 + 7*k. Let n(y) = f*l(y) + 5*t(y). Factor n(v).
3*v**2*(v - 1)
Let v = -899 + 903. Find c such that 0 + 8/3*c**2 + 8/3*c**v + 34/3*c**3 + 0*c = 0.
-4, -1/4, 0
Let a(k) be the third derivative of -k**6/120 - 3*k**5/10 + 85*k**4/24 - 11*k**3 + 2*k**2 - 68. Find q such that a(q) = 0.
-22, 1, 3
Suppose -3*d - 14 = -4*z, 0 - 4 = -5*z - 3*d. Factor -25*n + z*n**2 + 8 - 21*n + 36*n.
2*(n - 4)*(n - 1)
Let w(l) = -l**3 - 12*l**2 + 11*l + 3. Let n be w(-13). Let u = 33 - n. Factor -u*o - 2*o**4 - 2*o**4 + 12*o**2 + 6 + 4*o**3 - 14.
-4*(o - 2)*(o - 1)*(o + 1)**2
Let z = -68 - -75. Let h(g) = -2*g + 17. Let l be h(z). Factor 0 + 0*y + 2/7*y**2 - 4/7*y**l + 2/7*y**4.
2*y**2*(y - 1)**2/7
Let t(r) be the first derivative of 5*r**4/4 + 20*r**3/3 - 15*r**2/2 - 90*r + 64. Factor t(k).
5*(k - 2)*(k + 3)**2
Suppose 78723/2*f**2 + 483*f**3 + 38400 + 3/2*f**4 + 77280*f = 0. What is f?
-160, -1
Let h be 3/(-18)*((-56)/8 - -7)/2. Factor h - 4/7*y - 4/7*y**4 + 4/7*y**2 + 4/7*y**3.
-4*y*(y - 1)**2*(y + 1)/7
Factor -26/5 + 1/5*d**2 - 5*d.
(d - 26)*(d + 1)/5
Let j(h) be the second derivative of 5*h**4/12 + 40*h**3/3 + 195*h**2/2 - 693*h. Factor j(p).
5*(p + 3)*(p + 13)
Factor -39*v + 23*v + 0*v**4 - v**4 + 34*v + 4*v**4 - 21*v**2.
3*v*(v - 2)*(v - 1)*(v + 3)
Let i(s) be the third derivative of s**5/60 + s**4/4 - 7*s**3/6 - 26*s**2. What is m in i(m) = 0?
-7, 1
Let i = 28 + -53. Let b = i + 43. Find d, given that b - 18 + 2*d**3 + 2*d**2 = 0.
-1, 0
Let h(b) = -b - 10*b + 18*b - 3*b + 54. Let z be h(-13). Factor 0 - 5/6*q**z - 1/3*q.
-q*(5*q + 2)/6
Let 19 - 3*m**4 + 12*m - 23*m**3 + 34 + 15*m**2 + 3*m**5 - 65 + 8*m**3 = 0. What is m?
-2, -1, 1, 2
Let d(j) = -5*j**3 - 2*j**2 + 28*j - 12. Let p(w) = -90*w + 5*w + 5*w**2 + 52 - 17 + 15*w**3. Let g(z) = 10*d(z) + 3*p(z). What is n in g(n) = 0?
-3, 1
Let y(l) be the second derivative of -l**4/20 - 43*l**3/5 - 5547*l**2/10 - 3*l + 4. Find x such that y(x) = 0.
-43
Factor v + 1/5*v**3 + 4/5*v**2 + 2/5.
(v + 1)**2*(v + 2)/5
Suppose -2*z = 12 + 6. Let q be z/(-6) + (-20)/16. Determine l so that 0 + 0*l + q*l**3 - 1/4*l**2 = 0.
0, 1
Let n(s) be the first derivative of -5/8*s**4 + 13/4*s**2 - 3*s - 1/3*s**3 - 2. Factor n(k).
-(k - 1)*(k + 2)*(5*k - 3)/2
Let s(g) be the first derivative of g**5/70 - 5*g**4/42 + 8*g**3/21 - 4*g**2/7 - 7*g - 12. Let v(p) be the first derivative of s(p). Find n such that v(n) = 0.
1, 2
Let o(y) be the second derivative of -21*y**5/20 - 23*y**4/6 - 4*y**3 - 16*y - 1. Factor o(x).
-x*(3*x + 4)*(7*x + 6)
Let q(z) be the third derivative of -3*z**7/70 + 239*z**6/40 + 853*z**5/30 + 109*z**4/2 + 164*z**3/3 + 3*z**2 - 84*z. Solve q(a) = 0.
-1, -2/3, 82
Let d(r) = -4*r**3 + 2*r + 2. Let y = 21 - -17. Suppose 5*p = 8 - y. Let i(a) = a**4 - 4*a**3 + a**2 + 3*a + 3. Let x(t) = p*d(t) + 4*i(t). Factor x(m).
4*m**2*(m + 1)**2
What is s in 0 - 15/2*s + 3/2*s**3 + 6*s**2 = 0?
-5, 0, 1
Let d(w) be the third derivative of w**8/896 - w**7/560 - 3*w**6/160 + w**5/40 + w**4/8 - 168*w**2. Find r, given that d(r) = 0.
-2, -1, 0, 2
Let x(t) = t**2 - 27*t - 24. Let h(s) = 6*s**2 - 135*s - 120. Let g(i) = -4*h(i) + 21*x(i). Determine k so that g(k) = 0.
-8, -1
Let g(h) = h - 8. Let u be g(10). Let z(a) be the first derivative of 1 - a**4 - 1 + 6*a**u - 4*a**2 - 7. What is k in z(k) = 0?
-1, 0, 1
Let a(r) be the second derivative of r**4/12 - 10*r**3/3 - 21*r**2/2 + 5*r. Find k such that a(k) = 0.
-1, 21
Let l(z) be the first derivative of -4*z**3 + z**2/6 - 223. Suppose l(y) = 0. What is y?
0, 1/36
Suppose -116 = -8*l - 50*l. Suppose -4/13*s**l - 6/13*s**3 + 0*s + 0 - 2/13*s**4 = 0. Calculate s.
-2, -1, 0
Let x(m) = 4*m**4 + 9*m**3 - 6*m**2 + 9*m + 4. Let s(n) = 5*n**4 + 10*n**3 - 6*n**2 + 10*n + 5. Let z(g) = -5*s(g) + 6*x(g). Factor z(a).
-(a - 1)**4
Let i = -12 - -13. Let u be ((-294)/(-56))/(-21)*(-26)/3. Factor 7/6*n**3 - i + u*n + 13/3*n**2.
(n + 1)*(n + 3)*(7*n - 2)/6
Let o = 14541/4235 + -3/605. Determine f, given that -o*f**3 - 8/7*f**2 + 0 - 18/7*f**4 + 0*f = 0.
-2/3, 0
Let a be 6/(-21) + (-4)/(-14). Let j be 0 + (-18)/(-80) + 27/72. Factor 3/5*q**2 + j*q**3 + 0 + a*q.
3*q**2*(q + 1)/5
Let w(m) = -2870*m**2 + 4*m + 3. Let i be w(-1). Let o = i + 20155/7. Factor -18/7*h**4 - 66/7*h**2 - o*h**3 - 30/7*h - 4/7.
-2*(h + 1)**3*(9*h + 2)/7
Let b(k) = 35*k**3 - 35*k**2 - 25*k + 40. Let a(y) = -y**4 - 34*y**3 + 36*y**2 + 26*y - 39. Let n(u) = 5*a(u) + 4*b(u). Determine g, given that n(g) = 0.
-7, -1, 1
Let u(l) be the first derivative of -4*l**3 - 6*l + 7 - 27/2*l**2. Factor u(n).
-3*(n + 2)*(4*n + 1)
Suppose 0 = 2*m + 4, -2*k = 4*m - 562 + 550. Let t(b) be the first derivative of k + 2/11*b**2 - 2/11*b - 2/33*b**3. Suppose t(i) = 0. Calculate i.
1
Let l(z) = 5*z - 21*z + 12*z + 23 + 7*z. Let v be l(-7). Factor -2/11*b**4 + 0 + 6/11*b**3 - 6/11*b**v + 2/11*b.
-2*b*(b - 1)**3/11
Let r(y) be the first derivative of 15*y**6/2 - 47*y**5 + 455*y**4/4 - 135*y**3 + 80*y**2 - 20*y + 87. What is k in r(k) = 0?
2/9, 1, 2
Let l(s) = s**3 + 10*s**2 + 23*s + 13. Let a be l(-7). Let c be a + 5 - (3/6 + 3). Factor c*d**3 + 2*d**2 + 0 + 3/2*d.
d*(d + 1)*(d + 3)/2
Let x = -158 + 154. Let j be 4*6*(0 + x/(-32)). Factor -16/13*l**2 + 0 - 8/13*l - 2/13*l**4 - 10/13*l**j.
-2*l*(l + 1)*(l + 2)**2/13
Let m(j) be the second derivative of j**7/84 + 9*j**6/20 + 33*j. Factor m(w).
w**4*(w + 27)/2
Let l(b) be the third derivative of 0 + 0*b**4 + 0*b - 1/60*b**6 + 1/420*b**7 + 0*b**3 - 1/30*b**5 - 7*b**2 + 1/672*b**8. Factor l(a).
a**2*(a - 2)*(a + 1)*(a + 2)/2
Suppose 7*t - 14 = 4*t + m, -34 = -3*t + 5*m. Let -2*j**3 + t*j**3 - 12*j**4 + 13*j**4 = 0. Calculate j.
-1, 0
Let d = 1275 - 1275. Let z(j) be the second derivative of -3*j - 1/6*j**4 - j**3 - 2*j**2 + d. Determine n, given that z(n) = 0.
-2, -1
Let x(p) be the third derivative of p**6/960 - 161*p**5/480 + 2133*p**4/64 + 2187*p**3/16 - 124*p**2. Factor x(w).
(w - 81)**2*(w + 1)/8
Let l(f) be the first derivative of -1/26*f**4 + 4/13*f**2 + 0*f**3 + 0*f + 10. Factor l(p).
-2*p*(p - 2)*(p + 2)/13
Factor -9 - 15 + 14*r**3 - 13*r**3 - 47*r - 22*r**2.
(r - 24)*(r + 1)**2
Let m = -129555/4 - -32389. Suppose 0*a + 0 - m*a**3 + 1/2*a**2 - 1/2*a**4 + 1/4*a**5 = 0. What is a?
-1, 0, 1, 2
Let g(p) = -p**3 - 10*p**2 + 2*p + 24. Let v be g(-10). Determine u so that -v*u + 5*u + u + 4*u**2 + 2*u = 0.
-1, 0
Let a(s) be the first derivative of -1/3*s**2 - 1/5*s**5 + 1/3*s**4 - 3 + 1/9*s**3 + 0*s. Factor a(i).
-i*(i - 1)**2*(3*i + 2)/3
Let u(j) = 6*j**2 - 83*j - 46. Let y(x) = -9*x**2 + 84*x + 44. Let l(n) = 4*u(n) + 3*y(n). Suppose l(t) = 0. What is t?
-26, -2/3
Let k(r) be the second derivative of -r**4/3 + r**3/6 + r**2 + 13*r. Let j(m) = -m**2 + m + 1. Let v(w) = -12*j(w) + 4*k(w). Factor v(c).
-4*(c + 1)**2
Let q(i) be the first derivative of 5*i + 5*i**2 + 6 + 5/3*i**3. Determine b, given that q(b) = 0.
-1
Let m(n) = 30*n**2 - 60*n. Let t(z) = 1. Let u(k) = 5*k**2 - 10*k - 4. Let a(s) = 4*t(s) + u(s). Let h(i) = 25*a(i) - 4*m(i). What is b in h(b) = 0?
0, 2
Let n(l) be the first derivative of l**5/60 - l**4/12 - l**3/2 - 11*l**2 - 5. Let y(r) be the second derivative of n(r). Determine h, given that y(h) = 0.
-1, 3
Suppose 2*w - 1 = 5*q, 5*w + q + 2*q - 18 = 0. Suppose 2/5 + 4/5*s - 4/5*s**w - 2/5*s**4 + 0*s**2 =