et w(r) = -r - 4. Let k be w(-4). Let m = 3 - k. Factor 46*o**m + 4*o - 30*o**3 + 4*o**5 - 24*o**3.
4*o*(o - 1)**2*(o + 1)**2
Let x(b) be the second derivative of b**10/60480 - b**9/10080 + b**8/4480 - b**7/5040 - b**4/3 - b. Let f(m) be the third derivative of x(m). Factor f(q).
q**2*(q - 1)**3/2
Let z be -4 - (1 + -5 - 3). Let g be (9/(-12))/(6/(-16)). Find k, given that -5*k - k**g - z*k - 3*k**3 + 5*k + 7*k**2 = 0.
0, 1
Let z be 124/6 + -3*(-6)/(-27). Suppose -3*j + z = 7*q - 2*q, 2*j = 5*q - 20. Factor 3/4*c**3 + 1/4*c**2 - 3/4*c + 1/4*c**q - 1/2.
(c - 1)*(c + 1)**2*(c + 2)/4
Let q = 87294/11 + -7932. Let q*d + 0 + 6/11*d**2 = 0. What is d?
-7, 0
Solve -114/17*y**2 + 134/17*y**4 + 44/17*y + 0 - 12/17*y**3 - 12/17*y**5 = 0.
-1, 0, 1/2, 2/3, 11
Let v(h) be the first derivative of 1/20*h**5 + 2*h + 1/12*h**4 + 0*h**3 + 4 + 0*h**2. Let i(p) be the first derivative of v(p). Factor i(k).
k**2*(k + 1)
Suppose 0 = -5*i + 1 + 19. Suppose 9*q - 4*q - 15 = 0. Let c**q - 20*c**5 - i*c**3 + 23*c**5 = 0. What is c?
-1, 0, 1
Let d(j) be the second derivative of 2/45*j**3 + 1/90*j**4 - 7*j + 1/15*j**2 + 0. Factor d(n).
2*(n + 1)**2/15
Let l(o) = o + 11. Let a be l(-5). Let f(c) = c**3 - 5*c**2 - 6*c. Let p be f(6). Factor -2*g**5 + 5*g**5 + a*g + 6*g**2 - 6 + 3*g + p*g - 12*g**3.
3*(g - 1)**3*(g + 1)*(g + 2)
Let o(c) be the first derivative of 2*c**3/3 - 8*c**2 + 14*c - 34. Determine p, given that o(p) = 0.
1, 7
Suppose 0 = -5*f + 25, -3*d + 0*d - 3*f = -18. Factor -36*v - 3 - d - 23 - 12*v**2.
-3*(2*v + 3)**2
Let r(m) be the second derivative of -3*m**5/100 - m**4/5 - m**3/2 - 3*m**2/5 + 35*m + 1. Find u, given that r(u) = 0.
-2, -1
Suppose -2*t = -5*t + 3*y + 12, 0 = t - 5*y + 12. Find p such that -2*p**3 + p**5 + 5*p**2 + p + 0*p**2 + 7 - 3*p**2 - t - p**4 = 0.
-1, 1
Let r(h) be the second derivative of 5*h**7/42 + 2*h**6/3 + 3*h**5/4 - 5*h**4/3 - 10*h**3/3 + h + 12. Solve r(p) = 0 for p.
-2, -1, 0, 1
Suppose 0*c = 5*c - 15. Let -4*a**4 + 12*a**2 + 2*a**4 - 9*a**3 + 6*a**4 + 25*a**c = 0. Calculate a.
-3, -1, 0
Let r be 106/18 + 32/(-36) + 1. Let b be (-18)/(-28) + 3/r. Solve -8/7 + b*a - 2/7*a**2 = 0.
2
Let m(w) = 3 - w**2 - 3*w + 1 + 7*w. Let f be m(4). Let 3*q**2 + q**2 - 11*q + 2*q**5 + 9*q - 4*q**f = 0. What is q?
-1, 0, 1
Let o(i) be the first derivative of 15*i**4/8 - 43*i**3/6 + 6*i**2 + 2*i - 114. Factor o(d).
(d - 2)*(d - 1)*(15*d + 2)/2
Let p(c) = -c**3 - c**2. Let v(i) = -4*i**4 + 496*i**3 - 24592*i**2 + 524288*i - 4194304. Let x(w) = -16*p(w) + v(w). Solve x(n) = 0 for n.
32
Let b(y) be the first derivative of -y**6/30 + y**4/20 + 820. Factor b(q).
-q**3*(q - 1)*(q + 1)/5
Let x = 136 - 122. Factor -20*f**3 - x*f**2 + 35*f + 39*f**2 - 16 + 6.
-5*(f - 2)*(f + 1)*(4*f - 1)
Let z(b) be the second derivative of 5*b**7/42 - b**6/3 + 5*b**4/6 - 5*b**3/6 - 17*b + 2. Suppose z(h) = 0. Calculate h.
-1, 0, 1
Let k(l) = l**3 - 3*l**2 - 6. Let h be k(4). Let q = 34 - h. Let 12*f + 4*f**3 - 6*f**3 + q*f**2 + 2*f**3 + 9*f**3 = 0. What is f?
-2, -2/3, 0
Factor -j**5 - 78*j**4 + 64 + 112*j + 8*j**3 + 64*j**2 + 148*j**4 - 74*j**4.
-(j - 4)*(j + 2)**4
Let x(m) be the third derivative of -m**8/84 + 4*m**7/35 - 4*m**6/15 - 2*m**5/15 + 3*m**4/2 - 8*m**3/3 - 27*m**2. Factor x(j).
-4*(j - 4)*(j - 1)**3*(j + 1)
Let v(n) be the second derivative of n**6/360 - n**5/15 - 20*n**3/3 + 32*n. Let y(m) be the second derivative of v(m). Solve y(p) = 0 for p.
0, 8
Let l be (-22680)/(-6237) - 3/((-33)/4). Let -1/2*i**l + 0*i**3 - 1/4*i**5 + 0 + 1/4*i + 1/2*i**2 = 0. What is i?
-1, 0, 1
Let z(f) be the second derivative of -3*f**5/20 - 5*f**4 + 23*f**3/2 + 63*f**2 - 14*f. Factor z(a).
-3*(a - 2)*(a + 1)*(a + 21)
Let a(q) be the second derivative of 0 + 10*q - 1/150*q**6 - 4/15*q**3 + 0*q**2 - 1/5*q**4 - 3/50*q**5. Let a(n) = 0. Calculate n.
-2, 0
Let v(d) be the first derivative of -d**5/20 + d**4/4 + 3*d**3/2 + 9*d**2/2 - 11. Let y(x) be the second derivative of v(x). Factor y(f).
-3*(f - 3)*(f + 1)
Let p(a) = 9*a**3 + 11*a**2 + 25*a + 13. Suppose 8*z + 5 = 9*z. Let s(g) = -5*g**3 - 5*g**2 - 13*g - 7. Let k(r) = z*s(r) + 3*p(r). Factor k(m).
2*(m + 1)**2*(m + 2)
Let f = 64 + -61. Let i(h) be the third derivative of 0*h - 1/315*h**7 + 2*h**2 + 0*h**f + 0*h**4 + 0*h**6 - 1/504*h**8 + 0*h**5 + 0. Factor i(w).
-2*w**4*(w + 1)/3
Let q(h) be the second derivative of -1/90*h**6 + 1/30*h**5 - h + 0*h**2 + 0*h**3 - 1/36*h**4 + 0. Solve q(s) = 0.
0, 1
Let u(b) be the third derivative of -2*b**2 + 1/33*b**4 + 0 + 0*b + 1/330*b**5 + 1/11*b**3. Factor u(n).
2*(n + 1)*(n + 3)/11
Let x(u) be the second derivative of -u**6/60 + u**5/5 + 5*u**4/12 - 2*u**3/3 - 9*u**2/4 + 85*u + 1. Factor x(f).
-(f - 9)*(f - 1)*(f + 1)**2/2
Let w(n) be the third derivative of 2*n**6/75 - 17*n**5/75 + 8*n**4/15 - 2*n**3/5 + 48*n**2. Factor w(t).
4*(t - 3)*(t - 1)*(4*t - 1)/5
Let z(o) be the third derivative of o**5/70 - 41*o**4/7 + 6724*o**3/7 - 75*o**2 + 2*o. Factor z(t).
6*(t - 82)**2/7
Let o(b) = 5*b**2 - 21*b + 9. Let p(y) = 5*y**2 - 20*y + 9. Let i(m) = -2*o(m) + 3*p(m). Let i(z) = 0. What is z?
3/5, 3
Let m(t) be the second derivative of -8/5*t**3 + 0 - 16/5*t**2 + 24*t - 1/50*t**5 - 3/10*t**4. Factor m(r).
-2*(r + 1)*(r + 4)**2/5
Let o(t) be the first derivative of -2*t**3/3 - 66*t**2 + 441. Factor o(z).
-2*z*(z + 66)
Suppose -2 = -2*o + 21*b - 19*b, -2*o + 12 = 3*b. Factor 72/7 - 2/7*h**o - 22/7*h**2 - 48/7*h.
-2*(h - 1)*(h + 6)**2/7
Let f(j) be the first derivative of -24 + 56/27*j**3 + 4/9*j**2 + 28/9*j**5 + 25/27*j**6 + 0*j + 23/6*j**4. Let f(h) = 0. What is h?
-1, -2/5, 0
Factor 2/9*m**4 + 2/3*m + 8/9 - 2/3*m**3 - 10/9*m**2.
2*(m - 4)*(m - 1)*(m + 1)**2/9
Let h(d) be the first derivative of d**6/3 + 2*d**5/5 - 3*d**4 - 28*d**3/3 - 11*d**2 - 6*d + 89. Factor h(u).
2*(u - 3)*(u + 1)**4
Suppose 8*g + 10 = 26. Factor -4*v**4 + 100*v**2 + 3*v**3 + 5*v**4 - g*v - v**5 - 101*v**2.
-v*(v - 2)*(v - 1)*(v + 1)**2
Let x(h) be the second derivative of h**7/504 - 5*h**6/144 + h**5/6 + 2*h**4/3 + 11*h. Let g(l) be the third derivative of x(l). Find j, given that g(j) = 0.
1, 4
Let b be (-14)/144 + (-4)/(-18). Let r(u) be the third derivative of -3*u**2 + 0 + 2/5*u**6 + 0*u**3 + b*u**4 + 2/5*u**5 + 0*u. Suppose r(y) = 0. What is y?
-1/4, 0
Let l(k) be the second derivative of -k**5/4 - 25*k**4/12 - 20*k**3/3 - 10*k**2 - 27*k - 2. Factor l(w).
-5*(w + 1)*(w + 2)**2
Factor 1/2*l + 0 + 1/2*l**3 + l**2.
l*(l + 1)**2/2
What is d in -2*d**2 - 8*d**3 - 4*d**5 - 282 + 282 - 10*d**4 = 0?
-1, -1/2, 0
Suppose 52 = -7*l + 94. Let m(t) be the second derivative of 0*t**5 + 0*t**2 + 1/75*t**l + 0 + 0*t**3 - 9*t - 1/30*t**4. Determine z, given that m(z) = 0.
-1, 0, 1
Factor -110*z + 86 + 18 + 56 - 5*z**2 - 45.
-5*(z - 1)*(z + 23)
Let w = 7 - 5. Suppose 4 = 2*o - w. Factor 4/11*f**2 - 2/11*f**5 + 0*f - 10/11*f**o + 8/11*f**4 + 0.
-2*f**2*(f - 2)*(f - 1)**2/11
Let m = 1210/13661 + 12/719. Factor -2/19*v + 0*v**2 + 0 + m*v**3.
2*v*(v - 1)*(v + 1)/19
Suppose -2/13*r**5 + 0*r + 6/13*r**3 + 0 - 4/13*r**2 + 0*r**4 = 0. Calculate r.
-2, 0, 1
Let u(o) be the second derivative of -5/12*o**6 + 12*o - 5/6*o**3 + 0 + o**5 + 0*o**2 - 5/24*o**4. Factor u(i).
-5*i*(i - 1)**2*(5*i + 2)/2
Let j(b) be the third derivative of -b**6/24 - 2*b**5/3 + 95*b**4/24 - 25*b**3/3 + 1026*b**2. Factor j(m).
-5*(m - 1)**2*(m + 10)
Let p(m) be the second derivative of m**5/160 - m**4/12 - m**3/48 + m**2/2 + 891*m. Suppose p(d) = 0. Calculate d.
-1, 1, 8
Let o(a) be the first derivative of 0*a**2 - 25/6*a**6 - 5*a**4 + 0*a - 13*a**5 + 28 + 20/3*a**3. Determine g so that o(g) = 0.
-2, -1, 0, 2/5
Let o(a) be the first derivative of -a**4/12 - 8*a**3/9 - 10*a**2/3 - 16*a/3 - 108. Solve o(r) = 0 for r.
-4, -2
Let j(x) be the first derivative of -5*x**6/6 + 12*x**5 - 265*x**4/4 + 550*x**3/3 - 270*x**2 + 200*x - 15. Factor j(r).
-5*(r - 5)*(r - 2)**3*(r - 1)
Let y(k) = -k**3 - 3*k**2 - 2*k + 2. Let c be y(-2). Factor -5*d**c + 21 + 40 + 37 + 28*d + 7*d**2.
2*(d + 7)**2
Let a be -72*(-41)/1312*(50/9 + 0). Factor -a - 10*g + 5/2*g**2.
5*(g - 5)*(g + 1)/2
Let k(r) be the second derivative of 0 + 1/36*r**3 - 8*r + 0*r**2 + 1/72*r**4. Determine n so that k(n) = 0.
-1, 0
Suppose -2*q - 3*d + 21 = 0, 0 = -3*q - 0*q - 2*d + 24. Factor -15*p**2 + q*p**4 - 14*p**3 - 2*p + 1