*w**3. What is n in a(n) = 0?
-1, 2
Let f = -58 - -62. Let g(n) be the first derivative of -1/10*n**6 + 3/20*n**f - 2 + 1/5*n**3 - 3/25*n**5 + 0*n**2 + 0*n. Find x such that g(x) = 0.
-1, 0, 1
Let u(l) be the third derivative of 0 - 1/25*l**5 - 2/15*l**4 + 8/15*l**3 + 2/525*l**7 + 1/75*l**6 - 6*l**2 + 0*l. Let u(n) = 0. Calculate n.
-2, 1
Let b(v) be the first derivative of -v**5/80 + v**3/8 - v**2/4 + 4*v + 2. Let y(f) be the first derivative of b(f). Determine x, given that y(x) = 0.
-2, 1
Factor 3*i**2 + 32*i - 14*i - 12*i.
3*i*(i + 2)
Determine p, given that -5*p**2 + 13*p**2 - 24*p - 5*p**2 + 48 = 0.
4
Let a(i) be the first derivative of -i**7/2100 + i**5/100 - i**4/30 + 2*i**3/3 + 1. Let s(q) be the third derivative of a(q). Factor s(k).
-2*(k - 1)**2*(k + 2)/5
Let x(o) = o**2 - 8*o + 2. Suppose -3*z + 3*r + 23 = z, 0 = -2*z + 4*r + 4. Let i be x(z). Let -t**2 + 0*t + 3*t**2 + i*t = 0. What is t?
-1, 0
Let y(o) = o**3 - o**2 + o + 11. Let r be y(0). Suppose -r*u - 10 = -16*u. Factor 0 - 1/3*g**u + 2/3*g.
-g*(g - 2)/3
Let i(x) be the second derivative of x**4/16 - 7*x**3/8 + 9*x**2/4 + 47*x. Factor i(v).
3*(v - 6)*(v - 1)/4
Let z = 125 + -123. Let i(r) be the second derivative of 0*r**z - 1/60*r**6 + 0*r**3 + 1/20*r**5 + 0 + 0*r**4 - 2*r. What is u in i(u) = 0?
0, 2
Suppose 0*n = n + 5*o + 5, 2*n + 2*o - 6 = 0. Factor 0*k**4 - 15*k**5 + k**4 + 13*k**n.
-k**4*(2*k - 1)
Let v(n) be the second derivative of n**6/70 - n**4/28 - 11*n. Factor v(h).
3*h**2*(h - 1)*(h + 1)/7
Let j = -2 - -4. Let v(b) = 3*b**2 + 6*b + 2. Let n(l) = -6*l**2 - 12*l - 5. Let y(x) = j*n(x) + 5*v(x). Factor y(f).
3*f*(f + 2)
Determine d so that 40 - 2*d**2 + 6*d**2 + 2*d**3 - 40 - 6*d = 0.
-3, 0, 1
Let x(a) be the second derivative of 0*a**2 - 3/25*a**5 - 1/30*a**4 + a + 0*a**3 - 3/25*a**6 + 0 - 4/105*a**7. Suppose x(f) = 0. What is f?
-1, -1/4, 0
Let d(i) = i**4 - 2*i**3 - 2*i**2 - 17*i - 8. Let z(n) = n**4 - n**3 - 2*n**2 - 16*n - 8. Let o(l) = 4*d(l) - 5*z(l). Determine w so that o(w) = 0.
-2, -1, 2
Suppose 24/5*o - 18/5*o**3 + 6/5*o**5 - 24/5*o**2 + 0 + 12/5*o**4 = 0. Calculate o.
-2, 0, 1
Suppose 0 = 10*q - 140 + 110. Factor -q*m**2 - 33/4*m + 9/4.
-3*(m + 3)*(4*m - 1)/4
Let t be -2 - (-3)/(6/10). Let y(a) = -2*a - 13. Let k be y(-8). Factor -3*v + 2*v**2 + 3*v**3 + 0*v**k - t + v**2.
3*(v - 1)*(v + 1)**2
Let d(m) be the second derivative of -m**8/448 - m**7/105 - m**6/240 + m**5/20 - 5*m**4/12 - 4*m. Let l(x) be the third derivative of d(x). Factor l(o).
-3*(o + 1)**2*(5*o - 2)
Let i(p) = -p**2 + 7*p + 3. Let a be -1 - -1 - (-5 + -2). Let d be i(a). Solve 3*x + 4 + d*x - 8*x**2 - 2 = 0 for x.
-1/4, 1
Let b be (-326)/(-22) + 8/44. Suppose -2*a - 3*a + b = 0. Let h(d) = -2*d**2 + 6*d - 1. Let o(r) = -2*r**2 + 6*r - 2. Let g(y) = a*o(y) - 2*h(y). Factor g(l).
-2*(l - 2)*(l - 1)
Let a be ((-30)/(-70) - (-138)/21)/5. Factor 4/5*u**4 - a*u**2 + u**3 - 2/5*u + 0.
u*(u - 1)*(u + 2)*(4*u + 1)/5
Suppose 0*i**2 - 3*i**3 + 24 + 9*i**2 + 2*i**2 + 7*i**2 - 36*i = 0. Calculate i.
2
Let w(n) be the second derivative of 1/45*n**5 - 2/27*n**3 + 0 + 9*n + 0*n**4 + 1/9*n**2 - 1/135*n**6. Factor w(f).
-2*(f - 1)**3*(f + 1)/9
Factor z**4 + 0 + 1/5*z**2 + 2/5*z - 8/5*z**3.
z*(z - 1)**2*(5*z + 2)/5
Suppose -4*l + 9*l - 20 = 0. Suppose -23*a**2 + 3*a**l + 3*a**3 + 23*a**2 = 0. Calculate a.
-1, 0
Let v be (-4)/(-4) - -5 - 4. Suppose 0 = v*i + 2*i. Factor 2/7*r**5 - 2/7*r**3 + i*r**2 + 0*r**4 + 0 + 0*r.
2*r**3*(r - 1)*(r + 1)/7
Suppose -2/19*w + 0 + 2/19*w**2 = 0. What is w?
0, 1
Let u be 5 + -10*1/2. Factor -5*w**3 + 9/5*w**4 + u + 12/5*w**2 + 4/5*w.
w*(w - 2)*(w - 1)*(9*w + 2)/5
Suppose 0*l - 3*l = -15, 3 = -2*f - 3*l. Let t = -26/3 - f. Suppose -4/3*z**3 - 4/3*z + 2*z**2 + t*z**4 + 1/3 = 0. Calculate z.
1
Let i(q) be the first derivative of -q**3/3 - q**2/2 + 5. Factor i(d).
-d*(d + 1)
Let j(a) be the third derivative of -49*a**6/540 - 7*a**5/45 - a**4/9 + a**3/2 - 5*a**2. Let f(s) be the first derivative of j(s). Find y, given that f(y) = 0.
-2/7
Suppose -3*x - b + 17 = 0, 0 = -5*x + 5*b + 25 + 10. Let r = 1 + 0. Factor -4*t**3 + x*t**2 + 2 - 4*t + t**4 - r + 0.
(t - 1)**4
Suppose -3 = -2*w + 5*w. Let o(v) = -v**5 + v**4 + v**2 + v - 1. Let y(s) = -6*s**4 - 2*s**3 - 2*s**2 - 2*s + 2. Let k(j) = w*y(j) - 2*o(j). Solve k(u) = 0.
-1, 0
Let s(y) = -2*y**3 - 5*y**2 + 5*y - 5. Let x(k) = -k**3 - 2*k**2 + 2*k - 2. Let w(g) = 2*s(g) - 5*x(g). Suppose w(f) = 0. Calculate f.
0
Let j(p) = 30*p**3 - 65*p**2 - 150*p - 55. Let f(s) = -5*s**3 + 11*s**2 + 25*s + 9. Let v(t) = -35*f(t) - 6*j(t). Determine w so that v(w) = 0.
-1, 3
Suppose 14*w - 2 = 13*w. Let a(b) be the third derivative of -1/12*b**4 + 0*b**3 + 0 - 1/30*b**5 + 0*b + b**w. Let a(v) = 0. Calculate v.
-1, 0
Let d(i) be the first derivative of 4*i**5/35 - 4*i**3/7 - 4*i**2/7 - 30. Factor d(q).
4*q*(q - 2)*(q + 1)**2/7
Let z be 14/30*4/14. Let o(n) be the first derivative of 1/10*n**4 + 0*n + 0*n**2 - z*n**3 + 1. What is s in o(s) = 0?
0, 1
Let u = -240/11 - -1244/55. Determine x so that 2/5*x**3 - u*x**2 - 2/5*x + 4/5 = 0.
-1, 1, 2
Let g be ((-1)/2)/((-2)/4). Suppose u = -g + 3. Solve l - l**2 + 4*l**2 - u*l**2 = 0 for l.
-1, 0
Let k(b) be the first derivative of -b**4/12 + 10*b**3/9 - 3*b**2/2 - 42. Let k(g) = 0. Calculate g.
0, 1, 9
Suppose 11*b - 6*b = 0. Let r(q) be the second derivative of 1/3*q**3 + 0 + 3*q + b*q**2 - 1/12*q**4. Let r(x) = 0. Calculate x.
0, 2
Let n(a) be the second derivative of a**9/15120 + a**8/5376 + a**7/10080 + a**4/12 - 2*a. Let m(k) be the third derivative of n(k). Factor m(c).
c**2*(c + 1)*(4*c + 1)/4
Let b(s) be the first derivative of 5*s**6/6 - 15*s**4/4 + 10*s**3/3 - 10. Factor b(q).
5*q**2*(q - 1)**2*(q + 2)
Let m = -721 - -5065/7. Factor -2/7*i**2 + 12/7*i - m.
-2*(i - 3)**2/7
Let o(z) be the third derivative of -5*z**8/224 - z**7/42 + z**6/12 + z**5/12 - 5*z**4/48 + 9*z**2. Determine m, given that o(m) = 0.
-1, 0, 1/3, 1
Let n(f) be the second derivative of f**6/120 - f**4/6 + 2*f**2 + 17*f. Find p, given that n(p) = 0.
-2, 2
Let v(t) be the third derivative of -t**8/224 + t**7/35 - 3*t**6/40 + t**5/10 - t**4/16 - t**2. Factor v(l).
-3*l*(l - 1)**4/2
Suppose -8*t**5 - 55*t**3 + 22*t + 4 + 56*t**2 - 9*t**3 + 36*t**4 - 46*t = 0. Calculate t.
1/2, 1
Suppose 0 = -4*u - 5*k + 20, -3*k + 2*k = 0. Let p**3 - 4*p**2 - 5 + u*p + 1 + 2 = 0. What is p?
1, 2
Let r(o) be the second derivative of -2*o**2 + 0 - 1/5*o**5 - o**4 - 2*o**3 - 7*o. Factor r(z).
-4*(z + 1)**3
Let i(p) = 6*p**5 + 7*p**4 - 6*p**3 - 4*p**2 + 18*p - 11. Let w(o) = o**5 + o**4 + o - 1. Let u(a) = 2*i(a) - 10*w(a). Solve u(g) = 0 for g.
-3, -2, 1
Let n(k) = -23*k**3 + 6*k**2 + 29*k. Let c(w) = -4*w**3 + w**2 + 5*w. Let t be (-15)/(-1 - 2) - -1. Let d(r) = t*n(r) - 34*c(r). Factor d(s).
-2*s*(s - 2)*(s + 1)
What is x in -111/2*x**3 - 51/2*x**4 - 30*x - 6 - 117/2*x**2 - 9/2*x**5 = 0?
-2, -1, -2/3
Let z be 4/(-12) + 14/6. Let x(s) be the second derivative of -s - 1/18*s**4 + 0 + 1/9*s**3 + 0*s**z. Factor x(d).
-2*d*(d - 1)/3
Let n be 2 + 1 + (-123)/39. Let p = 21/52 + n. Let 1/4*q + 1/4*q**2 - 1/4 - p*q**3 = 0. Calculate q.
-1, 1
Let r be 2/(-9) - (-92)/9. Let j be r/24 - 3/(-12). Factor -2*i**2 - j*i**3 - 2/3 - 2*i.
-2*(i + 1)**3/3
Suppose k - 14 = o, -5*o + 7 = 4*k - 4. Let v be 1/k*12/2. Let 0 - 1/3*u**3 - 1/3*u - v*u**2 = 0. What is u?
-1, 0
Let c(w) be the third derivative of 0*w**5 - 1/300*w**6 + w**2 + 1/60*w**4 + 0*w**3 + 0 + 0*w. Solve c(o) = 0 for o.
-1, 0, 1
Suppose 16*k - 20 = 11*k. Factor -2/9 + 4/9*n**2 + 2/9*n**5 + 2/9*n - 4/9*n**3 - 2/9*n**k.
2*(n - 1)**3*(n + 1)**2/9
Suppose 5*z = -0*z. Let s(q) be the third derivative of 1/15*q**5 + z*q**3 - 1/60*q**6 + 0*q**4 + 0*q + 0 + 2*q**2. Factor s(i).
-2*i**2*(i - 2)
Let q(y) = y**3 + y**2 + 1. Let r(i) = 8*i**2 + 4. Let t(s) = 4*q(s) - r(s). Suppose t(h) = 0. Calculate h.
0, 1
Factor 80/7*t**2 + 0 - 12/7*t**3 - 50/7*t - 16/7*t**4 - 2/7*t**5.
-2*t*(t - 1)**2*(t + 5)**2/7
Suppose 2*j - 7 = -19. Let o be (-10)/j + 4/12. Let 0*u**2 + 10*u**o - 6 - 8*u + 6*u**3 - 2 = 0. Calculate u.
-2, -2/3, 1
Let m(g) be the second derivative of 5*g + 0 + 4*g**2 - 1/3*g**4 - 2/3*g**3. Determine b so that m(b) = 0.
-2, 1
Let i(m) be the third derivative of -m**5/15 + m**4/3 - 17*m**2. Find b such that i