+ 8*z**2. What is r in b(r) = 0?
4
Let w(q) be the third derivative of 49*q**6/780 - 21*q**5/130 + 5*q**4/52 - q**3/39 + 75*q**2. Factor w(j).
2*(j - 1)*(7*j - 1)**2/13
Let k(a) be the second derivative of 0 + 2/135*a**6 + 17*a - 4/27*a**3 + 0*a**5 + 0*a**2 - 1/9*a**4. Factor k(v).
4*v*(v - 2)*(v + 1)**2/9
Let f(z) = 16*z**4 + 5*z**3 - 15*z**2 - 5*z - 1. Let y(o) = o**3 + 4 + 1 - o - 5. Let t(m) = 2*f(m) + 6*y(m). Suppose t(a) = 0. What is a?
-1, -1/4, 1
Let a(l) be the second derivative of 0 + 11*l - 1/20*l**6 - 5/4*l**3 + 3/2*l**2 + 3/8*l**4 + 3/40*l**5. Suppose a(d) = 0. Calculate d.
-2, 1
Let q(u) be the first derivative of 4*u**5/5 - 56*u**4 + 3904*u**3/3 - 10752*u**2 + 36864*u + 356. What is t in q(t) = 0?
4, 24
Let q(y) = -y + 6. Let f = -12 + 16. Let v be q(f). Factor 4*d**v - 4*d - d**2 + 2*d - d**2.
2*d*(d - 1)
Let p(v) be the second derivative of -49*v**5/10 + 7*v**4 + 9*v**3/4 + v**2/4 + v - 15. Let p(f) = 0. What is f?
-1/14, 1
Let x(n) = 2*n**2 - 9*n - 84. Let l(c) = -c**2 + 12*c + 80. Let r(z) = 3*l(z) + 2*x(z). Factor r(o).
(o + 6)*(o + 12)
Let c = -7 - -9. Suppose 2*w - c = -0*w. Determine m so that m**4 - 7*m - 2*m**2 + 7*m + w = 0.
-1, 1
Let y(t) be the second derivative of t**4/36 + 16*t**3/9 + 128*t**2/3 + 2*t - 46. Determine l so that y(l) = 0.
-16
Let a(x) be the first derivative of 0*x - 2*x**2 - 12 + 1/2*x**4 + 2/3*x**3. Suppose a(b) = 0. Calculate b.
-2, 0, 1
Determine v, given that 0 + 16/7*v - 2/7*v**2 = 0.
0, 8
Factor d**2 + 262 + 13*d - d + 5*d - 322.
(d - 3)*(d + 20)
Suppose n + 77 = 80. Suppose 1/6*q**n + 0 + 1/6*q**2 + 0*q = 0. Calculate q.
-1, 0
Let u be (2 - 10) + (-380)/(-45). Factor 0*s + u - 4/9*s**2.
-4*(s - 1)*(s + 1)/9
Let i be (3712/580)/(0 + 1). Factor -4/5*h**3 - i - 24/5*h**2 + 12*h.
-4*(h - 1)**2*(h + 8)/5
Let n(z) be the third derivative of -z**8/90720 + z**7/22680 + 3*z**5/20 - z**2. Let f(i) be the third derivative of n(i). Let f(u) = 0. What is u?
0, 1
Suppose -9*y = -8*y. Let o(q) be the second derivative of 2*q + y*q**2 + 0*q**3 + 1/6*q**4 + 1/10*q**5 + 0. Suppose o(n) = 0. Calculate n.
-1, 0
Let x(a) be the third derivative of 1/340*a**6 + 0 - 1/51*a**3 - 4/1785*a**7 - 1/68*a**4 + 0*a + 1/102*a**5 + 6*a**2. Find h, given that x(h) = 0.
-1, -1/4, 1
Let n be ((-30)/24)/((-2)/(-8)). Let u = n - -10. Solve 5*a**2 + 11*a**2 + a - 5*a - 11*a**4 - u*a**3 - 14*a**4 = 0 for a.
-1, 0, 2/5
Suppose -5*z - 5 = -15. Let a be ((-40)/(-12) - 3)*18. Factor -a*k**4 + z*k**2 + k**4 + 2*k**4 + 2*k - 2*k**3 + k**4.
-2*k*(k - 1)*(k + 1)**2
Suppose -37*s = 244 - 318. Factor 0*o - 4/9 + 4/9*o**s.
4*(o - 1)*(o + 1)/9
Let k(o) = -2*o**5 + o**4 + 8*o**3 - 8*o**2 + 3*o. Let u(q) = -q**5 + q**3 - q**2 - q. Let y(f) = k(f) + u(f). Determine d, given that y(d) = 0.
-2, 0, 1/3, 1
Let m be (4/(-3))/(2/(-6)). Let p be 45/(-20) - (-1)/m - -4. Let -2/3 + 0*y + 2/3*y**p = 0. Calculate y.
-1, 1
Let -4*n**3 + 9412*n**2 - 18794*n**2 - 32*n - 64 + 9410*n**2 = 0. What is n?
-1, 4
Let v(d) be the first derivative of -2*d**3/39 - 434*d**2/13 - 94178*d/13 - 627. Let v(j) = 0. What is j?
-217
Let i(p) be the second derivative of 3/8*p**4 + 1/20*p**5 + 0*p**2 + 0 - 1/6*p**3 - 4*p - 3/20*p**6. Factor i(k).
-k*(k - 1)*(k + 1)*(9*k - 2)/2
Let j(o) be the second derivative of o**4/6 + 10*o**3 - 114*o. Find r such that j(r) = 0.
-30, 0
Let o(b) = 129*b + 261. Let k be o(-2). Let g(f) be the second derivative of 0*f**6 + 1/6*f**4 - k*f + 3/20*f**5 + 0*f**3 + 0 + 0*f**2 - 1/42*f**7. Factor g(t).
-t**2*(t - 2)*(t + 1)**2
Let y be (-88)/66 - 44/(-24). Suppose -1/4*z + y + 1/4*z**3 - 1/2*z**2 = 0. Calculate z.
-1, 1, 2
Suppose 1/2 + 19/4*c + 17/4*c**2 = 0. What is c?
-1, -2/17
Let -9*b**2 + b**2 + 79*b - 67*b - 4 = 0. What is b?
1/2, 1
Let m be -4*1/(-2 + (-8)/(-5)). Let a be -1*1/(-5) + (-2)/m. Determine w, given that 0 - 2/15*w**2 + a*w - 2/15*w**5 + 2/15*w**4 + 2/15*w**3 = 0.
-1, 0, 1
Let g be (2/2)/((-5)/5). Let k(q) = 3*q**2 - 1. Let p be k(g). What is s in -2*s**p - 4*s - s + 3*s = 0?
-1, 0
Let g = -3995/924 - 3/308. Let i = -4 - g. Factor 1/3*s**2 - 1/3*s**3 - 1/3*s**4 + 0 + i*s.
-s*(s - 1)*(s + 1)**2/3
Let g be (-8)/(-10)*(-40)/(-7 + 5). Factor -88*h**2 + 117 - 36*h**3 + g*h**4 - 20*h**4 + 11.
-4*(h - 1)*(h + 2)*(h + 4)**2
Let t(m) be the second derivative of -m + 0*m**2 + m**3 - 1/6*m**4 + 0. Suppose t(y) = 0. What is y?
0, 3
Let r(d) be the third derivative of -d**6/1320 - 3*d**5/110 - 4*d**4/11 - 64*d**3/33 - 91*d**2. Factor r(h).
-(h + 2)*(h + 8)**2/11
Factor -13/5*g**3 - 4/5*g + 6/5*g**4 + 0 - 1/5*g**5 + 12/5*g**2.
-g*(g - 2)**2*(g - 1)**2/5
Let r(j) = -j + 6. Let t be r(0). Suppose -23 = -2*g - 3*y, -3*g + 5*y - 5 - 8 = 0. Solve g*b**3 + 2*b + 12*b**4 - 9*b**2 + t*b**3 - 9*b**3 = 0.
-1, 0, 1/4, 2/3
Let t(i) = -i**2 + 3*i + 10. Let x be t(5). Suppose -5*h - 2*n + 2 = -x*n, -3*h = 3*n + 6. Find l, given that -3/4 - 9/4*l**h - 3*l = 0.
-1, -1/3
Let s(f) be the first derivative of 9/4*f + 1/12*f**3 + 3/4*f**2 + 5. Factor s(o).
(o + 3)**2/4
Suppose 0 = 5*z + 25, 19 = -2*t - 5*z - 0. Factor 0 - t + 9*g**4 - 4*g + 0 + 12*g**3 - 6*g**2 - 8*g.
3*(g - 1)*(g + 1)**2*(3*g + 1)
Let b(f) be the first derivative of f**4 - 4*f**3 - 8*f**2 - 200. Suppose b(y) = 0. Calculate y.
-1, 0, 4
Let q be (-4)/4 + 3 + 0 + 1. Suppose 4 = -q*v + 16. Find l such that 0*l**2 + 0 + 1/5*l**v + 0*l - 1/5*l**3 = 0.
0, 1
Let v(w) be the third derivative of -w**6/108 - 2*w**5/45 + 29*w**4/108 - 4*w**3/9 + 119*w**2. Determine r so that v(r) = 0.
-4, 3/5, 1
Let y(d) be the second derivative of d**4/36 - 37*d**3/18 - d - 18. What is s in y(s) = 0?
0, 37
Suppose 2*p + 5*h - 18 = 0, -4*h + 4 + 4 = 0. Factor -5/3*d**p - 25/3*d**2 + 0 + 20/3*d**3 + 10/3*d.
-5*d*(d - 2)*(d - 1)**2/3
Suppose 5*p + 2 = -4*m, -p = 2*m - 9 + 13. Let c(l) be the first derivative of l**4 - 10*l**p + 12*l + 2 + 4/3*l**3. Factor c(v).
4*(v - 1)**2*(v + 3)
Let y(o) = 13*o + 715. Let d be y(-55). Let a(l) be the second derivative of -7*l + 0*l**2 - 1/3*l**4 + 0*l**3 + d. Factor a(p).
-4*p**2
Let b(i) be the third derivative of 0*i + 1/270*i**5 + 0*i**3 + 0 + 9*i**2 + 1/108*i**4. Factor b(t).
2*t*(t + 1)/9
Let u = -7 + 8. Let p = -49 + 51. Factor -u + 21 - 8*f - 10*f - 5*f**p + 3*f.
-5*(f - 1)*(f + 4)
Factor -22*x**3 - 5*x**5 - 49*x**4 - 6*x**4 - 365*x**2 - 64*x**3 - 4*x**3 - 80 - 125*x**3 - 280*x.
-5*(x + 1)**3*(x + 4)**2
Let z be (2/(-4))/(-4 - 90/(-24)). Let y(w) be the first derivative of 0*w - 5/4*w**4 + 0*w**z - 5*w**3 - 2. Find l, given that y(l) = 0.
-3, 0
Let u(q) be the third derivative of -q**8/672 + q**7/10 - 97*q**6/48 - 34*q**5/15 + 432*q**4 + 5120*q**3/3 + 506*q**2. Factor u(p).
-(p - 16)**3*(p + 1)*(p + 5)/2
Let w(d) = -7*d**2 + 442*d - 3. Let j(p) = 22*p**2 - 1328*p + 10. Let a(s) = -3*j(s) - 10*w(s). Determine o, given that a(o) = 0.
0, 109
Suppose -10*m = 4*g - 12*m + 2, 2 = -3*g + 2*m. Let r be 3/(-5) + (-36)/(-10). What is v in -v**4 + 0*v**2 - 5/2*v**5 + 0*v**r + 0 + g*v = 0?
-2/5, 0
Let j(y) be the third derivative of 0*y**3 + 0*y + 0 + 1/270*y**5 - 18*y**2 + 1/27*y**4. Determine t, given that j(t) = 0.
-4, 0
Let h be (-8 + (-16)/24*-11)/(-2). Find a, given that -2/3 + 1/3*a**2 - h*a = 0.
-1, 2
Let j be ((-9)/84*-1)/((-3)/(-24)). Let -3/7*g + 3/7*g**2 - j = 0. What is g?
-1, 2
Solve -142*i**5 + 74*i**5 - 20*i**4 + i**2 + 19*i**2 + 5*i**3 + 63*i**5 = 0 for i.
-4, -1, 0, 1
Let f(r) be the second derivative of -3/80*r**5 + 5/8*r**3 - 9/4*r**2 + 7/48*r**4 - 1/120*r**6 + 0 - 9*r. Factor f(g).
-(g - 2)*(g - 1)*(g + 3)**2/4
Let a(q) be the second derivative of q**4/51 - 7*q**3/51 + 3*q**2/17 + 62*q - 2. Factor a(m).
2*(m - 3)*(2*m - 1)/17
Suppose 3*y = -l - 2, -2*l - 4 = -4*y - 0. Let a(h) = h**3 + h**2 - 1. Let o(g) = 6*g**2 - 2*g - 6. Let t(w) = l*a(w) - o(w). Factor t(c).
-2*(c - 1)*(c + 1)*(c + 4)
Let m(a) = 6 - 2 + 2*a - 5*a**2 - 2 - 3. Let q(l) = 6*l**2 - 3*l + 2. Let y(z) = 5*m(z) + 4*q(z). Factor y(o).
-(o - 1)*(o + 3)
Let l(w) be the second derivative of w**7/294 - w**6/105 - w**5/20 + 2*w**4/21 + 2*w**3/7 + 105*w. Find x such that l(x) = 0.
-2, -1, 0, 2, 3
Let g(d) be the second derivative of -d**4/60 + 2*d**3/5 - 18*d**2/5 - 23*d. Factor g(w).
-(w - 6)**2/5
Let f(q) = q**2 + 1. Let t be (-966)/27 - 8/36. Let u(k) = 16*k**2 - 2*k + 18. Let s(d) = t*f(d) + 2*u(d). Find p, give