 + 0*a**3 + 0*a**2 + 8*a + 0. Determine k so that v(k) = 0.
0
Let j(z) = z**3 - 3*z**2 + 2*z - 4. Let b be j(2). Let w be (b/24 + 0)*-4. Factor -7/3*p - 2*p**2 + 1/3*p**3 + 2/3*p**4 - w.
(p - 2)*(p + 1)**2*(2*p + 1)/3
Determine p, given that 3328*p**3 - 169*p**3 + 4*p**4 + 4020*p + 6102*p**2 + 77*p**4 + 888 = 0.
-37, -2/3
Let t(k) be the second derivative of -k**8/11760 + k**7/2940 + k**6/2520 - k**5/420 + 2*k**3 - 25*k. Let f(b) be the second derivative of t(b). Factor f(r).
-r*(r - 2)*(r - 1)*(r + 1)/7
Let m(u) = -13*u**4 + 76*u**3 - 123*u**2 + 28*u + 26. Let w(f) = -38*f**4 + 229*f**3 - 369*f**2 + 84*f + 77. Let z(j) = 17*m(j) - 6*w(j). Factor z(d).
(d - 10)*(d - 1)**2*(7*d + 2)
Suppose 0 = -5*g - 5, -4*g = z + z. Suppose -24 - t**z + 8*t + 4 + 4 = 0. What is t?
4
Factor -2/3*i**3 + 0 - 2/3*i**4 + 2/3*i**5 + 0*i + 2/3*i**2.
2*i**2*(i - 1)**2*(i + 1)/3
Factor -60/11*p**4 + 600/11*p**3 + 0*p + 2/11*p**5 - 2000/11*p**2 + 0.
2*p**2*(p - 10)**3/11
Let b(x) be the first derivative of 3*x**4/2 + 34*x**3/3 + 18*x**2 - 16*x - 162. Factor b(z).
2*(z + 2)*(z + 4)*(3*z - 1)
Let f(t) be the third derivative of 0 - 1/25*t**6 + 0*t**3 - 8/525*t**7 + 0*t**4 + 0*t - 3/100*t**5 - 5*t**2. Factor f(o).
-o**2*(4*o + 3)**2/5
Factor 5/2*x + 2*x**3 + 1/4*x**4 - 19/4*x**2 + 0.
x*(x - 1)**2*(x + 10)/4
Determine x, given that 3*x**2 - 5836 - x**3 + 5836 = 0.
0, 3
Solve -1 - 3*h**5 + 119*h + 10 - 265*h - 3*h**4 + 18*h**3 + 131*h - 6*h**2 = 0 for h.
-3, -1, 1
Let b = 5915 + -5913. Solve -2/5*s + s**b - 3/5 = 0 for s.
-3/5, 1
Let u(i) = 9*i**2 - 462*i + 10584. Let m(s) = 2*s**2 - s + 2. Let o(w) = -2*m(w) + u(w). Factor o(z).
5*(z - 46)**2
Let s(l) = l**2 + l + 1. Let c(h) = -2*h**2 - 17*h - 18. Let u(o) = -4*c(o) - 12*s(o). Factor u(y).
-4*(y - 15)*(y + 1)
Let g be (-5)/(70/(-32)) - 6/21. Let h(t) be the third derivative of 0*t**4 + 1/21*t**3 + 0*t - 5*t**g - 1/210*t**5 + 0. Factor h(i).
-2*(i - 1)*(i + 1)/7
Factor -7/6 + 1/6*n**2 + n.
(n - 1)*(n + 7)/6
Let h(d) = -4 + 7*d**2 + 898*d - 893*d + 7. Let a(w) = w**2 - 8*w + 1. Let c be a(7). Let y(t) = 8*t**2 + 6*t + 4. Let x(j) = c*h(j) + 5*y(j). Factor x(v).
-2*(v - 1)*(v + 1)
Let t(x) be the third derivative of -x**7/280 + x**6/160 + 3*x**5/80 - 5*x**4/32 + x**3/4 - 54*x**2. Factor t(b).
-3*(b - 1)**3*(b + 2)/4
Let x(p) = p**2 - p - 28. Let d be x(-5). Suppose 9 = d*z - 3*s, 2*s = -3*z + 6*z - 6. Factor 1/4*n**2 + 1/2*n + z.
n*(n + 2)/4
Let w(p) be the first derivative of -p**4/14 + 16*p**3/21 - 12*p**2/7 - 44. Determine o, given that w(o) = 0.
0, 2, 6
Let x = 15752/39405 + 2/7881. Factor 2/5 - 4/5*i**4 + x*i**2 + 1/5*i**5 + 4/5*i**3 - i.
(i - 2)*(i - 1)**3*(i + 1)/5
Suppose 2*a = -4, 5*u + 2*a - 23 = 3. Suppose 8*y = -18 - u. Let t(p) = p**2 - 1. Let o(b) = -b - 1. Let g(s) = y*o(s) + 3*t(s). Suppose g(d) = 0. Calculate d.
-1, 0
Let z(r) = -2*r**2 - r - 2. Let f(v) = -22*v**2 - 12*v - 16. Let b(m) = -f(m) + 10*z(m). Solve b(i) = 0 for i.
-2, 1
Let u(p) be the third derivative of 2/15*p**4 + 2/75*p**6 - 13*p**2 + 2/525*p**7 + 0 + 0*p + 2/15*p**3 + 2/25*p**5. Factor u(t).
4*(t + 1)**4/5
Suppose 0 = -2*r + 13 - 9. Factor -17*l**2 + 4 - 28*l**r - 16*l - 24*l**3 + l**2.
-4*(l + 1)**2*(6*l - 1)
Let m(z) = -2*z**2 - 21*z + 6. Let j be m(-10). Suppose -3*y - j + 4 = -3*u, 4*u = 5*y + 18. What is w in -4/5 + 8/5*w - 4/5*w**u = 0?
1
Let a(y) be the third derivative of y**7/315 - 17*y**6/180 + 31*y**5/30 - 175*y**4/36 + 98*y**3/9 + 22*y**2 - 3*y. Suppose a(d) = 0. What is d?
1, 2, 7
Let z(j) be the second derivative of -1/3*j**3 + 0 + 0*j**2 + 1/3*j**4 - 20*j. Suppose z(r) = 0. What is r?
0, 1/2
Find q, given that -36*q - 18*q**2 + 0*q - 28*q**3 + 54*q**3 - 29*q**3 - 24 = 0.
-2
Suppose 3*n = -n + 3*f + 9, -15 = 5*f. Factor -2/5*h**2 + 1/5*h + n + 1/5*h**3.
h*(h - 1)**2/5
Suppose -1/4*x**4 + 0 - 1/2*x**3 + 11/4*x**2 + 3*x = 0. Calculate x.
-4, -1, 0, 3
Let h = 756 + -754. Let x = -1 + 3. Factor 3*u + 14*u**x - h*u**3 - 19*u**3 - 8*u**2 + 12*u**4.
3*u*(u - 1)**2*(4*u + 1)
Factor -15*z**2 + 44 - 2*z**3 + 196 + 127 + 7*z**3 - 120*z + 33.
5*(z - 4)**2*(z + 5)
Let a(z) be the third derivative of -z**8/84 + 38*z**7/105 - 17*z**6/10 + 49*z**5/15 - 8*z**4/3 - z**2 + 564. Factor a(t).
-4*t*(t - 16)*(t - 1)**3
Suppose -7/2*p**4 - 5/2*p**5 + 3/2*p**3 + p + 7/2*p**2 + 0 = 0. What is p?
-1, -2/5, 0, 1
Factor -16*d + 40 - 54*d + 6*d**2 - 157*d**2 - 94*d**2.
-5*(7*d - 2)*(7*d + 4)
Let t(n) = -n**3 - 1. Suppose -3*v = 4*v + 7. Let f(u) = 6*u**3 - 20*u**2 + 28*u - 10. Let x(q) = v*f(q) - 2*t(q). Factor x(i).
-4*(i - 3)*(i - 1)**2
Let d(l) be the second derivative of -1/2*l**3 + 0 + 1/20*l**5 + 0*l**4 + 40*l - l**2. Factor d(x).
(x - 2)*(x + 1)**2
Suppose 0 = 8*o - 4*o - 3*c - 2, 4 = -o + 3*c. Find d such that -7*d**2 + d**3 + 8*d + 5*d**2 + 9*d**2 - o - 14 = 0.
-4, 1
Let p(h) = h**2 + 108*h + 711. Let w be p(-7). Find d such that 36/5*d**3 + 44/5*d**2 + 6/5 + 26/5*d + 14/5*d**w + 2/5*d**5 = 0.
-3, -1
Let y = 5/94 - -49/846. Factor 2/9*h**2 + 0 + 0*h - 1/9*h**4 + y*h**3.
-h**2*(h - 2)*(h + 1)/9
Let i be 284/12 - 2/(-6). Suppose -i = -2*r - 3*d, 0 = 2*r - 3*r + 5*d - 1. Factor -6*o - 3*o**3 + o**3 + o**2 - 18 + r*o**2.
-2*(o - 3)**2*(o + 1)
Let o(w) = 3*w**4 + w**3 - 8*w**2 - 4. Let a(r) = r**4 - r**3 - r - 1. Let q = -35 - -36. Let k(l) = q*o(l) - 4*a(l). Factor k(v).
-v*(v - 2)**2*(v - 1)
Let c(l) be the first derivative of l**5/5 - 2*l**3 + 4*l**2 + 4*l + 1. Let u(x) be the first derivative of c(x). Factor u(r).
4*(r - 1)**2*(r + 2)
Solve -15*x**3 + 482*x**4 - 15*x**5 - 15*x**3 - 401*x**4 = 0.
0, 2/5, 5
Let f(y) be the second derivative of -4*y + 1/63*y**7 + 0*y**2 + 0*y**3 + 0 - 1/5*y**6 + 1/2*y**5 + 25/18*y**4. Factor f(p).
2*p**2*(p - 5)**2*(p + 1)/3
Let j(r) be the second derivative of r**9/105840 - r**7/5880 - r**6/2520 + 25*r**4/12 - 24*r. Let b(h) be the third derivative of j(h). Let b(u) = 0. What is u?
-1, 0, 2
Factor 0 - 2/7*f**2 - 18/7*f.
-2*f*(f + 9)/7
Let a(t) = -t**2 - 3*t. Let i(u) = u**2 + 3*u - 1. Suppose 8 = -2*k + 4*k. Suppose -k*y = -0*y - 12. Let g(w) = y*a(w) + 2*i(w). Factor g(z).
-(z + 1)*(z + 2)
Solve 2/3*o**3 + 0*o + 0 - 20/3*o**2 = 0 for o.
0, 10
Suppose -16 = 6*h - 2*h. Let p be 5 - 3*(-3 - h). Determine i so that -i**2 + 5*i**p + i**2 - 3*i**2 = 0.
0
Let a(i) = i**2. Let f = -46 + 60. Let g(k) = -5*k**2 - 4*k. Let y(z) = f*a(z) + 2*g(z). Determine j, given that y(j) = 0.
0, 2
Let q(p) be the first derivative of 0*p**2 + 7 + 2/45*p**5 + 1/9*p**4 + 0*p + 2/27*p**3. Factor q(m).
2*m**2*(m + 1)**2/9
Let a(m) = -5*m**3 + 57*m**2 - 196*m + 176. Let v(t) = 10*t**3 - 116*t**2 + 393*t - 353. Let i(y) = -7*a(y) - 4*v(y). Factor i(l).
-5*(l - 9)*(l - 2)**2
Let a be 2/9 + (2 - (-68)/18). Let l(z) = z**2 - 9*z + 20. Let v be l(a). Factor 0*c + 0*c**3 - 1/4*c**v + 1/4*c**4 + 0.
c**2*(c - 1)*(c + 1)/4
Let q(k) = -2*k**2 + 4*k - 2. Let s(z) = 5*z - 48*z**2 + 45*z**2 - 3 - z. Let y(i) = -5*q(i) + 4*s(i). What is v in y(v) = 0?
-1
Let f(p) be the second derivative of -42*p - 2*p**5 + 0 - 15/4*p**3 + 0*p**2 + 5*p**4. What is u in f(u) = 0?
0, 3/4
Let v(k) = -15*k**3 - 24*k**2 + 21*k. Let x(l) = -3*l**3 - 5*l**2 + 4*l. Let z be (30/9)/2*12 + 1. Let m(w) = z*x(w) - 4*v(w). Factor m(i).
-3*i**2*(i + 3)
Let i(v) be the first derivative of -v**7/147 - v**6/60 - v**5/105 + 13*v**2 + 38. Let l(f) be the second derivative of i(f). Factor l(u).
-2*u**2*(u + 1)*(5*u + 2)/7
Suppose -2*q = 2*w - 7*q - 19, -q - 59 = -5*w. Suppose -v + 2*x + w = -x, 4*x + 15 = v. Factor -v*s - 10*s**2 + 0*s + 4*s**2.
-3*s*(2*s + 1)
Let w(i) be the third derivative of i**5/180 + 7*i**4/12 + 49*i**3/2 - 58*i**2. Solve w(z) = 0 for z.
-21
Let h = 9883 + -9881. Solve 1/5*s**h + 0 - 1/10*s - 1/10*s**3 = 0.
0, 1
Suppose 51 = 9*c - 12*c. Let o = c - -20. Solve -t**3 - t**2 - 5*t**3 + 9*t**3 - 4*t**o = 0 for t.
-1, 0
Let l(o) be the third derivative of -o**8/336 - o**7/21 - 11*o**6/40 - 11*o**5/15 - 5*o**4/6 - 6*o**2 - 17*o. Factor l(z).
-z*(z + 1)*(z + 2)**2*(z + 5)
Let o(u) be the second derivative of u**6/12 - 57*u**5/8 + 35*u**4/3 + 78*u + 1. Factor o(h).
5*h**2*(h - 56)*(h - 1)/2
Let w = -1030 + 1037. Let y(r) be the second derivative of 1/20*r**6 + 1/6*r**4 - 3/10*r**5 + 5/84*r**7 + 0*r**3 - w*r + 0*r**2 + 0. Solve y(b) = 0.
-2, 0, 2/5, 1
Let g(f) be the third der