ve of 1/5*h**5 + 0*h**2 + 0*h - 1 + 1/4*h**4 + 0*h**3. Factor b(x).
x**3*(x + 1)
Let m(y) be the second derivative of 0 - 2*y**2 - 1/6*y**4 + y - y**3. Let m(a) = 0. What is a?
-2, -1
Let s(f) be the third derivative of 0*f + 1/210*f**7 + 2/3*f**3 - 1/60*f**6 + 1/6*f**4 + 0 - 1/20*f**5 + f**2. Factor s(g).
(g - 2)**2*(g + 1)**2
Let r(u) be the third derivative of 0 - 1/18*u**4 - 3*u**2 + 0*u - 1/90*u**5 - 1/9*u**3. Suppose r(y) = 0. What is y?
-1
Let d be (-56)/(-96) - (-2)/(-8). Find h such that 1/3*h**2 - 1/3*h**4 + 0 + 0*h + 1/3*h**3 - d*h**5 = 0.
-1, 0, 1
Suppose 0 = -k - 4*f - 16, 18*k - 23*k - 16 = 4*f. Solve k*j**3 + 0 - 2/15*j**4 + 0*j**2 - 2/15*j**5 + 0*j = 0.
-1, 0
Let h(i) be the first derivative of i**4/9 + 20*i**3/9 + 50*i**2/3 + 500*i/9 - 17. Factor h(m).
4*(m + 5)**3/9
Let w(j) be the second derivative of -5*j + 0*j**2 - 3/8*j**4 + 1/4*j**3 + 3/20*j**5 + 0. Determine c so that w(c) = 0.
0, 1/2, 1
Let x(b) be the first derivative of 11/2*b**2 + b**3 - 2 + 6*b. Factor x(w).
(w + 3)*(3*w + 2)
Let t be -8*(0 + 1/(-4)). Let j(x) be the third derivative of 3*x**t - 1/105*x**5 + 1/84*x**4 + 0 + 0*x**3 - 1/140*x**6 + 0*x. Find a such that j(a) = 0.
-1, 0, 1/3
Let c(v) = v**3 + 10*v**2 + 2*v + 13. Let a be c(-10). Let o = 22/3 + a. Factor -1/3*r**2 + 1/3*r**3 + o - 1/3*r.
(r - 1)**2*(r + 1)/3
Let g be (-1203)/(-180) - 2/(-8). Let s = 48/5 - g. What is j in 14/3*j**2 - 8*j - s = 0?
-2/7, 2
Let z(f) = -f**2 + 1. Let i(y) = -2*y**2 + 2. Let k(r) = i(r) - z(r). Factor k(a).
-(a - 1)*(a + 1)
Suppose -2*d + 2 = -8. Let z(m) be the second derivative of 1/12*m**3 + 0 - 1/40*m**d - 1/4*m**2 + 3*m + 1/24*m**4. Find c, given that z(c) = 0.
-1, 1
Let g = -4 + 13. Determine s so that -16*s + 2*s - g*s**2 + 11*s = 0.
-1/3, 0
Let v(g) be the second derivative of g**7/252 - g**5/60 + g**3/36 + 46*g. Factor v(k).
k*(k - 1)**2*(k + 1)**2/6
Factor 1/7*u**3 + 0*u - 2/7*u**2 + 0 + 1/7*u**4.
u**2*(u - 1)*(u + 2)/7
Suppose 0*d - 5*d + 15 = 0. Let h be 0 - (-1)/(d/132). Suppose 30*b - 18*b**5 + 82*b**5 - 24*b**2 - 2 - 2*b**2 - 14*b + 64*b**4 - h*b**3 = 0. What is b?
-1, 1/4, 1/2
Suppose 10 = -3*z + 2*m, -2*m = 2*m - 20. Factor 2/7*c**2 + z*c + 0 - 2/7*c**3.
-2*c**2*(c - 1)/7
Suppose a + 8 = 2*k, a + 2 + 16 = 4*k. Let l(f) be the first derivative of -f**a + 4/3*f**3 - 1/2*f**4 + 0*f - 2. Find i such that l(i) = 0.
0, 1
Let p(v) = -6*v**3 + 2*v**2 + 12*v + 12. Let b(u) = -17*u**3 + 5*u**2 + 35*u + 35. Let x(j) = 4*b(j) - 11*p(j). Find h such that x(h) = 0.
-2, -1, 2
Let z(g) be the second derivative of g**7/63 + g**6/45 - g**5/5 - 7*g**4/9 - 11*g**3/9 - g**2 - 3*g - 9. Find n, given that z(n) = 0.
-1, 3
Suppose -188*b = -192*b + 8. Factor -9/4*q**b - 3/4 - 9/4*q - 3/4*q**3.
-3*(q + 1)**3/4
Factor -98/3 + 28/3*l - 2/3*l**2.
-2*(l - 7)**2/3
Determine w so that 4 + 51*w**3 - 20*w + 4 - 55*w**3 + 16*w**2 = 0.
1, 2
Let a(b) be the second derivative of 1/30*b**5 - 1/9*b**3 + 0*b**2 - b + 1/18*b**4 - 1/45*b**6 + 0. Suppose a(r) = 0. What is r?
-1, 0, 1
Let v = 14 - 10. Suppose -18 = -v*y - 6. Solve t**2 + t**2 - 2*t**3 + y*t + 2 + 2 - 3*t**4 - 3 - t**5 = 0 for t.
-1, 1
Factor -c + c**3 - 1/2*c**2 + 1/2.
(c - 1)*(c + 1)*(2*c - 1)/2
Let d be (9/(-2) - -2)*(-210)/125. Factor 2/5 + 72/5*l**2 + d*l + 16*l**3.
(4*l + 1)**2*(5*l + 2)/5
Let f(n) be the third derivative of n**6/300 - n**5/75 + n**4/60 + 2*n**2. Let f(x) = 0. What is x?
0, 1
Let n(o) be the third derivative of -o**6/160 - 3*o**5/80 - 3*o**4/32 - o**3/8 + 4*o**2. Factor n(d).
-3*(d + 1)**3/4
Factor 1 + 8*s**2 - 4 + 83*s**3 + 1 + s - 78*s**3.
(s + 1)**2*(5*s - 2)
Let t(o) be the second derivative of 0 + 0*o**2 - 1/18*o**4 + 0*o**3 - 3*o. Factor t(m).
-2*m**2/3
Let x(t) = -6*t + t**3 - 1 + 3 + 5*t - 1. Let n(p) = p**4 + 4*p**3 - 3*p**2 + 3. Let g(r) = n(r) - 5*x(r). Factor g(s).
(s - 1)**3*(s + 2)
Suppose 3 = 3*g - 5*x + 4*x, g - 3*x = -7. Let h = 6 - 4. Find w such that w + 2*w**h - w**g - 3*w**2 + 3*w = 0.
0, 2
Suppose -4*k + 15 = -2*u - 1, 3*u = 2*k - 16. Let z = -3/47 + 197/141. Determine a, given that 4/3*a + 1/3*a**k + z = 0.
-2
Let u(r) be the second derivative of 3/4*r**2 - 1/20*r**6 - 1/2*r**3 + 0*r**4 - 4*r + 0 + 3/20*r**5. Determine b, given that u(b) = 0.
-1, 1
Let k = 296/5 + -58. Solve -k*a + 0 - 2/5*a**2 = 0 for a.
-3, 0
Let j(o) = -7*o**3 + o**2 + 2*o + 1. Let l be j(-1). Suppose 3*s + 16 = l*s. Factor -2/7*z**s - 12/7*z**2 - 2/7 - 8/7*z - 8/7*z**3.
-2*(z + 1)**4/7
Let o(h) be the first derivative of -1/72*h**4 + 0*h + 1/180*h**5 - 1 + 1/2*h**2 + 0*h**3. Let d(s) be the second derivative of o(s). Find m such that d(m) = 0.
0, 1
Let l(o) be the second derivative of 3*o**5/40 + 3*o**4/8 - 3*o**2 - 4*o. Factor l(r).
3*(r - 1)*(r + 2)**2/2
Let w(k) = 2*k - 6. Let x be w(4). Factor -3*n**4 - 6*n**2 + 12*n**5 + 6*n**x.
3*n**4*(4*n - 1)
Let v(m) = -28*m**3 + 43*m**2 - 8*m - 7. Let l(y) = -14*y**3 + 21*y**2 - 4*y - 3. Suppose -6 = t + 1. Let j(c) = t*l(c) + 3*v(c). Factor j(z).
2*z*(z - 1)*(7*z - 2)
Let h(k) = k**3 + 5*k**2 - 6*k + 5. Let y be 70/(-12) - 7/42. Let b be h(y). Factor 2/9*u**b + 0*u + 0 - 2/9*u**2 + 2/9*u**4 - 2/9*u**3.
2*u**2*(u - 1)*(u + 1)**2/9
Suppose -c - 11 = 2*k, -4*c = -5*k - c. Let l(s) = s**3 + 3*s**2 - 3*s - 3. Let b be l(k). Factor -b*u**2 - 12*u**3 + 0 - 3/4*u.
-3*u*(4*u + 1)**2/4
Let j be (2/5)/(57/15 - 3). Determine i, given that -1/4*i**3 + 0*i + j*i**4 - 1/2*i**2 + 1/4*i**5 + 0 = 0.
-2, -1, 0, 1
Let h(o) = o**3 - o**2 - o - 1. Let s = -5 - -1. Let c(q) = 31*q**3 - 13*q**2 - 28*q + 8. Let t(d) = s*h(d) + c(d). Factor t(k).
3*(k + 1)*(3*k - 2)**2
Let u(r) be the second derivative of r**6/15 + 3*r**5/20 - r**4/12 - r**3/2 - r**2/2 - 5*r. Find a, given that u(a) = 0.
-1, -1/2, 1
Suppose 0 = d + 9 + 9. Let v = 18 + d. Factor -11/5*p**4 + 2/5*p**2 + 9/5*p**3 + v + 0*p.
-p**2*(p - 1)*(11*p + 2)/5
Suppose -2102*i - 5*i**5 - 5*i**2 + 15*i**3 + 10*i**2 - 5*i**4 + 2092*i = 0. Calculate i.
-2, -1, 0, 1
Let d(t) be the first derivative of -t**6/360 + t**5/120 + 2*t**3/3 - 4. Let h(q) be the third derivative of d(q). Find u, given that h(u) = 0.
0, 1
Let l(v) be the third derivative of v**7/1785 - v**6/340 + v**5/170 - v**4/204 - v**2. Factor l(r).
2*r*(r - 1)**3/17
Let p(q) be the second derivative of q**5/10 + q**4/3 - q**3/3 - 2*q**2 + 4*q. Factor p(m).
2*(m - 1)*(m + 1)*(m + 2)
Let k(l) = l**3 - 6*l**2 + 5*l. Suppose 1 = 3*z - 14. Let q be k(z). Factor 0 - 2/5*y**2 + q*y - 2/5*y**3 + 2/5*y**4 + 2/5*y**5.
2*y**2*(y - 1)*(y + 1)**2/5
Suppose -3*m + 5*h = 9*h + 8, 0 = -h - 2. Let 1/4*r**5 + 0 + 1/4*r**4 + m*r + 0*r**2 + 0*r**3 = 0. What is r?
-1, 0
Solve 0*m**3 + 3*m**5 + 2*m**3 - m**5 - 4*m**4 = 0 for m.
0, 1
Let w(y) = -y**2 - 1. Let r(z) = 8*z**2 + 6*z + 8. Let f(x) = r(x) + 5*w(x). Factor f(n).
3*(n + 1)**2
Suppose -10 = j + 5*h, 2*h - 12 = 2*j + 4*h. Let g(c) = -28*c**2 - 32*c - 36. Let t(v) = 9*v**2 + 11*v + 12. Let a(f) = j*g(f) - 16*t(f). Factor a(w).
-4*(w + 1)*(w + 3)
Let v be (2 - (-10 + 10))/1. Determine h, given that -10/3*h**3 - v*h**2 + 0 + 0*h = 0.
-3/5, 0
Let j(r) = -r**3 - 5*r**2 - r - 3. Let f be j(-5). Solve 2/5*h**3 + 0 - 6/5*h**f + 4/5*h = 0 for h.
0, 1, 2
Solve -1/3*o**3 + 1/3 + o**2 - o = 0.
1
Let r = -1/4 - -3/4. Factor 1/4 + r*g**3 + 1/4*g**5 - 3/4*g - 3/4*g**4 + 1/2*g**2.
(g - 1)**4*(g + 1)/4
Let w(d) = d**3 + 2*d**2 - 2*d. Let r be w(-2). Let o be -3 + 0 - (-7 - -4). Factor o*f + 1/2*f**3 + 1/4*f**2 + 0 + 1/4*f**r.
f**2*(f + 1)**2/4
Let p(u) be the first derivative of u**6/3 + 8*u**5/5 + 5*u**4/2 + 4*u**3/3 + 6. Factor p(k).
2*k**2*(k + 1)**2*(k + 2)
Suppose 3*r = 4*k + 3 + 1, 5*r - 4*k - 4 = 0. Let q be r + (-2 - -2) + 2. Solve 8 + 4*h**2 - 2*h**q + 0*h**2 + 8*h = 0.
-2
Let z(o) be the third derivative of -o**6/120 + o**5/15 - o**4/6 + 8*o**2. Factor z(a).
-a*(a - 2)**2
Let d(u) be the first derivative of -u**6/540 - u**5/45 - u**4/9 + 4*u**3/3 - 5. Let p(a) be the third derivative of d(a). Find x, given that p(x) = 0.
-2
Let l(h) be the first derivative of -h**5/20 + h**3/12 - 14. Factor l(s).
-s**2*(s - 1)*(s + 1)/4
Let n be (0 + 8)*(-36)/10. Let v = -412/15 - n. Factor 0 + 2/3*i**3 + 2/3*i - v*i**2.
2*i*(i - 1)**2/3
Let f = 32 + -3. Let k = f + -143/5. Factor 2/5 + 2/5*a - k*a**3 - 2/5*a**2.
-2*(a - 1)*(a + 1)**2/5
Let l(u) be the first derivative of u**