second derivative of n(z). Factor l(t).
t**2*(t - 1)/3
Let r(q) be the first derivative of -1/6*q**6 + 0*q - 1/4*q**4 + 0*q**2 + 2/5*q**5 - 3 + 0*q**3. Find a, given that r(a) = 0.
0, 1
Factor -7 - 2 - 2*r + 6 + r**2.
(r - 3)*(r + 1)
Let p(w) be the second derivative of -5*w + 0 + 0*w**3 + 1/24*w**4 + 0*w**2. Let p(y) = 0. Calculate y.
0
Factor 158*u**3 - 5*u**4 - 161*u**3 - 3*u**2 - u + 4*u**4.
-u*(u + 1)**3
Let j(a) = -10*a**4 - 10*a**3 + 10*a**2 + 3*a + 7. Let l(v) = 3*v**4 + 3*v**3 - 3*v**2 - v - 2. Let o(u) = -4*j(u) - 14*l(u). Factor o(i).
-2*i*(i - 1)*(i + 1)**2
Let t(f) be the second derivative of -2*f**7/63 - 2*f**6/45 + f**5/5 + 5*f**4/9 + 4*f**3/9 - 13*f. Solve t(s) = 0 for s.
-1, 0, 2
Let q(p) be the third derivative of -6*p**2 + 0 + 0*p + 0*p**7 - 1/60*p**6 + 0*p**5 + 1/336*p**8 + 1/24*p**4 + 0*p**3. Factor q(n).
n*(n - 1)**2*(n + 1)**2
Let g(f) = 17*f**2 - 9*f - 19. Let k(s) = -8*s**2 + 4*s + 9. Let c(p) = -4*g(p) - 9*k(p). Let i(x) = 6*x**2 - 7. Let d(r) = -7*c(r) + 5*i(r). Factor d(b).
2*b**2
Let u = 2/5 + -4/35. Factor 0*i**2 + u*i**3 - 2/7*i + 0.
2*i*(i - 1)*(i + 1)/7
Factor -2*f**3 + 6*f**3 - f**3 + 9*f**2 - 3 - 9*f**3.
-3*(f - 1)**2*(2*f + 1)
Suppose -3*k - 15 = -w, -3*w + 2*k - 2 + 19 = 0. Suppose -w*p = p - 8. Factor -4*v**2 - 3*v + 5 - 3 - v**p.
-(v + 1)*(5*v - 2)
Let l(v) be the second derivative of v**8/23520 - v**7/4410 + v**6/2520 - v**4/6 + v. Let a(r) be the third derivative of l(r). Determine n so that a(n) = 0.
0, 1
Let q be (0 + 1)*(-6)/2. Let y(f) = -5*f**4 - 5*f**3 - 7*f + 7. Let v(b) = 2*b**4 + 2*b**3 + 3*b - 3. Let o(w) = q*y(w) - 7*v(w). Find m such that o(m) = 0.
-1, 0
Suppose -17 = 3*c + 3*g - 74, 0 = -3*c + 4*g + 57. Let b = 22 - c. Let 14/3*p**4 + 8/3*p + 40/3*p**2 + 46/3*p**b + 0 = 0. Calculate p.
-2, -1, -2/7, 0
Factor -24/19*z**2 - 64/19*z + 8/19*z**3 + 128/19 + 2/19*z**4.
2*(z - 2)**2*(z + 4)**2/19
Let f(i) = -i + 13. Let b be f(11). Let p(q) be the first derivative of -1 - 1/6*q**3 - 1/2*q**b + 1/10*q**5 + 1/4*q**4 + 0*q. What is r in p(r) = 0?
-2, -1, 0, 1
Let n = 2/5 - 1/3. Let l(k) be the second derivative of -1/42*k**7 - 3*k + 0*k**4 + 0 + 0*k**2 + 0*k**3 - n*k**6 - 1/20*k**5. Determine z so that l(z) = 0.
-1, 0
Let h = 229 + -2057/9. Suppose 2/9 + 2/9*g**2 - h*g = 0. What is g?
1
Let a(s) be the second derivative of s**7/378 - s**6/270 - s**5/90 - 15*s. Factor a(k).
k**3*(k - 2)*(k + 1)/9
Let f be 28/(-13) - (-44)/286. Let o be 3 - (38/10 + f). Factor -2/5*l**2 - 4/5 + o*l.
-2*(l - 2)*(l - 1)/5
Suppose 0 = 6*u - 0 - 6. Let j(p) be the first derivative of -u - 1/3*p + 1/24*p**4 - 1/4*p**2 + 0*p**3. Factor j(f).
(f - 2)*(f + 1)**2/6
Let u(n) be the second derivative of -n - 3*n**2 + 0 + 1/30*n**5 + 5/18*n**4 + 1/3*n**3. Solve u(v) = 0 for v.
-3, 1
Factor 34*s**2 + s**3 - 9*s**2 - 15*s**2 + s**3 + 8*s.
2*s*(s + 1)*(s + 4)
Suppose -8 - 8 = -4*r. Factor 2*d**2 - 1 - 3*d**r + 2*d**4 + 0.
-(d - 1)**2*(d + 1)**2
Suppose -4*y + 42 = -2*k, y - 9 = 4*k + 12. Let h(t) = 3*t**2 + 9*t + 6. Let f(v) = -2*v**2 - 5*v - 3. Let a(b) = y*f(b) + 5*h(b). Find u, given that a(u) = 0.
-1, 1
Let p(a) be the second derivative of a**6/150 + a**5/100 - a**4/20 - a**3/30 + a**2/5 - 24*a. Find l, given that p(l) = 0.
-2, -1, 1
Let k be 6/15 + (-4)/10. Let y be 4 + -2 + k + 1. Factor -a - a**3 - y*a**3 + 0*a + 5*a**3.
a*(a - 1)*(a + 1)
Let s(v) be the second derivative of 19*v**4/21 + 34*v**3/21 - 4*v**2/7 + 31*v. Let s(f) = 0. Calculate f.
-1, 2/19
Suppose 0 = -k - 0 + 3. Factor -36*s**3 + 2 - 21*s**2 - 2 - k*s.
-3*s*(3*s + 1)*(4*s + 1)
Let r(v) be the first derivative of v**8/560 - v**7/280 - v**6/120 + v**5/40 + v**3/3 - 4. Let g(c) be the third derivative of r(c). Factor g(o).
3*o*(o - 1)**2*(o + 1)
Let -4/7*t**4 + 16/7*t**5 - 48/7*t**3 - 8/7*t + 0 + 44/7*t**2 = 0. What is t?
-2, 0, 1/4, 1
Let d(c) = -5*c**2 - 9*c. Let s(a) = -2*a**2 - 4*a. Let f(u) = -6*d(u) + 14*s(u). Determine w so that f(w) = 0.
0, 1
Factor 0 + 1/3*n**2 - n.
n*(n - 3)/3
Let r(m) be the second derivative of m**9/3780 + m**8/1680 - m**7/630 - m**6/180 + 5*m**4/6 + 10*m. Let y(h) be the third derivative of r(h). Factor y(v).
4*v*(v - 1)*(v + 1)**2
Let m = 23 - 20. Suppose 0*z - 2 = m*z - n, -n + 2 = 0. Factor 0*k**2 + z*k + 0 + 1/2*k**3 + 3/2*k**4 + k**5.
k**3*(k + 1)*(2*k + 1)/2
Determine r, given that -10*r**2 + 9*r**5 + 3*r + 40*r**3 + 28*r**2 + 30*r**4 - 4*r**3 = 0.
-1, -1/3, 0
Suppose 3*c = 1012 - 109. Factor -53*z**2 - 16 - 168*z + 87*z**2 - 686*z**3 - c*z**2 - 321*z**2.
-2*(7*z + 2)**3
Let -30 + 4*d + 21*d**2 - 19*d - d**2 - 10*d = 0. What is d?
-3/4, 2
Let d = -1 + 5. Let -d + 0*p**4 - 48*p**2 - 8*p**4 - 17*p - 9*p - 10*p**3 - 24*p**3 = 0. Calculate p.
-2, -1, -1/4
Factor t**5 + 8*t**2 - 26*t + 11*t + 12*t - 6*t**3.
t*(t - 1)**3*(t + 3)
Let n(r) = -5*r**4 + 48*r**3 + 53*r**2 - 65*r - 48. Let c(y) = -y**4 + 8*y**3 + 9*y**2 - 11*y - 8. Let x(t) = 34*c(t) - 6*n(t). Factor x(s).
-4*(s - 1)*(s + 1)*(s + 2)**2
Let r(s) be the third derivative of -s**5/120 + s**4/48 - 20*s**2. Factor r(c).
-c*(c - 1)/2
Let z(m) be the third derivative of -m**7/168 - m**6/32 - m**5/16 - 5*m**4/96 + 3*m**2. Factor z(r).
-5*r*(r + 1)**3/4
Let w = -3537/5 - -711. Factor -14/5*b**2 + w*b - 4/5.
-2*(b - 1)*(7*b - 2)/5
Solve 2/3*t + 5/6*t**2 + 0 + 1/6*t**3 = 0.
-4, -1, 0
Let j(l) = 2*l**3 - 2*l**2 + 6*l - 4. Let x be j(1). Factor -1/3*y**x - 4/3 - 4/3*y.
-(y + 2)**2/3
Let i(t) be the second derivative of -t**6/480 + t**4/32 - t**3/12 + t**2 + 3*t. Let z(q) be the first derivative of i(q). Let z(o) = 0. What is o?
-2, 1
Let z(d) = -2*d**4 + 2*d**3 + 4*d**2 - 2*d - 2. Suppose -3 + 0 = 3*f. Let l(o) = o**5 + o**2 - o - 1. Let x(b) = f*z(b) + 2*l(b). Let x(s) = 0. Calculate s.
-1, 0, 1
Suppose 3*j = 5*k - 122, -2*j = 2*j - k + 174. Let w = j - -111. Find y such that 30*y**4 - 90*y**3 - 56*y**2 - 8*y + 31*y**5 + w*y**5 + 26*y**4 = 0.
-1, -2/7, 0, 1
Let c(w) be the third derivative of w**5/210 + w**4/84 - 13*w**2. What is z in c(z) = 0?
-1, 0
Let j(u) = u + 1. Let z be j(-1). Determine y, given that z*y**3 + 5*y - 2 - 5*y**3 + y**2 + y**2 + 0*y**3 = 0.
-1, 2/5, 1
Solve -1/6*a**3 + 5/6*a + 1/6*a**2 + 1/2 = 0 for a.
-1, 3
Let p(t) be the first derivative of t**4/12 - t**2/2 + 2*t/3 - 20. Suppose p(g) = 0. What is g?
-2, 1
Let j(s) be the first derivative of s**3/12 - 3*s**2/8 - 6. Factor j(l).
l*(l - 3)/4
Let b be 27/(-6)*4/(-6). Suppose -4*a + 10 = -b*w, 2*a = 3*w + a - 2. Factor 5*h**2 - h - w*h**3 + h**3 - 3*h**2.
-h*(h - 1)**2
Let i(a) = 10*a**4 + 5*a**3 - 10*a**2 - 2*a - 3. Let b(y) = 29*y**4 + 14*y**3 - 29*y**2 - 6*y - 8. Let k(f) = -3*b(f) + 8*i(f). Solve k(v) = 0 for v.
-1, -2/7, 0, 1
Let u(t) = -6*t**2 - 6*t + 11. Let h be (-4)/18 + 364/(-63). Let s(y) = -y**2 - y + 2. Let i(z) = h*u(z) + 33*s(z). Factor i(q).
3*q*(q + 1)
Let p be 2*3/(-120) - 10/(-40). Find d, given that -2/5 + p*d**3 + 3/5*d**2 - 1/5*d - 1/5*d**4 = 0.
-1, 1, 2
Let v(w) = 3*w**3 + 5*w**3 + w - 2*w**2 - 2*w**3 + 0*w**3. Let b(t) = -2*t**3 + 0*t**3 + t**3. Let q(a) = -5*b(a) - v(a). Factor q(j).
-j*(j - 1)**2
Let b(h) be the third derivative of -h**2 + 0*h - 5/54*h**4 - 5/54*h**5 - 1/27*h**3 + 0. Factor b(z).
-2*(5*z + 1)**2/9
Factor 0*x**2 - 3/2*x**3 + 19/4*x**4 + 7/4*x**5 + 0 + 0*x.
x**3*(x + 3)*(7*x - 2)/4
Factor -1/3*h**5 + 0 + 1/3*h**3 - 1/3*h**4 + 1/3*h**2 + 0*h.
-h**2*(h - 1)*(h + 1)**2/3
Let m(r) = r. Let g be m(0). Suppose g*x = x. Find j such that -4 - j**2 + 2 - 3*j + x*j**2 = 0.
-2, -1
Let v(y) be the first derivative of -3/13*y**2 + 4/13*y - 7 + 2/39*y**3. Factor v(g).
2*(g - 2)*(g - 1)/13
Let u(a) = a**2 + 6*a + 3. Suppose -3*f + 4*c - 6 = 4, -4*f + c - 22 = 0. Let x be u(f). Factor z**3 - 3*z**x - 3 + 3*z + 3*z - 1.
-2*(z - 1)**2*(z + 2)
Let i be 4 - (-1 - -2)/1. Factor 2*k**2 + k**3 - i*k**3 + k**3.
-k**2*(k - 2)
Let b(l) be the third derivative of -l**8/6720 - l**4/8 + 2*l**2. Let v(x) be the second derivative of b(x). Factor v(q).
-q**3
Let k(j) = j**2 + 9*j - 20. Let v be k(-11). Factor -1/5*w**v + 1/5 + 0*w.
-(w - 1)*(w + 1)/5
Let j(l) = l - 4. Let i be j(8). Suppose i*u = 6 + 10. Factor 2*t**2 + u*t**3 - 3*t + 2*t**4 + 0*t + 3*t.
2*t**2*(t + 1)**2
Let f(t) be the first derivative of -1/16*t**4 + 0*t**2 - 3 + 0*t - 1/6*t**3. Factor f(u).
-u**2*(u + 2)/4
Let g(r) be the second derivat