be the third derivative of o**5/120 + 5*o**4/6 + 100*o**3/3 + 28*o**2 + 2*o. Factor t(q).
(q + 20)**2/2
Let v be (10/4 + -2)/(3/2). Let s(x) be the second derivative of 0*x**5 + 0 - 1/30*x**6 + 2*x - v*x**3 + 1/4*x**4 + 0*x**2. Factor s(r).
-r*(r - 1)**2*(r + 2)
Let v(f) be the first derivative of 6/5*f**5 - 15/4*f**4 + 4*f**3 - 4 + 0*f - 3/2*f**2. Factor v(x).
3*x*(x - 1)**2*(2*x - 1)
Let l(y) be the third derivative of -3*y**2 + 0 + 0*y - 1/105*y**5 + 1/84*y**4 + 1/420*y**6 + 0*y**3. Factor l(n).
2*n*(n - 1)**2/7
Determine i, given that -36/7*i**3 + 0 + 8/7*i - 20/7*i**5 + 52/7*i**4 - 4/7*i**2 = 0.
-2/5, 0, 1
Let j(c) be the second derivative of -3/8*c**3 + 1/40*c**6 + 9/80*c**5 + 4*c + 1/16*c**4 - 3/4*c**2 + 0. Factor j(m).
3*(m - 1)*(m + 1)**2*(m + 2)/4
Let a(b) = -b**5 - 13*b**4 - 21*b**3 - 19*b**2 - 7*b - 3. Let h(g) = 12*g**4 + 20*g**3 + 20*g**2 + 8*g + 4. Let o(p) = 4*a(p) + 3*h(p). Factor o(v).
-4*v*(v + 1)**4
Factor 0 - 7/6*o - 1/6*o**2.
-o*(o + 7)/6
Let k(g) be the first derivative of 4 + 4*g - 3*g**2 - 2/3*g**3 - 2/5*g**5 + 3/2*g**4. Let k(t) = 0. Calculate t.
-1, 1, 2
Let x(j) be the third derivative of -j**6/120 + j**4/24 + j**3/6 - 6*j**2. Let f(v) = 3*v**3 - 9*v**2 - 12*v - 6. Let r(l) = f(l) + 6*x(l). Factor r(z).
-3*z*(z + 1)*(z + 2)
Let o(m) = m**3 + 25*m**2 + 22*m - 48. Let q be o(-24). Factor q*h + 1/8*h**3 + 0 + 0*h**2 + 1/4*h**4 + 1/8*h**5.
h**3*(h + 1)**2/8
Let i(x) be the third derivative of x**9/68040 - x**4/12 - x**2. Let u(w) be the second derivative of i(w). Factor u(g).
2*g**4/9
Let u(g) = 44*g**3 + 204*g**2 + 540*g + 516. Let d(q) = -9*q**3 - 41*q**2 - 108*q - 103. Let v(x) = 24*d(x) + 5*u(x). What is y in v(y) = 0?
-3
Let w(b) be the third derivative of 0*b + 3*b**2 - 1/24*b**4 + 0 - 1/180*b**5 + 0*b**3. Let w(l) = 0. Calculate l.
-3, 0
Let k(s) be the second derivative of -s**4/6 + 4*s**3/3 - 3*s**2 - 4*s. Solve k(a) = 0 for a.
1, 3
Let z(s) be the first derivative of -2*s**3/15 + 3*s**2/5 - 4*s/5 + 3. What is v in z(v) = 0?
1, 2
Let o(h) = h**3 + 3*h**2 + h + 2. Let g be o(0). Factor -4/7 + 2/7*n**g - 2/7*n.
2*(n - 2)*(n + 1)/7
Let w(t) = -4*t**2 - 2*t + 8. Let h(m) = m**2 + m. Let q(y) = 2*h(y) + w(y). Factor q(j).
-2*(j - 2)*(j + 2)
Let o = -5 - -5. Let h(r) be the second derivative of o*r**3 + 0 - 1/48*r**4 - 1/120*r**6 - 1/40*r**5 + 2*r + 0*r**2. Find n, given that h(n) = 0.
-1, 0
Let b(i) be the second derivative of i**4/114 + 4*i**3/57 - 5*i**2/19 - 7*i. Factor b(v).
2*(v - 1)*(v + 5)/19
Let g be 5/4 - 1 - (-135)/324. Suppose 2/3*b**4 + g*b + 2/3 - 4/3*b**3 - 4/3*b**2 + 2/3*b**5 = 0. What is b?
-1, 1
Let g = -22 - -52. Let -g*q**3 - 8/3*q + 54*q**4 + 0 - 64/3*q**2 = 0. What is q?
-2/9, 0, 1
Let p be 0 + 1/((-1)/(-4)). Suppose 0 = t + t - p. Factor 0*m**4 - t*m + 5*m**4 + 2*m**2 - m**2 + 8*m**3.
m*(m + 1)**2*(5*m - 2)
Let n(x) be the second derivative of x**7/70 - x**6/40 - x**5/20 + x**4/8 + x**2 + x. Let s(l) be the first derivative of n(l). Factor s(d).
3*d*(d - 1)**2*(d + 1)
Let c(v) be the first derivative of 2 - 2/9*v**2 + 2/9*v + 2/27*v**3. Solve c(z) = 0 for z.
1
Let i(r) be the third derivative of 0*r**3 + 0*r - 1/20*r**4 + 6*r**2 + 0 - 1/20*r**5 + 3/200*r**6. Factor i(m).
3*m*(m - 2)*(3*m + 1)/5
Let b = 53 + -53. Factor -1/3*a**5 + b + 1/3*a**2 + a**4 + 0*a - a**3.
-a**2*(a - 1)**3/3
Let l(m) be the second derivative of m**8/840 + m**7/420 + m**3/6 + m. Let v(s) be the second derivative of l(s). Factor v(o).
2*o**3*(o + 1)
Let p(q) = -2*q + 18. Let i be p(8). Factor 0 - 14*h**2 + 1 - 3*h + i - 1.
-(2*h + 1)*(7*h - 2)
Factor 3/4*j**4 - 15/4*j**2 - 3/4*j**5 + 3/2*j + 9/4*j**3 + 0.
-3*j*(j - 1)**3*(j + 2)/4
Let p(g) be the third derivative of g**6/90 + g**5/30 + g**4/24 + g**3/36 - 16*g**2. Suppose p(z) = 0. What is z?
-1/2
Let j(s) = -s**2 + 0*s - s + 2*s + 2*s - 2. Let l(d) = 2*d**2 - 6*d + 4. Let c(p) = 11*j(p) + 6*l(p). Factor c(m).
(m - 2)*(m - 1)
Let f be ((-196)/12)/((-5)/(-21)). Let y = -68 - f. Factor 0*c**2 + y*c**3 + 0 + 3/5*c**4 + 0*c.
3*c**3*(c + 1)/5
Let h(a) be the second derivative of a**5/100 + a**4/40 - a**2/2 - a. Let g(c) be the first derivative of h(c). Factor g(w).
3*w*(w + 1)/5
Let c(u) be the first derivative of -2*u - 10*u**2 - 50/3*u**3 + 2. Factor c(f).
-2*(5*f + 1)**2
Let o be (-2)/(-10) + 1/10*3. Find c such that 3/4 - 1/4*c**2 - o*c = 0.
-3, 1
Let f(q) be the first derivative of -q**6/60 - q**5/30 - q**2 + 1. Let t(r) be the second derivative of f(r). Factor t(h).
-2*h**2*(h + 1)
Let y be 1/(-2)*0/4. Let g be y + (-2)/(2 - 8). Let g*f**4 + 0 - 1/3*f**2 - 1/3*f**3 + 1/3*f = 0. Calculate f.
-1, 0, 1
Let j be 16/10 - 2/(-5). Let z = j - -1. Factor -n**z - n + 4*n**5 - 5*n**5 + 3*n**3.
-n*(n - 1)**2*(n + 1)**2
Let w(l) = 2*l**3. Let j be w(1). Let q(u) be the third derivative of 0*u + 0 - 1/15*u**5 - 5/24*u**4 - 1/6*u**3 - 3*u**j. Factor q(z).
-(z + 1)*(4*z + 1)
Let l(a) be the second derivative of 0 + a**2 + 4/21*a**7 + 3*a - 4/3*a**4 + 7/15*a**6 - 2/3*a**3 - 1/5*a**5. Factor l(h).
2*(h - 1)*(h + 1)**3*(4*h - 1)
Factor 800*j + 87*j**2 + 15*j**2 + 500 + 64*j**3 + 4*j**4 - 30*j**2 + 288*j**2.
4*(j + 1)*(j + 5)**3
Let p(v) be the third derivative of v**9/15120 - v**7/840 + v**6/360 + v**4/6 + v**2. Let n(h) be the second derivative of p(h). Factor n(l).
l*(l - 1)**2*(l + 2)
Suppose -x - 3*x = -12. Suppose 0 = -2*s + 6*s - 8. Factor -x - 1 - s*k**2 - 4*k + 2.
-2*(k + 1)**2
Let s(o) = 6*o**2 - 9*o - 15. Let k(j) = j**2 - 2*j - 3. Let d(m) = -21*k(m) + 4*s(m). Solve d(f) = 0.
-1
Let h(n) be the third derivative of -n**6/210 + n**5/105 + n**4/42 - 2*n**3/21 - 8*n**2. Factor h(a).
-4*(a - 1)**2*(a + 1)/7
Let x(d) be the second derivative of -d**4/36 + d**3/6 + 5*d. Factor x(z).
-z*(z - 3)/3
Suppose -5*m = -5*s + 2*s + 11, -2*s - 2*m + 2 = 0. Let v(p) be the first derivative of 2/21*p**3 + 8/7*p - 4/7*p**2 + s. Factor v(f).
2*(f - 2)**2/7
Let o(r) be the second derivative of 1/42*r**3 - 7*r + 0*r**2 - 1/140*r**5 + 0 + 0*r**4. Factor o(j).
-j*(j - 1)*(j + 1)/7
Let o(y) be the first derivative of -1/4*y**5 - 1/3*y**3 - 1/2*y**4 - 1/24*y**6 - 5 + 0*y + 0*y**2. Factor o(a).
-a**2*(a + 1)*(a + 2)**2/4
Factor -2/3 - 2*y**3 - 3*y - 13/3*y**2.
-(y + 1)*(2*y + 1)*(3*y + 2)/3
Let v(c) be the third derivative of 1/420*c**7 + 1/672*c**8 - 1/120*c**6 + 0*c + 1/48*c**4 - 1/60*c**5 - c**2 + 0 + 1/12*c**3. Factor v(a).
(a - 1)**2*(a + 1)**3/2
Let v(l) be the second derivative of l**5/12 - 5*l**4/12 + 5*l**3/9 - 14*l. Solve v(y) = 0 for y.
0, 1, 2
Let g(q) be the third derivative of 0 - 1/30*q**3 + 1/60*q**4 + 2*q**2 - 1/300*q**5 + 0*q. Determine i, given that g(i) = 0.
1
Let c(w) be the second derivative of -w**5/30 + w**4/6 + w**2 - 6*w. Let j(y) be the first derivative of c(y). Factor j(h).
-2*h*(h - 2)
Let a(h) be the second derivative of -3*h**5/20 + 11*h**4/4 - 5*h**3 - 22*h. Factor a(s).
-3*s*(s - 10)*(s - 1)
Let s(i) be the first derivative of -i**3/3 - 7. Determine c so that s(c) = 0.
0
Suppose -4*f - 5*t = -5 - 7, 9 = 3*f + 3*t. Determine w, given that 1 - 9/2*w + 4*w**2 - 5*w**4 + 3/2*w**5 + f*w**3 = 0.
-1, 1/3, 1, 2
Determine j so that 0*j + 4/15*j**3 - 2/15*j**4 - 2/15*j**2 + 0 = 0.
0, 1
Let m(a) be the second derivative of 0*a**3 + 0 - 4*a - 1/14*a**7 - 9/20*a**5 + 0*a**2 - 1/4*a**4 - 3/10*a**6. Factor m(c).
-3*c**2*(c + 1)**3
Let r(y) be the third derivative of -1/96*y**4 + 1/240*y**5 + 0 + 0*y + 3*y**2 + 0*y**3. Factor r(m).
m*(m - 1)/4
Let f(n) be the second derivative of n**5/110 - 7*n**3/33 - 6*n**2/11 - 15*n. Let f(w) = 0. What is w?
-2, -1, 3
Let s(m) be the second derivative of -1/5*m**5 - m**4 + 0 - 2*m**3 - 2*m**2 + 8*m. Factor s(b).
-4*(b + 1)**3
Let 25*b**2 + 39*b - 45 - 32*b - 22*b - 5*b**3 = 0. What is b?
-1, 3
Let n = -20/3 - 51. Let v = n - -59. Find q, given that 1/3*q + 0 - 4/3*q**4 + 1/3*q**5 + 2*q**3 - v*q**2 = 0.
0, 1
Let l(z) be the first derivative of -2*z**3/33 + z**2/11 + 7. Let l(v) = 0. What is v?
0, 1
Let p = 12 - 14. Let s(n) = n**5 - 2*n**4 - n**3 + 2. Let y(w) = -w**4 + w**3 - w**2 + 1. Let i(o) = p*y(o) + s(o). What is b in i(b) = 0?
-2, 0, 1
Let f(h) = 9*h**2 + 3*h. Let l(y) be the third derivative of y**5/12 + y**4/12 + 5*y**2. Let t(v) = 4*f(v) - 7*l(v). Factor t(s).
s*(s - 2)
Let v(y) = 5*y**2 - 6*y - 1. Let r(d) = -d**2 + d + 1. Let z(h) = 6*