27. Factor i(p).
-2*p*(3*p + 1)*(5*p - 2)**2/15
Factor -2/3*x + 0 + 1/3*x**3 - 1/3*x**2.
x*(x - 2)*(x + 1)/3
Let k(y) be the first derivative of -2*y**3/15 + 3*y**2/5 - 18. Solve k(h) = 0.
0, 3
Let n(r) be the third derivative of -r**6/1980 - r**5/660 + r**3/6 - r**2. Let b(c) be the first derivative of n(c). Factor b(q).
-2*q*(q + 1)/11
Let z be (-5)/((-30)/3) - 4/8. Factor z*o - 2/7*o**3 - 2/7*o**2 + 0.
-2*o**2*(o + 1)/7
Let z(d) be the first derivative of d**8/504 + d**7/315 - d**6/180 - d**5/90 - 5*d**2/2 + 2. Let k(f) be the second derivative of z(f). Factor k(r).
2*r**2*(r - 1)*(r + 1)**2/3
Let u(a) = -3*a**5 - 4*a**3 - 5*a**2 + 2*a. Let y(z) = 2*z**5 + 2*z**3 + 3*z**2 - z. Let q = -18 + 15. Let w(j) = q*u(j) - 5*y(j). Factor w(i).
-i*(i - 1)**2*(i + 1)**2
Let o be (-116)/60 - ((-210)/(-9))/(-10). Determine a so that -2/5*a**4 + 0*a + 2/5*a**3 + 2/5*a**2 + 0 - o*a**5 = 0.
-1, 0, 1
Let f(z) be the first derivative of z**7/840 - z**6/180 + z**5/120 - z**3/3 - 3. Let l(k) be the third derivative of f(k). Factor l(u).
u*(u - 1)**2
Let g(d) be the third derivative of d**8/2520 + d**7/420 + d**6/270 + d**3/6 - d**2. Let r(k) be the first derivative of g(k). Factor r(x).
2*x**2*(x + 1)*(x + 2)/3
Let w be ((-10)/25*-5)/(4/6). Factor 3/4*t**2 + 5/4*t**w + 1/2*t**4 - 1/4 - 1/4*t.
(t + 1)**3*(2*t - 1)/4
Let a(m) be the second derivative of 1/48*m**4 - 1/24*m**3 + 0 + 3*m - 1/4*m**2. Factor a(f).
(f - 2)*(f + 1)/4
Let -3*b**3 - 574*b - 9*b**2 + 574*b = 0. What is b?
-3, 0
Suppose -6 + 2 = -2*f. Find u such that -1/2*u**f + 0 - 1/2*u = 0.
-1, 0
Let i be (0/(-1) + 0)/(-2). Suppose i*o + 2*o = 0. Factor 7*f - 2*f**3 + o*f + 4 - f.
-2*(f - 2)*(f + 1)**2
Let c(g) be the third derivative of 1/6*g**4 + 0*g + 0 - 1/3*g**3 - 3*g**2 - 1/30*g**5. Solve c(l) = 0 for l.
1
Let b(t) be the third derivative of t**8/252 + 2*t**7/63 + t**6/10 + 7*t**5/45 + t**4/9 + 12*t**2. Determine v so that b(v) = 0.
-2, -1, 0
Suppose 0*k = 4*k - 28. Suppose 3*u + 3*g - 9 = 0, -3*u + 0*u - 5*g + k = 0. Factor b**3 + 2*b**5 - 4*b**3 - u*b**4 + 9*b + 2*b**5 + 2*b**2 - 8*b.
b*(b - 1)**2*(2*b + 1)**2
Let m(q) be the second derivative of -q**8/2240 - q**7/840 + q**4/4 + 3*q. Let t(n) be the third derivative of m(n). Suppose t(k) = 0. Calculate k.
-1, 0
Let t = 14/13 - 29/39. Let t*c**5 - 1/3 + 2/3*c**3 + c**4 - c - 2/3*c**2 = 0. What is c?
-1, 1
Let v(l) = 3*l - 3*l + 11*l**2 - 10 + 3*l - 4*l**2. Let n(c) = 8*c**2 + 3*c - 11. Let s(f) = -4*n(f) + 5*v(f). Solve s(j) = 0 for j.
-2, 1
Let u(h) = -h**3 - 4*h**2 + 4*h - 2. Let r be u(-5). Factor -1/5*o**5 + 0 - 6/5*o**r - 4/5*o**4 - 1/5*o - 4/5*o**2.
-o*(o + 1)**4/5
Let x = -25 - -27. Let u be (x + -2)*2/(-2). Find c such that -6/7*c**3 + 6/7*c**2 - 2/7*c + u + 2/7*c**4 = 0.
0, 1
Let f = -181 - -99. Let d = 580/7 + f. Factor -d*n**3 + 2/7 - 2/7*n**2 + 6/7*n.
-2*(n - 1)*(n + 1)*(3*n + 1)/7
Let r(c) = 4*c**4 - 4*c**2 + 5*c - 5. Let k = -6 + 11. Let i(z) = 6*z**4 - 6*z**2 + 8*z - 8. Let s(d) = k*i(d) - 8*r(d). Factor s(w).
-2*w**2*(w - 1)*(w + 1)
Let q(t) be the first derivative of 0*t - t**2 + 2/3*t**3 + 4. Factor q(m).
2*m*(m - 1)
Let k(s) be the second derivative of 1/2*s**2 + 0 - 1/8*s**4 - 1/12*s**3 + 1/40*s**5 + 3*s + 1/60*s**6. Factor k(u).
(u - 1)**2*(u + 1)*(u + 2)/2
Let i be (7/(-126)*-4)/(6/9). Find c such that i*c**5 - 2/3*c**2 - 1/3*c + 2/3*c**4 + 0*c**3 + 0 = 0.
-1, 0, 1
Factor -2*x**2 - 8 - 6*x - 2*x + 0*x + 0*x.
-2*(x + 2)**2
Let t(v) = 15*v**4 + 25*v**3 - 5*v**2 - 25*v - 5. Let r(f) = 8*f**4 + 12*f**3 - 2*f**2 - 12*f - 3. Let y(g) = -5*r(g) + 3*t(g). Find j, given that y(j) = 0.
-3, -1, 0, 1
Suppose 2*x = -2 - 2. Let i be 1/(-2*x/32). Factor -1 + 19*l**4 - i*l**4 + 6*l**2 - 3*l + 2*l + 14*l**3 + 3*l**5.
(l + 1)**4*(3*l - 1)
Let g(u) be the third derivative of -27*u**8/112 + 39*u**7/70 - u**6/3 + u**5/15 + 3*u**2. Factor g(f).
-f**2*(f - 1)*(9*f - 2)**2
Let t = 1 - -4. Suppose -2*a + 1 = -t. Find v such that -1/4*v + 0*v**2 + 1/4*v**a + 0 = 0.
-1, 0, 1
Let v(d) be the first derivative of 4/9*d**2 + 2/27*d**3 + 8/9*d + 3. Suppose v(l) = 0. What is l?
-2
Suppose 4*b + 8 = -4. Let y(m) = m**2 - 4. Let k be y(b). Solve 0 + 2/7*n**3 + 12/7*n**4 + 0*n + 0*n**2 + 18/7*n**k = 0.
-1/3, 0
Suppose 4*q + 2*s + 3*s = 0, s = 0. Suppose q + 6 = 3*x. Factor 0 + 0*p + 1/4*p**3 - 1/4*p**4 + 0*p**x.
-p**3*(p - 1)/4
Let w(c) be the third derivative of c**7/840 - c**6/120 + c**5/40 - c**4/24 + c**3/24 - 3*c**2. Factor w(r).
(r - 1)**4/4
Suppose 2 + 1 = -2*x + 3*k, k = -5*x - 33. Let i = -6 - x. Factor i + 0*f - 1/4*f**2 + 1/4*f**3.
f**2*(f - 1)/4
Suppose 0 = -6*n + 5*n + 6. Factor b**5 + 2*b**3 + 3*b**5 + 0*b**3 - n*b**5.
-2*b**3*(b - 1)*(b + 1)
Let a(w) be the first derivative of w**6/240 - w**5/40 + w**3/3 - 5*w**2/2 + 6. Let c(p) be the second derivative of a(p). Factor c(k).
(k - 2)**2*(k + 1)/2
Let p be 1/(-2)*(-15)/108. Let d(b) be the third derivative of -1/9*b**3 - 2*b**2 + p*b**4 - 1/60*b**5 + 0 - 1/360*b**6 + 0*b + 1/630*b**7. Factor d(v).
(v - 1)**3*(v + 2)/3
Let 58*r**2 - 56*r**2 - 3*r**3 - 3*r**3 + 12*r + 4*r**3 = 0. Calculate r.
-2, 0, 3
Let r(v) be the second derivative of 3*v**5/40 + v**4/8 - v**3/2 - 7*v. Factor r(f).
3*f*(f - 1)*(f + 2)/2
Let s = 7/328 - 51/33128. Let y = s + 91/505. Solve -y*d - 1/5*d**3 - 2/5*d**2 + 0 = 0.
-1, 0
Let b(g) be the first derivative of 0*g**2 - 1/120*g**6 + 1 - 1/20*g**5 + 0*g - 4/3*g**3 - 1/8*g**4. Let x(n) be the third derivative of b(n). Factor x(i).
-3*(i + 1)**2
Factor -6*c**2 + 5*c**3 + 14 - 40*c**2 - 23*c + 14*c**2.
(c - 7)*(c + 1)*(5*c - 2)
Let f(v) be the second derivative of -11*v**5/100 + v**4/3 - 7*v**3/30 - v**2/5 - 3*v. Factor f(a).
-(a - 1)**2*(11*a + 2)/5
Let z(d) = 4*d**4 + 9*d**3 - 5*d**2 + 5*d - 5. Let x(v) = 6*v**4 + 14*v**3 - 8*v**2 + 8*v - 8. Let w(s) = 5*x(s) - 8*z(s). Solve w(o) = 0.
-1, 0
Factor 25*y**3 - 61*y**3 - 76*y + 6 - 30 - 4*y**4 - 84*y**2.
-4*(y + 1)**3*(y + 6)
Solve 5/6*x + 1/3*x**2 - 1/6*x**5 - 2/3*x**4 + 1/3 - 2/3*x**3 = 0.
-2, -1, 1
Let o(l) be the second derivative of -l**6/165 - l**5/55 - l**4/66 - 8*l. Determine v, given that o(v) = 0.
-1, 0
Let s = 830/7 - 47338/399. Let j = 80/57 + s. Determine i so that -j*i**5 - 2/3*i**2 + 11/3*i**3 - 2/3 - 7/3*i + 4/3*i**4 = 0.
-1, -1/2, 1, 2
Let p(x) be the first derivative of -x**6/1260 - x**5/210 - x**4/84 - 2*x**3/3 - 3. Let b(d) be the third derivative of p(d). Suppose b(h) = 0. Calculate h.
-1
Let d be -2*(-4)/(-44) - (-86)/110. Let t(a) be the first derivative of 2/15*a**3 + 4/5*a - d*a**2 + 2. Factor t(h).
2*(h - 2)*(h - 1)/5
Factor 2*k**2 - 9*k**3 - 7*k**2 + k**2 - 13*k**3.
-2*k**2*(11*k + 2)
Let x(y) = y**3 + y**2 - y. Let b(u) = 27*u**4 + 95*u**3 + 116*u**2 + 55*u + 12. Let n(f) = b(f) - 5*x(f). Factor n(t).
3*(t + 1)**2*(3*t + 2)**2
Let k(g) = 3*g**2 + g**2 - 5*g**2. Let v(m) = -3*m**4 + 18*m**2 - 3. Let p(z) = 12*k(z) + v(z). Factor p(y).
-3*(y - 1)**2*(y + 1)**2
Solve 9*g**2 + 5*g**2 - 2*g**2 - 14*g**3 + 4*g**5 - 2*g**5 = 0 for g.
-3, 0, 1, 2
Factor -1 - 1/2*x**4 - 9/2*x**2 - 5/2*x**3 - 7/2*x.
-(x + 1)**3*(x + 2)/2
Let m(t) = -3*t**3 + 13*t**2 - 10*t - 7. Let s(q) = 3*q**3 - 12*q**2 + 9*q + 6. Let b(f) = -6*m(f) - 7*s(f). Factor b(x).
-3*x*(x - 1)**2
Solve -15 + 11*w**3 + 6*w**3 - 24*w - 9*w**2 - 18*w**3 - 1 = 0.
-4, -1
Let f(l) be the first derivative of l**5/5 + l**4/2 - l**3 - 2*l**2 + 4*l + 11. Factor f(g).
(g - 1)**2*(g + 2)**2
Let m(s) = 3*s**2 - 4*s**2 - 5 + 6*s + 0*s**2. Let z be m(4). What is h in 9*h**2 + 5*h**z - 2*h**2 + 4*h - 2*h = 0?
-1, -2/5, 0
Suppose 3*p + p - 73 = -5*f, -3*f = -3*p + 21. Let 36*x + p*x**2 + 19*x**2 - 46*x**2 - 12 = 0. Calculate x.
2/5, 2
Let k be ((77/91)/(-11))/((-2)/4). Solve 32/13*n**2 - 14/13*n**5 + k*n + 4*n**4 - 68/13*n**3 - 4/13 = 0 for n.
-2/7, 1
Suppose -16 = 3*d + 89. Let k be 14/(-70) + (-17)/d. Factor k*j + 4/7 - 2/7*j**2.
-2*(j - 2)*(j + 1)/7
Let d(m) be the third derivative of m**8/560 - m**7/175 - 3*m**6/200 + m**5/25 + m**4/10 + m**2. Let d(x) = 0. What is x?
-1, 0, 2
Let i(h) be the first derivative of 49*h**6/10 - 357*h**5/25 + 201*h**4/20 + 23*h**3/5 - 24*h**2/5 - 12*h/5 - 24. Find j, given that i(j) = 0.
-2/7, 1
Suppose -p = -3*s + 5, 0 = 5*s + 5*p - p + 20. Let o(a) be the third derivative of 0*a**4 + 0*a**3 + 0 + 1/240*a**5 + 2*a**2 + s*a. Factor 