24. Factor 1/3*n**q - n**3 + n**2 + 0 - 1/3*n.
n*(n - 1)**3/3
Let c be -4*(-2)/4*3. Factor -9*k**4 - 2*k**3 + 4*k**5 - c*k**3 + 13*k**4.
4*k**3*(k - 1)*(k + 2)
Let b(n) = n**3 - n**2. Let o(y) = -3*y**5 + 7*y**3 - 4*y**2. Let z(r) = 2*b(r) + o(r). Factor z(u).
-3*u**2*(u - 1)**2*(u + 2)
Suppose -4*u + 2*l = -12 - 10, 17 = 4*u - l. Let s(p) be the second derivative of 0*p**2 + 1/30*p**4 - 1/15*p**u + 0 - 2*p. Factor s(g).
2*g*(g - 1)/5
Let p(q) be the third derivative of 0*q - 1/15*q**3 + 0 + 0*q**4 - 2*q**2 + 1/150*q**5. Find i such that p(i) = 0.
-1, 1
Let p be 1/(2 + (-1 - 0)). Let k = -1 + p. Determine t, given that k*t + 0 + 1/3*t**2 - 2/3*t**3 = 0.
0, 1/2
Factor -8*w - 16 + 20*w**2 + 24*w + 16*w.
4*(w + 2)*(5*w - 2)
Let d(v) = 6*v + 2. Let a be d(-9). Let y be 2/7 - a/14. Factor -2*c + y*c + 0*c - 2*c**2.
-2*c*(c - 1)
Let o(w) = 7*w**4 + 3*w**3 + 7*w**2 + 3*w + 7. Let x(q) = 8*q**4 + 2*q**3 + 6*q**2 + 2*q + 8. Let s(c) = 6*o(c) - 5*x(c). Factor s(y).
2*(y + 1)**4
Let z(f) be the first derivative of -4/21*f**3 + 0*f**4 - 1/21*f**6 + 4/35*f**5 + 0*f - 5 + 1/7*f**2. Factor z(a).
-2*a*(a - 1)**3*(a + 1)/7
Let c(r) be the first derivative of 6*r - 3 + 9/2*r**2 + r**3. Factor c(d).
3*(d + 1)*(d + 2)
Let g(v) = v**2 + 2*v - 3. Let y be g(1). Let p(j) be the first derivative of y*j - 1/7*j**2 + 0*j**5 + 0*j**3 - 2 - 1/21*j**6 + 1/7*j**4. Solve p(b) = 0 for b.
-1, 0, 1
Let b(f) = -f**3 + f**2 - 1. Let d(q) = 4*q**3 - 7*q**2 - q + 5. Let m(y) = -5*b(y) - d(y). Solve m(l) = 0.
-1, 0
Suppose 0 + 3/4*p + p**2 + 1/4*p**3 = 0. What is p?
-3, -1, 0
Let f(o) = -3*o**2 - 2*o - 6. Suppose -8 = -n - 4. Let c(u) = -n*u**2 - 7 + u**2 - u - u**2. Let q(p) = 4*c(p) - 6*f(p). Solve q(g) = 0.
-2
Let t(s) be the first derivative of -s**4/3 + 16*s**3/9 - 2*s**2 + 18. Factor t(q).
-4*q*(q - 3)*(q - 1)/3
Solve -32/11*a**3 - 16/11*a**2 - 14/11*a**4 + 32/11*a + 32/11 - 2/11*a**5 = 0 for a.
-2, 1
Let k(o) = -o**4 + o**3 - 1. Let m(s) = -10*s**4 + 14*s**3 - 6*s**2 + 2*s - 8. Let h(n) = -8*k(n) + m(n). Factor h(q).
-2*q*(q - 1)**3
Suppose 2*x = -1 + 7. Factor -1/3*b**2 + 1/3 - 1/3*b + 1/3*b**x.
(b - 1)**2*(b + 1)/3
Let t = 8 - 5. Let b be 132/(3/1)*2. Let 0*s**5 - b*s**2 + 82*s + 2*s**5 - 18*s - 17*s**4 + 56*s**t - 16 = 0. What is s?
1/2, 2
Let x(f) = -7*f - 32. Let n be x(-5). Suppose -2 + 49/2*z**4 + 14*z - 45/2*z**2 - 14*z**n = 0. Calculate z.
-1, 2/7, 1
Let i(s) = s**2 - 2. Let l be i(2). Suppose 3*c - l*p + 14 = -6*p, -c + p = -7. Find z, given that z**2 + 2*z**2 - z**2 + c*z = 0.
-1, 0
Let d be (-4)/(-12)*(3 + 3). Factor 0*y**2 + y**3 + 3*y - d*y**2 - 2*y.
y*(y - 1)**2
Suppose -4*v = -5*v + 2. What is z in 7*z + 54*z**5 + 30*z**3 - 16*z**2 - 7*z + v*z**2 - 4*z + 126*z**4 = 0?
-2, -1/3, 0, 1/3
Let r(j) = 2*j**5 + 2*j**4 + 6*j**3 + 6*j**2 - 8*j. Let u(q) = q**5 + q**4 + 6*q**3 + 5*q**2 - 7*q. Let s(t) = 3*r(t) - 4*u(t). Factor s(g).
2*g*(g - 1)**2*(g + 1)*(g + 2)
Let t = -3 - -3. Suppose -2*m = -t*m - 4. Suppose -4/5*f - 1/5*f**m - 4/5 = 0. Calculate f.
-2
Let p(r) = -13*r**3 - 8*r**2 + 11*r. Let u(o) = -20*o**3 - 12*o**2 + 16*o. Let v(m) = 8*p(m) - 5*u(m). Find h such that v(h) = 0.
-2, 0, 1
Let x = 12175 + -839956/69. Let y = x - 4/69. Factor -16/3*v**3 + 0*v - 4/3*v**2 - y*v**4 + 25/3*v**5 + 0.
v**2*(v - 1)*(5*v + 2)**2/3
Let g be (4 - -4)/(-4) - -2. Factor -1 - 2*w**2 + w**3 + w + 1 + g*w**3.
w*(w - 1)**2
Let d(p) be the third derivative of 1/180*p**6 - 1/1008*p**8 - 1/90*p**5 + 0 + 1/630*p**7 - 1/72*p**4 + 3*p**2 + 1/18*p**3 + 0*p. Factor d(z).
-(z - 1)**3*(z + 1)**2/3
Let g(o) = -1. Let a(l) = -l**3 - 4*l**2 + 6*l + 6. Let i(v) = -a(v) - g(v). Let u be i(-5). Factor -3*h**3 - h**5 + 2*h**2 + 5*h**3 - h**4 - h + u*h**5 - 1.
-(h - 1)**2*(h + 1)**3
Let w = 12/13 - 10/39. Solve -v - 1/3*v**2 - w = 0 for v.
-2, -1
Factor 2/3*b**2 + 2 + 8/3*b.
2*(b + 1)*(b + 3)/3
Let r(m) = -m - 2. Let o be r(-7). Suppose -o*w + 2*w = 2*i - 12, w = 2*i - 4. Factor 2*c**3 - c**2 + 0*c**3 + w*c**3.
c**2*(4*c - 1)
Let i(v) be the first derivative of 0*v - 1 + 2*v**2 - 10/3*v**3. Determine g so that i(g) = 0.
0, 2/5
Let f be -8 - -6 - (-2 - 2). Suppose -18*p + 9*p**f - 3/2*p**3 + 12 = 0. What is p?
2
Let p(b) = 2*b**2 - 6*b + 2. Let r(o) = -6*o**2 + 17*o - 4. Let m(c) = 14*p(c) + 4*r(c). Determine l, given that m(l) = 0.
1, 3
Let j(l) be the second derivative of 1/5*l**2 + 5*l - 1/100*l**5 - 1/30*l**4 + 0 + 1/30*l**3. Factor j(u).
-(u - 1)*(u + 1)*(u + 2)/5
Let n = -1331 + 4087/3. Let m = n - 461/15. Find v, given that 6/5*v**2 + 0 + 0*v + 3/5*v**3 - m*v**4 = 0.
-1, 0, 2
Let l = -5 - -7. Let t**l + 0*t**4 - 2*t**3 + 2*t**4 - 4*t**4 + 3*t**4 = 0. Calculate t.
0, 1
Determine t, given that 6*t**3 - 3 + 0*t**4 + 12*t + 6*t**3 - 3*t**4 - 18*t**2 = 0.
1
Suppose m - 2*z = -5 - 19, -m = -z + 19. Let b be (-35)/50*8/m. Determine i so that -b*i**3 - 2/5*i**2 + 2/5*i + 2/5 = 0.
-1, 1
Suppose -10*w + 1 + 19 = 0. Factor 2/3*o**4 + 8/3*o + 8/3 - 4/3*o**3 - w*o**2.
2*(o - 2)**2*(o + 1)**2/3
Let g(i) be the third derivative of 0 + 3*i**2 + 1/525*i**7 + 1/30*i**4 - 4/75*i**5 + 1/40*i**6 + 0*i + 0*i**3 - 1/336*i**8. What is d in g(d) = 0?
-2, 0, 2/5, 1
Suppose -1/2*w + 1/4*w**2 + 0 = 0. What is w?
0, 2
Factor -4*u**3 + 2*u**3 - 10*u**2 - 2 + 20*u**2 - 14*u + 8.
-2*(u - 3)*(u - 1)**2
Let q(f) be the third derivative of f**5/60 + f**4/6 - 2*f**3 - 28*f**2. Solve q(b) = 0 for b.
-6, 2
Determine g, given that 4/5 - 8/5*g + 4/5*g**2 = 0.
1
Let d(p) be the third derivative of -p**5/210 - p**4/84 + 2*p**3/21 + 3*p**2. Determine r, given that d(r) = 0.
-2, 1
Let c(z) = -z**2 - 5*z - 2. Let p be c(-4). Let l(j) be the third derivative of -2*j**p + 5/12*j**5 + 0 + 2/3*j**3 + 5/6*j**4 + 0*j. Solve l(o) = 0.
-2/5
Let u(z) = -2*z**3 + 14*z**2 - 12. Let h(d) = d**3 - 13*d**2 + 12. Let w(f) = -5*h(f) - 4*u(f). Let w(i) = 0. Calculate i.
-2, 1
Factor -2 + 4/3*m + 2/3*m**2.
2*(m - 1)*(m + 3)/3
Let b(f) = f + 7. Let h be b(-5). Factor -2*w**4 - 4*w**4 - 4*w**3 - 5*w**3 + 5*w**3 - h*w**5.
-2*w**3*(w + 1)*(w + 2)
Let 92/7*f**3 + 66/7*f**4 - 16/7*f + 0 + 24/7*f**2 + 2*f**5 = 0. Calculate f.
-2, -1, 0, 2/7
Let t be 3/48*((-13)/(-3) - 3). Let w(h) be the second derivative of 0 + h + 2*h**2 + 2/3*h**3 + t*h**4. Find j, given that w(j) = 0.
-2
Suppose a + a = 0. Let u(o) be the third derivative of 0*o + 0*o**7 + 0*o**4 - 1/1176*o**8 + 0*o**3 + 1/420*o**6 + 0 + 3*o**2 + a*o**5. Factor u(j).
-2*j**3*(j - 1)*(j + 1)/7
Let t(v) be the first derivative of v**7/1260 - v**6/135 + v**5/45 + 2*v**3/3 + 2. Let c(b) be the third derivative of t(b). Determine u so that c(u) = 0.
0, 2
Let o = 1/28 + 47/252. Factor -o*a**5 - 8/9*a**4 + 0 + 0*a - 10/9*a**3 - 4/9*a**2.
-2*a**2*(a + 1)**2*(a + 2)/9
Let h be 25/(-14) + 2/1. Let b = 1/14 + h. Suppose b - 2/7*z**2 + 0*z = 0. Calculate z.
-1, 1
Determine b, given that 195*b - 219*b**2 - 5*b**4 + 74*b**2 + 35*b**3 + 10*b**3 - 90 + 0*b**3 = 0.
1, 2, 3
Let y(r) = 6*r**2 - 2*r - 8. Let f(a) = 17*a**2 - 6*a - 23. Let z(v) = 4*f(v) - 11*y(v). Suppose z(u) = 0. What is u?
-1, 2
Let y = 20 + -17. Determine c so that 2*c**y - 6 - 8*c + 1 + 5 = 0.
-2, 0, 2
Let y(k) be the first derivative of 2 + 2/3*k + 2/15*k**5 + 0*k**4 + 0*k**2 - 4/9*k**3. Find p such that y(p) = 0.
-1, 1
Suppose 3*r - 15 = -15. Find m, given that -1/4*m**3 + r*m**2 + m**4 + 0 + 0*m = 0.
0, 1/4
Let d(x) be the second derivative of x**7/42 - x**5/5 - x**4/6 + x**3/2 + x**2 - 13*x. Factor d(n).
(n - 2)*(n - 1)*(n + 1)**3
Let j = 33/74 + 2/37. Factor -4*s + 8*s**2 + j.
(4*s - 1)**2/2
Let b = 1378/5 + -275. Factor -6/5*p**2 - b*p**3 + 6/5 + 3/5*p.
-3*(p - 1)*(p + 1)*(p + 2)/5
Let u(h) be the third derivative of -1/360*h**6 - 1/1260*h**7 + 0 - h**2 - 1/360*h**5 + 0*h**4 + 0*h**3 + 0*h. Suppose u(b) = 0. What is b?
-1, 0
Let n = -121/12 - -31/3. Let y be (-6)/8*4/(-6). Determine d so that y*d + 0 - 3/4*d**2 + n*d**3 = 0.
0, 1, 2
Suppose -38 = -3*p + p + s, -5*p + 3*s + 97 = 0. Suppose -2*r - 4*v + 13 = -3*v, 0 = 4*r - v - p. Factor 0*i - 6 - 3*i**2 + r*i + 5*i - i.
-3*(i - 2)*(i - 1)
Let n = 398 + -395. Factor 2*k**2 - 2/3*k**4 - 2/3*k**n + 4/3 + 10/3*k.
-2*(k - 2)*(k + 1)**3/3
Suppose 2 = 4*c - 5*a - 10, 0 = -3*c - a + 9. Suppose c*v + 2*v = 15. Factor -2*f + 4*f**3 - 3*f**4 + f**4 + 2*f**2 - 2*f**v.
-2*f*(f - 1)**2*(f + 1)
Factor 0 + 0*v - 2