- 28. Factor o(k).
-3*k*(k + 7)/7
Factor 0*k**3 + 9*k**2 - 9*k**3 - 6*k**2 + 4*k - 6 + 5*k + 3*k**4.
3*(k - 2)*(k - 1)**2*(k + 1)
Let b(t) = -8*t**2 - 20*t - 32. Let j(n) = -17*n**2 - 39*n - 63. Let s(w) = -9*b(w) + 4*j(w). Let s(k) = 0. Calculate k.
-3
Let j(u) = -u**2 + 4*u + 0 + 1 + 0*u**2 + 2*u**2. Let i(s) = -4*s - 1. Let q(g) = 6*i(g) + 5*j(g). Factor q(h).
(h - 1)*(5*h + 1)
Let c(j) = 9*j**4 + 6*j**3 + 4*j**2 + j - 1. Let r = -13 - -7. Let n(i) = 10*i**4 + 5*i**3 + 3*i**2 + i - 1. Let z(o) = r*c(o) + 5*n(o). Factor z(a).
-(a + 1)**3*(4*a - 1)
Let j = 159 - 156. Factor 1/3*p**3 + j*p - 2*p**2 + 0.
p*(p - 3)**2/3
Let i(k) be the first derivative of 3*k**4/4 + k**3 + 2. Factor i(p).
3*p**2*(p + 1)
Let s = 0 - -1. Suppose -y = -s - 1. What is c in -y*c - c - 3*c**2 + 8 - c**3 - 9 = 0?
-1
Let t(b) be the first derivative of 53/12*b**4 + 4/3*b + 7/18*b**6 - 8 + 0*b**2 - 11/5*b**5 - 31/9*b**3. Find z such that t(z) = 0.
-2/7, 1, 2
Let q(b) be the first derivative of -14*b**3/5 + 13*b**2/5 - 4*b/5 + 1. Determine d, given that q(d) = 0.
2/7, 1/3
Let w(v) be the first derivative of -1 - 1/16*v**4 - 1/20*v**5 + 1/8*v**2 + 0*v + 1/12*v**3. Solve w(s) = 0 for s.
-1, 0, 1
Let p(d) be the third derivative of -d**5/20 + 3*d**4/8 - d**3 - 6*d**2. Factor p(l).
-3*(l - 2)*(l - 1)
Suppose -o + 2*y + 20 = -y, 0 = o + 3*y - 44. Let n = o + -29. What is t in -1/4*t**n + 1/4*t + 1/4 - 1/4*t**2 = 0?
-1, 1
Let v(a) be the first derivative of -3*a - 1/7*a**2 + 1/42*a**4 - 3 - 1/21*a**3 + 1/70*a**5. Let y(k) be the first derivative of v(k). What is s in y(s) = 0?
-1, 1
Let o(t) = t**3 - 18*t**2 + 18*t - 20. Let i be o(17). Let m be (1/i)/(1/(-4)). Suppose -m - 2/3*c**2 + 2*c = 0. Calculate c.
1, 2
Let y(w) be the first derivative of 1/4*w**2 - 1/8*w**4 - 1/6*w**3 + 0*w + 1/10*w**5 + 6. Factor y(k).
k*(k - 1)**2*(k + 1)/2
Let n be (-2)/2 - 54/(-42). Factor -4/7 + 2/7*f**2 + n*f.
2*(f - 1)*(f + 2)/7
Let c = 422 - 6314/15. Solve 2/15*x**3 - 8/15*x + 4/15*x**2 - c = 0 for x.
-2, 2
Let l = -80 + 161/2. Factor l*a**3 - 1/2*a**2 + 0 + 0*a.
a**2*(a - 1)/2
Let s(u) be the third derivative of u**7/1680 - u**6/288 + u**5/120 - u**4/96 + u**3/3 + 4*u**2. Let f(y) be the first derivative of s(y). Factor f(k).
(k - 1)**2*(2*k - 1)/4
Factor 1/7*y**2 + 0*y + 0 - 1/7*y**3.
-y**2*(y - 1)/7
Let r(w) be the second derivative of -1/24*w**4 + 4*w - 1/4*w**2 + 0 - 1/6*w**3. Factor r(o).
-(o + 1)**2/2
Factor -1/7*o**5 + 0*o**2 + 0*o - 1/7*o**3 - 2/7*o**4 + 0.
-o**3*(o + 1)**2/7
Let i = 0 - -4. Suppose 0 = -i*y + 1 + 19. Solve v**3 - 4*v**4 + y*v**4 + 0*v**4 = 0.
-1, 0
Factor 2/3*v**3 + 0*v - v**2 + 1/3*v**4 + 0.
v**2*(v - 1)*(v + 3)/3
Let m(w) = 4*w**3 + 6*w**2 - 12*w + 8. Let h(x) = 5*x**3 + 6*x**2 - 12*x + 8. Let y(j) = 5*h(j) - 6*m(j). Suppose y(d) = 0. What is d?
2
Suppose 0 = -6*s - 7 + 19. Factor 1/3 + 2/3*z - 1/3*z**4 - 2/3*z**3 + 0*z**s.
-(z - 1)*(z + 1)**3/3
Let k(i) be the second derivative of 2*i**7/21 + 4*i**6/3 + 37*i**5/5 + 20*i**4 + 24*i**3 + 2*i. Factor k(p).
4*p*(p + 2)**2*(p + 3)**2
Suppose -3*f = 5*r + 20, 7*f - 3*f - 2*r = 8. Factor -1/2*c**5 - 1/2*c**3 + 0*c + 0 - c**4 + f*c**2.
-c**3*(c + 1)**2/2
Let k(g) be the second derivative of -g**4/12 + g**2/2 + 18*g. Factor k(l).
-(l - 1)*(l + 1)
Let o(r) be the third derivative of r**6/120 - 2*r**5/15 - r**4/24 + 11*r**3/6 + r**2. Let v be o(8). Solve v - 1 + 6 + 2*p**2 + 8*p = 0 for p.
-2
Let m(r) be the third derivative of r**5/30 - r**4/16 + 6*r**2. Factor m(n).
n*(4*n - 3)/2
Let o(a) be the first derivative of 8*a**4/11 - 112*a**3/33 - 31*a**2/11 - 8*a/11 + 1. Suppose o(t) = 0. What is t?
-1/4, 4
Let u(l) = -8*l**3 - 2*l**2 - 3*l. Let w(d) = 25*d**3 + 5*d**2 + 10*d. Let y(a) = 10*u(a) + 3*w(a). Let y(t) = 0. Calculate t.
-1, 0
Let g(p) be the second derivative of -4*p + 1/100*p**5 + 1/20*p**4 - 2/5*p**2 + 0 + 0*p**3. Factor g(y).
(y - 1)*(y + 2)**2/5
Factor 0 - 2/9*m**3 + 0*m**2 + 2/9*m.
-2*m*(m - 1)*(m + 1)/9
Determine r so that 5*r - 7*r**3 - r**3 - 56*r**5 - 44*r**4 - 5*r = 0.
-1/2, -2/7, 0
Factor 3/7*a**3 - 3/7*a**2 + 0*a + 0.
3*a**2*(a - 1)/7
Let l(y) be the third derivative of y**6/180 - 2*y**5/45 + y**4/9 + 3*y**2. Factor l(k).
2*k*(k - 2)**2/3
Suppose 2*n + u = 3, 12 = -5*n + n + 4*u. Let z = -2/293 + 604/2637. Find w, given that n*w + 2/9*w**4 + z*w**2 - 4/9*w**3 + 0 = 0.
0, 1
Let w(i) = 55*i**2 + 125*i - 55. Let c(p) = 4*p**2 + 9*p - 4. Let t(x) = 85*c(x) - 6*w(x). Factor t(j).
5*(j + 2)*(2*j - 1)
Let m(j) be the third derivative of -j**6/360 + j**5/60 - j**4/24 + j**3 + 5*j**2. Let p(b) be the first derivative of m(b). Find k, given that p(k) = 0.
1
Let x be (-3)/12 - 29/(-4). Factor 5*l - 3*l**2 + 0*l**2 + 2*l**3 + x*l**2 + 2 - l**3.
(l + 1)**2*(l + 2)
Let p(k) = -4*k**4 - 7*k**3 - 16*k**2 - k - 7. Let a(o) = -3*o**4 - 5*o**3 - 11*o**2 - o - 5. Let u(y) = 7*a(y) - 5*p(y). Factor u(i).
-i*(i - 1)**2*(i + 2)
Let f be 6 + 4/(-6)*3. Factor -112*x**3 - 8*x - 26*x**3 - 12*x**5 - 56*x**2 - 126*x**f - 14*x**4 - 38*x**5.
-2*x*(x + 1)**2*(5*x + 2)**2
Let d be (-6)/1 + (1368/(-27))/(-8). Factor 0 + d*l**3 + 1/3*l**2 + 0*l.
l**2*(l + 1)/3
Let l(m) be the third derivative of -m**8/10080 + m**7/1260 - m**5/45 - m**4/6 + 2*m**2. Let x(b) be the second derivative of l(b). Let x(n) = 0. Calculate n.
-1, 2
Let w(z) be the third derivative of z**8/120960 - z**7/30240 - z**6/2160 - z**5/20 - 2*z**2. Let f(r) be the third derivative of w(r). Factor f(l).
(l - 2)*(l + 1)/6
Factor 1568/3*t**3 - 128/3 - 4928/3*t**2 - 1472/3*t + 48020/3*t**5 + 35672/3*t**4.
4*(5*t - 2)*(7*t + 2)**4/3
Let f be ((-18)/(-14) - 2/7)*0. Solve f - 1/2*o**2 + 0*o - 1/2*o**4 + o**3 = 0.
0, 1
Determine i, given that 3*i - 2*i + 0*i - 9*i**2 + 5*i + 3*i**3 = 0.
0, 1, 2
Factor 2/5*c**3 + 4/5*c**2 - 2/5*c - 4/5.
2*(c - 1)*(c + 1)*(c + 2)/5
Let o(t) be the first derivative of t**7/525 - t**6/150 + t**5/150 - 2*t**2 - 1. Let i(m) be the second derivative of o(m). Let i(s) = 0. Calculate s.
0, 1
Let l be 5/(-6)*4/(-10). Find i, given that 1/3*i**2 + l*i - 2/3 = 0.
-2, 1
Let c be 1 - (1 - (2 - 3)). Let f be 5 - 2 - (c + 2). Determine o so that -2*o**4 - 4*o**3 + o**4 + 3*o**3 - o**f + o + 2*o**4 = 0.
-1, 0, 1
Let w(f) be the second derivative of -8*f**7/7 - 4*f**6/5 + 69*f**5/20 + 7*f**4/4 - 7*f**3/2 + 3*f**2/2 + 9*f. Let w(m) = 0. Calculate m.
-1, 1/4, 1
Let y(h) be the first derivative of -5*h**6/6 + h**5 + 5*h**4/4 - 5*h**3/3 - 9. Let y(c) = 0. What is c?
-1, 0, 1
Let y(t) = 4*t**2 + 2*t + 80. Let q(h) = -h**2 - h - 27. Let x(r) = 20*q(r) + 6*y(r). Factor x(u).
4*(u - 5)*(u + 3)
Suppose 0 = -6*n + 10 + 2. Let i(p) be the second derivative of n*p + 8/7*p**2 + 1/105*p**6 - 20/21*p**3 + 0 - 1/10*p**5 + 3/7*p**4. Factor i(d).
2*(d - 2)**3*(d - 1)/7
Let t = 229/705 - -2/235. Determine r so that -4/3*r**2 + r + t = 0.
-1/4, 1
Let r(b) be the first derivative of 5*b**4/16 + 5*b**3/4 + 5*b**2/4 + 7. Find t, given that r(t) = 0.
-2, -1, 0
Let h = 11 + -2. Let r be (-6 + h)*2/18. Solve -1/3*k**3 + 0*k**2 + 0 - r*k**5 + 2/3*k**4 + 0*k = 0 for k.
0, 1
Let p be 56/(-24) - (-5 - (1 + -3)). Solve p*y + 0*y**2 - 2/3*y**3 + 0 = 0.
-1, 0, 1
Let s be (-6)/(-3) + 1*(-12)/9. Solve 2/3*m**3 + 0 + 2/9*m**4 - 2/9*m**2 + 0*m - s*m**5 = 0.
-1, 0, 1/3, 1
Let z = -3 - -6. Let h = 5 - z. Suppose p + 5*p**2 - h*p**2 - 2*p**2 = 0. Calculate p.
-1, 0
Find x such that 9*x**5 - 4*x**5 + 0*x**5 - 43*x**4 + 33*x**4 + 5*x**3 = 0.
0, 1
Let s(b) be the third derivative of b**8/336 - 2*b**7/105 + b**6/24 - b**5/30 - 16*b**2. Suppose s(g) = 0. What is g?
0, 1, 2
Suppose -4 + 9 - 2 + 2*z**2 - 5 = 0. What is z?
-1, 1
Let f = 6 + -8. Let m = 2 + f. Factor 9*x + 12*x**3 + 5*x**2 + 2*x**5 - 8*x**4 - 13*x**2 + m*x**5 - 7*x.
2*x*(x - 1)**4
Find v, given that 0*v**2 + 0*v + 3/5*v**5 + 0*v**4 - 3/5*v**3 + 0 = 0.
-1, 0, 1
Suppose 0 = -5*j + 7 + 3. Let g be 287/(-63) - (-28)/4. What is l in j*l**2 - g*l + 4/9 = 0?
2/9, 1
Suppose u - 35 = -5*f + 6*u, -5*u = 5. Let r(x) be the third derivative of 0*x**3 + 0 + 0*x**5 + 1/180*x**f + 2*x**2 + 0*x - 1/36*x**4. Factor r(g).
2*g*(g - 1)*(g + 1)/3
Let x be -1 + 4 + 4664/55. Let f = x + -87. Let -4/5*a + f*a**3 - 2/5*a**2 + 2/5 = 0. What is a?
-1, 1/2, 1
Let d(i) = i**5 - i**3 - i**2 + i + 1. Let c(j) = j**5 + 8*j**4 + 7*j**3 + j**2 - j - 1. Let g(u) = -c(u) - d(u). S