 - 4. Factor -2/9*f**2 + 2/9*f**4 + 2/9*f**d - 2/9*f + n.
2*f*(f - 1)*(f + 1)**2/9
Let t(p) be the first derivative of 3*p**5/35 + 3*p**4/28 + 1. Factor t(o).
3*o**3*(o + 1)/7
Suppose 4 + 9*b**2 + 1/2*b**4 - 10*b - 7/2*b**3 = 0. What is b?
1, 2
Let a = 11 - 6. Let p(x) be the third derivative of x**2 - 1/120*x**a - 1/240*x**6 + 0 + 1/48*x**4 + 1/12*x**3 + 0*x. Factor p(c).
-(c - 1)*(c + 1)**2/2
Let t(z) be the third derivative of z**7/1890 - z**6/1080 + 18*z**2. Factor t(j).
j**3*(j - 1)/9
Let p(i) be the third derivative of -i**9/13608 + i**8/3780 - i**7/3780 - i**3/3 + 3*i**2. Let w(l) be the first derivative of p(l). Factor w(z).
-2*z**3*(z - 1)**2/9
Find b, given that -4*b**2 - b**2 - b**4 + 8*b**2 - 2*b**4 - 4*b**5 - b + 5*b**3 = 0.
-1, 0, 1/4, 1
Let i(o) be the first derivative of o**5/60 + o**4/24 - 3*o**2/2 - 1. Let m(h) be the second derivative of i(h). Factor m(c).
c*(c + 1)
Solve 2/5*d**2 - 2/5*d + 0 = 0.
0, 1
Let x = 1/16 - -27/80. Factor -6/5*s + 6/5*s**2 + x - 2/5*s**3.
-2*(s - 1)**3/5
Let r(x) be the second derivative of -x**4/3 - 8*x**3/3 + 10*x**2 + 35*x. Factor r(t).
-4*(t - 1)*(t + 5)
Factor l - 3/2 + 1/2*l**2.
(l - 1)*(l + 3)/2
Factor -9/5 + 6/5*c**3 - 24/5*c - 9/5*c**2.
3*(c - 3)*(c + 1)*(2*c + 1)/5
Let s(x) be the third derivative of -x**6/360 - x**5/120 - x**3/2 + 2*x**2. Let p(z) be the first derivative of s(z). Factor p(g).
-g*(g + 1)
Let a(c) = 3*c**3 - 7*c**2 + 3*c + 7. Let q(i) = -i**3 + i**2 + 1. Let k(r) = 2*a(r) + 4*q(r). Factor k(p).
2*(p - 3)**2*(p + 1)
Suppose 4*c - 17 = 15. Factor -c*k**3 + 2 - 15*k + 5*k**3 + 5 + 12*k**2 - 1.
-3*(k - 2)*(k - 1)**2
Factor -6/5 + 8/5*j - 2/5*j**2.
-2*(j - 3)*(j - 1)/5
Solve -2*s**3 - 2*s**5 + 4*s**5 + s**4 - 4*s**2 + 2*s**2 + s**4 = 0.
-1, 0, 1
Let g(a) be the second derivative of -a**6/60 + a**5/20 + a**4/24 - a**3/6 + 15*a. Suppose g(d) = 0. What is d?
-1, 0, 1, 2
Let t(d) be the first derivative of d**6/135 - d**5/90 - d**4/54 + d**3/27 - 2*d - 3. Let n(v) be the first derivative of t(v). Solve n(x) = 0 for x.
-1, 0, 1
Let g(o) be the second derivative of 1/42*o**4 + 0 + 1/21*o**3 + 2*o - 1/7*o**2 - 1/70*o**5. Determine z, given that g(z) = 0.
-1, 1
Let x(v) be the second derivative of -v**7/21 + 2*v**6/15 - v**4/3 + v**3/3 - v. Factor x(y).
-2*y*(y - 1)**3*(y + 1)
Let x(t) be the third derivative of -t**5/40 - 3*t**4/16 + t**3 + 26*t**2. Factor x(b).
-3*(b - 1)*(b + 4)/2
Let z be (2 + (-6)/(-6) - 3)/3. Factor 1/3*w**3 + 0*w**2 + 0 + z*w.
w**3/3
Let i be (-14)/(-8) - 1/(-4). Find q, given that 53 - 18*q**3 - 26*q**4 - 2*q**i - 53 - 8*q**5 + 2*q + 4*q**4 = 0.
-1, 0, 1/4
Let o(n) = -n - 7. Let v = -11 - -1. Let r be o(v). Suppose 1/4*m**4 + 1 - 1/2*m**r - 3/4*m**2 + m = 0. What is m?
-1, 2
Let p(t) = t**3 - 4*t**2 - 9*t + 7. Let i be p(6). Determine w, given that w + 29*w**3 - i*w**3 + 10*w**4 - w = 0.
-2/5, 0
Let b(z) be the third derivative of z**8/10080 + z**7/1260 + z**6/360 - z**5/15 - 4*z**2. Let c(g) be the third derivative of b(g). Factor c(a).
2*(a + 1)**2
Let m(j) be the second derivative of j**6/120 - j**5/80 - j**4/48 + j**3/24 + 4*j. Factor m(z).
z*(z - 1)**2*(z + 1)/4
Solve -1/2*s**2 + 0*s + 2 = 0.
-2, 2
Let c(j) be the third derivative of -1/24*j**4 + 0*j**3 + 0 + 4*j**2 + 0*j - 1/60*j**5. Factor c(o).
-o*(o + 1)
Let g(j) be the first derivative of 5*j**3/9 + 9*j**2/2 + 10*j/3 - 1. Factor g(i).
(i + 5)*(5*i + 2)/3
Let z(y) be the second derivative of 0 + 3/7*y**2 - 6*y - 1/42*y**4 - 2/21*y**3. Factor z(l).
-2*(l - 1)*(l + 3)/7
Let h = -15 + 137/9. Factor 4/9 + 2/9*d - h*d**2.
-2*(d - 2)*(d + 1)/9
Factor -162 - 30*b**2 + 142 + 38*b + 5*b**3 + 7*b.
5*(b - 4)*(b - 1)**2
Let y(v) = -v**3 + v**2 + v + 1. Let d(t) be the third derivative of -t**6/60 + t**5/60 + t**4/6 + t**3/2 + 5*t**2. Let l(z) = -d(z) + 3*y(z). Factor l(k).
-k*(k - 1)**2
Let s = 6 - 14. Let v(r) = r**3 + 7*r**2 - 10*r - 12. Let n be v(s). What is b in 28*b**5 + 36*b**3 - 6*b + 62*b**n + 2*b + 0*b - 2*b**2 = 0?
-1, -1/2, 0, 2/7
Let y = -6 + 12. Factor -1 + f**2 + y*f + 6 + 4.
(f + 3)**2
Let t(w) be the third derivative of -w**5/36 - w**4/72 + 2*w**3/9 - 4*w**2. Factor t(p).
-(p + 1)*(5*p - 4)/3
Let b(h) = -2*h**5 - 6*h**4 - 2*h**3 + 6*h**2 - 4*h + 4. Let j(a) = a**5 + a**4 - a**2 + a - 1. Let m(i) = -b(i) - 4*j(i). Factor m(y).
-2*y**2*(y - 1)**2*(y + 1)
Let c(k) = k**5 - 4*k**4 + 10*k**3 + 5*k. Let n(f) = 2*f**5 - 8*f**4 + 19*f**3 - f**2 + 9*f. Let h(o) = 7*c(o) - 4*n(o). Find j, given that h(j) = 0.
0, 1
Let r = -1 - 0. Let f be 1/(r/9*-3). Factor -3*p**2 + 18*p + 2 + p**2 - 14*p - 4*p**f.
-2*(p - 1)*(p + 1)*(2*p + 1)
Solve 37820 + 3308 - 240*p**3 + 109*p**4 - 104*p**4 + 62552 + 4320*p**2 - 34560*p = 0 for p.
12
Determine p so that 24 + 2*p**2 - 25*p**2 - 7*p**2 + 3*p + 9*p**3 + 9*p = 0.
-2/3, 2
Let b = 32 + -21. Factor b*a**5 + 52*a**4 + a**5 + 36*a**3 - 8*a - 4*a**2 + 8*a**5.
4*a*(a + 1)**3*(5*a - 2)
Let y(q) = -5*q - 88. Let z be y(-18). Let i(k) be the first derivative of 6*k - z + k**3 - 9/2*k**2. Factor i(w).
3*(w - 2)*(w - 1)
Factor -1/3*r**2 + r + 0 + 1/3*r**4 - r**3.
r*(r - 3)*(r - 1)*(r + 1)/3
Let y(t) be the third derivative of t**6/660 + 2*t**5/165 + 5*t**4/132 + 2*t**3/33 + 9*t**2. Find x, given that y(x) = 0.
-2, -1
Let p(z) = 7*z**4 - 11*z**3 + 31*z**2 - 25*z + 2. Let v be (2 + -8)*(-4)/6. Let j(k) = k**4 + k**3 + k**2 - k - 1. Let r(x) = v*j(x) - p(x). Factor r(h).
-3*(h - 2)*(h - 1)**3
Suppose -z - 5 = -4*b - 0*b, 5 = -3*b - z. Suppose b - 1/2*t**2 - 3/2*t**3 - 3/2*t**4 - 1/2*t**5 + 0*t = 0. What is t?
-1, 0
Suppose 5 = 2*z - 7. Let a = z + -3. Factor 5 + h**5 + a*h**4 - 5 + 3*h**3 + h**2.
h**2*(h + 1)**3
Solve -2*m + 2*m**2 - 2/3*m**3 + 2/3 = 0.
1
Suppose -3*n = -5*s + 9, -5*n - 3*s + 4*s = -7. Determine v, given that 0 + 8/5*v + 2/5*v**3 + 8/5*v**n = 0.
-2, 0
Let y(b) be the second derivative of -3*b + 0*b**2 - 1/27*b**3 + 0*b**5 + 1/27*b**4 + 0 + 1/189*b**7 - 2/135*b**6. Factor y(h).
2*h*(h - 1)**3*(h + 1)/9
Let x = 182 + -1087/6. Suppose 3/2 - 1/6*b**3 - x*b**2 - 1/2*b = 0. Calculate b.
-3, 1
Let x(c) = 14*c**3 + 6*c**2 - 2*c - 9. Suppose -2 - 2 = r. Let p = 2 + r. Let s(g) = -g**3 - g**2 + 1. Let n(a) = p*x(a) - 18*s(a). Find m, given that n(m) = 0.
-2/5, 0, 1
Suppose -o + 4*o + 2*o = 0. Let r(n) be the second derivative of o + n + 1/30*n**5 + 1/18*n**4 - 2/9*n**3 + 0*n**2. Let r(y) = 0. What is y?
-2, 0, 1
Let t be (2 - 2)*9/(-18). Let i(n) be the first derivative of t*n + 3 - 4/3*n**3 - n**2. Factor i(d).
-2*d*(2*d + 1)
Suppose -p + 0 = -2. Let j be (-2)/(5/(-2) + p). Factor -j*u**3 + 8*u + 0*u**2 - 4*u**3 + 2*u**2 + 1 - 3.
-2*(u - 1)*(u + 1)*(4*u - 1)
Suppose 4*g + 5 = k - g, -3*g - 3 = -5*k. Factor 3/2*o - 3/2*o**2 + k.
-3*o*(o - 1)/2
Let y be (2 - (-11)/(-4))/((-60)/40). Factor y*h**2 - 3/2*h + 1.
(h - 2)*(h - 1)/2
Let u = -199 + 9553/48. Let h(v) be the second derivative of 0 + 1/12*v**3 + 0*v**2 - 19/120*v**6 - 3/16*v**5 - 2*v - u*v**4 - 1/24*v**7. Factor h(d).
-d*(d + 1)**3*(7*d - 2)/4
Let n(r) be the first derivative of 2 - 4/7*r + 3/7*r**2 - 2/21*r**3. Factor n(i).
-2*(i - 2)*(i - 1)/7
Let m(l) = -5*l**4 - 80*l**3 - 384*l**2 - 560*l - 245. Let t(b) = -b**2. Let f(p) = -m(p) - 6*t(p). Factor f(s).
5*(s + 1)**2*(s + 7)**2
Let o(r) be the second derivative of r**6/15 - r**4/6 - 2*r. Let o(v) = 0. What is v?
-1, 0, 1
Suppose 2*a + 21 = w - a, 0 = 3*a + 12. Suppose 0 = 3*z - w. Factor -16/3*t**2 - 16/9*t**z - 64/9*t - 32/9 - 2/9*t**4.
-2*(t + 2)**4/9
Let m(s) = -4*s**2 + 4. Let l(j) = 8*j**2 - 8. Let y(h) = 4*l(h) + 7*m(h). Factor y(g).
4*(g - 1)*(g + 1)
Determine l so that -5*l**2 + 3*l**4 - 12 - 36*l - 4 - 8 - l**2 + 9*l**3 = 0.
-2, -1, 2
Let x(v) = 2*v + 16. Let j be x(-7). Factor 0*f**2 + j - 4*f + 8 - 2 - 4*f**2.
-4*(f - 1)*(f + 2)
Let v(o) be the third derivative of o**7/735 - o**6/70 + 3*o**5/70 - 26*o**2. Let v(k) = 0. Calculate k.
0, 3
Suppose 0 = k + 2*k - 6. Suppose v**k + 20*v - 20*v = 0. Calculate v.
0
Suppose -c = -6*c + 150. Let o be ((-8)/c)/(4/(-10)). Factor -o*l + 2/3*l**3 - 2/3*l**2 + 2/3.
2*(l - 1)**2*(l + 1)/3
Let t = 0 - -4. What is j in -5*j**3 - 2*j**2 + 5*j**5 + 2*j + 2*j**t - 2*j + 0*j**2 = 0?
-1, -2/5, 0, 1
Factor -y + y**2 + y - y - 2*y**2.
-y*(y + 1)
Suppose 8*i = 6*i + 5*b + 17, 4*i + 5*b + 11 = 0. Factor 1/2*d**2 + 3/2*d + i.
(d + 1)*(