20). Factor -1/5*c + 0 + 1/5*c**4 - 1/5*c**f + 1/5*c**3.
c*(c - 1)*(c + 1)**2/5
Suppose 0 = 3*g - 5*l + 40, 4*g - 4*l = 8*g. Let w(i) = i**2 + 6*i + 7. Let m be w(g). Find j such that -1/2 + 7/4*j**3 + 11/4*j - 4*j**m = 0.
2/7, 1
Let j = 20 - 18. Let 3/2*o**3 + 0 - 1/2*o + o**j = 0. Calculate o.
-1, 0, 1/3
Let o(y) be the third derivative of y**10/15120 + y**9/22680 + y**4/24 - 4*y**2. Let f(g) be the second derivative of o(g). Factor f(d).
2*d**4*(3*d + 1)/3
Let u = 37 + -71. Let c = u - -36. Suppose 1/2 - 1/2*q**c + 0*q = 0. Calculate q.
-1, 1
Let b(k) = -6*k**4 + 8*k**3 - 16*k**2 - 4*k - 6. Let v(l) = -12*l**4 + 15*l**3 - 33*l**2 - 9*l - 13. Let o(g) = -13*b(g) + 6*v(g). Factor o(h).
2*h*(h - 1)**2*(3*h - 1)
Solve j - 49*j**3 + 15*j**2 - 5*j + 13*j**2 = 0 for j.
0, 2/7
Let q(n) be the second derivative of -9*n**7/91 + 9*n**5/26 - 5*n**4/39 - 20*n**3/39 + 8*n**2/13 - 4*n. Factor q(f).
-2*(f + 1)**2*(3*f - 2)**3/13
Suppose 0 = 5*c - 5 - 5. Find j, given that -3*j**c + 19*j + 5 - 7*j - 8 - 9 = 0.
2
Let h be 1 + (-5 - -3) + 3. Find d such that 9*d**4 - 3*d**2 - 9*d**3 + 3*d**2 + 3*d**h - 3*d**5 = 0.
0, 1
Let n be (-84)/70 - (376/70)/(-4). Factor -1/7 - 3/7*j**2 - 3/7*j - n*j**3.
-(j + 1)**3/7
Let j = 217 - 2383/11. Factor 2/11*n**4 + 0*n**2 - 2/11 + j*n - 4/11*n**3.
2*(n - 1)**3*(n + 1)/11
Suppose -2*v**3 + 0*v + 0 + 0*v**2 + 1/2*v**5 + 0*v**4 = 0. Calculate v.
-2, 0, 2
Suppose 2*i - 2 = -4*z + 4, 2*z = 5*i + 9. Factor 4/13 - 2/13*r - 2/13*r**z.
-2*(r - 1)*(r + 2)/13
Let a(h) = -h**2 - 2*h. Let m(t) = -t**2 - 2*t. Let k(s) = -5*a(s) + 6*m(s). Factor k(g).
-g*(g + 2)
Let l(m) be the third derivative of -m**6/840 - m**5/105 - 5*m**4/168 - m**3/21 + m**2. Determine y so that l(y) = 0.
-2, -1
Let n = 1 - 1. Suppose 3*f = -0*f. Factor n + 1/4*w**3 - 1/4*w + f*w**2.
w*(w - 1)*(w + 1)/4
Factor 4*h**4 - 4*h**2 + 18*h**2 - 10*h**2 + 8*h**3.
4*h**2*(h + 1)**2
Suppose 18 = -0*h - 3*h. Let z be (h/(-9))/(1/3). Let -2*m**4 + 2*m**2 - 4*m**z + 4*m**4 = 0. Calculate m.
-1, 0, 1
Suppose -y - 4*y + 50 = 0. Suppose -l = 4*l - y. Factor l*f**3 - 8/3*f**2 + 0 - 8/3*f.
2*f*(f - 2)*(3*f + 2)/3
Factor -4*g**3 - 1/2*g**4 - 16*g - 12*g**2 - 8.
-(g + 2)**4/2
Let o(i) be the second derivative of -i**4/6 - 4*i**3 + 13*i**2 - 15*i. Suppose o(q) = 0. Calculate q.
-13, 1
Factor -6 + 12*q + 48*q**2 + 0 + 27*q**3 + 3*q.
3*(q + 1)**2*(9*q - 2)
Let n be (-5)/(-2)*3/30. Factor 0*k + 1/4*k**2 - n.
(k - 1)*(k + 1)/4
Let q(v) be the third derivative of v**7/42 - v**6/12 + 5*v**4/12 - 5*v**3/6 + v**2. Let q(n) = 0. What is n?
-1, 1
Let o(u) be the second derivative of 0*u**4 - 4*u + 0*u**5 + 0 + 0*u**3 - 1/135*u**6 + 0*u**2. Determine g, given that o(g) = 0.
0
Factor 1/8*d**4 + 0 + 1/8*d**3 + 0*d + 0*d**2.
d**3*(d + 1)/8
Let r(f) = -3*f**4 - 2*f**3 + 17*f**2 + 10*f + 2. Let v(b) = -b**4 + b**3 - b**2 - 1. Let z(n) = r(n) + 2*v(n). Factor z(x).
-5*x*(x - 2)*(x + 1)**2
Let y(g) be the third derivative of -g**7/420 - g**6/240 - 17*g**2. Find f such that y(f) = 0.
-1, 0
Let o be 0*(-2)/6 - -1. Let x(r) be the first derivative of 5/21*r**6 + 0*r - o - 26/35*r**5 + 9/14*r**4 - 2/7*r**2 + 2/21*r**3. Suppose x(t) = 0. What is t?
-2/5, 0, 1
Let q be (117/60 + -2)*-1. Let w(a) be the third derivative of 0*a + 0*a**3 - a**2 + 1/12*a**4 + 0 + 7/60*a**5 + q*a**6. Factor w(z).
z*(2*z + 1)*(3*z + 2)
Let w = 14 - 3. Let a = -7 + w. Let 0*v**3 + 18*v**2 + 10*v**4 + a*v + 13*v**3 + 11*v**3 = 0. Calculate v.
-1, -2/5, 0
Let d(f) be the second derivative of 0*f**4 + 0*f**2 - 8/15*f**6 + 2/15*f**5 + 5/9*f**7 + 0 + 0*f**3 - 3*f. Factor d(i).
2*i**3*(5*i - 2)*(7*i - 2)/3
Suppose 0 = 3*j - 15, -3*t + j = 6*j - 37. Suppose -2 = -2*o + t. Factor -3*q**2 + 4*q + q**2 + 4*q**2 - 4 - o*q**2.
-(q - 2)**2
Factor -2*t - 1/2*t**3 + 2*t**2 + 0.
-t*(t - 2)**2/2
Let a be ((-9)/(-18))/(3 - 1). Factor 0 - 1/4*r - r**2 - r**4 - 3/2*r**3 - a*r**5.
-r*(r + 1)**4/4
Suppose 3*l + 4 = -l - 5*s, 0 = -4*s. Let n = l - -3. Factor 2 + 0*d**3 - 2*d**2 + n*d**3 - 2*d**3 + d**3 - d.
(d - 2)*(d - 1)*(d + 1)
Factor 0 + 4*q - 7*q**2 + 5*q**2 + 3*q**4 - 4*q**3 - 1.
(q - 1)**2*(q + 1)*(3*q - 1)
Let z(a) = a**2 + 2. Let j(r) = 1. Let v = -8 - -2. Suppose -3 + 11 = 4*y. Let h(d) = v*j(d) + y*z(d). Factor h(w).
2*(w - 1)*(w + 1)
Factor -3/4*v - 3/2 + 3/4*v**2.
3*(v - 2)*(v + 1)/4
Let z(f) = 60*f**2 + 25*f - 35. Let y(o) = 20*o**2 + 8*o - 12. Let h(t) = 11*y(t) - 4*z(t). Factor h(c).
-4*(c + 1)*(5*c - 2)
Factor 10/7*o**2 + 0*o + 0 - 2/7*o**3.
-2*o**2*(o - 5)/7
Let p = -12 + 18. Suppose p*o = -0 + 12. Determine i, given that 8/9*i**o + 0 + 8/9*i + 2/9*i**3 = 0.
-2, 0
Let y(t) be the second derivative of -t**7/2520 + t**6/720 - t**4/6 + 4*t. Let d(v) be the third derivative of y(v). Factor d(g).
-g*(g - 1)
Let w = 6/65 + 183/130. Factor w*d**3 + 3/2*d**2 + 1/2*d**4 + 1/2*d + 0.
d*(d + 1)**3/2
Let f = 324 + -193. Let v = -915/7 + f. Factor -2/7*s**5 + 6/7*s**4 - 4/7*s**2 + 6/7*s - v - 4/7*s**3.
-2*(s - 1)**4*(s + 1)/7
Let k(t) be the third derivative of t**6/10 + 3*t**5/100 - t**4/20 + 11*t**2. Factor k(a).
3*a*(4*a - 1)*(5*a + 2)/5
Let f(a) be the third derivative of 8*a**7/21 + a**6/3 - 13*a**5/4 + 85*a**4/24 - 5*a**3/3 - 2*a**2. Factor f(t).
5*(t - 1)*(t + 2)*(4*t - 1)**2
Let r(a) be the third derivative of -a**6/720 - a**5/120 - a**4/48 - a**3/2 - 2*a**2. Let i(m) be the first derivative of r(m). Solve i(k) = 0 for k.
-1
Let m(q) = -q**4 + q - 1. Let o(a) = -a**5 - 2*a**4 - 9*a**3 + 7*a**2 + 5*a - 7. Let v(s) = 35*m(s) - 5*o(s). Let v(b) = 0. Calculate b.
0, 1, 2
Suppose 5*k - 3*k - 8 = 0. Let b(w) be the first derivative of -2*w**3 + 1 - 2*w - 1/2*w**k - 3*w**2. Let b(y) = 0. What is y?
-1
Let f be (-21483)/(-27)*2/7. Let p = f - 225. Determine h, given that 3*h**4 + 0*h**2 + 2/3*h**3 + p*h**5 + 0*h + 0 = 0.
-1, -2/7, 0
Let g(p) = -141*p**4 - 48*p**3 - 4*p**2 + 3. Let i(o) = -704*o**4 - 240*o**3 - 20*o**2 + 16. Let s(c) = -16*g(c) + 3*i(c). Factor s(q).
4*q**2*(6*q + 1)**2
Factor 16*k + 12*k**2 - 4*k - 9*k + 9*k**3.
3*k*(k + 1)*(3*k + 1)
Let g be ((-20)/(-36)*1)/(25/30). Solve g*r**2 - 2/3 + 2/3*r - 2/3*r**3 = 0.
-1, 1
Let m(w) be the second derivative of -w**4/6 + 7*w**3/3 - 6*w**2 - 21*w. Factor m(x).
-2*(x - 6)*(x - 1)
Let n(c) be the second derivative of c**5/30 - 2*c**4/9 - c**3/9 + 4*c**2/3 + c. Factor n(l).
2*(l - 4)*(l - 1)*(l + 1)/3
Let q(c) be the second derivative of 45*c**7/14 + 9*c**6 - 9*c**5/2 - 35*c**4/3 + 25*c**3/2 - 5*c**2 - 6*c. Factor q(f).
5*(f + 1)*(f + 2)*(3*f - 1)**3
Suppose 3*i - 36 = 7*i. Let v(y) = 15*y**3 - 21*y**2 + 6*y - 9. Let l(n) = -7*n**3 + 10*n**2 - 3*n + 4. Let w(c) = i*l(c) - 4*v(c). Factor w(h).
3*h*(h - 1)**2
Let g(m) be the third derivative of 7*m**6/24 - m**5/6 - 35*m**4/24 + 5*m**3/3 - 6*m**2. Determine r, given that g(r) = 0.
-1, 2/7, 1
Let w(n) be the second derivative of n**7/14 - 3*n**5/5 + n**4/2 + 3*n**3/2 - 3*n**2 + 18*n. Let w(h) = 0. What is h?
-2, -1, 1
Let s(w) = -w**2 + 7*w - 3 + 1 - 4. Let p be s(6). Let -m**2 - 2*m + p*m + m**2 - 2*m**2 = 0. What is m?
-1, 0
Let v(s) be the second derivative of -s**6/20 + s**5/10 + s**4/6 - 3*s. Factor v(h).
-h**2*(h - 2)*(3*h + 2)/2
Let r(z) be the third derivative of z**5/210 - 11*z**2. Factor r(d).
2*d**2/7
Let l(j) be the third derivative of -j**9/15120 - j**8/2520 - j**7/1260 + j**5/360 + j**4/12 + 3*j**2. Let d(p) be the second derivative of l(p). Factor d(o).
-(o + 1)**3*(3*o - 1)/3
Suppose -2/5*g**2 - 12/5*g**5 + 7/5*g**4 + 7/5*g**3 + 0*g + 0 = 0. Calculate g.
-2/3, 0, 1/4, 1
Let v(r) be the first derivative of -r**6/6 - 4*r**5/5 - r**4 + 48. Factor v(k).
-k**3*(k + 2)**2
Let n(l) be the second derivative of -l**6/90 - l**5/20 - l**4/18 - 8*l. Factor n(i).
-i**2*(i + 1)*(i + 2)/3
Suppose 5*g = -3*t + 7*t + 10, g - 3*t - 2 = 0. Factor h**g - 6 + 2*h**2 - 4*h + h.
3*(h - 2)*(h + 1)
Let b be (1 + (-5 - -3) - -1)*1. Let -6*i**3 + 4/3*i + 14/3*i**2 + b = 0. Calculate i.
-2/9, 0, 1
Suppose -11 + 36 = -5*t, -t - 18 = -b. Factor -5*x + x + 11*x**2 - 2 - b*x**2.
-2*(x + 1)**2
Let t = -6 - -3. Let l be t*3/((-27)/12). Solve -5*h**3 + 3*h**2 + 3*h**3 - h**2 + 0*h**4 - 2*h**l + 2*h = 0.
-1, 0, 1
Let c(x) be the first derivative of x**4/12 - x**2/2 + 3*x + 2. Let i(q) be the first derivative of c(q). Factor i(m).
(m - 1)*(m + 1)
Let q(s) be the third d