 - 2. Factor r(i).
-2*i**3*(i - 1)**2/3
Let w be 3 - 0/((-3)/(-3)). Determine n, given that -8/7*n**2 - 8/7*n**4 + 12/7*n**w + 0 + 2/7*n + 2/7*n**5 = 0.
0, 1
Let h(c) = -c**2 - 7*c - 4. Let m be h(-6). Let n(g) be the second derivative of 0 - 1/35*g**5 + 2/21*g**3 + 1/42*g**4 - g - 1/7*g**m. Factor n(z).
-2*(z - 1)*(z + 1)*(2*z - 1)/7
Factor 3/2*h + 9/4*h**2 + 0 + 3/4*h**3.
3*h*(h + 1)*(h + 2)/4
Factor -4*h - 6 - 2/3*h**2.
-2*(h + 3)**2/3
Let j = 13/70 - 3/35. Let s(w) be the second derivative of -4/45*w**6 - j*w**5 + 1/3*w**3 - 1/3*w**2 + 0 + 2*w + 5/18*w**4. Let s(r) = 0. Calculate r.
-1, 1/4, 1
Let v = -19 + 22. Suppose 2*p - 4 = 2*f - 2, v*f = -4*p + 11. Factor 0*g + 4/5*g**4 - 2/5*g**5 + 0*g**p + 0 - 2/5*g**3.
-2*g**3*(g - 1)**2/5
Factor 12 - d - 23 - 2*d**2 - d**3 + 11.
-d*(d + 1)**2
Determine r so that -4*r**2 + 3*r**2 - 20 + 0*r**2 - 4*r**2 + 20*r = 0.
2
Suppose 0 = -3*b - 31 - 8. Let x = -11 - b. Let -6/7*n**3 + 4/7*n**x + 0 + 2/7*n = 0. What is n?
-1/3, 0, 1
Let b(j) be the third derivative of -1/336*j**8 + 0*j + 1/210*j**7 - 1/60*j**5 + 3*j**2 + 0 + 0*j**3 + 1/120*j**6 + 0*j**4. Suppose b(h) = 0. What is h?
-1, 0, 1
Let g = 120 + -117. Let d(t) be the third derivative of 0*t + 0 + 1/105*t**7 - 1/30*t**6 - 1/840*t**8 - t**2 + 1/15*t**5 + 1/15*t**g - 1/12*t**4. Factor d(f).
-2*(f - 1)**5/5
Factor 8/7*r**3 - 6/7*r - 2/7 + 0*r**2.
2*(r - 1)*(2*r + 1)**2/7
Suppose 0 = -5*b + b + 12. Let t = -41 + 41. Factor -4/9*g**2 + 0*g - 2/9*g**b + t.
-2*g**2*(g + 2)/9
Suppose -5*a + 3*h = -16, a + 3 = -3*h - 1. Suppose -l + 2 = -0. Factor g**2 - 1 + 2*g - l*g**2 + 0*g**a.
-(g - 1)**2
Find r, given that -2/7*r - 5/7*r**2 - 3/7*r**3 + 0 = 0.
-1, -2/3, 0
Let b = 6/103 - -279/515. Determine a so that b*a + 3/5*a**2 - 6/5 = 0.
-2, 1
Let p(w) be the second derivative of w**7/168 - w**6/60 - w**5/80 + w**4/24 + w. Factor p(m).
m**2*(m - 2)*(m - 1)*(m + 1)/4
Let f(n) be the second derivative of -n**6/10 - 27*n**5/20 - 15*n**4/4 + 25*n**3/2 + n + 24. Factor f(r).
-3*r*(r - 1)*(r + 5)**2
Let n(h) be the third derivative of -h**5/30 + h**4/6 - h**3/3 + 7*h**2. Factor n(i).
-2*(i - 1)**2
Suppose -20*v**2 - 5*v**4 - 19*v**3 + 4*v + v**4 + 36*v**3 = 0. What is v?
0, 1/4, 2
Let b(t) = -3*t**3 + 3*t**2 + 3*t - 3. Let u(p) = -9*p**3 + 9*p**2 + 9*p - 9. Let i(f) = 7*b(f) - 2*u(f). Determine l so that i(l) = 0.
-1, 1
Let y(a) be the third derivative of -a**6/40 - a**5/5 - a**4/2 - 14*a**2. Factor y(u).
-3*u*(u + 2)**2
Let i(q) be the second derivative of q**9/15120 - q**8/2240 + q**7/1260 + q**4/6 + 2*q. Let d(y) be the third derivative of i(y). Factor d(h).
h**2*(h - 2)*(h - 1)
Let l(u) be the second derivative of u**3/6 - u**2/2 - u. Let r(g) = -86*g - 2*g**2 - 1 + 89*g + 0. Let v(o) = l(o) + r(o). Determine b so that v(b) = 0.
1
Let h(f) be the third derivative of -f**7/70 + 3*f**6/40 - f**4/2 + 28*f**2. Find d, given that h(d) = 0.
-1, 0, 2
Let y be 1 + -1 - (-2 + 3 + -1). Let -1/6*h**2 + 1/6 + y*h = 0. What is h?
-1, 1
Let f be ((-117)/(-156))/(9/24). Solve 2*m**f - 1 + 1/2*m - m**3 - m**4 + 1/2*m**5 = 0.
-1, 1, 2
Factor 24/5*l + 1/5*l**3 - 16/5 - 9/5*l**2.
(l - 4)**2*(l - 1)/5
Let n(b) be the first derivative of -11/8*b**2 + 8 + 11/16*b**4 - 7/12*b**3 + 9/20*b**5 - 1/2*b. Factor n(r).
(r - 1)*(r + 1)**2*(9*r + 2)/4
Let v = -445 + 1336/3. Factor -o**2 + v*o**3 + 4/3 + 0*o.
(o - 2)**2*(o + 1)/3
Let c(m) be the first derivative of -4*m**3/3 + 6*m**2 - 36. Find s such that c(s) = 0.
0, 3
Let k = 6 + -7. Let w(x) = x**3 + x**2 - x. Let s(p) = -5*p**3 - 9*p**2 - 3*p - 2. Let n(u) = k*s(u) - 3*w(u). Let n(q) = 0. Calculate q.
-1
Suppose -9*z + 72 = -7*z. Let v be 3/(-12) + 21/z. Factor 0 - 2/3*y + v*y**2.
y*(y - 2)/3
Let l(b) be the second derivative of 49*b**6/150 - 21*b**5/100 - 2*b**4/5 - 2*b**3/15 - 12*b. Factor l(o).
o*(o - 1)*(7*o + 2)**2/5
Suppose 6*k - 107 + 3*k**2 + 107 = 0. Calculate k.
-2, 0
Let b be ((-6)/4*1/(-3))/10. Let w(c) be the second derivative of b*c**5 + 2*c**2 + 5/12*c**4 - 3*c + 4/3*c**3 + 0. Factor w(l).
(l + 1)*(l + 2)**2
Determine k so that 6*k + 0 - 63/4*k**4 - 75/2*k**3 - 9*k**2 = 0.
-2, -2/3, 0, 2/7
Let x(z) be the second derivative of z**6/1620 + z**5/180 + z**4/54 + z**3/3 + 4*z. Let i(s) be the second derivative of x(s). Determine o, given that i(o) = 0.
-2, -1
Let g(v) = -3*v**3 + 3*v. Suppose -c + 5*o + 14 = 0, 3*c - 4*c - 3*o - 2 = 0. Let n(u) = -7*u**3 + 7*u. Let z(w) = c*n(w) - 10*g(w). Factor z(d).
2*d*(d - 1)*(d + 1)
Let u(x) be the third derivative of -x**6/24 - 3*x**5/20 - x**4/6 - 29*x**2. Factor u(c).
-c*(c + 1)*(5*c + 4)
Let q(x) be the second derivative of 0*x**4 + 3*x**2 - 4*x + 3/2*x**3 + 0 - 3/20*x**5. Determine m, given that q(m) = 0.
-1, 2
Let o(p) = -2*p**3 + 15*p**2 - 24*p + 19. Let y(i) = -2*i**3 + 14*i**2 - 24*i + 18. Let h(m) = 2*o(m) - 3*y(m). Factor h(z).
2*(z - 2)**3
Let y = -26 + 28. Let o(t) be the first derivative of 0*t**2 + y - 3/2*t**4 - 6/5*t**5 - 2/3*t**3 + 0*t - 1/3*t**6. Factor o(z).
-2*z**2*(z + 1)**3
Solve -5 + g**2 + 6 + 3 - 2*g**2 + 3*g = 0 for g.
-1, 4
Let j(f) be the first derivative of f**6/180 + f**5/30 + f**3 + 3. Let c(a) be the third derivative of j(a). Factor c(n).
2*n*(n + 2)
Let m(d) be the first derivative of 6*d + 2/9*d**3 - 2*d**2 - 2. Suppose m(g) = 0. Calculate g.
3
Let b be 5*1 - (7 + -5). Suppose b*o + 37 = 5*d, -29 = -5*d - 2*o + 3*o. Let m(p) = 1. Let t(n) = -4*n**2 - 5*n - 6. Let q(v) = d*m(v) + t(v). Factor q(w).
-(w + 1)*(4*w + 1)
Let q(p) be the third derivative of p**7/420 - p**5/60 + p**3/12 - 5*p**2. Factor q(z).
(z - 1)**2*(z + 1)**2/2
Let f(d) be the third derivative of d**6/24 + d**5/4 + 3*d**2. Solve f(w) = 0 for w.
-3, 0
Suppose -6/7*j**2 + 4/7 + 10/7*j = 0. Calculate j.
-1/3, 2
Suppose x + 5*g = 3*g - 8, 3*g = -15. Suppose 9 = 3*h - r, -4*r + x*r = 3*h - 18. Suppose 6*w**h - 6*w**4 + w**5 - w**3 = 0. What is w?
-1, 0, 1
Let b(h) be the third derivative of -h**6/60 - 7*h**5/60 - h**4/12 + h**3/2 - 31*h**2. Factor b(s).
-(s + 1)*(s + 3)*(2*s - 1)
Let o(p) be the second derivative of -1/14*p**7 + 4*p + 0*p**5 + 0 + p**4 - 3/10*p**6 + 0*p**2 + 0*p**3. Determine q so that o(q) = 0.
-2, 0, 1
Let r = 230/3 + -76. Factor -2/3 + r*b**2 + 0*b.
2*(b - 1)*(b + 1)/3
Factor 20*v**4 + 40*v**2 + 4 - 30*v**3 - 2*v**5 + 18*v**3 - 2*v**5 - 20*v - 28*v**3.
-4*(v - 1)**5
Suppose -q + 0*i + 13 = -2*i, 0 = 4*q - 5*i - 37. Let k(v) be the second derivative of -2*v + 1/12*v**4 + 0 + 1/20*v**5 + 0*v**q + 0*v**2. Factor k(s).
s**2*(s + 1)
Let j(w) be the third derivative of 2*w**2 + 0*w**5 + 1/60*w**6 - 1/4*w**4 + 2/3*w**3 + 0*w + 0. Factor j(b).
2*(b - 1)**2*(b + 2)
Solve 2/11*x**2 + 0*x + 0 = 0.
0
Let w(i) = -2*i + 2. Let l be w(0). Let -8/5*h - 8/5 - 2/5*h**l = 0. Calculate h.
-2
Factor 0 + 16/5*l**2 + 2*l**5 - 36/5*l**4 + 24/5*l**3 + 0*l.
2*l**2*(l - 2)**2*(5*l + 2)/5
Find c, given that -21*c**5 - 159/7*c**2 + 12/7 + 21*c**4 + 159/7*c**3 - 12/7*c = 0.
-1, -2/7, 2/7, 1
Suppose -4*h + 0 = 8. Let s be 3/(-18) + h/(-4). Let 4/3*k**2 - 5/3*k - s*k**3 + 2/3 = 0. Calculate k.
1, 2
Let q = -21/4 + 113/20. Factor q*u**2 + 0 + 0*u + 8/5*u**3.
2*u**2*(4*u + 1)/5
Factor 0*k + 2/5*k**2 + 0 + 3/5*k**3 + 1/5*k**4.
k**2*(k + 1)*(k + 2)/5
Suppose -3*g + 42 = 5*r, -g - 26 = -3*r - 3*g. Let b be -2 - (-2 - r/9). Factor -2/3*t**4 - 8/3*t**3 - 4*t**2 - 8/3*t - b.
-2*(t + 1)**4/3
Let y = -64 + 257/4. Suppose -r + 6 - 4 = 0. Factor -q - y - q**3 - 1/4*q**4 - 3/2*q**r.
-(q + 1)**4/4
Let y be (-1 - 1)*(4 + (-91)/21). Let d(w) be the first derivative of w**2 + 2/3*w**3 + 1 + y*w + 1/6*w**4. Factor d(b).
2*(b + 1)**3/3
Let c be (3/(-12))/((-190)/1216). Let -2/5*j**5 - 4/3*j**4 + 0 + 8/15*j - 2/5*j**3 + c*j**2 = 0. Calculate j.
-2, -1/3, 0, 1
Let r(h) = -h**3 - 4*h**2 + 2*h - 11. Let n be r(-5). Factor 2/3*l**3 + 2/3*l**n + 0 + 0*l + 0*l**2 - 4/3*l**5.
-2*l**3*(l - 1)*(2*l + 1)/3
Let n(t) = -4*t**3 - 2*t**2 - 3. Let c(z) be the first derivative of 1/3*z**3 + 2*z + 0*z**2 + 3/4*z**4 + 1. Let y(d) = 6*c(d) + 4*n(d). Factor y(l).
2*l**2*(l - 1)
Let g be 2/(-6)*(-6)/4. Let y(m) be the first derivative of 2*m + g*m**4 - 2/3*m**3 - m**2 - 1. Factor y(i).
2*(i - 1)**2*(i + 1)
Let b be (-10)/(-70) + 166/14. Let l = 16 - b. Factor 1/4*t**l + 0*t**2 - 1/4 + 1/2*t**3 - 1/2*t.
(t - 1)*(t + 1)**3/4
Let m(w) = -w - 17. Let n