(l) = 108*l**2 - 72*l + 12. Let h(w) = -27*w**2 + 18*w - 3. Let f(u) = 4*a(u) + 15*h(u). Factor f(g).
3*(3*g - 1)**2
Let z be (-5)/(-10)*-3 - 14/(-4). Solve 2/5*t**z + 0 - 4/5*t = 0 for t.
0, 2
Suppose 4 = 4*h - 12. Let g = 6 - h. Find o, given that -4*o**2 - 2*o**g - 2*o**3 + o - o + 8 = 0.
-2, 1
Let z(a) be the second derivative of a**8/1680 - a**7/280 + a**6/120 - a**5/120 + a**3/3 + 2*a. Let i(r) be the second derivative of z(r). Factor i(n).
n*(n - 1)**3
Factor 10/9*t**2 + 0 + 2/9*t**3 + 8/9*t.
2*t*(t + 1)*(t + 4)/9
Find l such that -2*l - 3*l + l + 10*l**2 + 0*l = 0.
0, 2/5
Let s(m) be the first derivative of 3*m**7/2 - 2*m**6 - 9*m**5/20 + m**4/2 - 3*m - 2. Let z(d) be the first derivative of s(d). What is y in z(y) = 0?
-1/3, 0, 2/7, 1
Find c, given that -7/4*c + 3/4 + 5/4*c**2 - 1/4*c**3 = 0.
1, 3
Suppose -5*c = 1 - 11, v = c. Factor 6*g**2 - 2*g**2 - 2*g**2 - v*g.
2*g*(g - 1)
Let z be ((-4)/(-30))/(-4 - (-216)/45). Factor -2/3*w**2 - 1/6*w - 2/3*w**4 - z*w**5 - w**3 + 0.
-w*(w + 1)**4/6
Let r = 978 + -976. Factor 0 - r*c - 4/3*c**2 - 2/9*c**3.
-2*c*(c + 3)**2/9
Let y(o) be the first derivative of o**8/420 + o**7/840 - o**6/90 - o**5/120 + o**3 + 9. Let g(m) be the third derivative of y(m). Factor g(n).
n*(n - 1)*(n + 1)*(4*n + 1)
Let r(a) be the third derivative of a**5/60 - 5*a**4/6 + 50*a**3/3 - 55*a**2. Factor r(o).
(o - 10)**2
Suppose -2*v - 7 = -11. Factor -v*k**3 - 5*k**4 - 18 + 18.
-k**3*(5*k + 2)
Let j(a) = a**3 + 4*a**2 + 4*a + 4. Let f be j(-3). Let p = 1 + f. Factor -o**3 - 2*o - o**3 + 2*o**p + 2*o**2.
-2*o*(o - 1)**2
Let d be (2/8)/(51/24 - 2). Let v(x) be the second derivative of x + 0 - 1/12*x**4 - 1/2*x**d - 1/3*x**3. Let v(t) = 0. Calculate t.
-1
Let f(m) be the third derivative of -7*m**2 + 0*m - 2/3*m**3 - 1/30*m**5 + 0 + 1/4*m**4. What is s in f(s) = 0?
1, 2
Factor 16*p + 44*p**2 + 36*p**2 + 579*p**3 - 487*p**3 + 28*p**4.
4*p*(p + 1)*(p + 2)*(7*p + 2)
Suppose 0 = s + 4*b + 239, -4*s - 876 = b - 5*b. Let m = 2011/9 + s. Factor 2/3*j**2 - 4/9 - m*j**3 + 2/3*j.
-2*(j - 2)*(j + 1)*(2*j - 1)/9
Let o = 3 + 0. What is y in y**o + 2 - 3*y**2 + 3*y - 7 + 4 = 0?
1
Factor 64/9 + 32/9*h + 4/9*h**2.
4*(h + 4)**2/9
Let t be 4/(-5) - (-90)/108. Let y(r) be the second derivative of 2/15*r**3 - 4*r - 1/10*r**2 + 0 - t*r**4 + 1/50*r**6 - 1/25*r**5. Factor y(c).
(c - 1)**2*(c + 1)*(3*c - 1)/5
Let a be (-4)/16*0 - -25. Suppose -4*v = -9*v + a. Suppose 12/7*w**2 - 8/7*w**4 + 2/7*w - 4/7 + 6/7*w**v - 8/7*w**3 = 0. What is w?
-1, -2/3, 1
Let m(w) = -5*w**2 - 30*w - 47. Let b(p) = -5*p**2 - 30*p - 48. Let z(c) = -2*b(c) + 3*m(c). Find f, given that z(f) = 0.
-3
Suppose -12/7*f**3 - 6/7 + 2/7*f**4 + 10/7*f + 4/7*f**2 + 2/7*f**5 = 0. What is f?
-3, -1, 1
Let o(k) be the first derivative of -28*k**3/3 - 60*k**2 - 32*k + 6. Factor o(c).
-4*(c + 4)*(7*c + 2)
Let k(p) be the third derivative of -p**5/135 - p**4/27 + 2*p**3/9 + 8*p**2. Suppose k(b) = 0. What is b?
-3, 1
Let -1/3*u**2 + 3 + 8/3*u = 0. What is u?
-1, 9
Let u be 1/(-1)*-2 - 14/8. Factor -1/2 - u*f**2 - 3/4*f.
-(f + 1)*(f + 2)/4
Let s = 12 - 10. Suppose -14*h - 11*h**2 - 9*h**3 + 10*h + 21*h**3 + h**s + 18*h**4 = 0. Calculate h.
-1, -1/3, 0, 2/3
Let k(s) = s**2 - 5*s + 6. Let u be k(4). Let f(i) be the second derivative of 5/6*i**4 + 0 + i + u*i**2 + 7/3*i**3. Suppose f(n) = 0. Calculate n.
-1, -2/5
Suppose -h - 3*p = -2, -5*p = -3*h - 4*p + 6. Solve -2/11*a**h - 2/11*a**3 + 2/11 + 2/11*a = 0.
-1, 1
Suppose 5*x - 14 + 4 = 0. Let g(l) be the first derivative of -2/5*l**5 - 2 + 2/3*l**3 - 1/2*l**x + 1/6*l**6 + 0*l**4 + 0*l. Factor g(i).
i*(i - 1)**3*(i + 1)
Solve 3 - 101*r**2 + 110*r**2 - 7 + 3*r**3 - 8 = 0 for r.
-2, 1
Suppose 9/7*b - 12/7*b**2 + 3/7*b**3 + 0 = 0. What is b?
0, 1, 3
Let m(h) be the second derivative of -1/10*h**5 - 1/15*h**6 + 1/6*h**4 + 0 + 1/21*h**7 + 0*h**3 - 4*h + 0*h**2. Solve m(k) = 0.
-1, 0, 1
Let o be -4 + 3 - 3/(-2). Factor 0 - 2*p**2 + p**4 + o*p**5 + 2*p - 3/2*p**3.
p*(p - 1)**2*(p + 2)**2/2
Suppose -5*f = -0*f - 30. Let k(w) be the third derivative of 0*w - 3*w**2 - 1/540*w**f - 2/27*w**3 + 0 - 5/108*w**4 - 2/135*w**5. Factor k(p).
-2*(p + 1)**2*(p + 2)/9
Let p be (15/(-6))/5*-68. Let m = 104/3 - p. Determine g so that 2/3 + m*g**2 + 4/3*g = 0.
-1
Let o be 5/(-6)*-1*8/10. Let o*u**5 - 2/3*u**3 + 0 + 2/3*u**4 + 0*u - 2/3*u**2 = 0. Calculate u.
-1, 0, 1
Let w(o) be the first derivative of 4*o**3/3 - 4*o**2 + 4*o - 7. Let w(l) = 0. What is l?
1
Let i(k) be the second derivative of -k**6/1980 + k**5/330 - k**4/132 - k**3 + 5*k. Let b(a) be the second derivative of i(a). Factor b(m).
-2*(m - 1)**2/11
Let 6*o + 0*o**3 - 15*o**2 - 3*o**4 - 3*o**3 + 15*o**3 + 0*o = 0. What is o?
0, 1, 2
Let t(h) be the first derivative of h**6/15 - h**4/10 - 1. Factor t(r).
2*r**3*(r - 1)*(r + 1)/5
Let g be -1 + 4/3 - (-77)/(-330). Let w(c) be the first derivative of 8/25*c**5 + 0*c**3 + g*c**4 + 0*c - 3 + 0*c**2. Factor w(n).
2*n**3*(4*n + 1)/5
Let i(p) be the second derivative of -p**6/180 + p**5/60 + p**3/3 - 5*p. Let s(q) be the second derivative of i(q). Factor s(y).
-2*y*(y - 1)
Let r(p) be the second derivative of 0*p**2 - 1/35*p**7 - 1/50*p**5 + 4/75*p**6 + 0*p**3 + p + 0*p**4 + 0. Solve r(o) = 0 for o.
0, 1/3, 1
Suppose -16*j**3 + 7*j**3 + 5 + 10*j - j**3 - 3*j**2 - 2*j**2 = 0. What is j?
-1, -1/2, 1
Let n(o) be the second derivative of 2*o - 1/21*o**3 - 2/7*o**2 + 0 + 1/42*o**4. Find r, given that n(r) = 0.
-1, 2
Let l(d) be the second derivative of 0*d**3 + 1/30*d**5 + 1/36*d**4 + 0 + 0*d**2 - d. Factor l(x).
x**2*(2*x + 1)/3
Let q(n) = n**4 + 3*n**3 + 10*n**2 + 15*n + 1. Let y = 6 + -3. Let a = 4 - 8. Let p(w) = w**4 + 2*w**3 + 9*w**2 + 16*w. Let v(r) = a*q(r) + y*p(r). Factor v(d).
-(d + 1)**2*(d + 2)**2
Let c be (-2)/3 - (-26)/39. Solve -6/7*t**2 + 4/7*t + c + 2/7*t**3 = 0.
0, 1, 2
Let n be (-16)/(-8) - (1 + -1). Factor 4/7*z + 22/7*z**2 + n*z**4 + 0 + 32/7*z**3.
2*z*(z + 1)**2*(7*z + 2)/7
Let p be (2 - (4 + -2))/(-1). Let c(r) be the first derivative of -2 + p*r**2 + 1/21*r**6 + 0*r + 0*r**5 + 4/21*r**3 - 3/14*r**4. Factor c(f).
2*f**2*(f - 1)**2*(f + 2)/7
Let a(k) be the first derivative of k**6/1440 + k**5/80 + 3*k**4/32 + k**3 + 5. Let v(o) be the third derivative of a(o). Factor v(n).
(n + 3)**2/4
Suppose 0*b + 20 = -4*l - 4*b, -5 = 5*l + b. Let p = l + 7. Factor 10*r**3 - 2 - 5*r**2 - 2*r**3 + 8*r - p*r**2 - 2*r**4.
-2*(r - 1)**4
Let n(q) be the third derivative of 0*q + 0 - 1/12*q**3 - 2*q**2 - 1/12*q**4 - 1/40*q**5. Suppose n(t) = 0. Calculate t.
-1, -1/3
Let o be ((-6)/40)/(24/(-60)). Let m(i) be the first derivative of o*i**2 + 3/4*i**3 - 4 - 3/2*i. Factor m(x).
3*(x + 1)*(3*x - 2)/4
Let m(h) = -2*h + 16. Let p be m(7). Solve -7*i**3 + 20*i - 4 - 15*i**2 + 3*i**p - 29*i**3 = 0.
-1, 1/3
Let p(k) be the first derivative of k**6/360 - k**5/60 - k**4/8 + 4*k**3/3 - 2. Let j(g) be the third derivative of p(g). Solve j(f) = 0.
-1, 3
Suppose 30 = 5*d + 4*t, -3*d = -0*d - 4*t + 14. Factor 16*s - 1 + 11 + 2*s**3 - d + 10*s**2.
2*(s + 1)*(s + 2)**2
Let h(y) be the first derivative of -y**5 - 15*y**4/4 - 5*y**3 - 5*y**2/2 - 12. Let h(r) = 0. Calculate r.
-1, 0
Let p(q) be the second derivative of q**5/20 - 7*q**4/24 + 7*q**3/12 - q**2/2 - 13*q. Let p(u) = 0. What is u?
1/2, 1, 2
Let y = -69 - -69. Let b(h) be the second derivative of y - 4/3*h**3 - 1/6*h**4 - 4*h**2 - h. Suppose b(q) = 0. Calculate q.
-2
Let m = -178 - -339. Let f = m + -641/4. Suppose -1/2 - 1/4*x**2 - f*x = 0. What is x?
-2, -1
Let a(l) = -l**4 + l**3 - l**2 - l. Let s(i) = 2*i**4 + 43*i**3 + 87*i**2 + 77*i + 25. Let y(w) = 3*a(w) - s(w). Factor y(u).
-5*(u + 1)**3*(u + 5)
Let z(k) = 2*k**2 - 12*k - 36. Let m(w) = -3*w**2 + 25*w + 71. Let s(t) = 4*m(t) + 7*z(t). Factor s(p).
2*(p + 4)**2
Let n be 28/(-40)*-5 + (-2)/4. Solve 0*s**2 + 3/2*s**4 - 3/2 + 3*s - n*s**3 = 0 for s.
-1, 1
Let i(q) be the first derivative of -2*q**5/85 + 3*q**4/34 - 4*q**3/51 + 18. Factor i(x).
-2*x**2*(x - 2)*(x - 1)/17
Let l(o) = 2*o**2 - o - 1. Let p be l(-1). Suppose s - p*s = -3. Let 4/5*y**4 + 9/5*y**s + 1/5*y + 0 + 6/5*y**2 = 0. What is y?
-1, -1/4, 0
Suppose 0 = 2*f + 2*s + 3*s - 1, -5*f - s + 14 = 0. What is r in 4*r**f + 3*r**4 - 4*r**3 + 6*r**3 + 0*r**4 = 0?
-2, 0
Let j be (-10 - 0)/(13/(91/(-14))). Find v, g