(w - 1)*(w + 1)**2
Let f be 90/(-81)*6/(-10). Solve -f*j + 0 + 2/3*j**3 + 0*j**2 = 0.
-1, 0, 1
Let c(g) be the third derivative of -5*g**8/336 - 2*g**7/21 - g**6/4 - g**5/3 - 5*g**4/24 + 10*g**2. Suppose c(d) = 0. What is d?
-1, 0
Let n(q) = -q**4 + q - 1. Suppose -2 = -3*g - z, 3*g - 3*z - 8 = 2*z. Let y(k) = 4*k**4 - 2*k**2 - 3*k + 4. Let h(m) = g*y(m) + 3*n(m). Factor h(a).
(a - 1)**2*(a + 1)**2
Suppose 0 = 8*l - 11*l + 12. Let h(k) be the second derivative of -1/6*k**3 + 1/20*k**5 - 2*k + 1/4*k**2 - 1/60*k**6 + 0 + 0*k**l. Factor h(a).
-(a - 1)**3*(a + 1)/2
Determine c, given that 1/7*c**3 + 4/7*c**2 - 4/7*c - 1/7*c**4 + 0 = 0.
-2, 0, 1, 2
Let i(r) = 5*r**3 - 2*r**2 + r. Let n be i(1). Let z be 4/6*18/n. Solve 0 - 2/7*c**2 + 2/7*c**z + 0*c = 0 for c.
0, 1
Let d(v) = v**3 - 5*v**2 - v + 7. Suppose 0*q - 10 = -2*q. Let t be d(q). Factor 0*a**4 + 0*a + 2/11*a**5 - 2/11*a**3 + 0 + 0*a**t.
2*a**3*(a - 1)*(a + 1)/11
Let m(i) = 52*i**2 + 38*i + 6. Let x(z) = -z**2 + z + 1. Suppose -3 = 2*r + 1. Let b(a) = r*x(a) - m(a). What is u in b(u) = 0?
-2/5
Let s be 92/230 - (-26)/10. Let 1/3*k**3 + 0 + s*k - 2*k**2 = 0. Calculate k.
0, 3
Let s(b) be the third derivative of -b**7/945 + b**6/540 + b**5/270 - b**4/108 - 6*b**2. Factor s(i).
-2*i*(i - 1)**2*(i + 1)/9
Let f(s) = -s**3 - 2*s**2 + 2*s + 3. Let g be f(-3). Let b be 4 - (-3)/g*2. Solve -1/2*k**b - k**4 + 1/2*k + 0 + k**2 + 0*k**3 = 0 for k.
-1, 0, 1
Suppose 1/2*f**3 - 1/4*f**5 - 1/4*f - 1/2 + f**2 - 1/2*f**4 = 0. Calculate f.
-2, -1, 1
Let i be 3/(-12) - (-21)/36. Let l(v) be the first derivative of -2/15*v**5 + 2 - i*v**2 + 2/9*v**3 + 1/6*v**4 + 0*v. Factor l(p).
-2*p*(p - 1)**2*(p + 1)/3
Let w(u) be the second derivative of -3*u**5/80 + u**4/8 + u**3/8 - 3*u**2/4 + 18*u + 2. Factor w(l).
-3*(l - 2)*(l - 1)*(l + 1)/4
Let -6*r**2 + 11*r**5 - 40*r**3 - 4*r**4 + 22*r**2 - r**5 = 0. What is r?
-2, 0, 2/5, 2
Let d(o) = -15*o + 92. Let f be d(6). Determine j, given that -1/5*j**4 - 1/5 + 2/5*j**f + 0*j + 0*j**3 = 0.
-1, 1
Let f be ((-28)/(-35))/(6/5). Let h(o) be the first derivative of 2*o**2 + 0*o - f*o**3 + 2. Factor h(g).
-2*g*(g - 2)
Let a(t) be the first derivative of -t**4/18 + 4*t**3/27 + 7*t**2/9 + 8*t/9 - 3. Solve a(b) = 0 for b.
-1, 4
Suppose 4*r + 0*x = 2*x + 18, -2*r = 5*x - 15. Factor -r*l - 4*l**3 + 2 - 7*l**2 + l**2 + 5*l.
-2*(l + 1)**2*(2*l - 1)
Factor -18/7*h - 2/21*h**3 + 18/7 + 6/7*h**2.
-2*(h - 3)**3/21
Suppose 2*v - 6 = -2. Solve -d**4 - 3*d**v + 5*d**3 - 2*d**4 + 2*d**2 + d - 2*d = 0 for d.
-1/3, 0, 1
Let x(m) = -6*m**5 + 12*m**4 - 12*m**3 - 30*m**2 - 3*m - 3. Let j(q) = q**5 + q**4 + q**3 + q**2 + q + 1. Let f(v) = -3*j(v) - x(v). Factor f(p).
3*p**2*(p - 3)**2*(p + 1)
Suppose -2*k = -6*k. Let u be 1/((-3)/(-12) + k). Factor u + 3*p**2 + 5*p - p**2 - 6*p - 5*p.
2*(p - 2)*(p - 1)
Let b(y) be the third derivative of -y**8/840 + 2*y**7/525 + y**6/100 - 4*y**5/75 + y**4/15 - 3*y**2. Let b(v) = 0. Calculate v.
-2, 0, 1, 2
Let p = 231/10 - 23. Let s(r) be the second derivative of 1/3*r**3 + 0 + 0*r**4 - 3*r + 0*r**2 - p*r**5. Factor s(w).
-2*w*(w - 1)*(w + 1)
Let j(l) be the second derivative of 0 + 0*l**2 + 4/5*l**6 - 1/3*l**4 + l - 1/3*l**7 - 3/10*l**5 + 0*l**3. Factor j(v).
-2*v**2*(v - 1)**2*(7*v + 2)
Let j be ((-3)/(-2))/((-6)/(-2)). Suppose -r - 3 = 3*i, -i = -2*i + 2*r + 6. Factor 1/2*o**2 - j*o + i.
o*(o - 1)/2
Suppose -5*o + 12 = b + 39, -2*b + 6 = 0. Let m be 2/(-1) + 12 + o. Factor -3*h**2 + 4 + 3*h**m - 4*h + 0*h**4 - 2*h**4 + 6*h**3 - 4*h**3.
(h - 1)**2*(h + 2)**2
Let y(j) be the second derivative of -3*j**6/20 - 3*j**5/10 + j**4/4 + j**3 + 3*j**2/4 - 2*j - 14. Find l such that y(l) = 0.
-1, -1/3, 1
Let c(h) = -h + 17. Let i be c(17). Let j(l) be the first derivative of i*l + 1/4*l**4 - 3 + 1/2*l**2 - 2/3*l**3. Factor j(d).
d*(d - 1)**2
Let x(v) = 36*v**4 - 28*v**3 - 28*v**2 + 36*v. Let b(p) = p**3 + 1. Let z = 20 + -12. Let u(g) = z*b(g) - x(g). Solve u(f) = 0.
-1, 1/3, 2/3, 1
Suppose -3*s + 10*s = 0. Solve s*c + 0 + 2/11*c**3 - 2/11*c**2 = 0 for c.
0, 1
Suppose -3*s - 4 = -4*b, 2*b - 1 = -4*s + b. Factor 1/3*g**2 + s + 2/3*g.
g*(g + 2)/3
Let -1/3*j**3 + 1/3*j**4 + 0 - 1/3*j**2 + 1/3*j**5 + 0*j = 0. Calculate j.
-1, 0, 1
Let d(j) be the second derivative of 6*j + 1/2*j**2 - 3/8*j**4 + 7/12*j**3 + 0. Find t, given that d(t) = 0.
-2/9, 1
Let w(j) = 4*j - 10. Let b be w(4). Let v(z) be the second derivative of 1/40*z**b + 0*z**2 - z + 0 + 3/80*z**5 + 1/48*z**4 + 1/168*z**7 + 0*z**3. Factor v(h).
h**2*(h + 1)**3/4
Let j be (-12)/4*1 + 8. Let u(t) be the second derivative of t + 0 - 1/12*t**4 - 1/20*t**j + 0*t**2 + 1/30*t**6 + 1/6*t**3. Determine b so that u(b) = 0.
-1, 0, 1
Let k(u) be the second derivative of u**4/6 + 2*u**3/3 - 9*u. Factor k(l).
2*l*(l + 2)
Let c(k) = k - 1. Let g be c(5). Factor 0*h**3 + 2/9*h**5 + 4/9*h**2 + 0 - 4/9*h**g - 2/9*h.
2*h*(h - 1)**3*(h + 1)/9
Let f(n) be the first derivative of n**7/70 - n**5/10 + n**3/2 - 7*n**2/2 - 1. Let j(g) be the second derivative of f(g). Suppose j(h) = 0. Calculate h.
-1, 1
Find r, given that 2/15*r**2 - 2/15*r + 0 = 0.
0, 1
Let v(p) be the first derivative of 2*p**3/9 + p**2 - 8*p/3 + 27. Suppose v(f) = 0. What is f?
-4, 1
Let i(p) be the first derivative of -5*p**6/2 + 5*p**5 + 5*p**4/4 - 25*p**3/3 + 5*p**2 + 23. Let i(z) = 0. Calculate z.
-1, 0, 2/3, 1
Let s be 6/(-15) + 37/5. Let n = s - 1. Factor -b**2 - b**2 + 0*b**2 + 4*b**4 + n*b**3 + 4*b**2.
2*b**2*(b + 1)*(2*b + 1)
Let -289/4 - 17/2*o - 1/4*o**2 = 0. What is o?
-17
Let c(j) be the third derivative of -j**8/100800 - j**7/6300 - j**6/900 + j**5/20 + j**2. Let o(z) be the third derivative of c(z). Find r, given that o(r) = 0.
-2
Suppose 0 = -4*d + 21 + 3. Suppose 22 - d = 4*g. Solve 1/4*m**g + 3/4*m**3 + 3/4*m**2 + 0 + 1/4*m = 0.
-1, 0
Let d = 2 + -2. Factor -2*t**3 + d*t**5 + 5*t**4 - 3*t**5 + t**5 - t**5.
-t**3*(t - 1)*(3*t - 2)
Suppose 3*s = 4*a - 0 - 20, 3*s = -12. Let o**4 - 2*o**3 + 2*o**4 + 0*o**3 - 2*o**2 - o**4 + a*o**5 = 0. What is o?
-1, 0, 1
Let f(s) = -s**3 - 8*s**2 - 2*s - 12. Let z be f(-8). Let g be z/20*(-3)/(-3). Factor 1/5 - g*i**2 + 0*i.
-(i - 1)*(i + 1)/5
Let q = 12 - 10. Let c = 6 - 3. Factor 2*r + c*r**3 + r**2 + 2*r**2 + q*r**2.
r*(r + 1)*(3*r + 2)
Let r(t) be the second derivative of -1/15*t**4 + 0*t**2 + 0*t**3 + 1/105*t**7 + 1/10*t**5 + 0 - 4/75*t**6 - t. Factor r(w).
2*w**2*(w - 2)*(w - 1)**2/5
Let g(h) be the first derivative of -4/3*h + h**2 + 5 + 0*h**3 - 1/6*h**4. Suppose g(l) = 0. What is l?
-2, 1
Let l be (-4)/(-6) + (-16)/(-12). Suppose r = -3 + l. Let m(p) = -3*p**3 + 2*p**2 + p - 4. Let d(n) = -n**3 + n**2 - 1. Let q(f) = r*m(f) + 4*d(f). Factor q(j).
-j*(j - 1)**2
Let h = 483/4 + -120. Let x(c) be the second derivative of -c - 7/40*c**5 + 0 + 1/60*c**6 + h*c**4 - 5/3*c**3 + 2*c**2. Factor x(i).
(i - 2)**3*(i - 1)/2
Let h be (-196)/105*(-6)/(-4) - -4. Find a such that -8/5*a**3 + 18/5*a - 4/5 - h*a**2 = 0.
-2, 1/4, 1
Let g(q) be the second derivative of -q**6/195 + 3*q**5/65 - q**4/6 + 4*q**3/13 - 4*q**2/13 - 14*q. Find j, given that g(j) = 0.
1, 2
Let k(f) be the third derivative of -f**6/120 + f**5/60 - f**4/24 + 3*f**2. Let a(x) = -x**2. Let n(u) = 6*a(u) + 2*k(u). Factor n(y).
-2*y*(y + 1)**2
Let q(s) be the first derivative of -s**3 + 19*s**2/2 + 14*s + 55. Factor q(p).
-(p - 7)*(3*p + 2)
Let q(j) be the first derivative of -j**4/4 - j**3/3 + j**2/2 + j + 4. Let h(x) = -5*x**3 - 4*x**2 + 5*x + 4. Let f(v) = h(v) - 4*q(v). Factor f(y).
-y*(y - 1)*(y + 1)
Factor -9/4*b**3 + 3*b**2 + 0 - b.
-b*(3*b - 2)**2/4
Let w(s) = 10*s**2 + 8*s - 12. Let o(v) be the third derivative of -11*v**5/60 - v**4/3 + 2*v**3 + v**2. Let g(k) = -6*o(k) - 7*w(k). Factor g(t).
-4*(t - 1)*(t + 3)
Let q be 0 - 245/30*-4. Let m = -32 + q. Factor 0*l**2 + 2/3*l**4 + 0*l + m*l**5 + 0*l**3 + 0.
2*l**4*(l + 1)/3
Let h(g) be the third derivative of -1/75*g**5 + 2/525*g**7 + 0 - 1/60*g**4 + 0*g**3 + 0*g**6 + 5*g**2 + 1/840*g**8 + 0*g. Let h(i) = 0. Calculate i.
-1, 0, 1
Let v = -779/3 + 261. Determine l so that -v*l + 2/3*l**2 + 2/3 = 0.
1
Let k(f) be the third derivative of f**7/350 + f**6/300 - f**5/300 + 4*f**2. Suppose k(r) = 0. What is r?
-1, 0, 1/3
Let t(o) be the second derivative of -1/6*o**3 - 1/2*o**2 + o + 0 + 1/12*o**4 + 1/20*o**5. Let s(j