s(a). Factor t(x).
-x**2*(x - 1)**2/2
Let b(u) = u**2 - 9. Let v be b(4). Let a(r) be the second derivative of 1/27*r**3 + 0*r**2 + r + 1/27*r**4 + 0*r**5 - 2/135*r**6 - 1/189*r**v + 0. Factor a(p).
-2*p*(p - 1)*(p + 1)**3/9
Suppose v - 2*t = -1, -5*t - 10 = -5*v - 5. Factor 4 - 2*h - 4*h**v + 0*h - 8*h**3 + 2*h**3 - 16*h**2.
-2*(h + 1)**2*(5*h - 2)
Let s be (12/15)/((-12)/(-30)). Suppose -s*x = -3*x. Solve x*t - 1/5*t**3 + 3/5*t**2 - 4/5 = 0.
-1, 2
Let m = 3 - 2. Suppose 0 = -s - k + 9, -3*k - m = -s - 3*s. Find p such that s*p - 4*p**2 + 4*p - 8 + 2*p**2 = 0.
2
Suppose 7*v - 4*v = -7*v. Factor v - 1/3*w - 2/3*w**2 + 1/3*w**5 + 0*w**3 + 2/3*w**4.
w*(w - 1)*(w + 1)**3/3
Let p(x) be the second derivative of x**5/20 + 5*x**4/12 + x**3 + 14*x. Factor p(i).
i*(i + 2)*(i + 3)
Let j = 94 - 92. Determine w so that 2/7 + 0*w**j - 4/7*w - 2/7*w**4 + 4/7*w**3 = 0.
-1, 1
Let v(j) = j**3 + j**2 - j + 1. Let f(g) = 4*g**3 + 8*g**2 - 2*g + 6. Suppose 3 - 27 = -4*q. Let p(a) = q*v(a) - f(a). Factor p(x).
2*x*(x - 2)*(x + 1)
Let v(z) be the second derivative of z**3/6 - z**2 - z. Let w be v(2). Factor 2/3*l + w*l**2 + 0 - 2/3*l**3.
-2*l*(l - 1)*(l + 1)/3
Let q(r) be the first derivative of 2 + 14/27*r**3 + 2/9*r + 5/9*r**2 + 1/6*r**4. Find k, given that q(k) = 0.
-1, -1/3
Let h = 1 - 6. Let i(s) = -s**3 - s**2 + 2*s. Let v(n) = 2*n**3 + 2*n**3 - 3*n - 2*n**3 + n**2. Let x(c) = h*i(c) - 3*v(c). Find o such that x(o) = 0.
0, 1
Solve 2*b - 18*b**2 + 3*b**5 - 12*b**4 + 6*b**2 + b + 18*b**3 = 0.
0, 1
Let h(y) be the first derivative of y**5/5 - y**3 + y**2 - 6. Determine c so that h(c) = 0.
-2, 0, 1
Suppose 4*h = w - 5*w + 8, 2*h - 6 = -w. Suppose h*u = 2*c + 6, u + c = -2*c + 12. Find b such that -1/2*b - 1/2*b**2 + 1/2 + 1/2*b**u = 0.
-1, 1
Let h(i) be the second derivative of -i**6/45 + 2*i**4/9 + 12*i. Factor h(l).
-2*l**2*(l - 2)*(l + 2)/3
Let f(l) be the third derivative of -1/12*l**3 + 0 - 1/120*l**5 + 0*l + 1/24*l**4 - 2*l**2. Factor f(m).
-(m - 1)**2/2
Let t(i) = 11*i**2 - 7*i + 2. Let m(u) = -2 - 3*u - 7*u**2 + 9*u - 5*u**2. Let w(v) = 3*m(v) + 4*t(v). Find p, given that w(p) = 0.
1/4, 1
Let k(q) be the third derivative of -q**7/420 + q**6/240 + q**5/120 - q**4/48 - 4*q**2. Solve k(j) = 0 for j.
-1, 0, 1
Let d(h) = -27*h**4 + 3*h**3 + 36*h**2 + 75*h + 39. Let g(o) = -7*o**4 + o**3 + 9*o**2 + 19*o + 10. Let z(x) = -4*d(x) + 15*g(x). Find f such that z(f) = 0.
-1, 2
Let s(f) be the third derivative of 0*f + 2/45*f**5 + 2*f**2 + 0 - 2/45*f**6 + 0*f**3 + 0*f**4 + 1/105*f**7. Let s(y) = 0. What is y?
0, 2/3, 2
Let 11*a**2 + 3*a**4 - 2*a**2 - 8*a**3 - 3*a - a**3 + 0*a**3 = 0. Calculate a.
0, 1
Suppose 2*n = k + 7, k - 4*n - 1 + 16 = 0. Suppose q - k = -4*b - 15, 0 = -4*q - 3*b - 4. Determine v so that 1/5*v - 1/5*v**q + 0 = 0.
0, 1
Let p(h) be the second derivative of -h**9/720 - h**8/448 + h**7/420 + h**4/12 + 4*h. Let z(b) be the third derivative of p(b). Factor z(k).
-3*k**2*(k + 1)*(7*k - 2)
Let j = 10 - 12. Let x be -2*(2/j + 0). Determine r so that -x*r**2 - 4/3 - 10/3*r = 0.
-1, -2/3
Suppose -1 = 4*d + 3*y, 2*d - y = 3 + 4. Let p(q) be the second derivative of 0 + 1/20*q**4 - 1/10*q**3 - 3*q - 3/5*q**d. Let p(w) = 0. What is w?
-1, 2
Let m(s) be the first derivative of 6*s**2 + 6/5*s**5 + 8*s**3 - 2 + 2*s + 5*s**4. Factor m(t).
2*(t + 1)**3*(3*t + 1)
Let v(b) = -b + 7. Let u be v(-8). Suppose -7 = 4*i - u. Factor 0 + h - 7/2*h**i.
-h*(7*h - 2)/2
Let a be -2 + (-102)/(-27) + 2/9. Let o(p) be the first derivative of -1/9*p**3 + 0*p + 2 + 0*p**a - 1/12*p**4. Factor o(l).
-l**2*(l + 1)/3
Suppose -8*i + 18 = -5*i. Let q(w) be the first derivative of 0*w - 10/21*w**3 - 1/7*w**2 + 4/21*w**i + 2/7*w**5 - 3/14*w**4 + 1. Let q(n) = 0. Calculate n.
-1, -1/4, 0, 1
Suppose -2*q + l = -56, -3*q + 0*q - 2*l = -70. Factor 4*j**2 + 25*j**4 - 3*j**2 - q*j**4.
-j**2*(j - 1)*(j + 1)
Let x(t) be the third derivative of -t**8/840 + t**7/525 + t**6/60 + t**5/50 - 28*t**2. Factor x(f).
-2*f**2*(f - 3)*(f + 1)**2/5
Factor 4/5*d**4 + 0 + 48/5*d**2 + 32/5*d + 24/5*d**3.
4*d*(d + 2)**3/5
Solve 0 - 1/5*l**3 + 0*l - 4/5*l**2 = 0.
-4, 0
Let h(f) = f**4 - f**2 - f. Suppose -8 = -x - x. Let a(s) = 6*s**5 + 12*s**4 + 8*s**3 - 8*s**2 - 10*s - 4. Let m(z) = x*h(z) + a(z). Factor m(i).
2*(i - 1)*(i + 1)**3*(3*i + 2)
Factor 1/7*c**2 + 0 - 9/7*c.
c*(c - 9)/7
Suppose -2*b - 1 + 5 = 0. Factor -2*g - 6 - 7*g - 20*g**2 + 17*g**b.
-3*(g + 1)*(g + 2)
Suppose -3*r + 0*s + 4*s - 8 = 0, -4*r = -4*s + 8. Find y, given that 3/5*y**4 - 3/5*y**3 + 3/5*y**5 + 0 + r*y - 3/5*y**2 = 0.
-1, 0, 1
Let 128/5 - 6*b**2 - 2/5*b**3 - 96/5*b = 0. What is b?
-8, 1
Factor -8*m - 4*m**3 + 12*m**2 - 44*m**2 + 20*m**2.
-4*m*(m + 1)*(m + 2)
Let u be ((-4)/10)/((-4)/40). Suppose 0 = u*x - 3*x. Factor -i + 0 + x + i**2.
i*(i - 1)
Suppose -3*y + 8 = -y. Factor -f**2 - 3*f**3 - 3*f**4 + 4*f**4 - f**5 + 0*f**4 - 4*f**y.
-f**2*(f + 1)**3
Suppose -4*r - 26 = -10. Let u be 1/4 + 1/r. Determine m so that 0*m**3 + 2/3*m**4 + u + 0*m**2 + 0*m = 0.
0
Let y(u) be the first derivative of -2*u**6/45 + 3*u**5/20 - u**4/6 + u**3/18 + 9*u - 7. Let f(o) be the first derivative of y(o). Factor f(z).
-z*(z - 1)**2*(4*z - 1)/3
Let u(g) be the first derivative of -g**3/4 - 3*g**2/4 - 3*g/4 - 3. Let u(w) = 0. Calculate w.
-1
Let o(m) be the second derivative of 5*m**4/3 + 5*m**3/6 - 15*m**2/2 + 70*m. Factor o(w).
5*(w + 1)*(4*w - 3)
Let l(h) be the third derivative of h**5/270 - h**4/27 + 4*h**3/27 - 11*h**2. Determine m so that l(m) = 0.
2
Let r(n) be the third derivative of -n**7/25 - 2*n**6/75 + 2*n**5/75 - 3*n**2. Suppose r(g) = 0. What is g?
-2/3, 0, 2/7
Find r, given that 0 + 0*r - 1/4*r**4 + 1/2*r**2 - 1/4*r**3 = 0.
-2, 0, 1
Factor -9*j - 2*j**2 + 4*j**3 + 27 - 25 + 5*j**3.
(j - 1)*(j + 1)*(9*j - 2)
Let w be (6/210*-12)/((-3)/10). What is v in w*v**2 - 2/7*v + 0 = 0?
0, 1/4
Let t(k) = k**3 - 7*k**2 + 2*k - 3. Let i be t(7). Suppose 2*u - i - 1 = 0. Factor -6 + 4*v**3 - v**2 + u.
v**2*(4*v - 1)
Suppose -2*s + 18 = -3*d, -4*d - 27 = -3*s + d. Factor m**3 + 2*m**4 + 7*m**3 + s*m**2 + 3*m**2 + 2 + 8*m.
2*(m + 1)**4
Let j be 1/(-70)*(-4)/6. Let m(q) be the second derivative of 1/25*q**5 - q + 0 + 2/75*q**6 - 4/15*q**4 - 2/5*q**2 + 7/15*q**3 - j*q**7. Factor m(c).
-2*(c - 1)**4*(c + 2)/5
Let y = 161/164 - 30/41. Suppose 0 - y*r**2 - 1/4*r = 0. Calculate r.
-1, 0
Let p be (-6826)/(-1056) + (-22)/(-121). Let w = -21/16 + p. Factor 3 + 8*b + w*b**2.
(4*b + 3)**2/3
Factor -16*i**2 - i**4 + 65*i**2 + 3*i**5 + 48*i + 23*i**2 + 3*i**3 - 17*i**4.
3*i*(i - 4)**2*(i + 1)**2
Let k(n) be the third derivative of -n**6/120 - n**5/180 + 2*n**3/3 - n**2. Let z(s) be the first derivative of k(s). Suppose z(h) = 0. Calculate h.
-2/9, 0
Factor 2*j**2 - 5*j**2 - 6*j + 2 - 2.
-3*j*(j + 2)
Let a be 2/4 - (-14)/4. Let t be (a/(-6))/((-16)/18). Factor -1/2*c - 3/4*c**2 + 0 + 1/2*c**3 + t*c**4.
c*(c - 1)*(c + 1)*(3*c + 2)/4
Let i = -33 - -101/3. Let f be (0 - -2)*30/20. Solve 2*p**f - i*p - 8/3*p**2 + 4/3 = 0 for p.
-2/3, 1
Suppose -4*y = 5*p - 10, -y - 4*y = 0. Solve 0 - 8/3*d - 10/3*d**3 - 16/3*d**p - 2/3*d**4 = 0.
-2, -1, 0
Let d(w) = -4*w**5 + 4*w**3 - 8*w**2. Let q(c) = 4*c**5 - c**4 - 4*c**3 + 7*c**2. Let y(x) = 3*d(x) + 4*q(x). Factor y(s).
4*s**2*(s - 1)**2*(s + 1)
Let v be (6/4)/((-6)/(-8)). Let a(p) = p - 1. Let h be a(3). What is b in 6*b**2 - h - 4*b**v + 0*b**2 = 0?
-1, 1
Let h = -35 - -39. Factor 2/5*o**2 - 12/5*o**3 + 0*o + 0 - 8/5*o**5 + 18/5*o**h.
-2*o**2*(o - 1)**2*(4*o - 1)/5
Let z(k) be the first derivative of k**5/5 + k**4/2 + k**3/3 - 13. Factor z(s).
s**2*(s + 1)**2
Solve 14 - 2*a**3 + 3 - 4*a**4 - 2*a**5 - 17 = 0 for a.
-1, 0
Let c(l) be the first derivative of 4 + 1/30*l**5 + 0*l + 1/6*l**2 - 1/6*l**3 + 0*l**4. Determine t so that c(t) = 0.
-2, 0, 1
Let a(d) be the third derivative of 0 - 1/60*d**4 + 0*d**3 + 1/300*d**6 + 1/525*d**7 - 1/150*d**5 + 3*d**2 + 0*d. Factor a(y).
2*y*(y - 1)*(y + 1)**2/5
Let g(z) = -2*z + z + 1 - z**2 + 2*z**2. Let r(q) = 9*q**3 + 9*q**2 - 14*q + 2. Let n be -1*(3 + -4)*-1. Let s(l) = n*r(l) + 6*g(l). Let s(a) = 0. What is a?
-2/3, 1
Let j(c) = c**2 + 7*c - 6. Let v be (-3 - -1)*4*1. Let z be j(v). Factor -r**2 - 3 + z + 7*r - 5*r.
-(r - 1)**2
Suppose 0*n - 24 = -3*n + 3*p, -5 = 5*n + 4*p. Suppose b = 4*j + n, -7