 third derivative of i**7/525 - i**5/50 - i**4/30 - 5*i**2. Factor z(r).
2*r*(r - 2)*(r + 1)**2/5
Let x(m) be the second derivative of -1/2*m**3 + 0*m**4 + 1/120*m**5 + 0*m**2 + 0 + 3*m + 1/180*m**6. Let a(g) be the second derivative of x(g). Factor a(v).
v*(2*v + 1)
Let w(x) be the first derivative of -x**5/35 + x**3/7 - x**2/7 + 35. Determine k, given that w(k) = 0.
-2, 0, 1
Let k(r) = -r**5 + r**4 + r**2. Let q(g) = -12*g**5 + 2*g**4 + 6*g**3 + 10*g**2. Let u = 2 - 3. Let j(x) = u*q(x) + 6*k(x). Let j(l) = 0. What is l?
-1, -2/3, 0, 1
Factor 270 - 270 - 4*t + 4*t**3.
4*t*(t - 1)*(t + 1)
Determine n, given that 0 + 10/3*n**4 + 4/3*n - 10/3*n**2 - 2*n**5 + 2/3*n**3 = 0.
-1, 0, 2/3, 1
Suppose 34*f = 8*f. What is s in -6/5*s**5 - 3/5*s**4 + 0*s + 0*s**2 + 3/5*s**3 + f = 0?
-1, 0, 1/2
Let o = -4 - -8. Let x = 7 - o. Factor s**2 - 5*s**2 + 2*s + x*s**2 + 3*s**2.
2*s*(s + 1)
Let s be 9/(-6) + (-2)/(-4). Let o be 170/(-17)*s*1. Suppose -1/3 - o*a**2 - 11*a**4 - 3*a**5 - 46/3*a**3 - 3*a = 0. Calculate a.
-1, -1/3
What is f in -8*f**2 + 4 + f**2 + f**2 - 2*f**4 + 8*f**3 - 8*f + 4 = 0?
-1, 1, 2
Suppose 2*j - 5*d + 4*d - 6 = 0, 5*d - 6 = -2*j. Factor -4/9 + 8*h**2 - 18*h**j + 2/3*h.
-2*(3*h - 1)**2*(9*h + 2)/9
Let x(w) = 5*w**3 - 4*w**2 - 40*w - 6. Let a(m) = -30*m**3 + 25*m**2 + 240*m + 35. Let r(z) = 6*a(z) + 35*x(z). Factor r(g).
-5*g*(g - 4)*(g + 2)
Let g(d) = d - 3. Let f be g(3). Let q be (-30)/(-18)*(-6)/(-5). Factor -1/4*s**q + 1/4*s**4 - 1/4*s**5 + 0*s + 1/4*s**3 + f.
-s**2*(s - 1)**2*(s + 1)/4
Let r be 1/6*2/7. Let i(z) be the first derivative of r*z**6 + 2 + 3/7*z**4 - 8/21*z**3 + 0*z + 1/7*z**2 - 8/35*z**5. Factor i(l).
2*l*(l - 1)**4/7
Solve -2*x**2 + 189*x**3 - 2*x**2 - 4*x - 190*x**3 = 0.
-2, 0
Factor -2*q - 3*q**3 + q**4 - 6*q**2 + 0*q + q**2 + q**5.
q*(q - 2)*(q + 1)**3
Let y(x) be the first derivative of 2*x**3/9 + x**2/3 - 4*x/3 - 8. Let y(q) = 0. Calculate q.
-2, 1
Let j(r) be the first derivative of -4/3*r**3 - 1/30*r**5 - r**2 + 2 + 1/3*r**4 + 0*r. Let x(g) be the second derivative of j(g). Factor x(p).
-2*(p - 2)**2
Suppose 0*k**3 + 2/3*k**5 + 0*k**2 + 0*k + 2/9*k**4 + 0 = 0. Calculate k.
-1/3, 0
Solve -21*s**2 - 15*s**2 + 36*s**2 - 2*s**4 + 6*s**3 = 0 for s.
0, 3
Let r be (-259)/(-74) - (-73)/(-22). Let -6/11*b + 0 + r*b**2 = 0. What is b?
0, 3
Let b(i) = -9*i**3 + 3*i**2 + 9*i - 9. Let q(g) = 8*g**3 - 4*g**2 - 8*g + 9. Let v(w) = -5*b(w) - 6*q(w). Let v(d) = 0. What is d?
-1, 1, 3
Let r(p) be the first derivative of p**6/1260 - p**4/84 + 2*p**3/3 + 3. Let h(v) be the third derivative of r(v). Factor h(a).
2*(a - 1)*(a + 1)/7
Let b be 20/(-8)*-1*2. Let v = b - 1. Factor 10*x**4 + 2*x - 4*x**3 - 6*x**3 + 2*x**2 - 4*x**v.
2*x*(x - 1)**2*(3*x + 1)
Let c(v) = -11*v**3 + 20*v**2 - 9*v + 8. Let x(i) = 4*i**3 - 7*i**2 + 3*i - 3. Let l(w) = -3*c(w) - 8*x(w). Suppose l(g) = 0. Calculate g.
0, 1, 3
Factor -1/4*x**2 + 1/2*x - 1/4.
-(x - 1)**2/4
Let m(b) be the first derivative of 1/2*b**2 - b + 1/3*b**3 - 1/4*b**4 - 7. Suppose m(k) = 0. What is k?
-1, 1
Let u(r) be the third derivative of -2*r**2 - 1/600*r**6 - 1/30*r**3 + 0*r + 0 + 1/120*r**4 + 1/300*r**5. Factor u(j).
-(j - 1)**2*(j + 1)/5
Determine g so that 1/6*g**3 + 1/6*g**2 - 1/6*g - 1/6 = 0.
-1, 1
Let s(y) be the third derivative of -y**5/210 + y**4/14 - 2*y**2 + 6*y. Factor s(f).
-2*f*(f - 6)/7
Let z(s) = 7*s - 3. Let n be z(1). Determine c, given that 6/7*c**n + 2/7*c**5 - 2/7 - 6/7*c + 4/7*c**3 - 4/7*c**2 = 0.
-1, 1
Suppose 4*r + 3*d + 3 = 0, 4*d + 20 = -0*d. Factor 8/7*t - 8*t**2 - 12*t**4 + 0 + 18/7*t**5 + 122/7*t**r.
2*t*(t - 2)**2*(3*t - 1)**2/7
Let t(d) = 3*d**2 + 12 - 7 - 2*d**2. Let v(o) = 2. Let x = -4 + 9. Let g(h) = x*v(h) - 2*t(h). Determine r so that g(r) = 0.
0
Let w(t) = -t**3 + t**2 + t - 1. Suppose -60 = 4*i - 9*i. Let r(v) = 68*v**3 - 52*v**2 + 8*v + 3. Let d(g) = i*w(g) + 3*r(g). Solve d(s) = 0.
1/4
Suppose 4*a - 8*a + 45 = -5*v, 0 = -2*a. Let q(i) = i**2 - 2*i - 3. Let m(h) = -2*h**2 + 4*h + 6. Let o(x) = v*q(x) - 4*m(x). Factor o(b).
-(b - 3)*(b + 1)
Factor 34/3*k**2 - 8/3*k**3 + 0 - 8/3*k.
-2*k*(k - 4)*(4*k - 1)/3
Let v(s) = s**3 + 6*s**2 - 6*s + 4. Let u be v(-7). Let y be u/((-1)/(2 + -1)). Factor 0 + 0*i**2 + 1/3*i - 1/3*i**y.
-i*(i - 1)*(i + 1)/3
Let u(p) be the second derivative of p**6/360 + p**5/90 + p**4/72 - 4*p**2 - 4*p. Let y(h) be the first derivative of u(h). Let y(o) = 0. What is o?
-1, 0
Suppose 5*c + 5*q - 20 = 0, 0*c + 7 = -2*c - 5*q. Factor -10*s + c*s + 18 + 2*s**2 - 11*s.
2*(s - 3)**2
Let a = 51 - 44. Let d(q) be the third derivative of 1/12*q**4 - 1/420*q**a + q**2 + 2/3*q**3 + 0*q - 1/48*q**6 - 1/20*q**5 + 0. Factor d(u).
-(u - 1)*(u + 2)**3/2
Let h(t) be the second derivative of 0*t**4 + 1/84*t**7 - 3*t + 1/30*t**6 + 1/40*t**5 + 0 + 0*t**2 + 0*t**3. Factor h(k).
k**3*(k + 1)**2/2
Let x be (-4)/6 + (-112)/(-24). Let v(f) be the third derivative of 0 + 0*f + 0*f**x + 0*f**3 - 2*f**2 - 1/210*f**5. Factor v(u).
-2*u**2/7
Let v(y) be the third derivative of 0 + 0*y - 1/5*y**5 - 1/70*y**7 + 0*y**4 - 3*y**2 + 0*y**3 - 1/10*y**6. Factor v(l).
-3*l**2*(l + 2)**2
Factor 2/5*a**2 - 2/5 + 8/5*a - 8/5*a**3.
-2*(a - 1)*(a + 1)*(4*a - 1)/5
Let s(m) = -m**3 + 10*m**2 + 10*m + 11. Let f be s(11). Let q be 18/14 - (1 - 0). Suppose 4/7*j**2 + f - 2/7*j**3 - q*j = 0. What is j?
0, 1
Let v be 26/12 - 10/60. Let u(w) be the third derivative of -1/30*w**5 - 3*w**v + 1/105*w**7 + 0 + 0*w + 1/60*w**6 - 1/12*w**4 + 0*w**3. Factor u(d).
2*d*(d - 1)*(d + 1)**2
Suppose 5*i - 4 = 3*i. Let b = -5 + i. Let m(g) = -g**2 + 6*g - 1. Let x(p) = 6*p. Let n(f) = b*m(f) + 2*x(f). Factor n(t).
3*(t - 1)**2
Suppose 0*t**3 + 0 + 4/7*t**4 + 0*t + 0*t**2 + 2/7*t**5 = 0. Calculate t.
-2, 0
Let v = 11 + -8. Factor 2/3 - 2*c - 2/3*c**v + 2*c**2.
-2*(c - 1)**3/3
Suppose -y**2 + 2*y - 5*y**3 - 3*y**3 + 5*y**2 + 2*y = 0. What is y?
-1/2, 0, 1
Solve -1/3*r + 2/3 - 1/3*r**2 = 0 for r.
-2, 1
Let c(p) be the third derivative of 3*p**6/200 - 3*p**5/100 - p**4/30 + 2*p**3/15 - 6*p**2. Solve c(h) = 0.
-2/3, 2/3, 1
Let j(p) be the third derivative of -2*p**7/525 - p**6/30 - 3*p**5/25 - 7*p**4/30 - 4*p**3/15 + 4*p**2. Suppose j(g) = 0. What is g?
-2, -1
Let -3*d**2 + 3*d**3 + 3*d**3 - 7*d - 9*d**4 + d + 12*d**2 = 0. Calculate d.
-1, 0, 2/3, 1
Let d(w) = w**2 + w - 1. Let b be d(1). Let h = b + -3/5. Suppose -6/5*g**4 - 8/5*g**3 + 8/5*g + 4/5*g**2 + h = 0. Calculate g.
-1, -1/3, 1
Suppose -8*r - 18 = -14*r. Factor -81/5*q + 27/5*q**2 - 3/5*q**r + 81/5.
-3*(q - 3)**3/5
Suppose 20 = 108*h - 103*h. Let b(j) be the second derivative of 0 + 0*j**2 + 1/3*j**3 - 1/2*j**h - 1/15*j**6 - 2*j + 3/10*j**5. Factor b(p).
-2*p*(p - 1)**3
Let x(q) be the third derivative of q**6/240 + q**5/20 + 11*q**4/48 + q**3/2 + 28*q**2. Factor x(r).
(r + 1)*(r + 2)*(r + 3)/2
Solve 4/7*o**3 + 17/7*o**2 + 3/7 + 16/7*o = 0 for o.
-3, -1, -1/4
Let z(g) = 11*g**4 - 36*g**3 + 83*g**2 - 72*g + 19. Let n(b) = -6*b**4 + 18*b**3 - 42*b**2 + 36*b - 9. Let i(k) = -5*n(k) - 3*z(k). Factor i(s).
-3*(s - 2)**2*(s - 1)**2
Factor 3*h - 11*h**2 + 6*h**3 + 5*h**2 - 3*h**3.
3*h*(h - 1)**2
Let i(c) = 4*c**3 - 5*c**2 + 4*c. Let y(j) = 4*j**3 - 4*j**2 + 4*j. Let f(u) = -4*i(u) + 3*y(u). Solve f(r) = 0.
0, 1
Let t = -3 - 8. Let s = -7 - t. Factor -6*a**4 + s*a**3 - 3*a**3 + 5*a**4.
-a**3*(a - 1)
Let v be 3 - (5 + ((-7)/2 - -1)). Factor -1/2 + v*s**4 - s**3 + 0*s**2 + s.
(s - 1)**3*(s + 1)/2
Let s = -1766/3 + 627. Let b = -37 + s. Factor -b*y**2 + 2/3 + 0*y**3 + 0*y + 2/3*y**4.
2*(y - 1)**2*(y + 1)**2/3
Let t be (18/7)/((-3)/(-14)). Let k be (t/(-15))/((-6)/15). Determine l, given that -2*l**2 - 2/3 + 2/3*l**3 + k*l = 0.
1
Let n be (-1 + 10)/(-2 + 3). Suppose v - n = -2*v. Find x, given that -4*x**2 + v*x**2 + 4*x**4 + x**2 - 14*x**5 = 0.
0, 2/7
Let u(a) be the first derivative of -a**5/10 - a**4/4 - a**3/6 + 1. Factor u(s).
-s**2*(s + 1)**2/2
Let u(d) be the first derivative of d**7/420 + d**6/60 + d**5/20 + d**4/12 - d**3 - 3. Let c(z) be the third derivative of u(z). Factor c(k).
2*(k + 1)**3
Suppose -57*x + 144 = -33*x. Find w such that -3/2*w**3 + x*w - 4 - 1/4*w**4 - 1/4*w**2 = 0.
-4, 1
Suppose 6*z = 3*z + 30. Factor 3 + 12*h**3 - z*h**3 - 2*h**5 - 3.
-2*h**3*(h - 1)*(h + 1)
Let n(l) be the second derivative of -l**4/20 - 2*l**3/5 - 9*