). Factor -40/3*n**2 - 8/3*n - 50/3*n**t + 0.
-2*n*(5*n + 2)**2/3
Suppose -1 - 8*d - 1 - 5*d**2 - 1 + 0 = 0. Calculate d.
-1, -3/5
Solve -27*w**2 + 10*w**3 + 48*w**2 - 21*w**2 + 5*w**4 = 0 for w.
-2, 0
Factor 0*z - 1/6*z**4 - 2/3*z**3 + 0 + 0*z**2.
-z**3*(z + 4)/6
Let w(c) be the first derivative of c**3 - 6*c**2 - 15*c + 2. What is m in w(m) = 0?
-1, 5
Let l be (57/45 + 3)*(4 - 1). Factor 2/5*q**4 + 48/5*q**2 - l*q + 32/5 - 16/5*q**3.
2*(q - 2)**4/5
Suppose -5*o + 4*n = 2, -3*o + 0*o + 2*n = 0. Let l(v) be the first derivative of -2/3*v**3 + 0*v**2 - o + 0*v. Factor l(x).
-2*x**2
Let k be -3*((-219)/108 - -2). Let o(u) be the third derivative of -1/60*u**5 + u**2 + 0 + k*u**4 - 1/6*u**3 + 0*u. Factor o(r).
-(r - 1)**2
Suppose 3*z + 5*y - 48 = 29, 117 = 5*z - 3*y. Let i be z/8 - (-5)/(-2). Factor -3/4*s**4 - i*s**3 + 1/2*s**2 - 1/4*s**5 + 3/4*s + 1/4.
-(s - 1)*(s + 1)**4/4
Factor 3*j + j**3 + 3*j**2 - 3*j**2 - 3*j**2 - j.
j*(j - 2)*(j - 1)
Suppose -1/2 - p**2 + 5/4*p + 1/4*p**3 = 0. Calculate p.
1, 2
Let r(h) be the first derivative of h**6/42 - h**4/28 + 22. Factor r(p).
p**3*(p - 1)*(p + 1)/7
Let z(s) = -s**2 + s. Let a(v) = -9*v - 13. Let k(c) = 2*c + 3. Let b(d) = 6*a(d) + 26*k(d). Let h(f) = b(f) + 2*z(f). Factor h(y).
-2*y**2
Let p(v) be the second derivative of -1/60*v**5 + 0*v**2 - v + 0 + 0*v**3 - 1/90*v**6 + 1/18*v**4. Factor p(s).
-s**2*(s - 1)*(s + 2)/3
Let q be (-1)/5 - (-1)/5. Let d = -158 + 478/3. Factor d*x**2 + q - 1/3*x**5 - 2*x**3 - 1/3*x + 4/3*x**4.
-x*(x - 1)**4/3
Let u be ((-96)/324)/((-2)/6). Let i(m) be the first derivative of 0*m - u*m**3 - 2 + 1/6*m**2 + 4/3*m**4. Find x such that i(x) = 0.
0, 1/4
Let c be 55/(-2)*(-8)/10. Let q(r) = -r**4 + r**2 - r - 1. Let h(a) = -12*a**4 - 2*a**3 + 11*a**2 - 9*a - 10. Let v(g) = c*q(g) - 2*h(g). Factor v(i).
2*(i - 1)*(i + 1)**3
Suppose 5*b - 5*b**2 + 0 - 15/4*b**3 + 5/4*b**5 + 5/2*b**4 = 0. What is b?
-2, 0, 1
Let c(s) be the third derivative of 2*s**7/105 - s**6/15 - s**5/5 + 4*s**4/3 - 8*s**3/3 - 2*s**2. Suppose c(o) = 0. Calculate o.
-2, 1, 2
Let c(k) = 31*k**3 - 2*k + 5*k + 0*k**2 - 8 - 2*k**2 - 20*k**3. Let d(w) = -4*w**3 + w**2 - w + 3. Let x(v) = 3*c(v) + 8*d(v). Factor x(z).
z*(z + 1)**2
Let j(q) be the third derivative of -1/1800*q**6 + 0*q + 0 - q**2 - 1/600*q**5 - 1/6*q**3 + 0*q**4. Let f(t) be the first derivative of j(t). Factor f(b).
-b*(b + 1)/5
Let u be 3/(-6) + (-56)/(-16). Factor 0 - 3/5*t**u - 2/5*t**2 + 0*t.
-t**2*(3*t + 2)/5
Let c(p) be the second derivative of -p**6/120 - p**5/16 - 3*p**4/16 - 7*p**3/24 - p**2/4 + 3*p. Factor c(t).
-(t + 1)**3*(t + 2)/4
Let h(i) = 3*i**2 + i - 1. Let y be h(1). Factor -l**2 + 3*l**3 - 5*l**y + 3*l**3.
l**2*(l - 1)
Let q be (-4)/3*(-15)/10. Let t(a) = 3*a - 14. Let c be t(6). Factor -2/9*v**c + 0 - 2/9*v**q + 4/9*v**3 + 0*v.
-2*v**2*(v - 1)**2/9
Solve -54*o**2 + 4*o**3 + 57*o**2 - 4 - 3*o**3 = 0 for o.
-2, 1
Let w(g) = g**2 + 9*g + 17. Let c be w(-9). Suppose c*m - 19*m = 0. Determine h, given that -1/2*h**2 - h + m = 0.
-2, 0
Let t be (-20)/(-25) + 0/(-5). Factor t*g**2 + 0 + 0*g - 16/5*g**3 + 12/5*g**4.
4*g**2*(g - 1)*(3*g - 1)/5
Suppose -5*h = 5*w + 10, -w - 4 = -4*w - h. Let c be ((-12)/9)/((-14)/w). Let c*a**3 + 2/7*a + 0 + 4/7*a**2 = 0. Calculate a.
-1, 0
Let a(k) be the third derivative of -6*k**2 + 3/100*k**6 + 0 + 9/350*k**7 + 2/5*k**3 - 11/100*k**5 - 1/10*k**4 + 0*k. Factor a(c).
3*(c + 1)**2*(3*c - 2)**2/5
Let f(b) = -2*b**2 + b. Let r(g) = -2*g**2 + 2*g. Let p(c) = 6*f(c) - 7*r(c). Suppose p(d) = 0. Calculate d.
0, 4
Let q(p) be the third derivative of 1/120*p**5 + 0 + 1/48*p**4 - 1/240*p**6 - p**2 + 0*p - 1/12*p**3. Solve q(w) = 0 for w.
-1, 1
Let o(s) be the first derivative of -s**5/5 + s**4/2 - s**2 + s - 6. Find f such that o(f) = 0.
-1, 1
Let u(w) be the second derivative of 1/12*w**4 + w + 0 - 1/2*w**2 + 0*w**3. Find a, given that u(a) = 0.
-1, 1
Let p = 2041/30 - 401/6. Determine q, given that 3/5*q**3 - p*q + 3/5*q**2 + 0 = 0.
-2, 0, 1
Suppose -2*w + 2 = 4*a - 2, 3*w = 5*a - 16. Suppose 6*q**4 + 1 + 2*q**5 + 2*q**a - 1 + 6*q**3 = 0. Calculate q.
-1, 0
Suppose 2*h + h = 0. Suppose -l = -4*t + 8, -4*t + 8 = -h*t + 3*l. Solve 0*p + 0*p**t - 1/5*p**3 + 0 = 0 for p.
0
Let c(r) be the second derivative of r**5/10 + r**4/6 - 2*r**3/3 + 5*r. Find l such that c(l) = 0.
-2, 0, 1
Let r(v) be the first derivative of v**7/630 - v**6/90 + v**5/45 + 2*v**2 - 1. Let o(s) be the second derivative of r(s). Factor o(p).
p**2*(p - 2)**2/3
Suppose 90 + 15 = 3*j. Let g = j + -243/7. Factor 6/7*s**3 + 0*s + 0 + g*s**5 + 2/7*s**2 + 6/7*s**4.
2*s**2*(s + 1)**3/7
Let m(d) be the second derivative of -d**4/48 - d**3/6 - d**2/2 - 3*d. Factor m(j).
-(j + 2)**2/4
Let o(v) be the third derivative of 0 - 3*v**2 - 1/15*v**3 + 0*v - 3/50*v**5 + 1/10*v**4. Suppose o(j) = 0. Calculate j.
1/3
Let k(n) = n**2 + 8*n + 9. Let i(j) = j**2 - 1. Let z(r) = -i(r) - k(r). Factor z(h).
-2*(h + 2)**2
Let f(y) be the third derivative of -y**8/50400 - y**7/2100 - y**6/200 - y**5/12 - 6*y**2. Let n(m) be the third derivative of f(m). Factor n(r).
-2*(r + 3)**2/5
Let h be -1 + 2 - 9373/35. Let n = 268 + h. Let -6/5*r**2 - 2/5*r**3 - 2/5 - n*r = 0. Calculate r.
-1
Suppose 20*j**3 - 8 + 4*j - 7*j + 7*j + 32*j**2 = 0. What is j?
-1, 2/5
Let x(n) be the third derivative of -3*n**6/40 + n**5 - 37*n**4/24 + n**3 - 3*n**2. Factor x(y).
-(y - 6)*(3*y - 1)**2
Let h(f) be the second derivative of f**6/1440 + f**5/240 + f**4/96 + f**3/2 - f. Let b(j) be the second derivative of h(j). Determine m, given that b(m) = 0.
-1
Let l be (-2)/11 - (-336)/396. Factor -2/3*h**2 + l*h + 0.
-2*h*(h - 1)/3
Let g be ((-24)/60)/(2/(-20)). Suppose 1 = r + 5, 0 = 5*b + g*r + 1. Factor 0 + 0*v + 0*v**2 + 2/3*v**4 - 1/3*v**5 - 1/3*v**b.
-v**3*(v - 1)**2/3
Suppose -6*j + 0*j = 12. Let o be 110/90 - j/(-2). Determine y, given that -2/9*y**2 + 4/9*y - o = 0.
1
Let q(u) be the third derivative of u**5/15 - 4*u**4/3 - 2*u**2. Factor q(j).
4*j*(j - 8)
Let i = 353 - 1411/4. Determine q, given that -1/2 - q**2 - i*q**3 - 5/4*q = 0.
-2, -1
Let s be (-8)/21 + (4 - 20/6). Factor -s*o**4 + 2/7 + 0*o**2 - 4/7*o + 4/7*o**3.
-2*(o - 1)**3*(o + 1)/7
Factor -2/9*t**3 + 0 + 0*t + 2/9*t**2.
-2*t**2*(t - 1)/9
Let m = -19 - -11. Let j(n) = 3*n**3 + 5*n**2 + 2*n. Let f(a) = 5*a**3 + 8*a**2 + 3*a. Let d(b) = m*j(b) + 5*f(b). Find r such that d(r) = 0.
-1, 0, 1
Determine o, given that 2 + 4*o**2 - o**3 + 0*o**2 - o + 4*o - 8*o = 0.
1, 2
Let r = 3 - 3. Let t(v) = -3*v. Let c be t(r). Find g, given that -4/11*g + 10/11*g**2 + c = 0.
0, 2/5
Let p(r) = r**4 + 15*r**3 - 9*r**2 + 5*r + 6. Let l(j) = j**4 + 29*j**3 - 17*j**2 + 9*j + 11. Let b(x) = -6*l(x) + 11*p(x). Factor b(s).
s*(s - 1)**2*(5*s + 1)
Let w(l) be the second derivative of -1/18*l**3 + 0*l**2 + 1/60*l**5 + 0 - 1/36*l**4 + 1/90*l**6 + 5*l. Factor w(k).
k*(k - 1)*(k + 1)**2/3
Let p(h) = h**3 + h - 10. Let r be p(0). Let b be 2/18*r + 2. Factor -b + 2/3*g**2 + 16/9*g - 2*g**3.
-2*(g + 1)*(3*g - 2)**2/9
Let c be ((-8)/6 + 1)*-6. Factor -1 - 1 + 0*i**3 + 0*i + i**3 - 4*i**c + 5*i.
(i - 2)*(i - 1)**2
Let n(h) be the first derivative of -2*h + 5/3*h**3 + 2 - 3/2*h**2. Find m, given that n(m) = 0.
-2/5, 1
Let w(o) be the second derivative of 2*o + 0*o**3 - 1/12*o**4 + 1/15*o**5 + 0 - o**2. Let j(l) be the first derivative of w(l). Solve j(r) = 0.
0, 1/2
Let o(r) be the first derivative of -4*r**7/105 - r**6/30 + 7*r**5/120 - r**4/48 + 3*r**2/2 + 3. Let c(t) be the second derivative of o(t). Factor c(i).
-i*(i + 1)*(4*i - 1)**2/2
Let q(u) = 10*u**5 + 20*u**4 - 10*u**3 - 20*u**2 + 5. Let l(t) = -5*t**5 - 10*t**4 + 5*t**3 + 10*t**2 - 2. Let s(r) = 5*l(r) + 2*q(r). What is c in s(c) = 0?
-2, -1, 0, 1
Let y(t) = 11*t**4 - 36*t**3 + 66*t**2 - 56*t + 21. Let p(g) = -g**4 + g**3 - g**2 + g - 1. Let q(l) = -6*p(l) - y(l). Solve q(j) = 0.
1, 3
Let u = -6 + 2. Let y be u/16 + (-9)/(-4). Solve 3*m**2 + y*m**2 + 4*m - 7*m**2 - 2 = 0.
1
Let i be ((-1)/(-9))/(1/3). Find p, given that 0*p**2 - i*p**3 - 1/3*p**4 + 0*p + 0 = 0.
-1, 0
Let n(y) be the first derivative of -y**4/12 + y**3/8 + y**2/8 + y - 2. Let d(f) be the first derivative of n(f). Factor d(w).
-(w - 1)*(4*w + 1)/4
Let h be (1/(-6))/((-2)/(-3)*-1). Let t(z) be the first derivative of -1/2*z**2 + 3 - 1/4*z**3