36*q - 36*q + q**3 - q**s + q**2.
-q**2*(q - 1)*(q + 1)**2
Let u(v) = 9*v**2 + 24*v - 36. Let m(l) = 7*l**2 + 4*l - 1 - 3*l**2 + 8*l - 17. Let j(s) = 13*m(s) - 6*u(s). Let j(k) = 0. Calculate k.
3
What is n in 25*n**3 - 26*n + 19*n - 5*n**4 + 42*n - 45*n**2 - 10 = 0?
1, 2
Suppose 4*h - 6*a + 1 = -3*a, 0 = 3*a - 9. Let m be (h/(-6))/(77/(-66)). Find l, given that 6/7*l**2 - 6/7*l + 2/7 - m*l**3 = 0.
1
Factor 0 - 2/11*p**3 + 4/11*p**2 - 2/11*p.
-2*p*(p - 1)**2/11
Let f(v) be the second derivative of -v**4/28 - v**3/2 - 15*v**2/7 - 27*v. Factor f(m).
-3*(m + 2)*(m + 5)/7
Let g be 3/6 - 55/10. Let f be g/(15/12)*-1. Determine x so that 4*x**4 - 2*x**4 + f*x**3 + 2*x**3 + x**4 + 3*x**2 = 0.
-1, 0
Let h = -35 + 35. Factor -2/7*s**2 + h*s + 2/7.
-2*(s - 1)*(s + 1)/7
Let z(s) be the third derivative of s**4/24 + s**3 + 6*s**2. Let o be z(-4). Factor -50/3*q**4 + 0 + 10/3*q**3 + 8/3*q + 32/3*q**o.
-2*q*(q - 1)*(5*q + 2)**2/3
Suppose -4 - 6 = -5*f. Suppose -l = 4*l. Factor d**f + l*d**3 - 2*d**3 + 3*d**3.
d**2*(d + 1)
Let y = -28 - -34. Let s(d) be the first derivative of 1/15*d**5 + 0*d - 1/18*d**y - 3 - 1/9*d**3 + 1/12*d**4 + 0*d**2. Let s(q) = 0. Calculate q.
-1, 0, 1
Let l(b) be the third derivative of -1/270*b**5 + 0*b + 4*b**2 + 0*b**3 + 1/108*b**4 + 0. Factor l(w).
-2*w*(w - 1)/9
Suppose -10 + 44*n**4 + 12*n + 8*n**2 - 82*n**4 - 12*n**3 + 40*n**4 = 0. What is n?
-1, 1, 5
Let s = 516 - 514. Suppose -h - 3*h = 0. Suppose h - 2/7*l**s + 0*l = 0. What is l?
0
Let x be 44 + -37 - 94/14. What is f in x*f**2 + 2/7*f + 0 = 0?
-1, 0
Let o = 3172/5 + -634. What is b in 0 + 0*b - 2/5*b**5 + 0*b**2 + o*b**4 + 0*b**3 = 0?
0, 1
Suppose 13*v - 7*v = 0. Factor 2/3*m**3 - 2/3*m + 0*m**2 + v.
2*m*(m - 1)*(m + 1)/3
Let l(c) be the first derivative of 5*c**6/6 + 6*c**5/5 - 11*c**4/20 - 4*c**3/5 + 2*c**2/5 + 3. Find d, given that l(d) = 0.
-1, 0, 2/5
Let p be (-3)/(-162)*-3*6/(-10). Let k(d) be the third derivative of 1/150*d**5 + 0 - 3*d**2 + 1/15*d**3 - p*d**4 + 0*d. Factor k(a).
2*(a - 1)**2/5
Let d(f) be the third derivative of -2*f**2 - 1/20*f**5 + 0*f - 1/20*f**6 + 1/8*f**4 + 0*f**3 + 0. Determine y so that d(y) = 0.
-1, 0, 1/2
Let p(z) be the third derivative of -1/108*z**4 + 1/27*z**3 + 0 + 0*z - 1/135*z**5 + 4*z**2 + 1/945*z**7 + 1/270*z**6 - 1/1512*z**8. Factor p(x).
-2*(x - 1)**3*(x + 1)**2/9
Suppose 0 = -p + 3*p - 4. Factor 4*j**4 - 28*j**2 - 3 + p*j**5 - 14*j - 1 + 12*j**2 - 4*j**3.
2*(j - 2)*(j + 1)**4
Let w(j) = 4*j - 7. Let d be w(7). Let s = -19 + d. Factor -48/7*k**3 + 18/7*k**s + 0 - 2/7*k + 32/7*k**4.
2*k*(k - 1)*(4*k - 1)**2/7
Let w(z) be the first derivative of -2*z**5/35 - 3*z**4/7 - 26*z**3/21 - 12*z**2/7 - 8*z/7 + 17. Factor w(y).
-2*(y + 1)**2*(y + 2)**2/7
Let v = 112 + -110. Factor 0 + 0*l + 2/9*l**3 + 0*l**v.
2*l**3/9
Let z be (-4)/28 + 86/14. Let l(w) be the third derivative of 0*w**5 - w**2 + 0*w + 1/80*w**z - 1/2*w**3 - 3/16*w**4 + 0. Factor l(s).
3*(s - 2)*(s + 1)**2/2
Factor -3/2*c + 21/8*c**3 + 9/2*c**2 + 0.
3*c*(c + 2)*(7*c - 2)/8
Let w(k) be the third derivative of 0 + 0*k - 1/40*k**6 - 4/9*k**3 - 7/18*k**4 - k**2 - 1/6*k**5. Let w(p) = 0. What is p?
-2, -2/3
Let p be 132/(-10)*(-28)/612. Let l = -1/255 + p. Factor -1/5 - 3/5*t**2 - l*t - 1/5*t**3.
-(t + 1)**3/5
Factor 0 + 1/8*v**2 - 2*v.
v*(v - 16)/8
Let r(i) be the third derivative of i**4/24 + i**3 + 2*i**2. Let t be r(0). Factor 7*k - t*k**3 + 3*k**5 + 3*k**4 + 3 - k - 3*k - 6*k**2.
3*(k - 1)**2*(k + 1)**3
Let s(p) be the third derivative of -1/20*p**6 + 0*p - 3/175*p**7 + 0 - 9*p**2 - 7/150*p**5 + 0*p**3 - 1/60*p**4. Find n such that s(n) = 0.
-1, -1/3, 0
Let n(y) = 7*y**2 + y + 9. Let i(k) = 8*k**2 + 10. Let x(h) = -5*i(h) + 6*n(h). Find g, given that x(g) = 0.
-2, -1
Let a(d) be the second derivative of 0 + 1/6*d**6 + 2/3*d**3 + 11/20*d**5 + 2*d**2 - 1/14*d**7 + 3*d - 7/4*d**4. Determine j, given that a(j) = 0.
-2, -1/3, 1, 2
Let g(s) be the first derivative of -3*s**4/14 + 8*s**3/21 + 5*s**2/7 - 4*s/7 - 33. Find z, given that g(z) = 0.
-1, 1/3, 2
Factor -75/2 + 27/2*l**2 + 3/2*l**3 + 45/2*l.
3*(l - 1)*(l + 5)**2/2
Factor -2/3*y - y**2 + 0 + 5/3*y**3.
y*(y - 1)*(5*y + 2)/3
Let z(h) = -9*h**3 + 51*h**2 - 84*h + 16. Let g(p) = 10*p**3 - 51*p**2 + 84*p - 14. Let j(v) = 2*g(v) + 3*z(v). Determine x so that j(x) = 0.
2/7, 2, 5
Let b be -3 + (-115)/(-50) + 1. Let k(y) be the first derivative of -b*y**4 + 0*y + 2 - 2/15*y**3 + 2/5*y**2. Factor k(v).
-2*v*(v + 1)*(3*v - 2)/5
Let d be ((-20)/(-8))/(1/2). Suppose 0 = -4*m + d*j + 26, 8*m = 3*m - 4*j + 12. Determine k, given that -7/2*k**m + 0 - k**2 + 9/2*k**3 + 0*k = 0.
0, 2/7, 1
Let y(w) be the first derivative of w**5/5 + 9*w**4/4 + 29*w**3/3 + 39*w**2/2 + 18*w - 47. Solve y(b) = 0 for b.
-3, -2, -1
Suppose 4*n = i + 18, 0 = n + 2*n - i - 14. Factor -1/2*f**2 + 0 + 1/2*f**5 - 3/2*f**n + 0*f + 3/2*f**3.
f**2*(f - 1)**3/2
Factor 2/17*j + 2/17*j**2 + 0.
2*j*(j + 1)/17
Let s = 16 - 15. Let t(l) be the first derivative of -2/5*l**3 + s - 4/5*l**2 + 2/5*l**4 + 8/25*l**5 - 2/5*l. Find u such that t(u) = 0.
-1, -1/2, 1
Factor 3*w**2 + 2*w**3 + 3*w - 6*w**3 - 3 - w**3 + 2*w**3.
-3*(w - 1)**2*(w + 1)
Factor 1/3*d**4 - 2/3 + d**3 + 1/3*d**2 - d.
(d - 1)*(d + 1)**2*(d + 2)/3
Let x(z) be the third derivative of z**8/1176 + 2*z**7/735 - z**5/105 - z**4/84 - 3*z**2. Factor x(n).
2*n*(n - 1)*(n + 1)**3/7
Factor 3/7*r**2 - 6/7*r + 0.
3*r*(r - 2)/7
Suppose -m - 2 = o - 2*m, -5*o = m + 22. Let u be 6/o*(-4)/9. Determine g, given that g**4 + 0 - 4/3*g**3 - 1/3*g**2 + u*g = 0.
-2/3, 0, 1
Let d(h) be the first derivative of -11*h**6/3 + 8*h**5/5 + 359*h**4/22 - 68*h**3/3 + 100*h**2/11 - 16*h/11 - 21. Let d(s) = 0. What is s?
-2, 2/11, 1
Factor 0 + 9/7*s**3 + 6/7*s**4 + 0*s + 0*s**2 - 3/7*s**5.
-3*s**3*(s - 3)*(s + 1)/7
Let g be -3*1/(-9)*108/5. Factor 4/5*i**2 - 24/5*i + g.
4*(i - 3)**2/5
Let r be (-2 - -2) + (0 - -2). Factor -2*d**r + 5*d**4 + 0*d**5 - 2*d**3 + 2*d**5 - 3*d**4.
2*d**2*(d - 1)*(d + 1)**2
Suppose -15*w + 208 = 208. Factor 1/5*s**4 + 2/5*s - 2/5*s**3 + w - 1/5*s**2.
s*(s - 2)*(s - 1)*(s + 1)/5
Let v(u) = -u**2 + 12*u - 11. Let k be v(11). Let c(i) be the first derivative of 0*i + 1/10*i**5 + k*i**2 - 1/6*i**3 + 0*i**4 - 4. Factor c(y).
y**2*(y - 1)*(y + 1)/2
Let m(g) be the second derivative of g**4/4 - 6*g**2 + 16*g. Factor m(i).
3*(i - 2)*(i + 2)
Let u be -1 - -2 - (1 + -2)/(-2). Factor -u*p**2 + 1/2 + 0*p.
-(p - 1)*(p + 1)/2
Let z(a) be the second derivative of -a**7/42 - a**6/10 + a**5/20 + 11*a**4/12 + 2*a**3 + 2*a**2 - 8*a. Factor z(c).
-(c - 2)*(c + 1)**3*(c + 2)
Let f be (0/(-3))/(-2 - -1). Let q(a) = -a**2 - a + 3. Let s be q(f). Factor -1/3 + m**s + 1/3*m**2 - m.
(m - 1)*(m + 1)*(3*m + 1)/3
Suppose 0*n = 4*p + 4*n - 16, 0 = 4*p + 5*n - 18. Let -3/4*u**4 + 3/4*u**p + 0 - 3/4*u**3 + 3/4*u = 0. Calculate u.
-1, 0, 1
Let p(r) be the first derivative of -r**4/4 + 2*r**3/3 + r**2 - r - 1. Let a be p(2). Find x such that x**a - x + 2/3 - 1/3*x**2 - 1/3*x**4 = 0.
-1, 1, 2
Let -4/3 + 2*k - 2/3*k**2 = 0. Calculate k.
1, 2
Factor 1/3*p**3 + 2/3 - p**2 + 1/3*p**4 - 1/3*p.
(p - 1)**2*(p + 1)*(p + 2)/3
Suppose 0*a - a + 2 = h, -4 = 3*h - 2*a. Let d(z) be the first derivative of 0*z**2 + 0*z**3 + 0*z + h*z**4 + 1/24*z**6 + 3 + 1/20*z**5. Factor d(k).
k**4*(k + 1)/4
Let t(l) be the second derivative of -l**5/70 - l**4/21 - l**3/21 - 18*l. Factor t(k).
-2*k*(k + 1)**2/7
Let g = -2 + 4. Solve -3*k + 3*k**g - 2*k**2 + 6*k + 2 = 0.
-2, -1
Let x be 2/(-4)*(7 + -19). Let k(g) be the first derivative of 7/3*g**3 - g**2 - 3/4*g**4 + 3 + 0*g - 7/5*g**5 + 5/6*g**x. What is v in k(v) = 0?
-1, 0, 2/5, 1
Let k(z) = -z**2 + 7*z - 4. Let y be k(5). Let i(b) = b - 2. Let h be i(y). Factor -2*p**4 + 4*p**h + p**3 - 3*p**3.
2*p**3*(p - 1)
Let r(y) be the second derivative of y**5/20 + y**4/6 + y**3/6 - 5*y. Factor r(n).
n*(n + 1)**2
Let c(f) be the second derivative of f**5/20 + f**4/12 - f**3/3 - 21*f. Factor c(t).
t*(t - 1)*(t + 2)
Let v(b) be the first derivative of b**8/5040 + b**7/1260 + b**6/1080 - b**3/3 + 1. Let i(d) be the third derivative of v(d). Factor i(n).
n**2*(n + 1)**2/3
Let w(h) be the second derivative of 1/20*h**6 + 1/40*h**5 - 1/6*h**3 + 0 - 1/8*h**4 - 7*h + 1/84*h**7 + 0*h**2. Factor w(o).
o*(o - 1)*(o + 1)**2*(o + 2)/2
Factor 5 + 2*w*