*3 - 1/6*a**6 - 3/5*a**g + 0*a**2. Factor j(h).
-h**2*(h + 1)**3
Let n be ((-4)/(-20))/(1/2). Factor -6/5*r**3 + n*r**2 - 2/5*r**5 + 6/5*r**4 + 0*r + 0.
-2*r**2*(r - 1)**3/5
Let n(a) be the third derivative of a**5/15 - a**4/3 - 2*a**3 + 8*a**2. Factor n(l).
4*(l - 3)*(l + 1)
Let y(x) be the second derivative of x**7/126 - x**6/45 + x**5/60 + 11*x. Suppose y(t) = 0. Calculate t.
0, 1
Let b be 5 - (2 - (-2 + 2)). Suppose 0 = -k + 5 - 1. Factor -r**b - k*r**3 + 2*r + 4*r**3 - r.
-r*(r - 1)*(r + 1)
Factor 4*p**2 - 4 - 12*p + 16 - 4.
4*(p - 2)*(p - 1)
Suppose -18 = 5*u + 2, 2*l - 3*u = 12. Factor l - 1/4*x**2 - 3/4*x.
-x*(x + 3)/4
Let y**2 + 1/3*y - 1/3*y**3 - 1 = 0. Calculate y.
-1, 1, 3
Let c(a) = -7*a**2 - 22*a - 2. Let y(f) = 36*f**2 + 111*f + 11. Let r(q) = 11*c(q) + 2*y(q). Determine d, given that r(d) = 0.
-4, 0
Find f such that 5*f**3 - 25*f**3 - 4*f**2 + 8*f**3 = 0.
-1/3, 0
Let k = -8/29 + 101/261. Let w(m) be the second derivative of -k*m**4 + 1/6*m**2 + 0 + 3*m + 1/6*m**3. Suppose w(v) = 0. Calculate v.
-1/4, 1
Let w(p) = p**3 - p**2 - 13*p. Let v be w(-3). What is t in 0 + 1/7*t**4 - 1/7*t - 1/7*t**2 + 1/7*t**v = 0?
-1, 0, 1
Let g(b) be the first derivative of -1/6*b**4 + 1 + 0*b - 2/9*b**3 + 0*b**2. Factor g(a).
-2*a**2*(a + 1)/3
Find j, given that -30*j**3 - 550 + 550 + 8*j**4 + 40*j**2 - 3*j**4 = 0.
0, 2, 4
Let o be (-28)/(-10)*(2 + 8). Suppose 0 = 4*z - 2*w - o, -2*z - z - 2*w = -7. Determine h, given that 3/5*h**4 + 0 + 1/5*h**2 + 0*h + 1/5*h**z + 3/5*h**3 = 0.
-1, 0
Let u = -7645/9 - -851. Let z(x) = x**2 - 17*x + 20. Let n be z(16). Suppose -u*m**3 - 8/9 - 2/9*m**2 - 2/9*m**5 + 10/9*m**n + 16/9*m = 0. What is m?
-1, 1, 2
Let y(b) be the first derivative of 2*b**3/15 - b**2/5 - 4*b/5 - 8. Solve y(t) = 0.
-1, 2
Let i(q) = q**3 - 8*q**2 - q - 7. Let h be i(9). Let d = h + -193/3. Factor -2/3*b + d*b**2 + 0.
2*b*(b - 1)/3
Let c = -20 + 28. Let b be (6 - c)/(2/(-2)). Suppose -4/7*x - 2/7*x**b + 0 = 0. Calculate x.
-2, 0
Factor 1/4*f**3 + 1 - f - 1/4*f**2.
(f - 2)*(f - 1)*(f + 2)/4
Let p(c) be the third derivative of 4*c**7/105 + c**6/12 - 7*c**5/30 - c**4/6 + 16*c**2. Factor p(s).
2*s*(s - 1)*(s + 2)*(4*s + 1)
Let o = 10 + -4. Let z(h) be the first derivative of -1/3*h**3 - 1/4*h**4 + 1/5*h**5 + 0*h + 0*h**2 + 1/6*h**o - 1. Factor z(n).
n**2*(n - 1)*(n + 1)**2
Let f(v) be the second derivative of -1/18*v**4 - v**2 + 0 + 2/9*v**3 + 2*v + 1/180*v**5. Let j(r) be the first derivative of f(r). Solve j(y) = 0 for y.
2
Factor -3/4*z**2 - 3*z + 0.
-3*z*(z + 4)/4
Let v(u) be the third derivative of 0*u + 0 + 0*u**3 + 7/60*u**5 + 1/12*u**4 + 1/24*u**6 - 2*u**2. Factor v(d).
d*(d + 1)*(5*d + 2)
Let c(l) be the first derivative of -2*l**5/15 - l**4/6 + 2*l**3/9 + l**2/3 - 5. Solve c(z) = 0 for z.
-1, 0, 1
Let n be 4/(-6)*9/2. Let l be n/5 + 14/15. Factor 2/3*i**4 - 2/3*i**2 + 0 - 1/3*i + 0*i**3 + l*i**5.
i*(i - 1)*(i + 1)**3/3
Let d = -44 - -26. Let q be ((-2)/4)/(d/27). Factor q*j**3 - 1/4*j**2 - 3/4*j**4 + 1/4*j**5 + 0 + 0*j.
j**2*(j - 1)**3/4
Find t such that 4 + 5*t + t**2 + 12*t - 13*t = 0.
-2
Let t(i) = -i**3 - 7*i**2 - 21*i - 86. Let a be t(-6). Suppose -1/3*f**2 + 0*f**3 + 0*f + 1/3*f**a + 0 = 0. What is f?
-1, 0, 1
Let m(i) be the second derivative of -2*i**6/135 + i**5/45 + i**4/27 - 2*i**3/27 + 4*i. Factor m(q).
-4*q*(q - 1)**2*(q + 1)/9
Suppose p - 1 = -j, 0*j + 5*p + 11 = 3*j. Let t be j/(-4) - 1/(-1). Factor 0 - 3*o**2 + t*o + 9/2*o**3.
o*(3*o - 1)**2/2
Let c = 94/115 - 2/115. Factor 2/5*z**2 - 2/5*z - c.
2*(z - 2)*(z + 1)/5
Let l = -29/3 - -557/57. Let t = l + 15/38. Factor 3/2*a**3 - 1/2*a**4 + t*a + 0 - 3/2*a**2.
-a*(a - 1)**3/2
Let f(w) = -w. Let r(z) = 6*z + 8. Let p(q) = -4*f(q) - r(q). Let j be p(-6). Let -2*d**2 + d + j*d - d = 0. What is d?
0, 2
Let a(o) be the third derivative of o**8/2352 + o**7/245 + o**6/105 - o**5/70 - 3*o**4/56 + 15*o**2. Suppose a(y) = 0. Calculate y.
-3, -1, 0, 1
Let k(h) = -3*h**3 - h**2 + 5*h + 1. Let y(p) = -12*p**3 - 3*p**2 + 21*p + 3. Let w(o) = -9*k(o) + 2*y(o). Factor w(g).
3*(g - 1)*(g + 1)**2
Find j, given that -25*j + 5*j**3 - 3 - 4 + 5*j**4 - 15*j**2 + 1 - 4 = 0.
-1, 2
Let o(s) be the third derivative of -2*s**7/105 - s**6/6 - s**5/5 + 3*s**4/2 + 13*s**2. Factor o(a).
-4*a*(a - 1)*(a + 3)**2
Let m(p) be the second derivative of 1/36*p**4 + 0*p**2 + 1/18*p**3 + 0 + 3*p. Factor m(x).
x*(x + 1)/3
Suppose 5*v - 13 - 8 = -3*l, 3 = -3*l + 3*v. Factor -14 + 0*j**4 + 18*j**3 + 3*j**5 + 14 - 12*j**l + 3*j - 12*j**4.
3*j*(j - 1)**4
Let n(v) be the second derivative of -v**7/420 + v**6/150 + 3*v**5/200 - v**4/30 - v**3/15 + 8*v. Suppose n(d) = 0. What is d?
-1, 0, 2
Let v(m) be the second derivative of 0*m**3 - 3/80*m**5 + 0 + 2*m - 1/16*m**4 + 0*m**2. Factor v(w).
-3*w**2*(w + 1)/4
Let v(f) be the third derivative of -1/90*f**5 + 0*f + 1/8*f**4 - 2/9*f**3 + 0 - 6*f**2. Factor v(j).
-(j - 4)*(2*j - 1)/3
Let o(b) be the first derivative of -b**6/6 + 2*b**5/5 + 3*b**4/4 - 8*b**3/3 + 2*b**2 - 16. Find j such that o(j) = 0.
-2, 0, 1, 2
Let k(n) = -n**3 + 5*n**2 - 4*n - 1. Let l be k(3). Suppose 0 = 2*s - l*h - 8, -h - 4*h = 0. Factor p**2 - 2*p**3 - 3*p**2 + s*p**3.
2*p**2*(p - 1)
Let s = 973/2445 - -1/489. Solve s*k**2 + 2/5*k + 0 = 0.
-1, 0
Let x(y) = y**2 - 6*y + 10. Let g be x(4). Solve 15*t**3 - 4*t**4 - 3*t**4 - 11*t**g + 2*t + t**3 = 0.
0, 2/7, 1
Factor 16*t**3 + 32 - 64 - 2*t**4 + 13*t + 51*t - 48*t**2.
-2*(t - 2)**4
Determine a, given that -6 - 3/2*a**2 + 6*a = 0.
2
Let p(f) = f. Let x(j) = 2*j**3 - 16*j**2 + 24*j - 12. Let a(n) = 4*p(n) + 2*x(n). Let a(l) = 0. What is l?
1, 6
Let t(o) be the second derivative of o**4/3 + 16*o**3/3 + 32*o**2 - 20*o. Solve t(v) = 0 for v.
-4
Let w = 16 + -2. Let h be (4/14)/(2/w). Factor -2/5 - 8/5*p**h - 2*p.
-2*(p + 1)*(4*p + 1)/5
Factor 2*i + 8*i + 2*i**2 + 27 - i**3 - 35 - 3*i**2.
-(i - 2)*(i - 1)*(i + 4)
Suppose -4*g + 2*g + 136 = -4*i, -3*i - 103 = -g. Let l be i/(-30) - (-2)/12. Solve -2/3 - 2/3*u**2 - l*u = 0.
-1
Determine d, given that -6 - 7674*d**3 - 4 - 8*d**5 - 14*d**2 - 8 + 32*d**4 + 42*d + 7640*d**3 = 0.
-1, 1, 3/2
Let a(m) be the second derivative of -m**6/70 - 3*m**5/35 - 5*m**4/28 - m**3/7 - 3*m. What is q in a(q) = 0?
-2, -1, 0
Factor -1/5*r**2 - 4/5 - 4/5*r.
-(r + 2)**2/5
Suppose 0 = -g + 2*h - 6, 4*g + h + 7 = -8. Let a be (g/(-15))/((-2)/(-5)). Suppose 0 + 1/3*u**4 + 1/3*u**2 + 0*u + a*u**3 = 0. Calculate u.
-1, 0
Let s(z) be the first derivative of z**4/3 - 4*z**3/3 + 2*z**2 + 4*z + 4. Let h(y) be the first derivative of s(y). Find q such that h(q) = 0.
1
Factor -15 - x**2 - 6*x + 0*x + 6.
-(x + 3)**2
Let n(k) be the first derivative of 3 - k**4 + 2/3*k**3 + 0*k**5 + 3/2*k**2 + 1/6*k**6 - 2*k. Factor n(t).
(t - 1)**3*(t + 1)*(t + 2)
Suppose r - 3*r = -6. Let q(f) be the third derivative of 1/90*f**5 - f**2 + 0*f**r - 1/180*f**6 + 0*f**4 + 0 + 0*f. Find z, given that q(z) = 0.
0, 1
Let i(f) = -5*f**3 - 15*f**2 + 6*f + 20. Let s(b) = 5*b**3 + 15*b**2 - 5*b - 20. Let l(k) = 5*i(k) + 6*s(k). Factor l(q).
5*(q - 1)*(q + 2)**2
Let f(s) be the third derivative of 0 + 0*s + 2*s**2 - 1/24*s**4 - 1/3*s**3 + 1/60*s**5. Factor f(a).
(a - 2)*(a + 1)
Let m(r) be the second derivative of -r**6/25 + 2*r**5/25 + r**4/30 - 2*r**3/15 - 3*r. Suppose m(l) = 0. Calculate l.
-2/3, 0, 1
Let z(k) = 19*k - 54. Let g be z(3). Suppose -5*p - 6 = 3*n, p + 10 = -p - 5*n. Determine r, given that 4/7*r**g + 0*r - 2/7*r**2 + p - 2/7*r**4 = 0.
0, 1
Let i(c) be the first derivative of c**6/180 - c**5/45 + c**4/36 + c**2/2 + 2. Let k(v) be the second derivative of i(v). Let k(f) = 0. Calculate f.
0, 1
Let a be (-12)/8*8/(-6). Let m = -14 + 14. Factor -6*p**a - 3*p + 2*p**3 + 9*p + m*p - 2*p.
2*p*(p - 2)*(p - 1)
Let g be 28/(-21)*6/(-4). Determine t so that 0*t + 2*t**2 + 3*t - 3*t**g - 4*t = 0.
-1, 0
Let l = -175/4 - -44. Find p such that l*p + 0 - 1/4*p**2 = 0.
0, 1
Let z(t) be the second derivative of 0*t**4 + 0 + 2*t + 0*t**2 + 1/231*t**7 + 0*t**6 - 1/55*t**5 + 1/33*t**3. Factor z(i).
2*i*(i - 1)**2*(i + 1)**2/11
Suppose 3*k - 8*k = -20. Find d such that 10*d**3 - 10*d**2 + k*d**2 - 8*d**3 - 29*d**3 = 0.
-2/9, 0
Let p = -12 + 17. Factor -p*i + 2 - 2*i**2 + 5*i.
-2*(i - 1)*(i + 1)
Let m be 4 - 1/(-1)*-1. Let -4*a**5 + 9*a**3 - 4*a**4 + m*a**2 - 4*a**3 + a**4 - a = 0