4/9*k = 0.
-2, 0
Let t be 6 + 6 + (-46)/4. Factor 1/2*x + 2*x**4 + 3*x**3 + 0 + t*x**5 + 2*x**2.
x*(x + 1)**4/2
Factor 0 - 1/5*g**2 + 0*g.
-g**2/5
Factor -49/2*j**4 - 2 - 109/2*j**2 - 63*j**3 - 18*j.
-(j + 1)**2*(7*j + 2)**2/2
Let y(g) be the second derivative of 0*g**2 + 3/25*g**5 + 3/25*g**6 - 3*g + 0*g**3 + 1/30*g**4 + 4/105*g**7 + 0. Factor y(x).
2*x**2*(x + 1)**2*(4*x + 1)/5
Let m(a) be the first derivative of 3 + 1/2*a**3 - 3/2*a + 0*a**2. Factor m(w).
3*(w - 1)*(w + 1)/2
Let b(o) be the second derivative of 2*o + 0 + 1/15*o**6 + 0*o**4 + 1/5*o**5 - 2/3*o**3 - o**2. Factor b(y).
2*(y - 1)*(y + 1)**3
Let o(a) = -a**3 - 6*a**2 + a - 1. Let r be o(-6). Let d = -4 - r. Suppose 2*z**4 - 2*z**2 + 4/3*z - 14/3*z**d + 0 + 10/3*z**5 = 0. Calculate z.
-1, 0, 2/5, 1
Suppose -3*b**4 + 6*b**2 + b**5 - 2*b**2 + 0*b**2 = 0. Calculate b.
-1, 0, 2
Let a = 140 - 1538/11. Factor 0 - 8/11*c**2 - a*c**3 - 8/11*c.
-2*c*(c + 2)**2/11
Let g = 7 - -1. What is f in -14*f**3 - 12*f**2 - 4*f + 1 + 10*f + 8*f**4 + 3 + g*f = 0?
-1, -1/4, 1, 2
Let z = 1752/4355 + -2/871. Factor -z*t**3 + 0*t + 2/5*t**2 + 0.
-2*t**2*(t - 1)/5
Let p(c) be the third derivative of -c**6/1440 - c**5/480 + 2*c**3/3 - 4*c**2. Let k(h) be the first derivative of p(h). Factor k(u).
-u*(u + 1)/4
Let w(t) = t**2 - 6*t + 3. Let b be w(6). Factor 2 + 0*q**b - 2 + 2*q**2 + q**4 - 3*q**3.
q**2*(q - 2)*(q - 1)
Determine w, given that -12/7*w**3 - 4/7*w**4 + 4/7*w**5 + 4/7*w**2 + 8/7*w + 0 = 0.
-1, 0, 1, 2
Let n(o) be the third derivative of -1/120*o**6 + 0*o**3 + 0 + 0*o**4 - 1/630*o**7 - 1/90*o**5 + 0*o - o**2. Let n(y) = 0. What is y?
-2, -1, 0
Let x be (-4)/(-12) - 12/40. Let y(r) be the third derivative of -2*r**2 + 1/4*r**4 + 0 + 0*r + x*r**5 + 2/3*r**3. Determine t so that y(t) = 0.
-2, -1
Let c be 24/(-44)*3 - -2. Let s = c - -32/33. Suppose -6*m**3 - 2/3*m**2 + 26/3*m**4 + 0 + s*m - 10/3*m**5 = 0. What is m?
-2/5, 0, 1
Factor 0 - 2/11*y + 0*y**2 + 2/11*y**3.
2*y*(y - 1)*(y + 1)/11
Let y(b) = b**2 + 4*b - 16. Let d be y(-7). Let f(w) be the second derivative of 7/60*w**d + 1/6*w**3 + w - 1/3*w**4 + 1/3*w**2 + 0. What is h in f(h) = 0?
-2/7, 1
Let k be 4/(-3)*(-6)/2. Factor 2*i**5 - 2*i**3 - 4 - 2*i**2 + 2*i**4 + k.
2*i**2*(i - 1)*(i + 1)**2
Let l(y) be the first derivative of 3 + 1/10*y**4 + 0*y - 4/25*y**5 + 0*y**2 + 0*y**3. Factor l(j).
-2*j**3*(2*j - 1)/5
Let u be (-2)/(-7) + 2/(-7). Suppose -v + 5*v = 3*m - 21, -5*m - 3*v + 64 = u. Factor 7*f**4 - m*f**4 - 2*f**2 + 0*f**2 - 5*f**3 - f**5.
-f**2*(f + 1)**2*(f + 2)
Suppose -15 = -5*d, -2*y - d - 32 = 25. Let o be (1 + -1)/(y/(-10)). Factor 4/7*w**3 + o - 2/7*w**5 - 2/7*w + 0*w**4 + 0*w**2.
-2*w*(w - 1)**2*(w + 1)**2/7
Let k be (-2)/(-5) + (-32)/(-20). Factor -w**k - 2*w + 2*w**2 + 2*w + w**3.
w**2*(w + 1)
Let f be (-5)/6*36/(-60). Factor 5/2*j**3 + f*j + 0 + 3*j**2.
j*(j + 1)*(5*j + 1)/2
Let c = -13/22 + 12/11. Let v = 1/10 + c. Find y such that 0*y - 3/5 + v*y**2 = 0.
-1, 1
Let g(n) = 36*n**2 - 56*n + 4. Let s(k) = 7*k**2 - 11*k + 1. Let m(a) = 3*g(a) - 16*s(a). Factor m(c).
-4*(c - 1)**2
Suppose -722 - 4*c + 722 + 14*c**2 = 0. What is c?
0, 2/7
Suppose -5*s + 3*c + 10 = 0, 5*c = -4*s + 2*c + 8. Let o(p) = 3 - 4*p**2 + 0*p**2 + p**s. Let k(h) = 7*h**2 - 7. Let j(d) = 2*k(d) + 5*o(d). Factor j(x).
-(x - 1)*(x + 1)
Solve 4 + 6*s**3 + 32*s**4 + 16*s**5 + 13*s**3 + 3*s - 15*s**3 - 7*s - 20*s**2 = 0.
-1, 1/2
Let j be (132/(-28) - -2) + 3. Suppose -n = -3*n. Suppose j*a**2 + 0 + n*a - 2/7*a**3 = 0. What is a?
0, 1
Let m(t) = t**5 - 6*t**4 + 15*t**3 - 14*t**2 + 4*t - 2. Let j(y) = y**5 - 6*y**4 + 16*y**3 - 15*y**2 + 4*y - 3. Let h(r) = 2*j(r) - 3*m(r). Factor h(k).
-k*(k - 2)**2*(k - 1)**2
Find b, given that 2*b**3 - 1/2*b**4 + 0 + 0*b - 3/2*b**2 = 0.
0, 1, 3
Let d(t) = -5*t - 45. Let i be d(-10). Let r(c) be the third derivative of -1/75*c**i + 0 + 0*c - 1/60*c**4 - c**2 + 0*c**3. Factor r(l).
-2*l*(2*l + 1)/5
Let f(a) = 5*a**4 - 3*a**3 - 3*a**2 - 3*a + 3. Let j(o) = 5*o**4 - 4*o**3 - 4*o**2 - 4*o + 4. Let y(k) = 4*f(k) - 3*j(k). Find z such that y(z) = 0.
0
Let g = 115 + -112. Let w(u) be the third derivative of 0*u**5 + 0 + 1/600*u**6 - 3*u**2 - 1/120*u**4 + 0*u + 0*u**g. What is j in w(j) = 0?
-1, 0, 1
Let j(m) be the first derivative of 0*m + 6 - 2/9*m**6 + 1/6*m**4 + 2/3*m**3 - 2/5*m**5 + 1/3*m**2. Suppose j(s) = 0. What is s?
-1, -1/2, 0, 1
Let q be ((-11)/154)/(2/(-16)). Let 0 + 2/7*u**3 - q*u - 2/7*u**2 = 0. What is u?
-1, 0, 2
Let k(n) be the third derivative of -1/10*n**5 + 3*n**2 + 3/70*n**7 - 1/2*n**3 + 3/8*n**4 + 0 + 0*n - 1/20*n**6 - 1/112*n**8. Factor k(w).
-3*(w - 1)**4*(w + 1)
Let t(q) = q**3 - q - 1. Let r(f) = 2*f**4 - 13*f**3 + 2*f**2 + 9*f + 9. Let g(v) = -2*r(v) - 18*t(v). Factor g(z).
-4*z**2*(z - 1)**2
Let f(q) = 2*q**3 + 3*q**2 + 4*q. Let k(c) = 3*c**3 + 4*c**2 + 5*c. Suppose -3*r - 9 = -3*y + 2*r, 0 = 4*y + 4*r - 12. Let h(o) = y*k(o) - 4*f(o). Factor h(j).
j*(j - 1)*(j + 1)
Let s be ((-36)/(-27)*(-18)/4)/(-3). Suppose -8/9*x - 8/9*x**3 + 4/3*x**s + 2/9*x**4 + 2/9 = 0. What is x?
1
Let z be (-2)/(-10) - (-120)/1400. Let k(r) = r**3 - 5*r**2 + 6*r - 6. Let h be k(4). Determine u, given that 0 + 4/7*u**h - z*u - 2/7*u**3 = 0.
0, 1
Let m(l) be the first derivative of -3*l**4/4 + 6. Determine z, given that m(z) = 0.
0
Let k(z) be the second derivative of z**5/120 + 5*z**4/72 + 2*z**3/9 + z**2/3 - 15*z. Solve k(r) = 0 for r.
-2, -1
Factor 12 - 27*i + 6*i**2 + 22*i**2 - 3*i**3 + 6*i**2 - 16*i**2.
-3*(i - 4)*(i - 1)**2
Let i(z) be the second derivative of z**7/5040 + z**6/576 + z**5/240 - z**4/6 - z. Let j(c) be the third derivative of i(c). Factor j(d).
(d + 2)*(2*d + 1)/4
Let s(o) be the third derivative of -o**6/1620 + o**5/540 + o**3 + 2*o**2. Let m(t) be the first derivative of s(t). Determine j, given that m(j) = 0.
0, 1
Let b = -3/4 - -17/12. Factor -2/3*r**2 - 2/3*r + b + 2/3*r**3.
2*(r - 1)**2*(r + 1)/3
Let g(p) = -p**4 + 2*p**2 + p - 2. Let k = 1 - 0. Let v(z) = -4 + z - 2*z + 5. Let r(o) = k*g(o) + v(o). Factor r(d).
-(d - 1)**2*(d + 1)**2
Let m(j) = j + 9. Let l be m(-6). Let g(w) be the third derivative of -1/180*w**5 - 3*w**2 + 0*w - 1/18*w**l + 0 - 1/36*w**4. What is v in g(v) = 0?
-1
Factor 1/3*k**5 + 5/3*k**3 + 0 - 2/3*k**2 + 0*k - 4/3*k**4.
k**2*(k - 2)*(k - 1)**2/3
Suppose 4*d + 34 = 6. Let b be (-10 - d) + 10/3. Suppose 0 - b*g**4 + 2/3*g**3 + 0*g - 1/3*g**2 = 0. What is g?
0, 1
Factor 0*q + 0 - 9/2*q**5 - 3*q**2 - 12*q**4 - 21/2*q**3.
-3*q**2*(q + 1)**2*(3*q + 2)/2
Let f(c) be the second derivative of -c + 1/30*c**5 + 0*c**4 + 0*c**2 + 0 - 1/9*c**3. Factor f(a).
2*a*(a - 1)*(a + 1)/3
What is c in 0*c + 5/2*c**5 + 0 + 0*c**2 + 5*c**4 + 5/2*c**3 = 0?
-1, 0
Let x be (-6)/15 - 34/(-10). Suppose -2*g**2 - x*g**4 - 6*g**3 + 0*g**2 - g**2 = 0. Calculate g.
-1, 0
Let m(h) be the third derivative of -h**8/672 + h**7/420 - 43*h**2. Factor m(c).
-c**4*(c - 1)/2
Let n(i) be the first derivative of i**6/48 - 3*i**5/40 + i**4/16 + i**3/12 - 3*i**2/16 + i/8 + 17. Find a such that n(a) = 0.
-1, 1
Let p(r) = 3*r**3 + r**2. Let z(c) = -2*c**3 - 2*c**2 + c. Let b(w) = -3*p(w) - 4*z(w). Factor b(s).
-s*(s - 4)*(s - 1)
Factor -45*u + 9 + 100*u + 3*u**2 - 43*u.
3*(u + 1)*(u + 3)
Let w(z) be the second derivative of -z**8/1400 - z**7/525 - z**6/900 + z**3/2 + 3*z. Let a(d) be the second derivative of w(d). Find g such that a(g) = 0.
-1, -1/3, 0
Let a = 67 + -199/3. Let o(r) be the second derivative of 0*r**2 + 0 + 0*r**3 - r + 77/15*r**6 + 16/5*r**5 + a*r**4 + 7/3*r**7. Factor o(h).
2*h**2*(h + 1)*(7*h + 2)**2
Let d = 10/23 + 187/46. Find o such that d*o**2 - 3/2*o**3 - 6 + 0*o = 0.
-1, 2
Let l(i) be the first derivative of -4/15*i**5 + 0*i - 1/12*i**4 + 0*i**2 + 7 + 0*i**3. Factor l(m).
-m**3*(4*m + 1)/3
Let i(v) = -2*v - 7. Let n be i(-5). Suppose -n*w = -4*w + 3. Factor 0 + 2/7*b**w - 2/7*b + 2/7*b**2 - 2/7*b**4.
-2*b*(b - 1)**2*(b + 1)/7
Let s = -5 + 9. Factor -2*h**4 + 5*h**2 - 3*h**2 + s*h + 3*h**2 + h**2.
-2*h*(h - 2)*(h + 1)**2
Let o = -9979/1495 - -87/13. Let z = o - -44/115. Factor -6/5*v - 4/5 - z*v**2.
-2*(v + 1)*(v + 2)/5
Let x(f) = 16*f**2 - 39*f + 15. Let o(k) = -65*k**2 + 155*k - 60. Let n(u) = 4*o(u) + 15*x(u). Solve n(t) = 0 for t.
3/4, 1
Suppose -t - c = -101, -21*t - 205 = -23*t + c. Factor 25*j**4 - 188/