18*a**4 - 1/126*a**7. Factor r(u).
-(u - 1)**4*(u + 1)/3
Let t(l) = -l - 1. Let h be t(4). Let y be 2/h - 4/(-10). Suppose 0*a**3 + 0*a**2 + 2/5*a**5 + 0 + y*a + 2/5*a**4 = 0. What is a?
-1, 0
Factor -3 - 21*v**2 + 19*v**2 + 3 - 2*v.
-2*v*(v + 1)
Let z = 7 + -3. Suppose 5*t + 4 = -k, 3*t + 3*k + 12 = -2*t. Factor t*a**2 + 3*a**2 - 4*a**2 + a**3 + a**z - a.
a*(a - 1)*(a + 1)**2
Let w(o) be the second derivative of -o**7/126 - o**6/90 + o**5/20 + 5*o**4/36 + o**3/9 - o - 18. Factor w(s).
-s*(s - 2)*(s + 1)**3/3
Suppose -14*j = -27*j + 39. Suppose 4/3*z**2 - 2/3*z**j - 2/3*z + 0 = 0. Calculate z.
0, 1
Let w(l) be the second derivative of 2*l + 1/2*l**3 + 1/4*l**4 + 0*l**2 + 0. Determine b, given that w(b) = 0.
-1, 0
Let s(d) be the third derivative of 0 - 7/15*d**4 + 4/15*d**3 + 1/21*d**7 - 3*d**2 + 23/50*d**5 - 7/30*d**6 + 0*d. Factor s(v).
2*(v - 1)**2*(5*v - 2)**2/5
Let a be (-6)/(-8) - (-54)/24. Let q(w) be the first derivative of 2/3*w - 2/9*w**a - 1 + 0*w**2. Determine n, given that q(n) = 0.
-1, 1
Factor -34*j**2 + 38*j**2 + 2*j**3 - 3*j**3 + 3*j**3.
2*j**2*(j + 2)
Let o = -3 + 5. Suppose -3*g + 4*x - 3*x = -o, -3*g - 2*x = -14. Let 2*c**g - 2*c - 3 - 2 + 2*c**3 + 3 = 0. Calculate c.
-1, 1
Let z(y) = -y**2 - 15*y - 32. Let t be z(-14). Let f be 21/t + (-9)/(-6). Factor 0 + 0*g + 1/3*g**3 - f*g**2.
g**2*(g - 1)/3
Determine c, given that -4*c + 4*c**3 - 8*c**2 - 138 + 2*c**4 + 144 + 0*c**3 = 0.
-3, -1, 1
Let s be (-2)/9 + 168/27. Factor -s - 5*m - 4*m**2 + 0*m**2 + 2 - m**3 + 2.
-(m + 1)**2*(m + 2)
Solve 1/5*u - 1/5*u**2 + 0 = 0 for u.
0, 1
Let b(z) be the second derivative of -z**5/60 + z**4/24 + 3*z**2/2 + 4*z. Let x(p) be the first derivative of b(p). Find w such that x(w) = 0.
0, 1
Let o = -3/596 + 225/298. Suppose -1/2*i + o - 1/4*i**2 = 0. What is i?
-3, 1
Suppose 26 + 0 = q + 5*f, 0 = -3*q + 2*f + 10. Let l = 8 - q. Find u such that -5*u + 3*u**2 + l*u - 2 + 2*u**2 = 0.
-2/5, 1
Suppose -2*d = 2*p - 8, 0*d + 2*d + p = 9. Factor r**2 + d*r - 2*r**4 - 2 - 3*r**3 + 2*r - 4*r + 3*r**4.
(r - 2)*(r - 1)**2*(r + 1)
Let c(q) be the third derivative of q**6/180 + q**5/20 + q**4/6 + q**3/6 + 2*q**2. Let k(f) be the first derivative of c(f). Factor k(n).
2*(n + 1)*(n + 2)
Let j(m) be the second derivative of -2*m**7/21 + 4*m**5/5 + 2*m**4/3 - 2*m**3 - 4*m**2 - 2*m. Solve j(v) = 0 for v.
-1, 1, 2
Let k(t) = -t**2 + t + 2. Let g be k(2). Let l(v) be the second derivative of 0*v**2 + 1/36*v**4 - 1/18*v**3 + g + v. Determine d, given that l(d) = 0.
0, 1
Suppose 17 = 4*q - 3. Suppose -q*d = 2*c - 18, d + 10 = 4*c - c. Determine x so that -x**2 + 3*x**d - 4 - x - x = 0.
-1, 2
Suppose -6 + 9/2*s**3 + 24*s - 39/2*s**2 = 0. Calculate s.
1/3, 2
Let -10*d**2 - 3*d**2 - d**3 + 4 + 10*d**2 = 0. What is d?
-2, 1
Let u be ((-12)/14)/((-18)/140). Let a(v) be the first derivative of 5*v**4 + 5*v**2 - 2*v**5 - 2 - 2*v - u*v**3 + 1/3*v**6. Factor a(i).
2*(i - 1)**5
Factor -2/7*o**3 + 4/7*o**2 + 0 - 2/7*o.
-2*o*(o - 1)**2/7
Let b be 22/5*15/6. Determine m so that 2*m**2 - 5*m + 20*m - 2*m**3 - b*m = 0.
-1, 0, 2
Let a(w) = 2*w + 14. Let z be a(-5). Let k(p) be the third derivative of p**2 - 1/3*p**z - 4/3*p**3 + 1/10*p**5 + 1/30*p**6 - 1/105*p**7 + 0*p + 0. Factor k(d).
-2*(d - 2)**2*(d + 1)**2
Let a be (1/25)/((-2)/(-10)). Factor 0 + 2/5*w**2 - 1/5*w**3 - a*w.
-w*(w - 1)**2/5
Let j be 2 + 4/(-6)*42/16. Let o(g) be the second derivative of 3*g - 1/20*g**5 + 1/12*g**3 - 1/60*g**6 + 1/12*g**4 - j*g**2 + 1/84*g**7 + 0. Factor o(s).
(s - 1)**3*(s + 1)**2/2
Suppose l = -0*d + 2*d + 22, 4*l - 138 = -2*d. Find o such that -3 + l*o**4 + o**4 + 18*o**2 - 9*o**5 - 2*o + 5*o - 42*o**3 = 0.
-1/3, 1
Factor -49*s - 67*s**2 + 14*s + 22 - 5*s**3 + 92*s**2 - 7.
-5*(s - 3)*(s - 1)**2
Let s(m) be the first derivative of m**4/6 - 10*m**3/9 + 7*m**2/3 - 2*m - 16. Determine z so that s(z) = 0.
1, 3
Let b be (2 - 4)*(-4 + 2). Suppose -3*c = 3*i - 0*c, b = -i - 2*c. Find k, given that -6/5*k**i + 2*k**3 - 8/5*k**5 - 2/5*k + 6/5*k**2 + 0 = 0.
-1, 0, 1/4, 1
Let s(g) be the first derivative of 2*g**5/5 + 7*g**4/6 + 10*g**3/9 + g**2/3 + 3. Factor s(h).
2*h*(h + 1)**2*(3*h + 1)/3
Let q(r) be the third derivative of r**5/20 + 5*r**4/24 + r**3/3 + 6*r**2. What is x in q(x) = 0?
-1, -2/3
Let h(w) = -w**3 - 2*w**2 + w - 4. Let l be h(-3). Suppose 3*q - l*s - 35 = 0, q - s - 2*s = 21. Factor -9 + 6*a - 3*a**2 + q.
-3*a*(a - 2)
Suppose -5/8*m**2 + 1/8*m**4 + 0 - 1/4*m + 1/8*m**5 - 3/8*m**3 = 0. What is m?
-1, 0, 2
Solve 0*y + 2/11*y**5 + 0 - 4/11*y**4 + 2/11*y**3 + 0*y**2 = 0 for y.
0, 1
Let s(b) be the first derivative of -2*b**6/27 - 2*b**5/45 + b**4/6 + 2*b**3/27 - b**2/9 - 22. What is t in s(t) = 0?
-1, 0, 1/2, 1
Let o be (0/(-3 - -2))/(-1). Let s = -23 + 25. Factor z - 1/2*z**s + o.
-z*(z - 2)/2
Suppose -14 = -2*g - 2*g + 3*n, g + 5 = 5*n. Let b(j) be the first derivative of 1/2*j**2 - 2 - j**3 - 1/5*j**g + 0*j + 3/4*j**4. Factor b(r).
-r*(r - 1)**3
Let f(l) be the second derivative of -l**8/6720 + l**7/2520 - l**4/6 - l. Let r(p) be the third derivative of f(p). What is v in r(v) = 0?
0, 1
Factor -3/8*g**2 - 147/8 - 21/4*g.
-3*(g + 7)**2/8
Let u(s) = -11*s**3 + 6*s**2 - 9*s - 8. Let p(c) = -8*c - 6 + 4*c + 3*c**2 - 5*c**3 + 2. Let f(w) = -9*p(w) + 4*u(w). What is m in f(m) = 0?
-1, 2
Let d be 0/(2/(-4 - -2)). Let t(w) be the first derivative of -1/8*w**4 + 1/12*w**3 + 0*w**2 + d*w - 2 + 1/20*w**5. Find a such that t(a) = 0.
0, 1
Let w(b) = -3*b + 5. Let f be w(0). Suppose -f*k + 20 = -k. Suppose -4/5*s**k - 14/5*s**4 - 18/5*s**3 - 2/5*s - 2*s**2 + 0 = 0. What is s?
-1, -1/2, 0
Let f be -8 + (0 - -3)/3. Let d be (f/(-5))/(12/15). Factor -4*v**2 - v - d*v**3 + 0.
-v*(v + 2)*(7*v + 2)/4
Let g(b) be the third derivative of 2*b**9/945 + b**8/525 + b**7/2100 - 5*b**3/6 + 10*b**2. Let i(v) be the first derivative of g(v). Factor i(h).
2*h**3*(4*h + 1)**2/5
Let j(q) be the second derivative of -2*q**6/45 - q**5/15 + q**4/9 + 2*q**3/9 - 3*q. Suppose j(s) = 0. What is s?
-1, 0, 1
Let o be 4 - 1 - (2 + -1). Let v(q) = -q**3 - 1. Let t(g) = -57*g + 2*g**2 + 3*g**3 + 2 + 57*g. Let j(b) = o*t(b) + 4*v(b). Factor j(m).
2*m**2*(m + 2)
Let r(w) be the third derivative of -w**8/1680 - w**3/2 - w**2. Let x(p) be the first derivative of r(p). Factor x(c).
-c**4
Let d(a) be the first derivative of -3*a + 4 - 4*a**3 + 15/2*a**2. What is k in d(k) = 0?
1/4, 1
Let k(w) be the second derivative of -22*w**6/15 + 9*w**5/5 + 13*w**4/3 - 6*w**3 - 4*w**2 - 13*w. Solve k(h) = 0.
-1, -2/11, 1
Suppose -21 = -3*o + 24. Let q be 48/20 - 6/o. Let -3*n + n**3 - n**q - n + 2*n = 0. What is n?
-1, 0, 2
Suppose 5*u = a - 25, 4*a + 2*u = -12 + 2. Let w(i) be the third derivative of 0*i - 1/24*i**4 + 2*i**2 - 1/12*i**3 + a - 1/120*i**5. Factor w(q).
-(q + 1)**2/2
Let u be 6/36*(-442)/(-21). Let r = u - 23/7. Factor -4/9*b + 0 - r*b**4 + 0*b**3 + 2/3*b**2.
-2*b*(b - 1)**2*(b + 2)/9
Let w = 418/3 - 138. Let c = w + -2/3. Factor 8/3*i**3 - 4/3*i**2 + 1/3 - c*i.
(2*i - 1)**2*(2*i + 1)/3
Let i(w) be the first derivative of w**6/27 + 4*w**5/45 + w**4/18 + 10. Determine h so that i(h) = 0.
-1, 0
Let j = -246/7 + 745/21. Determine f so that 1/2*f**2 + 0 - j*f - 1/6*f**3 = 0.
0, 1, 2
Let p be (-2)/(-2) - (1 + 29/(-3)). Factor 2/3 - p*u**2 + 1/3*u - 28/3*u**3.
-(u + 1)*(4*u - 1)*(7*u + 2)/3
Solve 8/7 + 10/7*r**3 + 32/7*r - 38/7*r**2 = 0 for r.
-1/5, 2
Let n = -283/4 - -71. Solve -1/4*z**2 - n - 1/2*z = 0 for z.
-1
Let t(k) = k**3 - 7*k**2 + 8*k - 8. Let n(o) = o**2 - 3*o - 4. Let w be n(5). Let i be t(w). Factor -4*z**4 - 2*z**5 + z**4 - 2*z**3 - z**i.
-2*z**3*(z + 1)**2
Let v(j) be the first derivative of 2*j**5/35 - 3*j**4/14 + 2*j**3/7 - j**2/7 + 6. Factor v(h).
2*h*(h - 1)**3/7
Let l = 431/3 + -143. Determine u so that 2/9*u + l*u**2 - 4/9*u**4 - 2/9*u**3 - 2/9 = 0.
-1, 1/2, 1
Let q(m) be the first derivative of -m**6/66 + m**5/11 - 5*m**4/22 + 10*m**3/33 - 5*m**2/22 + m/11 - 9. Find g such that q(g) = 0.
1
Let t(o) be the first derivative of o**5/60 - o**4/8 - 2*o**2 + 4. Let c(h) be the second derivative of t(h). Factor c(f).
f*(f - 3)
Let w(i) = i**2 - 5*i - 6. Let v be w(7). Let 6*t**2 - 16*t**2 - 8*t**3 - 6*t**3 - v*t**4 + 2*t**4 - 2*t = 0. Calculate t.
-1, -1/3, 0
Factor -13 - 2 + 26*f - 5*f**2 + 3 + 6*f.
-(f - 6)*(5*f - 2)
Let t(k