 1/2*b**4. Factor u(q).
2*(q - 2)*(3*q + 1)
Suppose 40*a - 12 = 38*a. Let x(t) be the third derivative of 1/60*t**a + 1/315*t**7 - 3*t**2 + 0*t**3 + 0 + 1/36*t**4 + 0*t + 1/30*t**5. Factor x(z).
2*z*(z + 1)**3/3
Suppose -2*j - 4*w + 10 = -j, -2*j + 6 = w. Let 1/4 - 1/4*v**3 - 1/4*v**j + 1/4*v = 0. What is v?
-1, 1
Let z(u) be the third derivative of u**7/280 - 3*u**6/160 + u**5/40 - u**2. Find t such that z(t) = 0.
0, 1, 2
Let z(g) be the third derivative of g**7/84 - g**6/80 - g**5/60 + 15*g**2. Factor z(s).
s**2*(s - 1)*(5*s + 2)/2
Let n = 13/6 + -3/2. Factor 4/3*i + 2/3*i**2 + n.
2*(i + 1)**2/3
Let o(b) = -b**3 + b. Let z be o(-1). Factor 1/3*t**4 + 0*t**3 - 2/3*t**2 + 1/3 + z*t.
(t - 1)**2*(t + 1)**2/3
Suppose 5*g - 8 = 4*j, -3*g = -0*j - 2*j - 6. Suppose 2*q + j = 7. Factor -1/2*m**3 + 0 - 1/2*m**4 + 1/2*m + 1/2*m**q.
-m*(m - 1)*(m + 1)**2/2
Let b be 68/(-16) + 3/12. Let r be ((-6)/(-18))/(b/(-3)). Suppose -1/4*m**5 + 1/4*m**3 - 1/4*m**2 + r*m**4 + 0*m + 0 = 0. What is m?
-1, 0, 1
Let x(b) be the second derivative of b**7/315 + b**6/180 + b**2/2 + 2*b. Let y(q) be the first derivative of x(q). Find l, given that y(l) = 0.
-1, 0
Let m be 38/(-95) - (-9)/15. Let 0*a**4 - 1/5*a - m*a**5 + 2/5*a**3 + 0*a**2 + 0 = 0. Calculate a.
-1, 0, 1
Determine p so that -28*p**2 - 32*p + 54*p + 2*p**4 - 2*p**5 + 0*p**5 - 6 + 12*p**3 = 0.
-3, 1
Let u = -11 + 15. Find a, given that 3*a**3 + 4*a**2 + 3*a**5 + 0*a**3 - 4*a**2 + 6*a**u = 0.
-1, 0
Let q(s) be the first derivative of 6*s**5/5 - 4*s**4 + 8*s**3/3 + 4. Factor q(i).
2*i**2*(i - 2)*(3*i - 2)
Let d(m) be the second derivative of 2*m**4 - 2*m**3 + 0 + m + 9/20*m**5 - 9/10*m**6 + 0*m**2. Determine s so that d(s) = 0.
-1, 0, 2/3
Factor -3/2*y - 1 - 1/2*y**2.
-(y + 1)*(y + 2)/2
Let r(j) be the first derivative of -2*j**3 + 6*j + 6 - 9/2*j**2. What is s in r(s) = 0?
-2, 1/2
Let u(s) be the first derivative of 3 + 0*s**2 + 0*s - 1/15*s**5 + 1/6*s**4 + 0*s**3. Solve u(w) = 0 for w.
0, 2
Suppose c - 6*c + 8 = 4*s, 0 = c + 5*s - 10. Factor -1/2*x**3 + c + 1/2*x**5 + 0*x + 1/2*x**4 - 1/2*x**2.
x**2*(x - 1)*(x + 1)**2/2
Let r(z) be the third derivative of 2*z**7/105 + z**6/15 - z**4/3 - 2*z**3/3 - 20*z**2. Factor r(v).
4*(v - 1)*(v + 1)**3
Suppose 2*k + 2*k = 0. Let d be k/(1*(2 + -3)). Suppose -o**5 - 3*o**3 + d*o**3 - 2*o**4 - o**2 - o**4 = 0. Calculate o.
-1, 0
Let v(m) = -m**3 + 5*m**2 + 7*m - 3. Let w be v(6). Let c = -1 - -3. Solve -5*f**3 + 4*f**w - c*f**2 + f**2 + f**5 + f**4 = 0.
-1, 0, 1
Let p = -11/4 + 13/4. Let v(i) be the second derivative of 0*i**3 - i + 0 + p*i**2 - 1/12*i**4. Factor v(x).
-(x - 1)*(x + 1)
Let m(i) = -i**3 - 5*i**2 - i - 5. Let k be m(-5). Factor -1 + k - 4*r + 3 + 2*r**2.
2*(r - 1)**2
Let 15/2*a**2 - 3/2*a**3 - 9/2*a + 0 - 3/2*a**4 = 0. Calculate a.
-3, 0, 1
Let q(x) = -8*x + 16. Let o be q(2). Suppose 2/7*z**2 + 0*z + o = 0. What is z?
0
Let r = 368/3 - 1469/12. Determine a so that -1/4*a**5 + 3/4*a**2 - r*a**3 + 1/2*a - 3/4*a**4 + 0 = 0.
-2, -1, 0, 1
Let t(y) be the third derivative of y**7/210 + y**6/40 + y**5/20 + y**4/24 - 14*y**2. Determine j so that t(j) = 0.
-1, 0
Factor -27*t**5 + 239*t**2 - 579*t**3 + 73*t**2 + 269*t**4 - 35*t**4 - 48*t.
-3*t*(t - 4)**2*(3*t - 1)**2
Suppose 16*a - 12*a = -13*a. Factor -2/7*i**3 + 0 + 0*i**2 + a*i.
-2*i**3/7
Let s be (-16)/19 - (2 + -3). Let z = s + 7/76. Factor -v**4 - 7/4*v**3 + z*v + 0 - 1/2*v**2.
-v*(v + 1)**2*(4*v - 1)/4
Suppose 0 = f - 5 + 2. Suppose f + 6 = 3*o. Factor -o*q**4 - 9/4*q**3 + 0*q + 3/4*q**2 + 0.
-3*q**2*(q + 1)*(4*q - 1)/4
Let b be -1 + 3 + -3 + 7. Factor -6 + 3 + 3*t**3 - b*t + 15*t - 9*t**2.
3*(t - 1)**3
Factor 0*f + 16/3*f**3 + 0 - 2*f**4 + 2*f**2.
-2*f**2*(f - 3)*(3*f + 1)/3
Suppose m + 5*m - 12 = 0. Factor -2*l**2 - 131*l**3 - 2*l**m + 127*l**3 + 8*l.
-4*l*(l - 1)*(l + 2)
Let i(s) = -7*s + 289. Let f be i(41). Let -n**3 - 12/7*n**f - 3/7*n + 2/7 = 0. Calculate n.
-1, 2/7
Let i be 2/7 - (609/(-98) + 6). Determine m so that m + i*m**2 + 0 = 0.
-2, 0
Let v be 9*((-423)/(-81) + -5). Let 2/5*m**3 - 4/5*m**v + 0 + 2/5*m = 0. Calculate m.
0, 1
Let q(z) be the third derivative of z**8/80640 + z**7/10080 + 7*z**5/60 - 7*z**2. Let b(m) be the third derivative of q(m). Let b(k) = 0. What is k?
-2, 0
Suppose -30 = -v - 5*v. Suppose 2*z + 2*b + 13 = 5*z, -5*b = -v*z + 25. Let 2/7*m + 2/7*m**2 - 2/7 - 2/7*m**z = 0. What is m?
-1, 1
Let v = 37 + -37. Let r(a) be the first derivative of 0*a**2 + v*a - 2/9*a**3 - 1/6*a**4 + 4. Factor r(t).
-2*t**2*(t + 1)/3
Let o(k) = k**3 + 7*k**2 + 5*k - 2. Let h be o(-6). Let y(l) = 4 - 2*l**2 - h. Let a(s) = 5*s**2 - s. Let m(v) = -4*a(v) - 9*y(v). Solve m(u) = 0.
0, 2
Let o = -134 - -134. Find d such that o + 1/2*d**3 + 1/2*d**2 - d = 0.
-2, 0, 1
Factor 2/5*u**3 - 4/5*u + 2/5*u**2 + 0.
2*u*(u - 1)*(u + 2)/5
Let c(w) be the second derivative of -w**6/540 + w**4/108 - w**2 - 3*w. Let b(o) be the first derivative of c(o). Factor b(r).
-2*r*(r - 1)*(r + 1)/9
Let t(r) = r**2 - 19*r + 92. Let h be t(10). Determine a so that 0 + 0*a + 1/3*a**h = 0.
0
Let s(m) = -m + 3*m + 4*m**2 + 8*m**3 + m**4 + m**4. Let z(q) = 3*q**4 + 17*q**3 + 9*q**2 + 5*q. Let n(y) = 5*s(y) - 2*z(y). Determine j, given that n(j) = 0.
-1, -1/2, 0
Let p(j) = -j**3 + 6*j**2 - 5*j + 2. Let q be p(5). Suppose 7*i - 6 = 4*i. Factor -2*u**i + 10*u - q*u**3 - 10*u.
-2*u**2*(u + 1)
Let m(d) = 2*d**2 + 3*d + 2. Let w be m(-2). Let t be 0*w*4/32. Factor -2/3*p**4 - 2/3 + 4/3*p**2 + t*p + 0*p**3.
-2*(p - 1)**2*(p + 1)**2/3
Let j(y) = y + 8. Let p be j(-7). Let n(s) be the first derivative of 0*s**2 + 0*s + 1/9*s**3 - 1/12*s**4 - p. Find i, given that n(i) = 0.
0, 1
Let y = 88/9 - 422/45. Factor -y*f + 0 - 2/5*f**2.
-2*f*(f + 1)/5
Let a = -1/253 - -1015/759. Let m be (12/9)/(1 + 1). What is n in -m + a*n - 2/3*n**2 = 0?
1
Let x(h) be the second derivative of h**8/8400 - h**7/1800 + h**6/1800 + h**5/600 - h**4/4 + 3*h. Let k(y) be the third derivative of x(y). Factor k(i).
(i - 1)**2*(4*i + 1)/5
Factor 2/7*o**2 - 6/7 - 4/7*o.
2*(o - 3)*(o + 1)/7
Let x(j) be the third derivative of j**8/13440 - j**7/1680 + j**6/480 - j**5/240 - j**4/6 + 3*j**2. Let m(i) be the second derivative of x(i). Factor m(l).
(l - 1)**3/2
Suppose 2*s + 10 = 5*v, -3*v + 2*v + 2 = 3*s. Suppose -v*z - 8 = -2*n - n, -4*z = 5*n - 6. Let 0 - 4/7*m - 2/7*m**n = 0. What is m?
-2, 0
Let s(k) be the second derivative of -k**7/147 + k**6/105 + k**5/70 - k**4/42 + 6*k. Factor s(a).
-2*a**2*(a - 1)**2*(a + 1)/7
Let a(m) be the third derivative of m**10/30240 - m**9/7560 + m**7/1260 - m**6/720 + m**4/24 + 3*m**2. Let v(x) be the second derivative of a(x). Factor v(s).
s*(s - 1)**3*(s + 1)
Let r(v) be the second derivative of -v**7/6 + 3*v**6/10 - v**5/10 + 20*v. Factor r(t).
-t**3*(t - 1)*(7*t - 2)
Let h(w) be the second derivative of 0 + 3/2*w**2 + 1/48*w**4 + 1/120*w**5 + 0*w**3 + 3*w. Let s(r) be the first derivative of h(r). Factor s(y).
y*(y + 1)/2
Factor 94*f - 11*f**3 + 4*f**4 - 27 + 220*f**5 - 30*f - 219*f**5 - 26*f**2 - 5.
(f - 2)*(f - 1)**2*(f + 4)**2
Let d(l) be the second derivative of -10*l**7/21 + 11*l**6/6 - 9*l**5/4 + 5*l**4/12 + 5*l**3/6 - 2*l. Let d(y) = 0. What is y?
-1/4, 0, 1
Let l(k) = -k**2. Let m(d) = -d**2 - 6*d - 6. Let a be m(-4). Let o(j) = 5 - 2*j - 5 + j + j**a. Let i(z) = 2*l(z) + o(z). Factor i(y).
-y*(y + 1)
Let f(p) be the first derivative of p**4/10 - 4*p**3/15 + p**2/5 + 1. Find x, given that f(x) = 0.
0, 1
Let o be -2 + -1 + (113/11 - 6). Factor -o*l**2 - 4/11 + 18/11*l.
-2*(l - 1)*(7*l - 2)/11
Let b(y) be the third derivative of y**6/24 - 5*y**4/24 + 15*y**2. Find s, given that b(s) = 0.
-1, 0, 1
Suppose 171*c = 172*c - 3. Factor 0 - 9/2*r**c + 3/2*r**2 + 3*r.
-3*r*(r - 1)*(3*r + 2)/2
Factor 1/3*t**3 - 1/6*t**4 + 2/3*t + 0 + 7/6*t**2.
-t*(t - 4)*(t + 1)**2/6
Let m be 5 - ((-6)/1)/(-2). Suppose 15 = m*f + f. Factor 0*w**2 - 2/5*w**4 - 7/5*w**f + 0 + 0*w**3 + 0*w.
-w**4*(7*w + 2)/5
Let g(x) be the first derivative of x**6/360 + x**5/60 + x**4/24 - x**3/3 + 4. Let s(u) be the third derivative of g(u). Factor s(q).
(q + 1)**2
Let r(j) be the first derivative of 2*j**3/57 - 2*j/19 + 4. What is u in r(u) = 0?
-1, 1
Let k(h) = -84*h**4 + 228*h**3 - 180*h**2 - 4*h + 40. Let f(t) = -28*t**4 + 76*t**3 - 60*t**2 - t + 13. Let p(q) = 16*f(q) - 5*k(