, -u - 29 = -2*p + 4*u. Let q(f) = -f**2 + 6*f - 3. Let n be q(3). What is i in -13*i + n + i**2 + 5*i + i**p = 0?
1, 3
Suppose 4*b - 20 = 4*y, 2*b - 14 = -2*b + 2*y. Let i(v) be the first derivative of 1/12*v**4 + 0*v - 1/6*v**b + 0*v**3 + 2. Factor i(a).
a*(a - 1)*(a + 1)/3
What is n in -3/5*n**3 + 0 + 0*n + 3/5*n**4 + 3/5*n**5 - 3/5*n**2 = 0?
-1, 0, 1
Let 1/6*p**3 + 0*p**2 - 1/2*p + 1/3 = 0. What is p?
-2, 1
Determine l, given that -6*l + 3/2*l**2 + 3/2*l**3 - 6 = 0.
-2, -1, 2
Let d(i) = i**2 - 1. Let z(v) = v**3 - 20*v**2 + 15*v + 36. Let l(k) = 22*d(k) + 2*z(k). What is b in l(b) = 0?
-1, 5
Let t = -13 - -12. Let p = t + 4. Solve 2/7*m**4 + 2/7*m**2 + 0 - 4/7*m**p + 0*m = 0.
0, 1
Let g = -6/31 + 173/93. Let f(o) be the first derivative of g*o**3 + 4*o + 3 - 1/4*o**4 - 4*o**2. Factor f(t).
-(t - 2)**2*(t - 1)
Let a be ((-2)/(-6))/((-5)/(-30)). Let h(j) be the first derivative of -2 + 2/3*j**3 + 2*j - a*j**2. Suppose h(k) = 0. Calculate k.
1
Suppose -4*n - 2 = 2*m, -m = -6*m + 4*n + 23. Suppose -2*b - m = 3*q - 6*b, -24 = -5*q - 3*b. Factor 3*w**4 - w**5 - 5 + 4*w + 2 - 2*w**2 - w - 2*w**q + 2.
-(w - 1)**4*(w + 1)
Let x(c) = c**3 + 4*c**2 + 4*c + 3. Let j be x(-2). Suppose j*z = 8 - 2. Suppose -5*v**z + 3*v**2 + 3*v**2 - 2*v = 0. What is v?
0, 2
Suppose 2*c + 3*n = 6*c - 15, 0 = -2*c - 4*n + 2. Factor g**3 - 3*g + 3*g**c + 4*g**4 - 5*g**2 + 5*g - 5*g**4.
-g*(g - 2)*(g - 1)**2
Let l(o) be the first derivative of -4/3*o**3 + 8/5*o + 6/5*o**2 - 8. Factor l(u).
-4*(u - 1)*(5*u + 2)/5
What is m in -4/7*m**3 + 6/7*m**4 - 2/7*m**5 - 2/7 + 6/7*m - 4/7*m**2 = 0?
-1, 1
Factor 3/7*t - 2/7 - 1/7*t**3 + 0*t**2.
-(t - 1)**2*(t + 2)/7
Let o be 4/(-6)*7/(-140). Let v(k) be the second derivative of -o*k**4 + 0 + 2*k - 1/15*k**3 + 2/5*k**2. Determine n so that v(n) = 0.
-2, 1
Let r(a) = -a**3 - 8*a**2 - 2*a - 11. Let f be r(-8). Factor 2*h**3 + 0*h**4 + h**3 - h**2 - h**4 - f*h**3.
-h**2*(h + 1)**2
Let v(z) be the third derivative of -z**8/1512 + z**7/945 + z**6/180 - z**5/54 + z**4/54 - 6*z**2. Suppose v(k) = 0. What is k?
-2, 0, 1
Solve 2*m**3 + 0*m**2 - m**2 - 3*m**2 = 0.
0, 2
Let r(p) = 4*p**3 - 2*p**2 + 2*p + 1. Let v(l) = -3*l**3 + l**2 - l - 1. Let h(u) = -4*r(u) - 5*v(u). Suppose h(j) = 0. What is j?
1
Solve 0*r + 93/4*r**3 - 12*r**5 - 3*r**2 + 0 - 42*r**4 = 0 for r.
-4, 0, 1/4
Let a(q) = q**2 + 10*q - 9. Let l be a(-11). Let 0 - 1/2*t - 1/4*t**l = 0. What is t?
-2, 0
Factor -4/3 + 2/3*j**4 - 2*j**2 - 10/3*j + 2/3*j**3.
2*(j - 2)*(j + 1)**3/3
Let x(d) be the first derivative of d**6/66 - 2*d**5/55 + 2*d**3/33 - d**2/22 - 17. Factor x(f).
f*(f - 1)**3*(f + 1)/11
Let v = 25 - 27. Let q be v - 0 - 2 - -6. Solve 4/5*u**3 - 6/5*u + 2/5 + 2/5*u**5 + 4/5*u**q - 6/5*u**4 = 0 for u.
-1, 1
Suppose 4*t - 2*r - 4 = 0, -4*r - 2 - 6 = 5*t. Factor 2/3*c**3 + 0*c**2 - 2/3*c + t.
2*c*(c - 1)*(c + 1)/3
Suppose 0*l + 6/5*l**3 - 2/5*l**2 + 0 = 0. Calculate l.
0, 1/3
Let u = 12 - 11. Let b(m) be the first derivative of 0*m - 3/2*m**4 - 1/3*m**6 - u + 0*m**2 - 2/3*m**3 - 6/5*m**5. Let b(q) = 0. What is q?
-1, 0
Let w(x) be the second derivative of 8*x + 1/50*x**5 + 0*x**3 + 0 + 0*x**4 + 0*x**2 + 0*x**6 - 1/105*x**7. Suppose w(d) = 0. What is d?
-1, 0, 1
Let c(l) = 7*l**2 - 1. Let f be c(1). Suppose -f*a + 9 = -3*a. Factor 1/3*j**2 - 1/3*j - 1/3 + 1/3*j**a.
(j - 1)*(j + 1)**2/3
Let h(d) = -d**2 + 7*d - 8. Let z be h(6). Let v = 1 - z. Solve -1/4*f - 1/4 + 5/4*f**2 - 3/4*f**v = 0 for f.
-1/3, 1
Let l(z) = -z - 5. Let b be l(-10). Find j, given that 11*j**2 - b*j**2 + 1 + 4*j - 1 = 0.
-2/3, 0
Let c(o) = 2*o - 6. Let b be c(5). Suppose -b*d = -4*u - 20, 2 = 5*d - 2*u - 14. Factor -3*g**d + g + 8*g**3 + 4*g**2 - 3*g + 5*g**4.
g*(g + 1)**2*(5*g - 2)
Factor 127*j + 4*j**2 + 130*j - 35 - 265*j + 3.
4*(j - 4)*(j + 2)
Suppose -2/5*i**2 + 0 + 2*i = 0. Calculate i.
0, 5
Let i(p) be the first derivative of -p**4 + 2 - 8*p**2 + 16/3*p**3 + 0*p. Solve i(a) = 0 for a.
0, 2
Let s(p) be the third derivative of p**7/1890 + p**6/360 + p**5/540 - p**4/72 - p**3/27 + 6*p**2. Factor s(q).
(q - 1)*(q + 1)**2*(q + 2)/9
Suppose 4*w + 10 = 26. Let z(v) be the third derivative of -1/280*v**7 - 1/96*v**w + 1/480*v**6 + 0*v + 0*v**3 + 1/80*v**5 - 2*v**2 + 0. Factor z(p).
-p*(p - 1)*(p + 1)*(3*p - 1)/4
Factor -45*w**2 - 2*w**4 - 10*w**3 + 3*w - 4 + 25*w + 51*w**4 - 18*w**3.
(w - 1)*(w + 1)*(7*w - 2)**2
Find w such that -1 - 1/3*w**2 + 4/3*w = 0.
1, 3
Factor 1/4*u**2 + 1/2 - 3/4*u.
(u - 2)*(u - 1)/4
Let r = -47057 + 13505427/287. Let g = r + 2/41. Factor -2/7 + 2/7*c**2 + 2/7*c - g*c**3.
-2*(c - 1)**2*(c + 1)/7
Let r be (-2)/10 - (-77)/35. Factor p**3 + 8*p**r + 3*p**3 + 0 - 16 + 4*p**2.
4*(p - 1)*(p + 2)**2
Factor 8/11*c + 2/11*c**2 + 8/11.
2*(c + 2)**2/11
Let c(o) = o**2 - 8*o + 5. Let s(l) = 3 + 3*l**2 + 3*l**2 - 5*l**2 + 0 - 4*l. Let w(p) = -6*c(p) + 10*s(p). Factor w(n).
4*n*(n + 2)
Factor 0*w + 1/2 - 1/2*w**2.
-(w - 1)*(w + 1)/2
Suppose 7 = -20*z + 7. Factor 9/7*t**4 + z*t + 0 + 0*t**3 - 12/7*t**2 - 3/7*t**5.
-3*t**2*(t - 2)**2*(t + 1)/7
Let g(u) = u**2 - 9*u + 20. Let v be g(5). Let k(o) be the first derivative of -2 - 2/9*o + 2/27*o**3 + v*o**2. Factor k(h).
2*(h - 1)*(h + 1)/9
Suppose 15 = -5*t, -3*t - 2 - 7 = 4*v. Suppose 0 = m - r - r - 10, 4*r + 20 = 3*m. What is l in 1/3*l**2 + m*l + 1/3*l**3 + v = 0?
-1, 0
Let v(p) = 11*p**2 + 2*p - 1. Let h be v(1). Let z = h + -8. Factor -5*w**2 + w**4 - 2*w**z + 2*w**4 + 4*w**2.
w**2*(w - 1)*(w + 1)
Let k be (-2)/(-9) - -3 - 3. Let y(u) = 2*u - 10. Let t be y(6). Solve -2/9 - 4/9*f - k*f**t = 0.
-1
Let r = -13 + 15. Suppose -r*z = 4*c - 6, -5*c - 2*z = -4*z + 6. Factor 2/3*f**2 - 2*f**3 + c*f + 0.
-2*f**2*(3*f - 1)/3
Suppose 0 - 2/7*h**2 - 2/7*h**3 + 4/7*h = 0. What is h?
-2, 0, 1
Let k = -768 + 770. Find y such that -2/3 + 5/3*y**3 - 1/3*y**4 - 3*y**k + 7/3*y = 0.
1, 2
Let i(w) = -w**2 - 5*w - 2. Let u be i(-4). Let b(l) = -5 + l**2 - 3*l + 10 - 6. Let s(m) = m**2 - 2*m - 1. Let j(d) = u*b(d) - 3*s(d). What is v in j(v) = 0?
-1, 1
Suppose -3*o + 8 = o. Suppose -r + 6 = o. Factor m**3 + m**4 + m**r - m - m**4 - m**2.
m*(m - 1)*(m + 1)**2
Let v(q) be the third derivative of 0 + 7/120*q**8 + 16/25*q**5 + 0*q**3 + 4/15*q**4 - 8/25*q**7 + 0*q + 22/75*q**6 + 3*q**2. Factor v(t).
2*t*(t - 2)**2*(7*t + 2)**2/5
Factor -6/17*n + 0 + 2/17*n**3 - 4/17*n**2.
2*n*(n - 3)*(n + 1)/17
Let z(s) = 16*s**5 - 26*s**4 + 10*s**3 + 11*s**2 - 11*s + 11. Let y(h) = -3*h**5 + 5*h**4 - 2*h**3 - 2*h**2 + 2*h - 2. Let i(b) = 11*y(b) + 2*z(b). Factor i(r).
-r**3*(r - 2)*(r - 1)
Let z = -2/29 + 482/261. Find u such that -28/9*u**4 + 10/3*u**5 + 0 + 8/9*u - 26/9*u**3 + z*u**2 = 0.
-2/3, -2/5, 0, 1
Let h be (-2)/10 + (-190)/50 - -6. Let f = -1 + 5/4. Factor -f + 0*u + 1/4*u**h.
(u - 1)*(u + 1)/4
Suppose 3*s - 79*s**4 - 5*s - 86*s**4 - 23*s**3 + 13*s**2 + 177*s**4 = 0. What is s?
0, 1/4, 2/3, 1
Let w be 2/(-6) + 136/(-60) + 3. Factor -w*p**3 - 6/5*p - 6/5*p**2 - 2/5.
-2*(p + 1)**3/5
Suppose -6*f + 4*t = -3*f + 42, -2*f + 2*t - 28 = 0. Let l be -2 + (-4)/(24/f). Factor 0*c + 0 + l*c**3 - 2/3*c**2.
c**2*(c - 2)/3
Factor 6*g**3 - g**2 + 7*g**2 - 8 - 8*g + 5*g**3 + 2*g**4 - 3*g**3.
2*(g - 1)*(g + 1)*(g + 2)**2
Let q be 0/(-2 + 1 + -1). Suppose -2*u + 7*u - 5 = q. Factor -3 + u + 0 + 2*p**2.
2*(p - 1)*(p + 1)
Let u be 14/4*(1 - -1). Suppose -4*d = -3*g - u, -23 = -2*d - 3*g - 2*g. Suppose -14*l + 31*l**2 - 56*l**3 - 12*l - d - 16*l**4 - 91*l**2 = 0. Calculate l.
-2, -1/2
Let z = -3 + 65. Factor -24*x + 81*x**4 + 29*x + 278*x**3 + 216*x**2 + 91*x + 16 - z*x**3.
(3*x + 2)**4
Let -44*f - 4 + 4 + 5*f**2 + 29*f = 0. What is f?
0, 3
Solve -3/5 - 6/5*n**3 - 12/5*n - 3*n**2 = 0 for n.
-1, -1/2
Let c be (-2 + 1)/(-2)*0. Let r be (-2)/(-5) + (-32)/(-120). Factor -1/3*u**3 + c - r*u**4 + 0*u - 1/3*u**5 + 0*u**2.
-u**3*(u + 1)**2/3
Let h(d) be the second derivative of 3*d**6/70 - 4*d**5/35 + 5*d**4/84 + d**3/21 + 3*d. Factor h(u).
u*(u - 1)**2*(9*u + 2)/7
Let d(i) = -i**2 - 10*i + 4. Let b be d(-10). Let x be (18/12)/(2/b). Factor -2/9*n**4 - 2/9 - 8/9*n**x - 4/3*n**2 - 8/9*n.
-2*(n + 1)**4/9
Factor 4/3 + 4/3*g + 1/3*g**2.
(g + 2)**2/3
Suppose -4*y = 3*d - 2 - 0, d - 8 = -5*y. Factor 1/2*a**y + 1/2 + a.
(a + 1)**2/2
Suppose -z = w - 0*z - 3, -4 = -3*w - 4*z. Factor -2*j**2 - 2*j**3 + 0*j**5 - 10*j*