**2/5
Let w(i) be the first derivative of 1/6*i**5 + 0*i**2 + 4/9*i**3 - 2*i - 3 - 4/9*i**4 - 1/45*i**6. Let a(k) be the first derivative of w(k). Factor a(v).
-2*v*(v - 2)**2*(v - 1)/3
Suppose -10 = r - 6*r. Solve -y**4 - 3*y**5 + y**3 + 2*y**5 + y**r - y**3 + y**3 = 0 for y.
-1, 0, 1
Determine w, given that 8*w - 8*w**3 - 14*w**4 - 16*w**4 - 2*w**2 + 32*w**4 = 0.
-1, 0, 1, 4
Factor -21*u - 49/4 - 1/4*u**4 - 11/2*u**2 + 3*u**3.
-(u - 7)**2*(u + 1)**2/4
Suppose 0 = 4*j + j - 50. Factor 6*g + 4*g**3 + 4*g + 8*g**2 - j*g.
4*g**2*(g + 2)
Suppose -y = -5, x + 4*y = 3*x + 10. Let a be 9/12 + (x - 2). Factor -3/4*w**4 + 3 + 3/4*w**2 + 3/4*w**5 + 6*w - a*w**3.
3*(w - 2)**2*(w + 1)**3/4
Factor -7*w**3 + 0*w**3 - 4*w**4 - 9*w**3.
-4*w**3*(w + 4)
Let s(k) = 15*k**5 - 10*k**4 - 40*k**3 + 15*k**2 + 15*k - 5. Let z(l) = l**5 + l**4 - l**2 + l. Let h(w) = s(w) + 5*z(w). Determine t, given that h(t) = 0.
-1, 1/4, 1
Let o(d) = -d**2 - 4*d + 4. Let h be o(-4). Suppose 3*k - 2*y = 0, h*k + 3*y - 19 = -2. Determine s, given that -2/3 + 7/3*s**k - 5/3*s = 0.
-2/7, 1
Let j(t) be the second derivative of 3*t**6/40 + t**5/5 + t**4/6 + t**2/2 - t. Let l(p) be the first derivative of j(p). Solve l(f) = 0 for f.
-2/3, 0
Suppose 0 = 4*a + v - 14, 5 = 3*a - 4*a + 4*v. Let n be ((-18)/(-3))/(36/8). What is d in 0*d**2 - n*d**a + 4/3*d + 2/3 - 2/3*d**4 = 0?
-1, 1
Let r(z) be the third derivative of -z**7/4200 - z**6/600 - z**5/200 - z**4/120 + 2*z**3/3 - 5*z**2. Let h(g) be the first derivative of r(g). Factor h(c).
-(c + 1)**3/5
Let l = 55 - 47. Let y be 40/(-16)*l/(-10). Factor -2/3*j**y + 2/3 + 0*j.
-2*(j - 1)*(j + 1)/3
Let w(j) = -5*j**2 - 7*j. Let i(n) = n**2 + 2*n. Let f(s) = 9*i(s) + 2*w(s). Find v such that f(v) = 0.
0, 4
Let z(g) be the first derivative of -2*g**3/15 - 12. Let z(c) = 0. What is c?
0
Let r(n) = n**2 - 6*n - 3. Let w(v) = -v**3 - 2*v**2 - 2. Let z be w(-3). Let o be r(z). Factor 0*c + 2/9*c**o + 0 - 4/9*c**3 + 2/9*c**2.
2*c**2*(c - 1)**2/9
Let f(b) be the second derivative of b**6/70 + 9*b**5/140 - 3*b**4/14 - 4*b**3/7 + 25*b. Solve f(t) = 0 for t.
-4, -1, 0, 2
Let l(j) be the third derivative of 7*j**6/720 - j**5/180 - 7*j**4/144 + j**3/18 + 20*j**2. Factor l(q).
(q - 1)*(q + 1)*(7*q - 2)/6
Suppose -4*j = -y - 8, 3*j + y = 4 + 2. Suppose -2 + 4*h + h**j - 7*h**2 + 2 + 2*h**3 = 0. What is h?
0, 1, 2
Determine a so that -4*a**3 + 4*a + 4*a**2 + 0*a**4 - 4*a**4 - a**3 + a**3 = 0.
-1, 0, 1
Let l(w) be the second derivative of -1/2*w**4 + 0 - 2*w + 1/14*w**7 + 0*w**2 + 0*w**5 - 1/2*w**3 + 1/5*w**6. Factor l(u).
3*u*(u - 1)*(u + 1)**3
Factor 4/3 - 14/9*d + 0*d**2 + 2/9*d**3.
2*(d - 2)*(d - 1)*(d + 3)/9
Factor -3/5*y**2 + 0 + 6/5*y - 3/5*y**3.
-3*y*(y - 1)*(y + 2)/5
Let j be (-81)/18*(-4)/6. Let o(p) be the second derivative of -1/5*p**5 - 7/3*p**j - p**2 + p**6 + p + 3/7*p**7 - 7/3*p**4 + 0. Solve o(t) = 0.
-1, -1/3, 1
Let r(a) = -3 + 2*a**3 + 2*a + 3*a**3 - 6*a**2 - 4*a**3. Let v be r(6). Determine w, given that 6*w**2 - v*w**3 - 4 - w + 3 + 1 + 4*w**4 = 0.
0, 1/4, 1
Let s(k) be the first derivative of 8*k**3/9 - k**2 - 2*k/3 - 1. Factor s(o).
2*(o - 1)*(4*o + 1)/3
Let s be 9/3 - (1 - 0). Factor 5/3*z**3 - 1/3*z**4 - 3*z**s + 7/3*z - 2/3.
-(z - 2)*(z - 1)**3/3
Factor -5 - 2*t**2 + 1 + 6 - 4 + 4*t.
-2*(t - 1)**2
Suppose -2*q + 10 = 3*m, 3*m + 2*q = -2*q + 14. Factor 6 + 4*y + 2/3*y**m.
2*(y + 3)**2/3
Let c(h) be the first derivative of -h**4/4 - h**3 + 5*h - 4. Let k(b) be the first derivative of c(b). Factor k(f).
-3*f*(f + 2)
Suppose 5*c - c = 20. Let m(b) = b**2 + b - 1. Let q(z) = -2*z**3 - z**2 - 7*z + 5. Let l(t) = c*m(t) + q(t). Let l(d) = 0. Calculate d.
0, 1
Suppose 3*r - 275 = -2*r. Let g be r/75 - (-1)/(-3). Factor g*f**2 - 6/5*f + 4/5.
2*(f - 2)*(f - 1)/5
Let k(m) = 45*m**3 + 8*m**2 - 40*m - 13. Let t(f) = -23*f**3 - 4*f**2 + 20*f + 7. Let o(j) = 3*k(j) + 5*t(j). Factor o(q).
4*(q - 1)*(q + 1)*(5*q + 1)
Let i(l) be the first derivative of l**4/9 + 16*l**3/27 + 10*l**2/9 + 8*l/9 - 12. Factor i(x).
4*(x + 1)**2*(x + 2)/9
Let g = -2/77 - -81/154. Let y(t) = -t**3 - 5*t**2 + 5*t - 3. Let k be y(-6). What is f in 1/2*f**4 - 1/2*f + 1/2*f**k + 0 - g*f**2 = 0?
-1, 0, 1
Let b be (1 - 3) + 5 - 1. Suppose b*j = 5 - 1. Factor -1/4*k**j - 1/4*k + 0.
-k*(k + 1)/4
Let y = 463/9 + -51. Solve -4/9*a**4 + 0*a - 2/9*a**5 + 2/9*a**3 + y*a**2 + 0 = 0.
-2, -1, 0, 1
Let z be (-3 - (-186)/26) + -4. Let v(p) be the first derivative of 1/26*p**4 + 3/13*p**2 - 2/13*p**3 - 3 - z*p. Suppose v(j) = 0. Calculate j.
1
Let q(s) be the first derivative of s**8/1680 - s**7/280 + s**6/180 - s**3/3 + 1. Let g(l) be the third derivative of q(l). Factor g(z).
z**2*(z - 2)*(z - 1)
Let k(i) = -3*i + 2*i + 1 - 2. Let t(b) = -b**2 + b + 2. Let f(g) = -6*k(g) - 4*t(g). Suppose f(l) = 0. Calculate l.
-1, 1/2
Let u be 17/17 - (-14)/(-18). Let z(b) = -b**3 + 6*b**2 - 2*b - 12. Let v be z(5). Factor 2/9*y**v + 2/9*y**2 - 2/9*y - u.
2*(y - 1)*(y + 1)**2/9
Let h be 13 + 6 + -3*1. Suppose 0 = 3*c + 2*w + 8, 4*w + 0 = 5*c - h. Suppose c + 2/5*z - 2/5*z**2 = 0. Calculate z.
0, 1
Let r = -43 - -49. Let z(b) be the third derivative of 0*b - 3*b**2 + 1/240*b**r - 1/840*b**7 - 1/48*b**4 + 0 + 1/24*b**3 + 0*b**5. Factor z(x).
-(x - 1)**3*(x + 1)/4
Let i be ((-10)/(-5))/((-2)/3). Let f = 3 + i. Factor 2/3*s**3 + f*s + s**4 - 1/3*s**2 + 0.
s**2*(s + 1)*(3*s - 1)/3
Let m be (3 + -2 - -1) + (-9)/(-3). Let u(k) be the third derivative of -3*k**2 - 2/3*k**3 - 1/30*k**m + 1/4*k**4 + 0*k + 0. Factor u(s).
-2*(s - 2)*(s - 1)
Let q(d) be the third derivative of -d**6/60 - 4*d**5/15 - 7*d**4/12 + 19*d**2. Factor q(w).
-2*w*(w + 1)*(w + 7)
Let r(x) = -6*x**2 - 14*x - 6. Let t(f) = 31*f**2 + 71*f + 29. Let m(o) = 11*r(o) + 2*t(o). Factor m(p).
-4*(p + 1)*(p + 2)
Factor -4*p + 2*p**4 - 5*p**4 + 8*p**2 - 5*p**4 + 4*p**5.
4*p*(p - 1)**3*(p + 1)
Determine r, given that 35 - 14*r**2 + 19*r**2 + 26*r + 14*r = 0.
-7, -1
Let l(v) be the first derivative of -2/15*v**5 - 1/3*v**2 + 1/27*v**6 + 4/27*v**3 + 1/9*v**4 + 2/9*v - 4. Factor l(s).
2*(s - 1)**4*(s + 1)/9
Let w(r) = -29*r**2 - 8*r - 9. Let v(u) = 14*u**2 + 4*u + 4. Let j(a) = -9*v(a) - 4*w(a). Let j(i) = 0. Calculate i.
-2/5, 0
Let c = -222 - -667/3. Suppose 2/3 - i**4 + 5/3*i + c*i**2 - 5/3*i**3 = 0. What is i?
-1, -2/3, 1
Let s(y) be the first derivative of y**5/20 + 7*y**4/16 + 3*y**3/2 + 5*y**2/2 + 2*y + 6. Let s(q) = 0. Calculate q.
-2, -1
Let b(o) = 5*o**3 + 9*o**2 + 7*o. Let n(y) = -y**3 - y**2 - y. Let r(d) = 2*b(d) + 6*n(d). Suppose r(w) = 0. Calculate w.
-2, -1, 0
Factor 2/3 - 1/2*a**2 - 2/3*a - 1/6*a**4 + 2/3*a**3.
-(a - 2)**2*(a - 1)*(a + 1)/6
Let m = -3739/20 + 187. Let r(i) be the third derivative of 1/210*i**7 + 0 - i**2 + 0*i + 0*i**3 - 1/24*i**4 + m*i**5 - 1/40*i**6. Factor r(v).
v*(v - 1)**3
Let a be (-6 - -8) + 6*(-5)/20. Suppose a*m**3 - 3/2*m**2 + 1 - 1/2*m + 1/2*m**4 = 0. What is m?
-2, -1, 1
Solve 34*s + 8*s**2 - 21 - 15 - 20 + 64 = 0.
-4, -1/4
Factor 0*q + 3*q**2 + 2*q + 2*q**4 + 4*q + 2*q**3 - 13*q**2.
2*q*(q - 1)**2*(q + 3)
Solve -2*c**2 + 2*c - 2*c**4 - 21*c**3 + 4*c**4 + 19*c**3 = 0 for c.
-1, 0, 1
Let u(s) be the first derivative of -s**8/462 - 3*s**7/385 - s**6/110 - s**5/330 - 2*s**2 + 7. Let g(l) be the second derivative of u(l). Solve g(r) = 0.
-1, -1/4, 0
Let m(c) = -c**2 + 17*c - 21. Let v be m(14). Suppose -4*x + 5*s = 3 + 14, -3*x - 3*s + v = 0. Factor 2*t**5 + 14/3*t**4 + 2*t**3 - 4/3*t + 0 - 2*t**x.
2*t*(t + 1)**3*(3*t - 2)/3
Suppose -8 + 0 = -4*g. Suppose -g*q = 5*s + 1, -4*q = -5*q + 4*s + 6. Suppose 2/7*d - 2/7*d**5 + 0 + 4/7*d**4 + 0*d**3 - 4/7*d**q = 0. Calculate d.
-1, 0, 1
Suppose 2*z + 20 = 3*x, -4*z - 7 = -x + 13. Suppose 0*q + x*q - 5*j = -12, 5*q - 14 = -j. What is n in 2*n**q + 2*n - 2 - 4*n + 2*n**3 + 0 = 0?
-1, 1
Let z be (-20)/90 - 40/(-18). Factor -4*d + 35*d**2 - 36*d**z - 4 + 0.
-(d + 2)**2
Let p = 15 - 8. Suppose 18 = 5*k - p. Factor 3*f**3 - 4*f**4 - 2*f**4 + 3*f**3 - 2*f**2 + 2*f**k.
2*f**2*(f - 1)**3
Let m(d) = 7*d**2 - 12*d - 1. Let b be m(2). Let w(s) be the third derivative of -1/24*s**4 - 1/120*s**5 + 0 + 0*s + 0*s**b + 3*s**2. Factor w(o).
-o*(o + 2)/2
Let d(j) be the second derivative of -j**7/280 + j**6/40 - j**4/2 - j**3/2 - 8*j. Let g(t) be the second derivative of d(t). Factor g(k).
-3*(k 