 = -7*p**4 + 23*p**3 + 78*p**2 + 85*p + 37. Let m(j) = -6*r(j) - 13*y(j). Factor m(u).
3*(u + 1)**2*(u + 2)**2
Let j(q) be the first derivative of -q**6/165 - q**5/22 - 3*q**4/22 - 7*q**3/33 - 2*q**2/11 + q + 5. Let r(f) be the first derivative of j(f). Factor r(x).
-2*(x + 1)**3*(x + 2)/11
Factor -v**2 + 0*v - 1/3*v**4 + 0 + 4/3*v**3.
-v**2*(v - 3)*(v - 1)/3
Suppose 16/3*i + 64/3 + 1/3*i**2 = 0. Calculate i.
-8
Suppose -4*m + 4*y + 21 = 3*y, 3*m = -y + 21. Let t be (6 - 3)/m*3. Let o**4 + 0 - 1/4*o + o**2 - 1/4*o**5 - t*o**3 = 0. What is o?
0, 1
Let k(a) be the first derivative of -27*a**5/5 + 9*a**4 + 5*a**3 - 18*a**2 + 12*a + 3. Find h, given that k(h) = 0.
-1, 2/3, 1
Factor 1/7*t**2 + 1/7 - 2/7*t.
(t - 1)**2/7
Suppose 3*h**3 + 22*h**4 + 3*h**3 - h**3 - 27*h**4 = 0. Calculate h.
0, 1
Let h(w) be the first derivative of -w + 0*w**2 - 7 + 1/3*w**3. Factor h(k).
(k - 1)*(k + 1)
Let v = 21/5 - 83/15. Let a = -1 - v. Solve a + 1/3*q**2 - 2/3*q = 0.
1
Let z(v) be the second derivative of 0*v**2 + 2/15*v**3 + 2*v + 1/100*v**5 + 0 + 1/15*v**4. Factor z(c).
c*(c + 2)**2/5
Let z = 75 - 133/2. Let b = z + -8. Factor 0 - y**4 + 0*y + 1/2*y**5 + 0*y**2 + b*y**3.
y**3*(y - 1)**2/2
Let k(s) be the first derivative of -s**6/900 + s**4/60 + s**3 + 3. Let m(q) be the third derivative of k(q). Factor m(t).
-2*(t - 1)*(t + 1)/5
Determine a so that -2*a**4 + 2*a**2 + 4*a**3 - 9*a + 6*a - a = 0.
-1, 0, 1, 2
Let d(x) be the second derivative of -x**7/84 + x**6/60 + x**5/40 - x**4/24 + 3*x. Factor d(s).
-s**2*(s - 1)**2*(s + 1)/2
Let o(d) = d**3 - 7*d**2 + d - 5. Let v be o(7). Let p(r) be the first derivative of 1/9*r**3 + 0*r - 1/12*r**4 - 1/15*r**5 + 1/6*r**v - 2. Factor p(y).
-y*(y - 1)*(y + 1)**2/3
Let r = -5 - -9. Suppose -s - s + r = 0. Suppose 0*g - 2/9*g**s + 2/9 = 0. Calculate g.
-1, 1
Determine t so that t + 4/3 - 1/3*t**2 = 0.
-1, 4
Factor 14*q**3 - 2*q**3 + 8*q + 9*q**2 + 11*q**2.
4*q*(q + 1)*(3*q + 2)
Let d(b) be the third derivative of -b**5/15 - 4*b**4/15 + 8*b**3/15 + 15*b**2. Determine f so that d(f) = 0.
-2, 2/5
Let w(i) be the third derivative of -1/6*i**3 - 1/240*i**5 + 0*i + 0*i**4 - 4*i**2 + 0 - 1/720*i**6. Let g(c) be the first derivative of w(c). Factor g(b).
-b*(b + 1)/2
Let t(y) = -y**3 - 24*y**2 + 53*y + 26. Let a be t(-26). Let k(u) be the third derivative of -1/6*u**3 + 1/60*u**5 + a*u**4 + 0 + 0*u - 3*u**2. Factor k(r).
(r - 1)*(r + 1)
Let h(i) = i**3 + 2*i**2 - 6*i - 7. Let v be h(-3). Suppose -y = -4*f + 4, -f + 4*y - 1 - 13 = 0. Factor -o**f + 2*o + 0*o + v*o**3 + 5*o**2.
2*o*(o + 1)**2
Let d be (-70)/(-9)*54/90. Factor 9/2 + 18*i + d*i**3 + 15*i**2 + 1/2*i**4.
(i + 3)**3*(3*i + 1)/6
Solve -27 - 32 - 2*y**4 + 59 = 0 for y.
0
Let t be ((-15)/(-10))/((-15)/4*-1). Suppose 0 - t*p**3 + 2/5*p**2 + 4/5*p = 0. What is p?
-1, 0, 2
Let z(g) = 3*g**4 - 6*g**2 + 3*g + 3. Let h(p) = -9*p**4 - p**3 + 18*p**2 - 8*p - 8. Let m(o) = 3*h(o) + 8*z(o). Factor m(a).
-3*a**2*(a - 1)*(a + 2)
Let l(t) be the second derivative of 1/6*t**5 + 4/9*t**3 + 1/45*t**6 - 5*t + 0 + 4/9*t**4 + 0*t**2. Find h such that l(h) = 0.
-2, -1, 0
Let c(s) be the third derivative of -s**7/1575 - s**6/90 - 2*s**5/25 - 3*s**4/10 - 3*s**3/5 - 5*s**2. Suppose c(k) = 0. Calculate k.
-3, -1
Let z(f) be the first derivative of 0*f**2 + 0*f + 2 + 0*f**3 - 1/6*f**4 + 4/15*f**5 - 1/9*f**6. Factor z(q).
-2*q**3*(q - 1)**2/3
Let w(p) be the second derivative of -p**7/14 - p**6/6 - p**5/10 + p. Factor w(g).
-g**3*(g + 1)*(3*g + 2)
Let h(k) be the third derivative of 0*k - 4*k**2 + 0*k**6 + 0*k**4 + 1/105*k**7 + 0 - 1/15*k**5 + 1/3*k**3. Factor h(g).
2*(g - 1)**2*(g + 1)**2
Suppose 2*c - 2 = 4. Suppose 3*h**4 - 5*h - c - 5*h**2 + 2*h**3 + 2*h**3 + 5 + h**3 = 0. What is h?
-2, -1, 1/3, 1
Suppose 3*o = -3*f - 3, 0 = -f + 4*f + 9. Suppose -4*a = -o - 6. Factor 9*i - 4*i**a - 7*i + 2*i**2.
-2*i*(i - 1)
Let a be 2 + 24/(-16) + (-10)/(-4). Suppose 3/2*u**2 + 0 + 1/2*u**a + u = 0. Calculate u.
-2, -1, 0
Suppose 0 = 44*s - 47*s + 6. Let z(j) be the second derivative of 1/15*j**6 + 2*j - 1/84*j**7 - 3/20*j**5 + 0*j**s + 0 + 1/6*j**4 - 1/12*j**3. Factor z(o).
-o*(o - 1)**4/2
Let r(q) = 4*q**3 + 8*q**2 + 2*q - 6. Let y(d) = 21*d**3 + 41*d**2 + 11*d - 29. Let x = 0 + 2. Suppose 0 = t - 6 + 17. Let u(a) = t*r(a) + x*y(a). Factor u(b).
-2*(b - 1)*(b + 2)**2
Determine v, given that -6/7*v**2 + 0 + 6/7*v**4 + 3/7*v**5 + 0*v**3 - 3/7*v = 0.
-1, 0, 1
Let o(c) be the first derivative of c**3/18 - c**2/6 + c/6 + 9. Factor o(r).
(r - 1)**2/6
Suppose 15 = 5*q + w - 0*w, 0 = -2*q - 2*w + 14. Suppose 3/4*a**3 + 5/4*a**4 - a**5 + 0 + 1/4*a - 5/4*a**q = 0. Calculate a.
-1, 0, 1/4, 1
Factor 1/3*i - 1/3*i**3 - 2/3*i**2 + 2/3.
-(i - 1)*(i + 1)*(i + 2)/3
Let p(u) be the first derivative of 0*u**3 - u**2 + 0*u - 1/240*u**6 + 0*u**4 - 2 - 1/120*u**5. Let v(i) be the second derivative of p(i). Factor v(c).
-c**2*(c + 1)/2
Suppose 4*t - 14 = w, -3*w - 7 = -4*t + 11. What is s in 0*s**t + 0 - 1/3*s**5 + 2/3*s**4 + 1/3*s - 2/3*s**2 = 0?
-1, 0, 1
Factor 1/3*j**3 - 8/3 + 4*j - 2*j**2.
(j - 2)**3/3
Let y be 6 + 1 + -3 - -12. Suppose 0 = 7*p + 2 - y. Factor -2/3 + 4/3*v**p + 2/3*v.
2*(v + 1)*(2*v - 1)/3
Let d(y) be the first derivative of -y**7/14 - y**6/10 - 4*y - 2. Let u(n) be the first derivative of d(n). Solve u(x) = 0 for x.
-1, 0
Let w(f) be the third derivative of f**7/945 + f**6/180 + f**5/270 - f**4/36 - 2*f**3/27 - 5*f**2. Factor w(u).
2*(u - 1)*(u + 1)**2*(u + 2)/9
Let n be (-55)/(-10) - (-6)/(-4). Factor 0*m + 65*m**2 - 64*m**2 - n*m + 4.
(m - 2)**2
Let r(w) be the first derivative of w**3/3 + w**2/6 - 13. Solve r(t) = 0 for t.
-1/3, 0
Factor 0 - 4/3*d + 2/3*d**4 - 8/3*d**3 + 10/3*d**2.
2*d*(d - 2)*(d - 1)**2/3
Suppose 2*d - b - 4 = 7*d, 4*d = -2*b - 8. Suppose 15 = 5*t - d*t. Factor t*k**2 - 5 - 4*k**2 + 6.
-(k - 1)*(k + 1)
Let q(c) = -6*c**3 + 6*c**2 - 4*c. Suppose -2*o - 5 + 9 = 0. Let h(i) be the second derivative of i**6/30 + i**3/6 + i. Let d(l) = o*h(l) + q(l). Factor d(x).
2*x*(x - 1)**3
Let a(r) be the first derivative of -4*r**4 - 20/3*r**3 - 9 + 12/5*r**5 + 4*r**2 + 0*r. Suppose a(x) = 0. What is x?
-1, 0, 1/3, 2
Let c be -1 - 0 - (-1352)/(-10). Let g = -135 - c. Determine p, given that 2/5*p**4 - 2/5*p**2 + g*p**3 + 0 - 6/5*p**5 + 0*p = 0.
-1, 0, 1/3, 1
Suppose 3 + 13 = 2*c. Find f such that -3 + c*f - 2*f + 0*f - 3*f**2 = 0.
1
Let l(b) be the second derivative of -2*b + 1/42*b**4 - 2/21*b**3 + 0 + 1/7*b**2. Let l(k) = 0. Calculate k.
1
Let d(w) = 2*w**2 - 2*w - 1. Let n be d(2). Let j be ((-48)/18)/((-5)/n). Solve 0 + 2/5*o + 8/5*o**4 + 2/5*o**5 + 12/5*o**3 + j*o**2 = 0.
-1, 0
Let b be 1/1 - 1/3. Let u(j) be the second derivative of 0 - j - 1/18*j**4 - b*j**2 - 1/3*j**3. Find o, given that u(o) = 0.
-2, -1
Let l(d) be the third derivative of d**8/1176 + d**7/147 + d**6/42 + d**5/21 + 5*d**4/84 + d**3/21 + 7*d**2. Factor l(g).
2*(g + 1)**5/7
Factor 6*y**2 + 0*y**3 - 4*y + 12 - 12 - 2*y**3.
-2*y*(y - 2)*(y - 1)
Let q(o) = o**2 - 6*o - 3. Let l be q(7). Suppose -l = -t - 2. Factor -2*w**3 + t*w**2 + 0 + 0.
-2*w**2*(w - 1)
Let d(v) be the second derivative of -v**7/63 + 4*v**6/45 - v**5/10 + 30*v - 1. Factor d(u).
-2*u**3*(u - 3)*(u - 1)/3
Let v(f) be the first derivative of -f**4/8 - 5*f**3/6 - 7*f**2/4 - 3*f/2 + 25. Factor v(z).
-(z + 1)**2*(z + 3)/2
Let z(s) = -10*s**2 + 19*s - 2. Let d(v) = 7*v**2 - 13*v + 1. Let k(y) = 7*d(y) + 5*z(y). Determine o, given that k(o) = 0.
1, 3
Let n(o) = 3*o + 7 - 2*o + 7. Let f be n(-11). Suppose -2*x**4 + 3*x**4 - 3*x**f + x**2 + 0*x**4 + 5*x**3 = 0. Calculate x.
-1, 0
Let -2/7*u**4 - 2/7*u**2 + 4/7 - 6/7*u + 6/7*u**3 = 0. Calculate u.
-1, 1, 2
Factor -36*s**2 + 6*s**2 - 6 - 4*s**2 - 12*s**3 - 33*s - 5*s**2.
-3*(s + 1)*(s + 2)*(4*s + 1)
Let x(a) be the third derivative of a**8/151200 + a**7/12600 + a**6/2700 - a**5/15 - 6*a**2. Let s(t) be the third derivative of x(t). Factor s(n).
2*(n + 1)*(n + 2)/15
Let p(q) be the first derivative of -q**6/5 + 6*q**5/5 - 3*q**4 + 4*q**3 - 3*q**2 + 6*q/5 - 12. Find j, given that p(j) = 0.
1
Let j(q) be the second derivative of -1/96*q**4 + 1/12*q**3 + 0 + 2*q + 1/480*q**6 + q**2 - 1/120*q**5. Let c(f) be the first derivative of j(f). Factor c(s).
(s - 2)*(s - 1)*(s + 1)/4
Suppose d = -0*d - 1. Let q = d - -3. Factor x**2 + x +