(-3)). Let p(n) = -n**3 - 4*n**2 - 4*n - 3. Let y be p(x). Factor y - 1/2*q**2 - 1/2*q.
-q*(q + 1)/2
Factor 0*n + 0 - 2/15*n**2 - 2/15*n**3.
-2*n**2*(n + 1)/15
Let j = 0 - -3. Find l such that -5*l - 15*l**2 - 6*l**j + 2*l**2 - 2 - 4*l = 0.
-1, -2/3, -1/2
Let y(k) be the second derivative of 1/10*k**4 - 3/10*k**3 + 7*k + 0 - 3/50*k**6 + 1/70*k**7 + 3/50*k**5 + 3/10*k**2. Solve y(l) = 0 for l.
-1, 1
Let f(d) = d**3 - 7*d**2 - 8*d + 2. Let v be f(8). Suppose -5 = -s - z, z - v - 3 = 0. Factor -14/5*m**4 + s + 0*m + 0*m**2 - 4/5*m**3.
-2*m**3*(7*m + 2)/5
Let z = 7 - 18. Let w(s) = 4*s**3 - 10*s**2 + 16*s - 6. Let j(n) = -21*n**3 + 50*n**2 - 80*n + 29. Let a(f) = z*w(f) - 2*j(f). Factor a(i).
-2*(i - 2)**2*(i - 1)
Let r(q) be the first derivative of -q**4 + 16*q**3/3 - 8*q**2 + 29. Find v such that r(v) = 0.
0, 2
Let 1/2*i + i**2 - 1/2*i**4 - 1/2 - i**3 + 1/2*i**5 = 0. Calculate i.
-1, 1
Let z be (4 + -1)*115/15. Let m = 47/2 - z. Factor 0*o - o**3 + m*o**4 + 1/2*o**2 + 0.
o**2*(o - 1)**2/2
Let c = -37/4 - -11. What is u in -3/4*u**2 - 1/2*u + c*u**3 + 0 + 3/4*u**4 - 5/4*u**5 = 0?
-1, -2/5, 0, 1
Let m = 17 - 27. Let l be -1*1/(m/4). Factor 0 + 0*i + 0*i**2 + l*i**5 - 2/5*i**3 + 0*i**4.
2*i**3*(i - 1)*(i + 1)/5
Let w(o) = o**2 - 2*o. Let x be (-4)/(-12) - (-10)/6. Let s be w(x). Suppose -2/7*r + 2/7*r**5 + 4/7*r**2 + s - 4/7*r**4 + 0*r**3 = 0. Calculate r.
-1, 0, 1
Determine w, given that 0*w**2 + 1/5*w**3 + 2/5 - 3/5*w = 0.
-2, 1
Let r(t) = -t**2 + 7*t - 3. Let w be r(6). Let 3*o - 2*o**2 - 2*o**2 - 2 + w*o**2 = 0. Calculate o.
1, 2
Let k = 4/53 + 70/477. Let i be -2*(-9)/(-21)*21/(-6). Factor -8/9 + 0*n + 2/3*n**2 + k*n**i.
2*(n - 1)*(n + 2)**2/9
Suppose 2*y + 1 = 4*h - 57, 2*y = -3*h + 47. Let -9*b + 4*b**3 + 8*b**2 + 3 + h*b + b**2 - 2 = 0. What is b?
-1, -1/4
Let i be (30/(-16))/(1 - (-52)/(-16)). Let s(m) be the first derivative of 1/18*m**6 + 1/3*m + 10/9*m**3 + 5/6*m**2 + 1/3*m**5 + 2 + i*m**4. Factor s(n).
(n + 1)**5/3
Suppose 2*m + 65 = -3*m. Let f = 15 + m. Determine d, given that 18/5*d**f + 0 + 24/5*d**3 + 2*d**4 + 4/5*d = 0.
-1, -2/5, 0
Let s = -248/5 - -50. Let x be ((-2)/5)/2*-8. Find n such that -2/5*n + 0 + s*n**3 - x*n**4 + 8/5*n**2 = 0.
-1, 0, 1/4, 1
Suppose -5*k + i + i = -16, 0 = -k - 4*i + 12. Suppose 0 = -2*l + 4*c + 20, -21 = -3*l - k*c + 7*c. Suppose -s - l*s + 13*s - 1 - 16*s**2 = 0. What is s?
1/4
Factor 2/3 - 10/3*p + 16/3*p**2 - 8/3*p**3.
-2*(p - 1)*(2*p - 1)**2/3
Suppose 0 = 4*h + u - 13, -8 = -3*h + 5*u - 4. Let 1/4*c - 1/2 + 9/4*c**2 - 13/4*c**h + 5/4*c**4 = 0. Calculate c.
-2/5, 1
Find c such that 0*c + 3/2*c**2 - 27/2 = 0.
-3, 3
Factor 26/5*c**3 + 8/5*c + 2/5*c**5 - 12/5*c**4 + 0 - 24/5*c**2.
2*c*(c - 2)**2*(c - 1)**2/5
Let x(k) be the third derivative of -k**10/50400 + k**9/10080 - k**5/60 + 9*k**2. Let j(y) be the third derivative of x(y). Determine f so that j(f) = 0.
0, 2
Let h be 6/(-10)*30/(-9). Let r(a) be the first derivative of 2*a**3 + h*a**2 + 0*a + 1/2*a**4 - 3. Factor r(t).
2*t*(t + 1)*(t + 2)
Let x(u) = 1 + 0 - 3*u**2 + 2*u**2 - u. Let b(s) = 4*s**2 + 6*s - 1. Let m(i) = -2*b(i) - 6*x(i). Factor m(j).
-2*(j + 1)*(j + 2)
Let u(c) be the third derivative of -c**5/20 + 2*c**3 - 4*c**2. Factor u(n).
-3*(n - 2)*(n + 2)
Let h(t) be the second derivative of 3*t**5/10 - t**4/4 - 5*t**3/2 - 3*t**2 + 19*t. Factor h(y).
3*(y - 2)*(y + 1)*(2*y + 1)
Suppose 0 = 2*l - 5*q - 9, -16 = -5*q - 21. Factor -9/5*s**l + 3/5*s**3 + 0 + 6/5*s.
3*s*(s - 2)*(s - 1)/5
Let c be 2*(-2 + 12/(-8)). Let i be (-6)/28*c/6. Find j such that -1/4*j**3 + 0 + 0*j + 0*j**2 + i*j**4 = 0.
0, 1
Suppose 1/8*i**2 - 1/8*i + 0 = 0. What is i?
0, 1
Let q(i) be the third derivative of -9*i**6/40 + 3*i**5/20 + i**4/4 + 3*i**2. Factor q(w).
-3*w*(3*w - 2)*(3*w + 1)
Let x(j) = 6*j - 1. Let f be x(-1). Let u = f - -9. What is a in u*a**3 + 0*a + 8/3*a**4 - 2/3*a**2 + 0 = 0?
-1, 0, 1/4
Suppose -3*z + 26 = -5*n, -2*z + 3*n - 4 + 20 = 0. Factor 17*p - 17*p + 3*p**z.
3*p**2
Let f(j) be the second derivative of -j**6/1080 + j**5/360 + j**3/2 + 4*j. Let d(c) be the second derivative of f(c). Factor d(r).
-r*(r - 1)/3
Let w = 25675/21 + -3637/3. Let w*y**2 - 24/7*y + 2/7 = 0. Calculate y.
1/6
Let n(z) = -z**2 - z - 1. Let q(m) be the second derivative of 2*m**4/3 + 5*m**2 - 5*m. Let f(u) = 6*n(u) + q(u). Solve f(k) = 0 for k.
1, 2
Let s be (2/6)/(20/30). Suppose 14 = 5*o + 4. Find u such that -s - 1/2*u**o + u = 0.
1
Let o(w) be the second derivative of 0 + w - 1/12*w**4 + 2/3*w**3 - 2*w**2. Determine j, given that o(j) = 0.
2
Let r(a) be the third derivative of a**7/735 + a**6/140 + a**5/210 - a**4/28 - 2*a**3/21 - 38*a**2. Factor r(w).
2*(w - 1)*(w + 1)**2*(w + 2)/7
Suppose 4*y - 30 = -y. Let v(l) = l**2 - 5*l - 4. Let j be v(y). Suppose 4*r - r - r - r**j = 0. Calculate r.
0, 2
Let d(z) be the second derivative of 2*z**7/21 + 2*z**6/5 + 2*z**5/5 - 2*z**4/3 - 2*z**3 - 2*z**2 + 11*z. Factor d(c).
4*(c - 1)*(c + 1)**4
Let w be (2 + (-573)/285)*1. Let y = w + 98/285. Factor 0*l + 1/6*l**3 + y*l**2 + 0.
l**2*(l + 2)/6
Let t(o) = -o - 20. Let a be t(-23). Suppose 14/9*g**4 - 2/9*g + 10/9*g**2 + 0 - 4/9*g**5 - 2*g**a = 0. Calculate g.
0, 1/2, 1
Let x = -894 + 8048/9. Factor x*h**2 - 2/9 + 0*h.
2*(h - 1)*(h + 1)/9
Let f(r) be the first derivative of -r**4/10 + r**2/5 + 1. Determine m so that f(m) = 0.
-1, 0, 1
Let s(w) = w**3 + w**2 - w + 1. Let j(i) = 3*i**3 + 5*i**2 - 2*i + 4. Suppose 2*p + 10 = 2. Let d(z) = p*s(z) + j(z). Find o, given that d(o) = 0.
-1, 0, 2
Let u(d) = 78*d - d**2 + 7 - 2*d**2 - 5*d**2 - 11*d**3 - 82*d. Let q(j) = 6*j**3 + 4*j**2 + 2*j - 4. Let s(b) = -7*q(b) - 4*u(b). Factor s(o).
2*o*(o + 1)**2
Let r = -130 - -394/3. Factor 1/3*p**4 - p**2 - 2/3*p**3 + r + 4/3*p.
(p - 2)**2*(p + 1)**2/3
Factor -12/5 - 4/5*n**2 - 16/5*n.
-4*(n + 1)*(n + 3)/5
Let v(q) be the third derivative of q**8/336 + q**7/70 + q**6/60 - q**5/30 - q**4/8 - q**3/6 + 6*q**2. Factor v(j).
(j - 1)*(j + 1)**4
Suppose -j**3 + 16*j**3 + 12*j**4 - 17*j**4 - 20*j = 0. What is j?
-1, 0, 2
Let v(n) be the first derivative of 7 + 2*n - 5/2*n**2 - 1/4*n**4 + 4/3*n**3. Solve v(h) = 0 for h.
1, 2
Let m = -1070/11 - -100. Let 8/11*a**5 + 20/11*a**2 + 0*a - 2/11 + m*a**4 + 40/11*a**3 = 0. Calculate a.
-1, 1/4
Let n = 3 - 1. Factor -n*s + 2 + 3*s**3 - s - s**4 + 2*s**2 - 3*s**2.
-(s - 2)*(s - 1)**2*(s + 1)
Suppose 0 = i + 2*i - 4*f - 4, -i + 5 = -5*f. Factor i*b - 2/7*b**3 - 4/7*b**2 - 10/7*b**5 + 0 + 16/7*b**4.
-2*b**2*(b - 1)**2*(5*b + 2)/7
Let z(a) be the first derivative of -1/3*a**3 - 1/3*a**6 - 2 + 0*a + 1/2*a**2 + a**5 - 3/4*a**4. Factor z(v).
-v*(v - 1)**3*(2*v + 1)
Suppose -45 = -7*l + 2*l. Suppose 0 = 4*x - f - 48, -f - 60 = 4*x - l*x. Suppose -3 + x*k**2 - k**5 + 3 + 0 - 4*k + 6*k**4 - 13*k**3 = 0. Calculate k.
0, 1, 2
Let x(a) be the second derivative of 2*a**7/21 - 4*a**6/15 + 2*a**4/3 - 2*a**3/3 - 5*a. Factor x(w).
4*w*(w - 1)**3*(w + 1)
Suppose -4*i + 0*a = -5*a + 12, -4*i + 2*a = 0. Let y = i - -2. Suppose 7/5*u**3 - 9/5*u**2 - 1/5 - 2/5*u**y + u = 0. Calculate u.
1/2, 1
Let p(g) = -g**4 + g**3 + g**2 + 3*g - 2. Suppose -9 = -0*i - 3*i. Let o(s) = -s**4 + 2*s**3 + s**2 + 4*s - 3. Let t(f) = i*p(f) - 2*o(f). Factor t(b).
-b*(b - 1)*(b + 1)**2
Let o(c) be the first derivative of 7*c**3/12 + 5*c**2 - 3*c + 13. Factor o(h).
(h + 6)*(7*h - 2)/4
Let t(b) be the third derivative of -b**9/3024 - b**8/2520 + b**3/3 - b**2. Let f(v) be the first derivative of t(v). Factor f(d).
-d**4*(3*d + 2)/3
Let h(p) be the first derivative of 1/100*p**5 + 0*p**3 + 0*p**4 + 0*p**2 - 2 + 2*p. Let k(q) be the first derivative of h(q). Solve k(t) = 0 for t.
0
Let o be -2 + 3 - (-19 + 1). Suppose 5*m**3 - 10*m**4 + 1 + o*m**3 - 18*m**2 - 1 + 4*m = 0. What is m?
0, 2/5, 1
Let i(h) = h. Let x(d) = -d**2 - d - 2. Let z(w) = w**3 + 10*w**2 - w - 9. Let m be z(-10). Let p(k) = m*x(k) - 2*i(k). Factor p(q).
-(q + 1)*(q + 2)
Let d(n) be the second derivative of n**4/12 - n**3/6 - 3*n**2 + 13*n. Factor d(m).
(m - 3)*(m + 2)
Let s(a) be the third derivative of -a**8/1344 + a**6/240 - a**4/96 - 4*a**2. Factor s(q).
-q*(q - 1)**2*(q + 1)**2/4
Let d be (36/48)/((-3)/(-12)). Let b(a) be the second derivative of 1/42*a**7 + 0*a**5 + 0*a**2 + 1/15*a**6 - 1/6*a**4 + d*a - 1/6*a**3 + 0. Factor b(h).
h*(h - 1)*(