y**2.
-y*(y - 3)
Let t(a) be the second derivative of -2*a**6/15 + a**5 - a**4 - 10*a**3/3 + 8*a**2 + 6*a. Factor t(x).
-4*(x - 4)*(x - 1)**2*(x + 1)
What is m in 0 + 4/3*m + 44/3*m**2 = 0?
-1/11, 0
Let k(x) be the second derivative of -6*x**2 + 4/3*x**3 - 2*x + 1/3*x**4 + 0. Suppose k(i) = 0. Calculate i.
-3, 1
Let z(j) be the third derivative of 1/18*j**4 - 3*j**2 - 1/3*j**3 + 0*j - 1/270*j**5 + 0. Factor z(a).
-2*(a - 3)**2/9
Let t(o) be the second derivative of -o**6/15 + 3*o**5/10 + o**4/6 - o**3 - 42*o. What is v in t(v) = 0?
-1, 0, 1, 3
Factor -2/11*q**2 - 2/11*q**5 + 0 - 6/11*q**3 + 0*q - 6/11*q**4.
-2*q**2*(q + 1)**3/11
Let h = -1585/7 + 227. Let n = 699/7 + -99. Let -6/7*z**3 + h + 10/7*z**4 - 2*z**2 + n*z = 0. What is z?
-1, -2/5, 1
Let t(d) = -d**3. Let s(p) = p**3 - 2*p**2 + p + 4. Let a(u) = 1. Let h(q) = 2*a(q) - s(q). Let z(f) = -2*h(f) + 4*t(f). Factor z(i).
-2*(i - 1)*(i + 1)*(i + 2)
Let f(t) be the first derivative of t**8/2240 - t**7/1120 - t**6/480 + t**5/160 - t**3 - 1. Let j(x) be the third derivative of f(x). Factor j(k).
3*k*(k - 1)**2*(k + 1)/4
Let l(y) be the second derivative of -5*y**6/12 + 3*y**5/4 + 3*y**4/2 + 2*y**3/3 - 5*y. What is b in l(b) = 0?
-2/5, 0, 2
Let d be (-6 - (-165)/10)*(4 + -2). Find s such that -49/2*s**3 - 9/2*s + d*s**2 + 0 = 0.
0, 3/7
Let g = -19 + 58/3. Determine m so that -g*m**3 + 0 + 1/3*m + 1/3*m**4 - 1/3*m**2 = 0.
-1, 0, 1
Let m(a) be the second derivative of a**5/70 + a**4/14 - 4*a**3/21 - 12*a**2/7 + 26*a. Let m(n) = 0. What is n?
-3, -2, 2
Let y(g) = 4*g**5 + 4*g**4 - 18*g**3 + g**2 - 5*g + 7. Let v(x) = -x**5 + x**4 + x**3 + x - 1. Let m(u) = 14*v(u) + 2*y(u). Find o such that m(o) = 0.
-1/3, 0, 1, 2
Suppose s = -s + 12. Let u be s/(-20)*10/(-12). Let 3/4*g**3 + 1/4*g**5 - 3/4*g**4 - u*g**2 + 0 + 0*g = 0. What is g?
0, 1
Suppose 0 = -5*w - 2*l - 2580, 2*l + 0*l = 0. Let c be (w/(-18))/(1 - -2). Determine s so that 40/9*s**4 - c*s**2 - 8/9 - 16/3*s - 8/3*s**3 = 0.
-1/2, -2/5, 2
Let l(i) be the first derivative of i**8/336 - 2*i**7/105 + i**6/20 - i**5/15 + i**4/24 + i**2 - 3. Let j(a) be the second derivative of l(a). Factor j(n).
n*(n - 1)**4
Let z(x) be the second derivative of -3*x**4/16 - 5*x**3/8 + 3*x**2/4 + 14*x. What is c in z(c) = 0?
-2, 1/3
Let z = -11 - -56/5. Let o(k) be the first derivative of 3/4*k**4 + z*k**5 - 1 + k**3 + 1/2*k**2 + 0*k. Let o(w) = 0. Calculate w.
-1, 0
Let s(r) = r**2 - 6*r + 7. Let o be s(5). Factor 8*q**2 - 6*q**2 - 2*q**o + 3*q**5 - 3*q**3.
3*q**3*(q - 1)*(q + 1)
Let 12*q - 2*q + 8*q - 3*q - 5*q**3 + 10*q**2 = 0. What is q?
-1, 0, 3
Factor -29*i**5 + 58*i + 65*i**2 - 21*i**5 - 138*i**3 - 66*i - 9*i**2 + 140*i**4.
-2*i*(i - 1)**2*(5*i - 2)**2
Let k(m) = m + 14. Let d be k(11). Let s = -73/3 + d. Factor 0 - s*l**3 + 4/3*l**2 - 2/3*l.
-2*l*(l - 1)**2/3
Let t be (-18)/(-10) - 1/(-5). Factor 6/5*i**t - 6/5*i + 2/5 - 2/5*i**3.
-2*(i - 1)**3/5
Suppose 4*u - 8 = s - 3*s, -3*s - u + 2 = 0. Factor 3 - 3*a**5 + s*a + 3*a**4 - 3*a - 6*a**2 - 20*a**3 + 26*a**3 + 0.
-3*(a - 1)**3*(a + 1)**2
Let v(x) = 25*x**4 + 65*x**3 + 40*x**2 - 40*x + 40. Let w(h) = -2*h**4 - 5*h**3 - 3*h**2 + 3*h - 3. Let o(q) = 3*v(q) + 40*w(q). Find g such that o(g) = 0.
-1, 0
Let z(c) = -4*c**3 + 8*c**2 + 16*c - 11. Let v(k) = 3*k**3 - 9*k**2 - 15*k + 12. Let f(n) = 3*v(n) + 2*z(n). Let s be f(12). Factor 1/2 + 1/2*q**s + q.
(q + 1)**2/2
Let u(r) = 8*r**4 + 16*r**3. Let b(y) = 2*y**4 + 4*y**3. Let x = 13 - 35. Let s(m) = x*b(m) + 6*u(m). Determine l so that s(l) = 0.
-2, 0
Let s(l) be the third derivative of l**6/180 + 2*l**5/45 + l**4/12 - 6*l**2. Let s(a) = 0. Calculate a.
-3, -1, 0
Let u(l) be the second derivative of -2*l**6/15 + l**5/5 - 24*l. Let u(k) = 0. Calculate k.
0, 1
Suppose 6*w - 8*w = -10*w. Factor w - 2/3*n**3 + 2/3*n**2 + 0*n.
-2*n**2*(n - 1)/3
Let v = -225 - -2477/11. Suppose 4/11*u - v - 2/11*u**2 = 0. What is u?
1
Let r(q) = 0*q - 3*q**2 + 2*q**2 + 7 - 4*q. Let h be r(-5). Factor -4*x - x**2 + 6*x + 3*x**h.
2*x*(x + 1)
Let j(u) = -3*u**5 - 8*u**4 + 8*u**3 + 3*u**2 - 17*u. Let r(i) = -i**5 - 3*i**4 + 3*i**3 + i**2 - 6*i. Let p(g) = -6*j(g) + 17*r(g). Factor p(s).
s**2*(s - 1)**3
Let o(d) be the first derivative of d**6/10 + d**5/5 - d**4/12 - d**3/3 + 8*d - 3. Let g(j) be the first derivative of o(j). Factor g(s).
s*(s + 1)**2*(3*s - 2)
Let f(m) be the first derivative of 1/8*m**4 - 3 - 1/4*m**2 + 1/2*m - 1/6*m**3. What is x in f(x) = 0?
-1, 1
Let b be 77/140 - (-2)/10*1. Let -b*t**3 + 1 + 2*t + 1/4*t**2 = 0. Calculate t.
-1, -2/3, 2
Determine f so that 0 + 3/2*f**3 + 0*f + 3*f**2 = 0.
-2, 0
Let r be (-44)/(-23) + -2 - (-8610)/6440. Factor i**2 + r*i + 1/2 + 1/4*i**3.
(i + 1)**2*(i + 2)/4
Let 16 - 40*c + 4 + 35*c**4 + 2*c**3 - 105*c**2 - 13*c**3 + c**3 = 0. Calculate c.
-1, 2/7, 2
Let u(s) = -8*s**5 - 17*s**4 - 20*s**3 - 6*s**2 + 5. Let b(i) = 9*i**5 + 18*i**4 + 21*i**3 + 6*i**2 - 6. Let c(r) = 5*b(r) + 6*u(r). Factor c(f).
-3*f**2*(f + 1)**2*(f + 2)
Let h(q) be the third derivative of 1/3*q**3 + 0 + 1/60*q**5 + 3*q**2 + 0*q - 1/8*q**4. Find k, given that h(k) = 0.
1, 2
Let p(b) be the second derivative of b**10/15120 - b**9/7560 - b**4/4 + 3*b. Let f(c) be the third derivative of p(c). Suppose f(y) = 0. Calculate y.
0, 1
Let z(c) = 5*c**2 + 2*c - 3. Let d be z(1). Determine x, given that 2*x**d - 20/3*x**3 + 8/3*x**2 + 16/3*x + 0 = 0.
-2/3, 0, 2
Factor -5*z**3 - 30 + 0*z**3 - 55*z - 36*z**2 + 6*z**2.
-5*(z + 1)*(z + 2)*(z + 3)
Factor -4 - z**2 + 4 - 4 + 6*z - z**2.
-2*(z - 2)*(z - 1)
Let m(u) be the second derivative of -1/32*u**4 - 1/240*u**5 - 1/12*u**3 + 0 + u**2 + u. Let a(q) be the first derivative of m(q). Factor a(g).
-(g + 1)*(g + 2)/4
Let f(q) be the second derivative of 0 - 9*q + 3/20*q**5 + 0*q**2 + 1/4*q**4 - q**3. Factor f(d).
3*d*(d - 1)*(d + 2)
Suppose -4*j = -z - 12, -8*j + 3*j - 5*z + 15 = 0. Suppose j*y - 3/2*y**2 + 0 = 0. What is y?
0, 2
Let o(i) be the second derivative of -i**7/105 + i**5/50 - 3*i. Suppose o(k) = 0. What is k?
-1, 0, 1
Let w = 10 + -7. Let -4*k**2 + 2*k**2 + k - 2 + w*k = 0. What is k?
1
Let x = -22 - -38. Suppose 4 - x = -4*r. Determine k, given that -2/7 + 8/7*k - 12/7*k**2 - 2/7*k**4 + 8/7*k**r = 0.
1
Let y(p) be the second derivative of 1/4*p**4 - 1/10*p**6 + 0*p**2 + 1/14*p**7 + 8*p - 3/20*p**5 + 0 + 0*p**3. Let y(j) = 0. What is j?
-1, 0, 1
Let j(o) be the first derivative of 1/12*o**3 + 1/16*o**4 - 1/8*o**2 + 3 - 1/4*o. Factor j(k).
(k - 1)*(k + 1)**2/4
Let q(p) be the second derivative of -p**4/24 + 7*p**3/3 - 49*p**2 + 5*p + 2. Find f, given that q(f) = 0.
14
Suppose 4*x + 146 - 42 = 0. Let m be x*1/(-8) - 3. Factor m*h**2 - 1/4*h**3 - 1/4 + 1/4*h.
-(h - 1)**2*(h + 1)/4
Let x(u) be the first derivative of 0*u - 6/5*u**5 + 0*u**2 + 8/3*u**3 + 1/3*u**6 + 0*u**4 + 1. Determine r, given that x(r) = 0.
-1, 0, 2
Suppose -79*k + 78*k = 0. Let m(d) be the third derivative of k*d + 4*d**3 + 3/2*d**4 + 0 + 2*d**2 + 3/10*d**5 + 1/40*d**6. Factor m(h).
3*(h + 2)**3
Let h(m) be the first derivative of 3/2*m**4 + 2/5*m**5 - 2 + 2*m**3 + m**2 + 0*m. Factor h(x).
2*x*(x + 1)**3
Let g = -4 + 7. Let 10*k**4 + 6*k**3 - 2*k**g - 4*k**4 = 0. What is k?
-2/3, 0
Let r(a) be the first derivative of 1/21*a**6 + 0*a**4 + 2 + 4/21*a**3 - 1/7*a**2 - 4/35*a**5 + 0*a. Factor r(h).
2*h*(h - 1)**3*(h + 1)/7
Let c(q) be the first derivative of 1/2*q**2 + 1/3*q**3 - 2*q + 1. Find k, given that c(k) = 0.
-2, 1
Let b(i) be the third derivative of -i**5/24 + 5*i**4/48 + 5*i**3/6 + 9*i**2. Factor b(p).
-5*(p - 2)*(p + 1)/2
Let y(g) be the second derivative of -g**7/49 - 8*g**6/105 - 3*g**5/70 + g**4/21 - 38*g. Solve y(k) = 0 for k.
-2, -1, 0, 1/3
Let w(m) be the first derivative of 1/10*m**5 - 1/6*m**3 - 1/4*m**2 + 3 + 1/8*m**4 + 0*m. Factor w(z).
z*(z - 1)*(z + 1)**2/2
Let l be (31/(-124))/(6/(-32) - 0). Let w be 15/6*4/5. Solve -l + 4/3*n**w - 2/3*n**3 + 2/3*n = 0 for n.
-1, 1, 2
Let s = -330 + 991/3. Factor 2/3*o**4 + 1/3 + 1/3*o**3 - o**2 - s*o.
(o - 1)*(o + 1)**2*(2*o - 1)/3
Suppose 8*g = 7*g + 2. Let z(d) be the first derivative of 1/3*d**3 + g*d - 1 + 3/2*d**2. Let z(u) = 0. What is u?
-2, -1
Let d(z) = -z**2 - z - 1. Let m(i) = -8*i**2 - 4*i - 24. Let p(h) = 12*d(h) - m(h). Factor p(g).
-4*(g - 1)*(g + 3)
Let m be (-9)/3 - 42/(-10). Determine b, gi