*a(m) + 4*c(m). Factor y(j).
4*(j - 6)*(j + 1)*(4*j + 1)
Suppose -2*w + 5*l - 7 = 0, -w + 0*l = -l - 1. Suppose w*z - 4 - 4 = 0. Factor -2/3*h + 4/3 - 2/3*h**z.
-2*(h - 1)*(h + 2)/3
Let o(y) = y**2 + 3*y + 2. Let s be o(-3). Factor -3*l**s - 4*l**3 + 4*l + 2 - 4*l**2 - 2*l**4 + 7*l**2.
-2*(l - 1)*(l + 1)**3
Let w be 1 + 5/(-2)*(-16)/80. Factor 9/4*y**3 + 0*y - w*y**2 + 0.
3*y**2*(3*y - 2)/4
Let i be 1/((-8)/10 + 1). Suppose 0 = 4*v + 3*j - 24, 0 = 2*v + j - i - 5. Factor 6*a**4 + v*a**3 - 5*a**4 - 2*a**3.
a**3*(a + 1)
Let s(t) be the first derivative of -24/35*t**5 + 0*t + 3/14*t**4 + 1/3*t**6 + 0*t**2 + 2 + 4/21*t**3. Factor s(n).
2*n**2*(n - 1)**2*(7*n + 2)/7
Suppose -4 - 5 = 3*s. Let o = s + 6. Determine k, given that 1/3*k**o - 2/3 + 2/3*k**2 - 1/3*k = 0.
-2, -1, 1
Let s(z) be the second derivative of z**7/5040 - z**6/480 + z**5/120 - z**4/3 + 2*z. Let l(g) be the third derivative of s(g). Factor l(d).
(d - 2)*(d - 1)/2
Let w(x) = 10*x**4 - 2*x**3 - 12*x**2 - 5*x + 13. Let r(h) = h**4 - h**2 - h + 1. Let k(f) = 36*r(f) - 4*w(f). Factor k(l).
-4*(l - 2)**2*(l + 1)**2
Let s(k) = -k**2 - 6*k + 7. Let n(y) = y**2 + 12*y - 13. Suppose -4*l + 6 = -5*l + f, 5*l = -3*f - 14. Let r(j) = l*n(j) - 7*s(j). Solve r(x) = 0.
1
Let q(l) = l**2 + 4*l + 11. Let m be q(-3). What is j in -2/3 - m*j - 24*j**2 = 0?
-1/6
Suppose 22*q = 21*q. Find i, given that q*i + 1/4*i**5 - 1/4*i**3 + 0 + 1/4*i**4 - 1/4*i**2 = 0.
-1, 0, 1
Let -2*p - p - 7 - 3*p**2 + 13 = 0. Calculate p.
-2, 1
Let b(l) = 4*l**5 - 9*l**4 - 4*l**3 - l**2. Let y(j) = 2*j**5 - 5*j**4 - 2*j**3 - j**2. Let o(p) = -3*b(p) + 5*y(p). Let o(r) = 0. What is r?
-1, 0, 1
Let y(p) be the second derivative of 1/84*p**7 - 1/2*p**2 - 1/10*p**5 + 0 + 1/12*p**4 + 8*p + 0*p**6 + 1/4*p**3. Suppose y(o) = 0. What is o?
-2, -1, 1
Suppose q = 5*q - 152. Let s = q + -36. Factor 4/5*g + 0 + 2/5*g**s.
2*g*(g + 2)/5
Let w be ((-50)/20)/((-1)/10). Suppose 4*n + n = -3*o - 25, -5*n = -o + w. Factor 2/3*i**2 + o + 4/3*i.
2*i*(i + 2)/3
Let d(b) be the first derivative of -b**4/24 - b**3/18 - 11. Suppose d(n) = 0. What is n?
-1, 0
Let n(x) be the first derivative of 2 - 1/2*x**2 + 0*x**3 + 1/4*x**4 + 0*x. Let n(v) = 0. What is v?
-1, 0, 1
Let b(j) be the third derivative of j**9/272160 - j**7/22680 - j**5/20 - 3*j**2. Let u(t) be the third derivative of b(t). Suppose u(s) = 0. Calculate s.
-1, 0, 1
Let k(u) = 4*u**3 - 11*u**2 + 13*u - 5. Let g(x) = x**2 + x - 1. Let a(d) = g(d) - k(d). Factor a(i).
-4*(i - 1)**3
Find s such that -2/3 + 1/3*s + 1/3*s**2 = 0.
-2, 1
Let h = -740 + 740. Factor h + 2/5*v**2 + 2/5*v.
2*v*(v + 1)/5
Let j(s) be the third derivative of -s**6/60 - s**5/10 + s**4/12 + s**3 + 40*s**2 - 1. Factor j(v).
-2*(v - 1)*(v + 1)*(v + 3)
Let b(h) be the third derivative of 1/6*h**4 + 0*h**3 + 1/21*h**7 - 1/6*h**5 + 0*h - 1/30*h**6 + 0 + 4*h**2. Find s, given that b(s) = 0.
-1, 0, 2/5, 1
Suppose 10*c = 12*c + 252. Let z be 2/(-14) - 60/c. Suppose 0*y**4 + 1/3*y + z*y**5 + 0*y**2 - 2/3*y**3 + 0 = 0. Calculate y.
-1, 0, 1
Let s(t) be the third derivative of t**8/50400 - t**7/6300 + t**5/30 + 8*t**2. Let g(m) be the third derivative of s(m). Factor g(i).
2*i*(i - 2)/5
Let u(x) be the second derivative of x**4/12 - x**2/2 + x. Let c be u(2). Determine m so that -4 - 3*m**3 + c*m**3 + m**3 - 3*m**2 + 8*m - 2*m**2 = 0.
1, 2
Let g = -50 + 101/2. Factor 0 + 1/2*d**2 - 1/2*d**3 + g*d - 1/2*d**4.
-d*(d - 1)*(d + 1)**2/2
Solve 0 - 4/3*f**2 + 0*f - 2/3*f**4 - 2*f**3 = 0 for f.
-2, -1, 0
Let s = 172 + -1200/7. Let y(o) be the first derivative of -s*o + 2/21*o**3 - 1/7*o**2 - 2. Factor y(j).
2*(j - 2)*(j + 1)/7
Let y be (-2)/(-5) + (-1)/(-5). Let f = -2/331 - -672/1655. Find l such that f*l + 1/5*l**3 - y*l**2 + 0 = 0.
0, 1, 2
Let l be 2*(-4 - 17/(-4)). Let i be (6/8)/((-6)/(-4)). Factor -i*z**2 - l*z + 0.
-z*(z + 1)/2
Let w(m) be the first derivative of m**4/2 - 2*m**3/3 + 1. Factor w(j).
2*j**2*(j - 1)
Let c(a) be the second derivative of 7*a**6/15 - 11*a**5/10 + 16*a**4/21 - 4*a**3/21 + 6*a. Factor c(b).
2*b*(b - 1)*(7*b - 2)**2/7
Factor 45/4*c + 3*c**2 + 27/4.
3*(c + 3)*(4*c + 3)/4
Let y(u) = -8*u**4 - 3*u**3 + 21*u**2 + 5*u - 5. Let r(b) = -12*b**4 - 4*b**3 + 32*b**2 + 8*b - 8. Let j(f) = -5*r(f) + 8*y(f). Solve j(m) = 0 for m.
-2, 0, 1
Let m(i) be the second derivative of -i**5/70 - 5*i**4/42 - i**3/3 - 3*i**2/7 - 2*i. Factor m(b).
-2*(b + 1)**2*(b + 3)/7
Suppose 2/9*l - 4/9 + 2/9*l**2 = 0. What is l?
-2, 1
Let j(b) = b**2 + 6*b + 3. Let c be j(-5). Let x be -1 - (4/c - 1). Factor -2*a**2 - x*a**3 - 1 - 5 + 6.
-2*a**2*(a + 1)
Let q = -33 - -33. Let t(u) be the third derivative of 0 - 1/135*u**5 - 1/108*u**4 - 1/540*u**6 + u**2 + q*u**3 + 0*u. Determine o, given that t(o) = 0.
-1, 0
Suppose -5*v - 2*z = -10, 4*v - 2 = -5*z + 6. Factor -2*g + 1 - g**v + 3*g**2 - g**2.
(g - 1)**2
Let y(r) be the third derivative of -r**7/1260 - r**6/360 + r**4/12 + 2*r**2. Let o(i) be the second derivative of y(i). Factor o(z).
-2*z*(z + 1)
Let u = 13 + -7. Let a = u + -3. Factor -a*s**2 - s**3 + 3*s**2 + s**5.
s**3*(s - 1)*(s + 1)
Factor -11/2*a**4 + 1/2*a - 2*a**5 - 9/2*a**3 - 1/2*a**2 + 0.
-a*(a + 1)**3*(4*a - 1)/2
Let j(q) = q**2 - q - 1. Let l be j(-2). Suppose l*z - 1 = 9. Determine n, given that 39/4*n**z - 9*n**3 - 1 - n = 0.
-1/4, 2/3
Let g(d) = d**4 - d + 1. Let z(y) be the first derivative of 6*y**5/5 + 9*y**4/4 + 3*y**3 + 3*y + 6. Let r(l) = 3*g(l) - z(l). Factor r(c).
-3*c*(c + 1)**3
Let h(s) = -s**3 - 6*s**2 - 2*s - 7. Let l be h(-6). Suppose -6*x + l*a + 35 = -x, -19 = -x + 5*a. Factor -8/3*b - 32/3*b**2 + 50/3*b**x - 10/3*b**3 + 0.
2*b*(b - 1)*(5*b + 2)**2/3
Let q be (-17)/(-4) + (-4)/16. Factor 6*p + 2*p**2 - q*p**2 - 1 - 3 + 0*p.
-2*(p - 2)*(p - 1)
Let z(k) be the second derivative of k**6/5 + 4*k**5/5 + k**4/2 - 2*k**3/3 + 12*k. Factor z(p).
2*p*(p + 1)*(p + 2)*(3*p - 1)
Let h(z) = -z**3 - 11*z**2 + 15*z + 11. Let g(l) = -6*l**2 + 8*l + 6. Suppose 0*d - 3*j = 3*d, 3*d + 5*j - 8 = 0. Let o(a) = d*h(a) + 7*g(a). Factor o(y).
2*(y - 1)*(y + 1)*(2*y + 1)
Let x = -3/26 + 8/13. Let j(z) be the first derivative of -1 + 2*z + 1/5*z**5 - z**3 - x*z**2 + 1/4*z**4. Let j(n) = 0. What is n?
-2, -1, 1
Let j(n) = -4*n**3 + 5*n**3 + 6*n + 0*n - 5*n**2 - 3. Let f be j(4). What is c in -f*c**3 + 17*c**3 - 2*c - 16*c**4 - 3*c**5 + 9*c**5 = 0?
-1/3, 0, 1
Let b(r) = -r + 8. Let q be b(4). Let o(w) be the second derivative of 0 + w - 1/35*w**5 + 0*w**2 - 1/21*w**3 - 1/14*w**q. Factor o(z).
-2*z*(z + 1)*(2*z + 1)/7
Let s(l) = 20*l**3 - 32*l**2 - 12. Let h(z) = 8*z**3 - 13*z**2 - 5. Let d(g) = 12*h(g) - 5*s(g). Determine y so that d(y) = 0.
0, 1
Suppose -16/7*z**2 - 2*z - 6/7*z**3 - 4/7 = 0. Calculate z.
-1, -2/3
Let a be 28/20 - 4/10. Factor a + 2*i + 4*i**2 - 3 + 2.
2*i*(2*i + 1)
Let v = 4/7 + -1/14. Factor 1/2*u**3 + 0*u**2 - v*u + 0.
u*(u - 1)*(u + 1)/2
Let k(v) = -v**3 - 6*v**2 + 10*v + 10. Let n be k(-7). Let b = -9 - n. Factor 0*w**b + 1/4*w - 1/4*w**3 + 0.
-w*(w - 1)*(w + 1)/4
Let b(q) be the second derivative of -1/9*q**2 + 0 + 1/27*q**3 + 1/54*q**4 - 2*q - 1/90*q**5. Let b(l) = 0. What is l?
-1, 1
Let n(w) be the second derivative of -1/25*w**5 + 2/15*w**3 - 1/5*w**2 + 0 + 8*w + 0*w**4 + 1/75*w**6. Solve n(b) = 0 for b.
-1, 1
Let d(a) be the second derivative of 3/10*a**5 + 0 + 2*a**2 + 5*a - a**3 - 1/15*a**6 - 1/6*a**4. Factor d(b).
-2*(b - 2)*(b - 1)**2*(b + 1)
Let z(u) be the second derivative of u**5/5 - 4*u**4/3 - 2*u**3/3 + 8*u**2 - 2*u + 30. Determine x so that z(x) = 0.
-1, 1, 4
Find k, given that -4*k**3 + 10*k**3 - 3*k**3 - 3*k = 0.
-1, 0, 1
Factor 3/2*s - 9/2 + 1/2*s**3 + 5/2*s**2.
(s - 1)*(s + 3)**2/2
Let i(g) be the third derivative of 0*g + 0 - 3*g**2 + 1/210*g**5 - 1/84*g**4 + 0*g**3. Solve i(t) = 0.
0, 1
Let z = 3 - 1. Let j be 4*-5*z/(-8). Solve -5*t**2 + 6*t**4 - 3*t**j - t**2 + 2*t**3 + t**3 = 0.
-1, 0, 1, 2
Factor 18/17*w - 36/17*w**2 + 4/17.
-2*(3*w - 2)*(6*w + 1)/17
Let y = 7374/35207 + 2/1853. Let j = y - -7/57. Determine o so that -3*o**2 + j - 1/3*o - 11/3*o**3 - 4/3*o**4 = 0.
-1, 1/4
Let g(w) = w**3 + 6*w**2 - 6*w - 1. Let f(n) be the third derivative of -n**5/60 + n**4/24 - 2*n**2. Let l(c) = 5*f(c) + g(c). Factor l(q).
(q - 1)*(q + 1)**2
Let o(s) = -9*s**3 - 19*s**2 - s - 3. Let a(p) = 19*p**3 + 37*p**2 