) be the first derivative of 5*n**3/3 - 25*n**2/2 + 30*n - 57. Factor s(y).
5*(y - 3)*(y - 2)
Let r(y) be the first derivative of 245*y**6/2 + 182*y**5 + 95*y**4/4 - 100*y**3/3 - 10*y**2 - 15. Find w such that r(w) = 0.
-1, -2/7, 0, 1/3
Let c = -2/27 - -97/945. Let y(j) be the second derivative of -1/105*j**6 + 0*j**2 + 0*j**3 - 1/42*j**4 - c*j**5 + 0 + j. Factor y(p).
-2*p**2*(p + 1)**2/7
Let a(g) be the third derivative of 0*g + 2*g**2 + 1/240*g**6 + 0*g**4 + 0 - 1/3*g**3 + 1/40*g**5. Find c such that a(c) = 0.
-2, 1
Suppose -4*w = w + 2*h - 46, 4*w + h - 35 = 0. Let c be (w/12)/(1/3). Factor 4*f**3 + 2*f**4 + 3*f**c - 2 - 4*f - 3*f**2 + 0.
2*(f - 1)*(f + 1)**3
Find c, given that 8/5*c - 4/5 - 4/5*c**2 = 0.
1
Let b(x) = -2*x**3 - 2*x**2 + 3*x - 3. Let c(t) = 5*t**3 + 5*t**2 - 7*t + 7. Let d(y) = -7*b(y) - 3*c(y). Factor d(p).
-p**2*(p + 1)
Suppose -4*l - l - 2*z + 25 = 0, -4*l - 4*z + 20 = 0. Suppose r - l = -0*r. Factor 0 + r*a**5 + 2 - 4*a**3 - 3*a**2 - 7*a**2 - a + 8*a**4.
(a - 1)*(a + 1)**3*(5*a - 2)
Let j be ((-5)/2)/5*-10. Factor 2*g**2 - 2*g**3 - g - 4 - 3*g + j*g**2.
-(g - 2)**2*(2*g + 1)
Let a(c) be the second derivative of 0*c**3 + 0 + 3*c + 1/12*c**4 - 1/2*c**2. Solve a(z) = 0 for z.
-1, 1
Factor 0 + 0*z**2 + 1/4*z**3 - 1/4*z**4 + 0*z.
-z**3*(z - 1)/4
Suppose 0 = 4*z - 8*z. Let o(x) be the third derivative of 0*x - 1/60*x**5 + 1/3*x**3 - 1/24*x**4 - x**2 + z. Find k, given that o(k) = 0.
-2, 1
Suppose 0 = h - 5 - 10. Let p be (8/(-10))/((-18)/h). Factor 2/3 - p*l**2 + 0*l.
-2*(l - 1)*(l + 1)/3
Let b be (-6 - -3) + (5 - 1 - -1). Factor 2*m**4 + 1/3*m**5 + 14/3*m**3 + 16/3*m**b + 2/3 + 3*m.
(m + 1)**4*(m + 2)/3
Let y(u) = -10*u**3 - 10*u**2 - 3*u + 10. Let i(z) = -5*z**3 - 5*z**2 - z + 5. Let o(k) = -13*i(k) + 6*y(k). Factor o(h).
5*(h - 1)*(h + 1)**2
Suppose -3*f + 5*f = 6. Let t(l) be the first derivative of -1/2*l - 3/8*l**2 + 2 - 1/12*l**f. Factor t(x).
-(x + 1)*(x + 2)/4
Let g(o) be the first derivative of o**4/2 - 3*o**2 - 4*o - 8. Find d, given that g(d) = 0.
-1, 2
Let a(m) = -4*m + 28. Let l be a(6). Suppose 12/5 - 36/5*b + 39/5*b**2 + 3/5*b**l - 18/5*b**3 = 0. What is b?
1, 2
Let l = -67729/2598 + -42/433. Let v = -51/2 - l. Factor v*z + 2/3*z**3 + 4/3*z**2 + 0.
2*z*(z + 1)**2/3
Suppose 109 = 4*x + 5*m, 4*x + 64 = -2*m + 170. Suppose -5*b + 4*h = -14, -5*b - h + 2*h = -x. Factor o**2 + 2 + o**2 - b*o + o.
(o - 2)*(2*o - 1)
Let a(f) = 3*f**2 - f + 2. Let c be a(1). Let r(y) be the first derivative of -11/6*y**3 - 1/4*y - y**2 - 3/2*y**c - 2 - 9/20*y**5. Factor r(s).
-(s + 1)**2*(3*s + 1)**2/4
Let v(o) be the second derivative of o**8/420 + o**7/210 - o**6/90 - o**5/30 + o**3/2 - 2*o. Let a(z) be the second derivative of v(z). Factor a(j).
4*j*(j - 1)*(j + 1)**2
Let p(q) = -q**3 - q**2 - q + 4. Let k be p(0). Let g(i) = -4*i + 104. Let o be g(26). Factor 4/9*c**3 + o*c + 2/9*c**2 + 2/9*c**k + 0.
2*c**2*(c + 1)**2/9
Factor 0*k**2 + 2/21*k**5 + 0 + 0*k + 0*k**4 + 0*k**3.
2*k**5/21
What is f in -10/3*f**4 - 14/3*f**3 + 0*f + 0 - 2/3*f**5 - 2*f**2 = 0?
-3, -1, 0
Let z = 3 + 1. Let g be (1 - -5)*z/12. Determine y, given that -g*y + 4 - 5 + 3 - y**2 + y = 0.
-2, 1
Let n(x) be the first derivative of x**9/7560 + x**8/1400 + x**7/700 + x**6/900 + 4*x**3/3 - 5. Let u(t) be the third derivative of n(t). Factor u(i).
2*i**2*(i + 1)**3/5
Let j(l) be the first derivative of 12*l**6/5 + 246*l**5/25 + 16*l**4 + 196*l**3/15 + 28*l**2/5 + 6*l/5 - 25. Determine h, given that j(h) = 0.
-1, -3/4, -1/3
Let q(n) = n**2 + n. Let j(p) = -3*p**4 + 6*p**3 + p**2 + 4*p. Suppose x + 1 = -2. Let y = -7 - x. Let w(k) = y*q(k) + j(k). Factor w(z).
-3*z**2*(z - 1)**2
Suppose t - 3*n + 8 = 0, -3*n + 24 = -3*t - 0*n. Let u be 2/t + (-75)/(-108). Determine c so that -2*c**2 + 14/9*c**4 - 10/9*c + u + 10/9*c**3 = 0.
-1, 2/7, 1
Let z(p) = p**3 - p**2 - 1. Let k(m) = -16*m**3 + 32*m**2 + 22*m + 1. Let x(b) = -2*k(b) - 18*z(b). Factor x(a).
2*(a - 4)*(a + 1)*(7*a - 2)
Let l(i) = -i. Let r(k) = 2*k**2 + 18*k + 32. Let g(w) = -2*l(w) - r(w). Factor g(c).
-2*(c + 4)**2
Factor 1 - 3 + 9*d + 4*d**2 - 7*d.
2*(d + 1)*(2*d - 1)
Determine a, given that -21*a**3 + 5*a**4 - 12*a**4 - 2*a**4 + 21*a**2 + 9*a = 0.
-3, -1/3, 0, 1
Let x(c) = 10*c - 4*c - 11 + 10*c - 16*c**4 + 16*c**2 - 3*c**3 - 2*c**3. Let z(m) = -3*m**4 - m**3 + 3*m**2 + 3*m - 2. Let u(h) = 2*x(h) - 11*z(h). Factor u(o).
o*(o - 1)*(o + 1)**2
Let v = 2/143 + 280/429. Factor 0 - 4/3*f**2 + 2/3*f**3 + 0*f + v*f**4.
2*f**2*(f - 1)*(f + 2)/3
Find k such that 0*k**4 + 16*k**2 - 5*k**2 - 2*k**2 + 6*k**3 - 6*k - 9*k**4 = 0.
-1, 0, 2/3, 1
Let m(d) be the first derivative of -136/45*d**3 - 7 - 27/5*d**4 + 0*d + 49/9*d**6 - 14/75*d**5 - 8/15*d**2. What is v in m(v) = 0?
-2/5, -2/7, 0, 1
Let p(o) = o**5 - o**4 + o**3 + o**2 - o. Let v(t) = 6*t**5 - 4*t**4 + 4*t**3 + 4*t**2 - 5*t. Let s(m) = -5*p(m) + v(m). Factor s(g).
g**2*(g - 1)*(g + 1)**2
Let c(i) be the first derivative of i**4/7 - 4*i**3/7 - 24. Factor c(x).
4*x**2*(x - 3)/7
Suppose 8*i - 4*i = -12. Let u be 1/i + (-14)/(-15). Factor 0 + 0*v + 3/5*v**3 - u*v**2.
3*v**2*(v - 1)/5
Suppose -3 - 7 = -5*k. Let q(o) be the first derivative of 0*o**2 - o + k + 1/3*o**3. Factor q(x).
(x - 1)*(x + 1)
Let c(z) be the third derivative of z**6/40 + 3*z**5/4 + 63*z**4/8 + 49*z**3/2 - 3*z**2 + 11. Suppose c(f) = 0. What is f?
-7, -1
Let p(z) be the first derivative of -z**5/3 - 13*z**4/12 - z**3 + z**2/6 + 2*z/3 + 8. Factor p(o).
-(o + 1)**3*(5*o - 2)/3
Let n(l) be the second derivative of -5/3*l**3 + 3/2*l**4 + 0 - 2*l**2 + 1/2*l**5 - 7/15*l**6 + 4*l. Let n(j) = 0. Calculate j.
-1, -2/7, 1
Let v(d) = d**2 - 3*d + 2. Let x be v(3). Factor 1/2*q**4 - 1/2*q**x + 0 + 1/2*q - 1/2*q**3.
q*(q - 1)**2*(q + 1)/2
Let y = -7/4 - -45/28. Let n = y + 10/21. Determine r so that 0 + r**2 + 1/3*r**4 - r**3 - n*r = 0.
0, 1
Let x(f) be the second derivative of 0*f**3 - 1/40*f**5 + 0*f**2 - 2*f + 0 - 1/48*f**4 - 1/120*f**6. Factor x(u).
-u**2*(u + 1)**2/4
Factor 0*z - 6*z**3 + 2*z**5 + 3*z**3 + z**4 + 2*z + z**2 - 3*z**3.
z*(z - 1)**2*(z + 2)*(2*z + 1)
Let r(i) be the third derivative of -4*i**2 + 0 + 0*i - 1/50*i**5 + 1/40*i**4 + 0*i**3. Determine n so that r(n) = 0.
0, 1/2
Let v = -260 - -266. Factor v*w**2 + 2/3*w**4 + 10/3*w**3 + 14/3*w + 4/3.
2*(w + 1)**3*(w + 2)/3
Let f be (111/(-8))/(165/(-22)). Let p = 9/4 - f. Find t such that -2/5*t**4 - 2/5*t**5 + 0 + 0*t + p*t**3 + 2/5*t**2 = 0.
-1, 0, 1
Let n = 10 - 1. Factor m**5 - n*m**4 - m**3 + 2*m**5 - 3*m**2 + 4*m**3 + 6*m**3.
3*m**2*(m - 1)**3
Let x(v) = 11*v + 57. Let y be x(-5). Let i(q) be the second derivative of 0*q**3 + 3/4*q**4 + 0 - q - 6*q**y + 3/20*q**5. Solve i(z) = 0 for z.
-2, 1
Let o(n) be the first derivative of 0*n + 0*n**3 + 0*n**2 - 1/5*n**4 + 1 - 2/25*n**5. Factor o(b).
-2*b**3*(b + 2)/5
Suppose 5*f = -3*l + 19, 3*f - 1 = 4*l - 7. Find j, given that 4/3*j + 0 - 2/3*j**3 - 2/3*j**f = 0.
-2, 0, 1
Let h be (-4)/10 + (-10)/(-15). What is x in -2/15*x**3 + 0 - h*x**4 + 0*x + 0*x**2 = 0?
-1/2, 0
Suppose 3*r = -2*r. Let g(l) be the second derivative of r - 5/4*l**5 - 5/12*l**4 + 8/3*l**3 - 2*l**2 - 2*l. What is v in g(v) = 0?
-1, 2/5
Let s(v) be the first derivative of -1/3*v**3 - 1/3*v + 2/3*v**2 + 3. Factor s(x).
-(x - 1)*(3*x - 1)/3
Determine l, given that 0 + 1/3*l**3 + 2*l + 5/3*l**2 = 0.
-3, -2, 0
Factor -2*q**2 - 7*q**3 + q**2 + 4*q**2 + 6*q**3.
-q**2*(q - 3)
Let a = -167 + 167. Let u(f) be the second derivative of 3/2*f**2 - 12/5*f**6 + 21/5*f**5 - 3/2*f**4 + a - 3/2*f**3 - 3*f. Factor u(l).
-3*(2*l - 1)**3*(3*l + 1)
Let g be (-4 - -1)/((-2)/(-20)). Let a = -59/2 - g. Suppose -a*u - 1/2*u**2 + 0 = 0. Calculate u.
-1, 0
Let p(q) = -q - 5. Let x be p(-7). What is v in 3*v - v**x - 4*v + 0*v**2 = 0?
-1, 0
Let d = -2 + 4. Factor -v**3 + 2*v - 3*v**2 + 6*v**2 + d*v**3.
v*(v + 1)*(v + 2)
Let n(l) be the first derivative of 1/6*l**6 - 1/5*l**5 + 1/3*l**3 + 0*l**2 - 6 + 0*l - 1/4*l**4. Find x, given that n(x) = 0.
-1, 0, 1
Let d(h) be the first derivative of -h**6/480 + h**5/48 - h**4/12 + h**3/6 + h**2/2 + 2. Let u(c) be the second derivative of d(c). Factor u(i).
-(i - 2)**2*(i - 1)/4
Let s(o) = 11*o**2 + 3*o**2 + 14*o + 9 - 2*o**2. Let t(w) = -w**2 - w - 1. Suppose -l = 4*l + 70. Let b(x) = l*t(x) - 2*s(x). Factor b(i).
-2*(i 