. Factor -247*w**3 - 19*w**2 - 6*w - 2*w + d + 240*w**3.
-(w + 1)*(w + 2)*(7*w - 2)
Let k(v) be the first derivative of -v**3/3 - 9*v**2 - 81*v + 24. Determine f so that k(f) = 0.
-9
Let c(u) = -u**2 + 1. Let g(h) = 3*h**3 - 6*h**2 - 9*h. Let t(o) = -6*c(o) + g(o). Factor t(x).
3*(x - 2)*(x + 1)**2
Let v(a) be the first derivative of a**6/6 + 4*a**5/5 + 5*a**4/4 + 2*a**3/3 + 16. Find x, given that v(x) = 0.
-2, -1, 0
Let d(c) be the first derivative of c**8/672 - c**7/420 - c**6/240 + c**5/120 + c**2/2 + 2. Let l(f) be the second derivative of d(f). Solve l(s) = 0 for s.
-1, 0, 1
Let w(p) be the first derivative of p**8/840 - p**7/84 + 7*p**6/180 - p**5/20 + p**3 - 10. Let i(k) be the third derivative of w(k). Let i(y) = 0. What is y?
0, 1, 3
Let c(b) = b**2 - b. Let o(p) = -5*p**3 - p**2 + 16*p + 20. Let a(d) = 4*c(d) - o(d). Find g such that a(g) = 0.
-2, -1, 2
Factor 6/11*n**2 + 2/11*n**3 + 0 + 4/11*n.
2*n*(n + 1)*(n + 2)/11
Let y = 5 - 2. Let h(f) be the second derivative of -2/5*f**6 + 1/6*f**7 + 7/6*f**4 - 1/5*f**5 + f - 1/2*f**y - f**2 + 0. Factor h(i).
(i - 1)**3*(i + 1)*(7*i + 2)
Suppose -5*r + 0*i - 4*i = -28, 3*r = -i + 14. Suppose -5*p + r*l = l - 21, 4*l = 5*p - 18. Solve 3*h + 0*h - h - p*h + 2*h**2 = 0 for h.
0, 2
Let q = 237/788 - 10/197. Factor 0*x**4 - 1/4*x + 0 + 0*x**2 + 1/2*x**3 - q*x**5.
-x*(x - 1)**2*(x + 1)**2/4
Let b(p) be the third derivative of -p**5/630 + p**4/126 + p**3/21 + 14*p**2. Factor b(x).
-2*(x - 3)*(x + 1)/21
Suppose -704*k + 713*k = 0. Find d such that 3/2*d**3 + 3/2*d**2 + 0*d - 3/2*d**4 + k - 3/2*d**5 = 0.
-1, 0, 1
Let n be (-6 - -8) + 1 + -4. Let v be (-10)/20*(n - -1). Suppose v - 1/2*c + 1/4*c**3 - 1/4*c**2 = 0. Calculate c.
-1, 0, 2
Let d(p) = -p**3 + p**2 + p. Let g(a) = a - 1. Let k be g(3). Let i(w) = -3*w**3 + 2*w**2 + 3*w - 1. Let x(u) = k*d(u) - 2*i(u). Suppose x(o) = 0. What is o?
-1, 1/2, 1
Let l = 22 - 20. Let u(h) = -2*h**4 + 6*h**3 + 6*h**2 - 2*h - 2. Let r(j) = j**4 + j**3 + j**2 + j - 1. Let p(f) = l*r(f) - u(f). Factor p(k).
4*k*(k - 1)**2*(k + 1)
Let q(a) = -2*a**2 + 2*a - 2. Let c(n) = n. Suppose -3*p - 8 = -2*r - 5*p, 3*r + 2*p - 9 = 0. Let x(t) = r*q(t) - 6*c(t). Factor x(z).
-2*(z + 1)**2
Let g(r) = -r**2 + 4*r + 3. Let o be g(4). Factor 2*c**3 + 3*c**5 - c**5 - o*c**3 - c**3.
2*c**3*(c - 1)*(c + 1)
Let p(x) be the first derivative of 1/60*x**5 + 0*x**2 + 0*x**3 + 2*x + 2 + 0*x**4. Let k(b) be the first derivative of p(b). Factor k(d).
d**3/3
Let g(a) be the second derivative of -a**5/10 - a**4/6 + 4*a**3/3 + 4*a**2 - 9*a. Factor g(u).
-2*(u - 2)*(u + 1)*(u + 2)
Factor 2 - 45*k**2 - 24*k + 49*k**2 - 2.
4*k*(k - 6)
Let r(s) be the third derivative of s**5/360 + 5*s**4/144 + s**3/9 - 11*s**2. Find z such that r(z) = 0.
-4, -1
Suppose 81*g = 86*g - 10. Factor 5*o - 1 - 9/4*o**g.
-(o - 2)*(9*o - 2)/4
Find t such that 6/7*t**3 - 6/7*t + 3/7*t**2 - 3/7*t**4 + 0 = 0.
-1, 0, 1, 2
Find v, given that 15*v**2 - 54*v**3 + 20*v**4 + 25*v**2 - 20*v + 14*v**3 + 4 - 4*v**5 + 0*v**5 = 0.
1
Let u be (-9)/(-6) - (-86)/4. Let s = u + -23. Factor -2/5*g**3 + 0*g + 2/5*g**2 + s.
-2*g**2*(g - 1)/5
Let l be 2*((-3)/(-3) + 0). Let g be (l/5)/((-1)/(-5)). Factor 1 + 2*z**g - 7*z + 1 + 7*z**3 - 4*z**2.
(z - 1)*(z + 1)*(7*z - 2)
Let n = 973/6 + -315/2. Let y(s) = s**3 - 6*s**2 - 7*s + 2. Let k be y(7). What is w in 6*w + 4/3 + n*w**k = 0?
-1, -2/7
Determine j, given that -4/7*j**2 - 4/7*j + 8/7 = 0.
-2, 1
Let l = 80 + -398/5. Let m = 17/70 + -3/70. Factor 0*k**2 + 0*k + 1/5*k**4 - l*k**5 + m*k**3 + 0.
-k**3*(k - 1)*(2*k + 1)/5
Let i(d) be the second derivative of -5*d - d**2 + 1/90*d**5 - 2/9*d**3 + 1/36*d**4 + 0. Let g(c) be the first derivative of i(c). Let g(x) = 0. What is x?
-2, 1
Let k(z) = z**2 - 2*z - 3. Let n be k(3). Suppose -l - 2*q - 3*q + 20 = 0, n = 2*q - 6. Factor -1/2*r**2 + 1/2*r**l - 1/2*r**3 + 1/2*r**4 + 0*r + 0.
r**2*(r - 1)*(r + 1)**2/2
Factor 4/5*z**3 + 0 - 16/5*z + 0*z**2.
4*z*(z - 2)*(z + 2)/5
Suppose 0 = 3*a + 2*w - 22, 3*a - 6*w = -2*w + 10. Suppose -a*n + n = 0. Factor i**2 + 1/2*i**3 + n + 1/2*i.
i*(i + 1)**2/2
Let x(z) = -z**2 + 3*z + 20. Let s be x(6). Solve 5/4*r**3 + 1/4*r**5 + 0 - 1/2*r**s - r**4 + 0*r = 0.
0, 1, 2
Let g(m) be the first derivative of -1/6*m**3 - 3 + 1/20*m**5 + 1/8*m**2 + 1/24*m**6 - 1/8*m**4 + 1/4*m. Factor g(d).
(d - 1)**2*(d + 1)**3/4
Factor -1/4*n**3 + 0 + 1/4*n**2 + 1/4*n - 1/4*n**4.
-n*(n - 1)*(n + 1)**2/4
Let v = 26 - -10. Let w be 279/v + 2/(-8). Factor -6*u + 6 - w*u**2 + 9/2*u**3.
3*(u - 2)*(u + 1)*(3*u - 2)/2
Let l(g) be the first derivative of g**5/45 - g**4/36 - g**3/9 + g**2/18 + 2*g/9 - 27. Factor l(p).
(p - 2)*(p - 1)*(p + 1)**2/9
Let f be (2 + (2 - 3))*0. Suppose 2*j + 4*i + 96 = 7*j, -4*j + 3*i + 76 = f. Find x such that -j*x**5 - 15*x**3 - 8*x**2 - 42*x**4 - 2*x**5 - 17*x**3 = 0.
-1, -2/3, 0
Let f be (-4 - 38/(-8))*(-32)/(-84). Suppose f*m**3 - 4/7 - 2/7*m + 4/7*m**2 = 0. What is m?
-2, -1, 1
Let r = -158 + 158. Let 0 + t**3 - 1/3*t**5 + 2/3*t**2 + 0*t**4 + r*t = 0. What is t?
-1, 0, 2
Suppose -5*g = -5*x + 10, 4*x - 10 = 2*x - 4*g. Factor w**4 - w**2 + 0 + 1/2*w - 1/2*w**5 + 0*w**x.
-w*(w - 1)**3*(w + 1)/2
Let a(q) = q**3 - 7*q**2 + 9*q + 5. Let s be a(5). Factor -4/5*l**3 + 4/5*l**4 - 4/5*l**2 + s + 4/5*l.
4*l*(l - 1)**2*(l + 1)/5
Let i = -1 + 3. Let y(j) = -j - 4. Let h be y(-7). Factor -h + 5 + l - l**3 - i.
-l*(l - 1)*(l + 1)
Let n be 1 + 1 + 96/(-28) + 2. Find d, given that -2/7*d**5 + 8/7*d**4 + n*d**2 + 0 - 10/7*d**3 + 0*d = 0.
0, 1, 2
Let i(l) be the second derivative of -2*l**6/15 + l**5/5 + l**4/3 - 2*l**3/3 - l. Factor i(j).
-4*j*(j - 1)**2*(j + 1)
Let v be (-6)/5*(-85)/68. Suppose -3/2*f - 3/2 + 3*f**2 - v*f**4 - 3/2*f**5 + 3*f**3 = 0. Calculate f.
-1, 1
Let l be 2 - (96/28 - 1 - 1). Factor 0 + l*x + 2/7*x**2.
2*x*(x + 2)/7
Let z be 13/18 + (-2)/9. Let l(y) be the first derivative of -z*y**2 + 2 + 1/3*y**3 + 0*y. Factor l(j).
j*(j - 1)
Let u(o) be the first derivative of -o**4/30 + 2*o**3/15 - o**2/5 + 2*o/15 - 13. Determine h so that u(h) = 0.
1
Let h(b) be the second derivative of -5*b**7/14 + 4*b**6/3 - 3*b**5/2 + 5*b**3/6 + 40*b. Suppose h(p) = 0. What is p?
-1/3, 0, 1
Let w(d) = d + 26. Let a be w(-19). Suppose a*r - 24 = -r. Factor 0 - 2/5*b**r - 2/5*b**2 + 2/5*b**4 + 2/5*b.
2*b*(b - 1)**2*(b + 1)/5
Factor 2/11 + 0*u - 2/11*u**2.
-2*(u - 1)*(u + 1)/11
Let r(b) = 7*b**2 + 3*b - 2. Let c be r(-2). Let s be (c/(-2))/((-9)/6). Factor -s*w**3 + 0*w + 4/3*w**2 + 25/3*w**4 + 0.
w**2*(5*w - 2)**2/3
Let x = -1/21 + 1/3. Let z be 2/(-4) - 15/(-6). Factor -4/7*r + 2/7 + x*r**z.
2*(r - 1)**2/7
Let p(u) be the second derivative of u**4/24 + u**3/6 + u**2/4 - 6*u. Solve p(b) = 0 for b.
-1
Let o(b) = -2*b + 15. Let a be o(10). Let q be a - -6 - 3/9. Find s, given that -2/3*s**3 + 2/3*s**2 + q*s - 2/3 = 0.
-1, 1
Let v(y) be the third derivative of y**8/13440 - y**7/5040 - y**4/8 + 2*y**2. Let s(c) be the second derivative of v(c). Factor s(p).
p**2*(p - 1)/2
Let x be 2 - (-5 + 2)*1. Let o(l) be the third derivative of -l**2 - 4/15*l**3 - 1/150*l**x + 1/15*l**4 + 0*l + 0. Find n such that o(n) = 0.
2
Let d = -8779/170 - -12/85. Let i = d - -54. Find z, given that -z**2 + 0*z - i*z**4 + 7/2*z**3 + 0 = 0.
0, 2/5, 1
Let b(y) = -y**2 + 12*y - 19. Let r be b(10). Let w(v) be the first derivative of 0*v + 3/8*v**4 - 1/6*v**3 - 3/10*v**5 + 0*v**2 - r + 1/12*v**6. Factor w(m).
m**2*(m - 1)**3/2
Let u be 2*(6 + -2 - 3). Suppose -u*q = -q. Solve 1/4*o + 0*o**2 - 1/4*o**3 + q = 0 for o.
-1, 0, 1
Let l(h) be the first derivative of 2/3*h**3 - 1 + 0*h - h**2. Factor l(b).
2*b*(b - 1)
Factor -4/3*t**2 - 16/9*t - 4/9.
-4*(t + 1)*(3*t + 1)/9
Let y(i) be the third derivative of 1/40*i**5 - 4*i**2 + 0*i**3 + 0 + 3/140*i**7 + 3/80*i**6 + 0*i**4 + 1/224*i**8 + 0*i. Factor y(l).
3*l**2*(l + 1)**3/2
Factor 1/3 - 4/3*x**3 + 4/3*x - 1/3*x**2.
-(x - 1)*(x + 1)*(4*x + 1)/3
Let g(j) = -8 + 7*j**2 + 0 + 2*j**3 - 7*j + 5 + 1. Let i(z) = -z**2 + z. Let s(m) = -g(m) - 5*i(m). Suppose s(o) = 0. Calculate o.
-1, 1
Suppose -7 - 5 = -4*g. Factor y**4 - 2*y**g - 5*y**3 + 3*y**3 + y**4 + 2*y**2.
2*y**2*(y - 1)**2
Let q = 5 + -1. Solve -2 + 16*v**3 - 14*v - 6*v + 4*v + 19*v**q - 30*v**2 + 13*v**4 = 0.
-1, -1/4, 1
Let -8*w - 37 + 4*w**2 + 37 = 0. What is w?
0, 2
Factor 0 