a). Factor f(m).
-(m - 2)*(m + 1)**2/6
Let h(g) be the third derivative of g**7/1680 + g**6/120 + 3*g**5/80 - g**4/4 - 2*g**2. Let w(u) be the second derivative of h(u). Factor w(a).
3*(a + 1)*(a + 3)/2
Let x(c) = -2*c - 4. Let f be x(-3). Solve -3*w**f + 1 - 1 = 0.
0
Let s(c) = -51*c - 4. Let g be s(-4). Let f be g/132 + (-4)/22. Solve f*z**2 + 2/3*z - 2/3 = 0.
-1, 1/2
Suppose -2*c + 7*c = -4*w + 16, 2*w - 8 = 4*c. Suppose c*z**2 + z**3 - 3/4*z - 1/4 = 0. What is z?
-1/2, 1
Let t(q) = -q**3 + 10*q**2 - 17*q + 8. Let u(w) = -4*w**3 - 53*w - 18*w - 3 - 15*w + 44 + 49*w**2. Let a(b) = -11*t(b) + 2*u(b). Factor a(r).
3*(r - 2)*(r - 1)**2
Let h(m) = -6*m**2 - 27*m - 116. Let a(k) = 7*k**2 + 28*k + 115. Let p(s) = -5*a(s) - 6*h(s). Factor p(b).
(b + 11)**2
Suppose -l = -3, -a + 4*l - 12 = 2*a. Suppose t = -a*t. Factor 2/9*q**2 + 2/3*q**4 - 2/3*q**3 - 2/9*q**5 + 0 + t*q.
-2*q**2*(q - 1)**3/9
Let p = -7 - -7. Let w(q) be the third derivative of 1/120*q**5 + 1/480*q**6 - 3/70*q**7 + 0*q**4 + 0 + p*q**3 + 0*q - 2*q**2. Solve w(f) = 0.
-2/9, 0, 1/4
Let o = 7 + 9. What is s in 8*s**2 + 4*s**5 - 18*s**4 + 2*s**4 - 18*s - 2*s + 8 + o*s**3 = 0?
-1, 1, 2
Let d(t) be the second derivative of -5*t**4/12 - t**3/3 + 5*t. Let w(x) = 6*x**2 + 2*x. Let q(a) = -5*d(a) - 4*w(a). Solve q(o) = 0 for o.
-2, 0
Let i(o) be the second derivative of -1/10*o**4 + 0 + 1/50*o**6 - 3/50*o**5 + 1/10*o**3 + 1/70*o**7 + 3/10*o**2 + 3*o. Factor i(v).
3*(v - 1)**2*(v + 1)**3/5
Let o(f) be the first derivative of -1/20*f**5 - 1/6*f**4 - 1/6*f**3 + 0*f + f**2 + 2. Let x(z) be the second derivative of o(z). Factor x(p).
-(p + 1)*(3*p + 1)
Suppose a**2 + 17*a**2 + 4*a**3 - 14*a**2 = 0. What is a?
-1, 0
Let q = 8 + -6. Let s = -43/5 - -91/10. Determine a so that 1/2*a**q - s*a + 0 = 0.
0, 1
Let n = -33/52 + 18/13. Factor 1/4*x**3 + n*x**4 - 3/4*x**2 + 0 - 1/2*x + 1/4*x**5.
x*(x - 1)*(x + 1)**2*(x + 2)/4
Let d(o) be the second derivative of o**4/4 - 2*o. Find p such that d(p) = 0.
0
Let r be 0/(2/(-1) + 0). Suppose -24*p**4 + 7*p + r*p + p - 10*p**5 + 2*p**3 + 24*p**2 = 0. What is p?
-2, -1, -2/5, 0, 1
Let b(g) be the second derivative of -g**6/1260 - g**5/140 - g**4/42 + g**3 - g. Let z(o) be the second derivative of b(o). Solve z(q) = 0 for q.
-2, -1
Let o(s) = -4*s**4 + 14*s**3 + 2*s**2 - 20*s - 2. Let j(l) = l**3 - l**2 - 1. Let r(t) = -10*j(t) + o(t). Determine z, given that r(z) = 0.
-2, 1
Suppose -3*h - 13 = -4*m, 4*h - 3*m + 9 = h. Find d, given that d + 1/4*d**2 + h = 0.
-2
Factor 1/2*b**2 + 1 + 3/2*b.
(b + 1)*(b + 2)/2
Let s(m) = -13*m**2 + m - 7. Let a(n) = 9*n**2 - n + 5. Let b(c) = 7*a(c) + 5*s(c). Solve b(r) = 0.
-1, 0
Let z(f) be the first derivative of -f**5/25 + f**4/20 + 2*f**3/15 - 3. Solve z(g) = 0 for g.
-1, 0, 2
Let d(f) be the first derivative of 0*f + 2/3*f**3 + 0*f**2 - 5. Factor d(r).
2*r**2
Let w(r) be the first derivative of r**6/2 + 18*r**5/5 + 39*r**4/4 + 12*r**3 + 6*r**2 + 33. Solve w(j) = 0.
-2, -1, 0
Let m(u) = -u**3 + 8*u**2 + 10*u - 7. Let b be m(9). Suppose 5*x = p + 10, -3*x = -p + 5*p - 29. What is j in -2*j - b*j**x - j**3 + 0*j + 5*j**3 = 0?
-1, 0, 1
Let l(m) be the first derivative of -m**4/4 + 7*m**3/3 - 8*m**2 + 12*m + 12. What is f in l(f) = 0?
2, 3
Suppose 59 + 61 = 30*v. Factor 0*n + 0*n**v + 8/7*n**5 + 2/7*n**2 + 0 - 6/7*n**3.
2*n**2*(n + 1)*(2*n - 1)**2/7
Let h = 199/4 + -497/10. Let g(w) be the second derivative of 2*w + 0*w**3 + 1/6*w**4 + 0*w**2 + h*w**5 + 0. Find r, given that g(r) = 0.
-2, 0
Let p(q) = -q**3 + q - 1. Let f(a) = -a**3 + 9*a**2 - 8*a - 2. Let r be f(8). Let x(o) = 5*o**3 + 2*o**2 - 11*o - 5. Let s(m) = r*x(m) - 6*p(m). Factor s(i).
-4*(i - 2)*(i + 1)*(i + 2)
Suppose -4*v + 45 = -u, 3*u - u + 30 = 2*v. Suppose -4 = 2*m - v. Let -2/7*i**m + 0 + 2/7*i + 0*i**2 = 0. What is i?
-1, 0, 1
Let r(p) be the second derivative of -p**7/84 - p**6/20 - 3*p**5/40 - p**4/24 + 3*p. Find w, given that r(w) = 0.
-1, 0
Let w(i) = -i**2 + 4. Let c be w(0). Suppose 2*a = -0*a + c. Let -d + d + d**a - 1 = 0. What is d?
-1, 1
Let d(n) be the second derivative of -1/30*n**5 - 3*n - 1/2*n**2 + 0 - 2/3*n**3 - 1/4*n**4. Let k(a) be the first derivative of d(a). Solve k(t) = 0 for t.
-2, -1
Let u(m) be the second derivative of m**4/36 + m**3/6 + m**2/3 + 6*m. Suppose u(l) = 0. Calculate l.
-2, -1
Let y(x) = -14*x**3 - 3*x**2 - 20*x - 14. Let t(b) = -5*b**3 - b**2 - 7*b - 5. Let m(r) = -17*t(r) + 6*y(r). Solve m(s) = 0.
-1, 1
Suppose d - 8 = 2*c - 7*c, 0 = -5*c - 3*d + 4. Factor 4*j**4 - 12*j**5 - c*j**3 + 18*j**5 - 8*j**5.
-2*j**3*(j - 1)**2
Let z = 56 - 26. What is m in -16/7*m + z*m**4 + 0 - 40/7*m**2 + 116/7*m**3 = 0?
-2/3, -2/7, 0, 2/5
Let z(j) = j**2 + 9*j + 14. Let b be z(-7). Suppose -5 = 3*v - 14. Determine w so that -v + b*w**2 - 4*w + 2*w**2 + 5 = 0.
1
Let t(v) be the first derivative of v**6/21 + 4*v**5/35 - 4*v**4/7 + 4*v**3/21 + v**2 - 8*v/7 + 16. Factor t(i).
2*(i - 1)**3*(i + 1)*(i + 4)/7
Let h(s) be the third derivative of 0*s + 0 + 1/4*s**5 - s**3 - 3/8*s**4 - 9*s**2. Factor h(b).
3*(b - 1)*(5*b + 2)
Let m be 1/6 - 736/(-192). Suppose 2/5*j**m - 6/5*j**3 + 0*j + 0 + 4/5*j**2 = 0. Calculate j.
0, 1, 2
Let v be (-18)/3 - -2 - 25/(-6). Factor 1/2 + 5/6*h + 1/6*h**2 - v*h**3.
-(h - 3)*(h + 1)**2/6
Let d(n) be the second derivative of -n**9/1512 - n**8/420 - n**7/420 + n**3/6 + 4*n. Let r(i) be the second derivative of d(i). Suppose r(h) = 0. What is h?
-1, 0
Let o(q) be the first derivative of q**3/18 + 2*q**2/3 + 5*q/2 - 58. Factor o(c).
(c + 3)*(c + 5)/6
Let w(s) = 0 - 2*s - s**3 - 11*s**2 + 7*s + 7*s + 2. Let t be w(-12). Factor 2*i**3 - t*i - 4/7*i**2 + 4/7.
2*(i - 1)*(i + 1)*(7*i - 2)/7
Let y = -18 + 28. Factor 2*z**2 - 7*z**2 + 0*z**3 - 7*z**3 + 16*z - y + 6.
-(z - 1)*(z + 2)*(7*z - 2)
Suppose -3*c + 20 + 16 = 0. Suppose -5*d + 0*t - 2*t = 1, -4*t - c = 0. Factor -1 + d - w**5.
-w**5
Let t(b) be the first derivative of b**5/5 + 2*b**4 + 8*b**3 + 16*b**2 + b + 8. Let d(c) be the first derivative of t(c). Factor d(s).
4*(s + 2)**3
Suppose 3*r + 3*u + 15 = 0, 5*u + 40 = r + 15. Factor -1/2*l**4 + r*l + 0 - 3/2*l**3 - l**2.
-l**2*(l + 1)*(l + 2)/2
Let s = 11 + -11. Suppose 0*c + 12 = 2*g - 2*c, -2*g - 4*c = s. Factor 5*x**5 + 9*x**3 + 7*x**2 + 0*x**g - 4*x**5 + 5*x**4 + 2*x.
x*(x + 1)**3*(x + 2)
Let t be (-3)/((-9)/4)*9. Factor -t*f + 22 - 5*f**2 + 0*f**2 - 26.
-(f + 2)*(5*f + 2)
Let w = 3 - 1. Let t(d) be the third derivative of 0*d + 0*d**4 + 0 - 1/90*d**5 - 1/90*d**6 + d**w + 0*d**3. Factor t(x).
-2*x**2*(2*x + 1)/3
Let k(s) be the first derivative of 16*s**3/3 - 2*s**2 - 19. Suppose k(o) = 0. What is o?
0, 1/4
Determine d so that 7/3*d**4 + 2/3*d**2 - 1/3*d**5 - 14/3*d**3 - 3 + 5*d = 0.
-1, 1, 3
Suppose -1/4*c**2 + 1/4*c**5 + 1/2*c + 0 - 3/4*c**3 + 1/4*c**4 = 0. Calculate c.
-2, -1, 0, 1
Let d be (-4)/10 + (18/10)/3. Factor 0 + 2/5*p - d*p**2.
-p*(p - 2)/5
Let o(r) be the first derivative of -r**7/21 + 2*r**6/15 - r**5/10 - 10*r + 5. Let f(w) be the first derivative of o(w). Determine n, given that f(n) = 0.
0, 1
Suppose a = 1 + 3. Let y(r) = r**2 + 6*r + 5. Let j be y(-6). Factor -x + 3*x**j + 3*x + 4*x**2 - 2 - x**5 - 2*x**3 - 2*x**a - 2*x**3.
2*(x - 1)**3*(x + 1)**2
Let t be -5*((-46)/10 - -4). Factor -1/2*b - 1/2*b**2 + 1/2*b**4 + 0 + 1/2*b**t.
b*(b - 1)*(b + 1)**2/2
Let c(b) be the second derivative of -4*b + 0*b**2 + 0 - 1/42*b**4 - 1/21*b**3. Find g, given that c(g) = 0.
-1, 0
Let w = 13 + -8. Factor -4*o**4 + o**w - o**2 - o**2 - 2*o**2 + 0*o**5 + o + 6*o**3.
o*(o - 1)**4
Factor 11/4*v + 3/2 + 1/4*v**2 - v**3.
-(v - 2)*(v + 1)*(4*v + 3)/4
What is c in 2*c**2 + 3*c + 5 - 2*c - c**3 + 0*c**3 - 7 = 0?
-1, 1, 2
Let n be 2/(-5)*(-22)/22. Factor n + 0*g - 2/5*g**2.
-2*(g - 1)*(g + 1)/5
Suppose 0 = 5*s - 10 - 0. Let g = 4 - s. Factor -1/2*d**g - d - 1/2.
-(d + 1)**2/2
Let m(j) be the second derivative of -1/10*j**6 - 9/20*j**5 + 0*j**2 + 2*j + 0 - 3/4*j**4 - 1/2*j**3. Let m(t) = 0. Calculate t.
-1, 0
Suppose 4*p + 7 = 19. Suppose 10 = p*l - 2. Find g such that 2/3*g**5 + 2/3*g - 8/3*g**l + 0 + 4*g**3 - 8/3*g**2 = 0.
0, 1
Let w be (10/8)/(3/12). Let b(f) = 6*f**5 + 2*f**4 + 3*f**3 - f**2. Let j(v) = 7*v**5 + 3*v**4 + 3*v**3 - v**2. Let k(h) = w*j(h) - 6*b(h). Factor k(d).
-d**2*(d - 1)**3
Let j = -100 + 502/5. Suppose j*f + 6/