 = 5*m(x) - z(x). Determine y so that o(y) = 0.
-1, 1, 2
Let g(y) = y**3 - 37*y**2 + 97*y + 3. Let t(h) = -36*h**2 + 96*h + 4. Let a(o) = 4*g(o) - 3*t(o). Suppose a(n) = 0. What is n?
0, 5
Let b(z) be the first derivative of z**5/25 - 3*z**4/10 + 13*z**3/15 - 6*z**2/5 + 4*z/5 - 10. Factor b(g).
(g - 2)**2*(g - 1)**2/5
Let x(p) be the second derivative of -p**6/10 - 3*p**5/2 - 13*p**4/4 + 30*p**3 - 54*p**2 + 7*p + 2. Determine g, given that x(g) = 0.
-6, 1
Let r(k) be the second derivative of -k**5/35 - 2*k**4/7 - 6*k**3/7 - 4*k. Suppose r(h) = 0. Calculate h.
-3, 0
Let h(u) be the first derivative of u**6/2 + 9*u**5/5 - 3*u**4/4 - 7*u**3 + 12*u - 10. What is n in h(n) = 0?
-2, -1, 1
Suppose 15*k - 3*k = 0. Suppose -5*m = -5*f + 20, f = 6*f + 4*m - 2. Factor -1/2*o**f + k*o + 0.
-o**2/2
Factor 2/9*l**3 + 0 + 0*l**2 - 8/9*l.
2*l*(l - 2)*(l + 2)/9
Let v(f) be the second derivative of f**7/1890 - f**6/270 + f**4/3 + 3*f. Let h(w) be the third derivative of v(w). Factor h(p).
4*p*(p - 2)/3
Let f(q) be the second derivative of 0*q**3 + 0*q**2 + 0 - 1/20*q**5 + 3*q + 0*q**4. Factor f(y).
-y**3
Let j(f) be the second derivative of f**5/20 + f**4/3 + 5*f**3/6 + f**2 + f. Factor j(p).
(p + 1)**2*(p + 2)
Let x be 153/86*7/42. Let z = x - 2/43. Let 1 + z*r**2 + r = 0. What is r?
-2
Factor -b**2 + 4*b + 2*b**3 + 2*b**2 - 12*b**3 + 5*b**2.
-2*b*(b - 1)*(5*b + 2)
Suppose -11*m = -2*g - 15*m, -3*g = -m. Let n(b) be the third derivative of b**2 + 0 + 1/105*b**7 + 0*b**4 + 0*b**3 + 2/15*b**5 - 1/15*b**6 + g*b. Factor n(a).
2*a**2*(a - 2)**2
Let w be (2/(-2))/(2/(-8)). Let c(x) be the second derivative of 1/9*x**3 - x - 1/36*x**w + 0 - 1/6*x**2. What is o in c(o) = 0?
1
Let x(f) be the third derivative of -2*f**7/105 - f**6/5 - 3*f**5/5 + 4*f**2. Solve x(s) = 0 for s.
-3, 0
Let s(g) be the second derivative of 2/15*g**3 + g + 0 - 1/30*g**4 - 1/5*g**2. Determine r so that s(r) = 0.
1
Let q(y) be the first derivative of -y**4/6 - 2*y**3/3 - y**2 - 2*y/3 - 3. Factor q(b).
-2*(b + 1)**3/3
Let q(m) be the first derivative of -1/6*m**4 + 0*m + 4 - 1/9*m**6 + 0*m**3 + 0*m**2 - 4/15*m**5. Solve q(y) = 0.
-1, 0
Let n be 4/(3 - 1) - 0. Let z be (n - 3)*1*-2. Factor z*r + 2*r**2 - 2 + 2.
2*r*(r + 1)
Let g(v) = 3*v**2 + v - 3. Let n(w) = w**2 - w - 1. Let k(i) = g(i) + n(i). Determine j, given that k(j) = 0.
-1, 1
Let w(j) be the first derivative of -j**4/16 + j**3/12 + j**2/8 - 2*j - 2. Let o(d) be the first derivative of w(d). Factor o(a).
-(a - 1)*(3*a + 1)/4
Let l(d) be the third derivative of 0 - 1/8*d**4 - 1/3*d**3 + 0*d + 1/40*d**6 + 1/60*d**5 - 4*d**2 + 1/210*d**7. Factor l(q).
(q - 1)*(q + 1)**2*(q + 2)
Let j(s) = -4*s**5 - 8*s**4 - 7*s**3 + 3*s**2 + 3. Let q(h) = -5*h**5 - 9*h**4 - 8*h**3 + 4*h**2 + 4. Let i(m) = -4*j(m) + 3*q(m). Factor i(l).
l**3*(l + 1)*(l + 4)
Factor -1/2*c + 1/2*c**3 - 1/4*c**4 + 1/4 + 0*c**2.
-(c - 1)**3*(c + 1)/4
Let g(h) be the first derivative of 3*h**4/4 - 2*h**3 - 1. Suppose g(z) = 0. What is z?
0, 2
Let b(s) be the first derivative of -s**6/600 + s**5/150 - s**4/120 + 3*s**2/2 - 3. Let i(f) be the second derivative of b(f). Suppose i(n) = 0. Calculate n.
0, 1
Let w(r) = -4*r**2 + 22*r + 2. Let u(m) = -m - 1. Let c(j) = 2*u(j) + w(j). Solve c(i) = 0 for i.
0, 5
Let v(z) = 4 - 6 + 3 + z**2 - z**3 - 4*z**2. Let b(h) = -h**2 + h + 1. Let x(p) = -b(p) + v(p). Factor x(l).
-l*(l + 1)**2
Let b(f) = f**4 + 6*f**3 + 4*f**2 - 6*f - 5. Suppose -r - 20 = 3*r. Let v(o) = -o**2 + o + 1 - 3*o**2 + 3*o**2 - o**3. Let y(z) = r*v(z) - b(z). Factor y(x).
-x*(x - 1)*(x + 1)**2
Suppose 0 = -13*n + 5*n. Let o(m) be the third derivative of 0*m + 1/12*m**4 + m**2 + 0 + 1/30*m**5 + n*m**3. Factor o(j).
2*j*(j + 1)
Let h = -76 - -126. Suppose -5*x + 4*x = 3*o - 20, -h = -5*x - 5*o. Factor s**x - s**4 + 2*s**4 + s**4 - 2*s**5 - s**3.
-s**3*(s - 1)**2
Let m(v) be the first derivative of -3*v**5/5 - 3*v**4/4 + 2*v**3 - 3. Factor m(y).
-3*y**2*(y - 1)*(y + 2)
Let u(a) be the first derivative of a**4/18 + 2*a**3/27 - a**2/9 - 2*a/9 + 1. Factor u(q).
2*(q - 1)*(q + 1)**2/9
Let u(n) be the second derivative of 0*n**2 + 0*n**4 + 0 + 1/60*n**6 + 0*n**3 + 1/40*n**5 + n. Factor u(d).
d**3*(d + 1)/2
Let o(h) be the third derivative of -h**7/525 - h**6/300 + 2*h**5/75 + h**4/15 + 3*h**2. What is s in o(s) = 0?
-2, -1, 0, 2
Let b(s) = s**2 + 9*s - 3. Let v be b(-10). Solve -15*q**5 + 2*q**4 + 9*q**5 + q**5 + v*q**5 = 0 for q.
-1, 0
Let n(t) be the second derivative of t**8/20160 - t**6/720 - t**5/180 + t**4/3 - 2*t. Let h(y) be the third derivative of n(y). Let h(x) = 0. What is x?
-1, 2
Let k(z) be the first derivative of -2*z**5/5 - 2*z**4/3 - 8*z**3/27 - 14. Factor k(m).
-2*m**2*(3*m + 2)**2/9
Let p(n) = -11*n**4 + 58*n**3 - 12*n**2 - 72*n + 16. Let d(f) = 6*f**4 - 29*f**3 + 6*f**2 + 36*f - 8. Let g(q) = 14*d(q) + 6*p(q). Factor g(v).
2*(v - 2)**2*(v + 1)*(9*v - 2)
Suppose n = -4*u + 20, -2*u + n = -0*n - 4. Factor 4/9*r**2 + 0 + 16/9*r**u + 14/9*r**3 + 2/3*r**5 + 0*r.
2*r**2*(r + 1)**2*(3*r + 2)/9
Let q = 509/2331 + 1/259. Solve 2/9*p**4 + 0 - q*p**2 + 2/9*p - 2/9*p**3 = 0 for p.
-1, 0, 1
Let f be -4*(-2)/7*24/96. Solve f*z**2 + 6/7 - 8/7*z = 0.
1, 3
Factor 10*k**3 + 6*k**3 - 9*k**2 - 19*k**3 + 1 + 3*k + 8.
-3*(k - 1)*(k + 1)*(k + 3)
Let s be (-10)/6 - (-12)/6. Let l(y) be the second derivative of 0 + s*y**3 + 1/15*y**6 + 0*y**2 + 2*y - 1/10*y**5 - 1/6*y**4. Find h, given that l(h) = 0.
-1, 0, 1
Let f(u) be the third derivative of u**7/630 - u**6/180 + u**5/180 + 17*u**2. Factor f(m).
m**2*(m - 1)**2/3
Let w = -15 + 19. Let w*p**2 - 16*p**2 - 63*p**4 + 21*p**3 + 27*p**3 + 7*p**5 + 20*p**5 = 0. Calculate p.
0, 2/3, 1
Let q = -19/100 - -11/25. Suppose -q*a + 0*a**2 + 1/4*a**3 + 0 = 0. Calculate a.
-1, 0, 1
Let d(o) be the third derivative of o**8/8960 - o**7/10080 - o**6/960 + o**5/480 - 5*o**4/24 + 3*o**2. Let s(f) be the second derivative of d(f). Factor s(v).
(v - 1)*(v + 1)*(3*v - 1)/4
Let q = -34 + 205/6. Let o(l) be the second derivative of -1/18*l**3 - 1/36*l**4 + q*l**2 + 1/60*l**5 + l + 0. Determine i so that o(i) = 0.
-1, 1
Let m(s) be the first derivative of s**5/5 + s**4/4 - s**3 - s**2/2 + 2*s - 7. Factor m(y).
(y - 1)**2*(y + 1)*(y + 2)
Suppose -o - o = -6. Let t = 1 - -1. Factor 2 + 6*z - 6*z**4 - 2*z**5 - 3*z**3 + 4*z**t - z**o + 0*z.
-2*(z - 1)*(z + 1)**4
Let w(q) be the second derivative of 3*q**5/35 + 4*q**4/7 + 13*q**3/14 + 9*q**2/14 + 2*q. Solve w(x) = 0.
-3, -1/2
Let f = -86 - -86. Let q(v) be the second derivative of f*v**2 + 0 + 2/3*v**3 - 1/6*v**4 + 2*v. Factor q(s).
-2*s*(s - 2)
Let g(j) = -2*j**4 - 9*j**3 + 2*j**2 + 3*j. Let d(f) = -f**4 - f**3 - 2*f**2 + f. Let t(z) = -3*d(z) + g(z). What is h in t(h) = 0?
0, 2, 4
Let p(w) = -w**3 - 6*w**2 - 5*w - 10. Let a be p(-6). Let x be (8/a)/(2 + 0). Suppose 0*f + 0 + x*f**2 = 0. What is f?
0
Let a(w) be the third derivative of -4*w**7/1575 - w**6/900 + 7*w**5/450 + w**4/180 - w**3/15 - 2*w**2. Suppose a(y) = 0. What is y?
-1, 3/4, 1
Let z(k) be the first derivative of 1 + 0*k + 3/2*k**2 - k**3. Factor z(y).
-3*y*(y - 1)
Let s(l) = 3*l**3 + 3*l**2 - 6*l. Let v(d) = 3*d**3 + 4*d**2 - 7*d. Let k(q) = 5*s(q) - 6*v(q). Factor k(x).
-3*x*(x - 1)*(x + 4)
Let t be 32/10 + (-1)/5. Let w(s) be the first derivative of -3/2*s**4 + 0*s + 4/3*s**6 - 10/3*s**3 - t - s**2 + 2*s**5. Let w(k) = 0. Calculate k.
-1, -1/4, 0, 1
Let z = -26 + 28. Factor 4/9 - 2/9*l**z + 2/9*l.
-2*(l - 2)*(l + 1)/9
Let w be 16/(-12)*(-3)/2. Let v(n) = -6*n**w + 2 + 5 - 3*n**2 - 9*n. Let m(a) = 6*a**2 + 6*a - 5. Let i(z) = 7*m(z) + 5*v(z). Determine p, given that i(p) = 0.
-1, 0
Find x, given that -6*x + 7*x + x**3 + 2*x**2 - 2 - 2*x = 0.
-2, -1, 1
Let p = -1 - 4. Let y = 8 + p. Suppose 6*x**2 - y*x**2 + x - 2*x**2 = 0. What is x?
-1, 0
Let j be (-640)/(-15)*12/10. Let r = j - 51. Factor 0 - 1/5*b**2 + 1/5*b**3 - 1/5*b + r*b**4.
b*(b - 1)*(b + 1)**2/5
Find y such that -4/7*y**3 + 0 - 2/7*y + 5/7*y**2 + 1/7*y**4 = 0.
0, 1, 2
Let f be (-111)/(-12)*(-48)/(-2). Let z be (-4 - f/(-27)) + -4. Find g, given that 0*g**4 + 0 - z*g + 4/9*g**3 + 0*g**2 - 2/9*g**5 = 0.
-1, 0, 1
Let z(o) be the first derivative of 8*o**5/5 - 2*o**4 - 2*o**3 + 2*o**2 + 2*o - 6. Let z(m) = 0. What is m?
-1/2, 1
Let g = -6655/24 + 278. Let o = g + -1/24. Factor o*l + 2/3*