- 2*w**5/15 + w**2 + 5. Let f(g) be the second derivative of o(g). Factor f(s).
2*s**2*(s - 2)**2*(s - 1)
Suppose -4 = -j + 1. Suppose 2*g**4 - j*g**4 + 2*g**2 - 2*g + 2*g**3 + g**4 = 0. What is g?
-1, 0, 1
Suppose 0 = r - 2*z + 2, r + r + 16 = z. Let y be r/28*24/(-30). Factor -2/7*c**3 + y*c + 0 + 2/7*c**2 - 2/7*c**4.
-2*c*(c - 1)*(c + 1)**2/7
Suppose 0 = 5*f - 6 + 61. Let h be 12/4 - f/(-5). Solve h - 14/5*o**3 - 24/5*o**2 - 6/5*o = 0 for o.
-1, 2/7
Suppose 2*j = -10, 5*j = -5*z - 9 - 1. Let h(c) be the third derivative of 0*c**4 - 1/120*c**6 + z*c**2 + 0 - 1/60*c**5 + 0*c + 0*c**3. Factor h(r).
-r**2*(r + 1)
Let a be (4 + -4)/(-2 - -1). Suppose a = -f - 0*f - 5, 4*f + 28 = 4*p. What is g in -1/2*g**4 + 1/2*g**p - 1/2*g**5 - g + 0 + 3/2*g**3 = 0?
-2, -1, 0, 1
Let c(a) be the third derivative of -a**5/20 - a**4/2 + 5*a**3/2 + 3*a**2. Solve c(i) = 0 for i.
-5, 1
Let x(u) be the first derivative of -4 - 3/4*u**4 + 6*u + 3/10*u**5 + 3*u**2 - 3/2*u**3. Find a such that x(a) = 0.
-1, 2
Let w(p) = -p**2 + 2*p + 5. Let j be w(4). Let u be (7 + j)/(-1 - -2). Factor -10*n**u + 0*n + 14*n**3 - 4*n**2 + 0*n.
-2*n**2*(n - 1)*(5*n - 2)
Let j(o) be the second derivative of -7*o**6/15 - 9*o**5/5 - 10*o**4/7 - 8*o**3/21 + 40*o. Factor j(a).
-2*a*(a + 2)*(7*a + 2)**2/7
Let u(a) be the second derivative of 2*a**6/105 + 3*a**5/35 + 13*a**4/84 + a**3/7 + a**2/14 - 7*a. Suppose u(b) = 0. Calculate b.
-1, -1/2
Suppose 13*x = 18*x - 15. Let n(f) be the first derivative of -x + 0*f - 1/4*f**4 + 0*f**2 + 2/3*f**3. Solve n(o) = 0 for o.
0, 2
Let m = 2 + -6. Let p be (-2 + 0 + 1)*m. Factor -2*j**p - 2*j**3 + 0*j**3 - 3*j**4.
-j**3*(5*j + 2)
Let v be (-10)/(-6) + 3/9. Suppose 4*n - 8 - 16 = 0. Determine p so that 0*p**3 - 3*p**4 + 2*p - v*p**3 - 5*p**2 - n*p**5 + 14*p**4 = 0.
-2/3, 0, 1/2, 1
Let w(l) = l**4 - 7*l**3 - 3*l**2 + 7*l - 6. Let x(v) = 7*v**3 + 3*v**2 - 7*v + 7. Suppose 0 = -2*i + i + 4. Let n(s) = i*x(s) + 5*w(s). Factor n(o).
(o - 1)**2*(o + 1)*(5*o - 2)
Let l be (7/(-3) + 2)*10/(-35). Let i(n) be the third derivative of -5/84*n**4 + 0*n + 5*n**2 + 0 - 1/30*n**5 + l*n**3. Solve i(u) = 0.
-1, 2/7
Let x(j) = -11*j**3 + 10*j**2 - 2*j. Let n(m) = -54*m**3 + 50*m**2 - 10*m. Let c(q) = -3*n(q) + 14*x(q). Solve c(k) = 0.
0, 1/4, 1
Let i = 6 - 5. Suppose i - 2*v + v**3 - v**4 + 4*v + 0*v**4 - 3*v**3 = 0. What is v?
-1, 1
Let l(z) = z + 9. Let k = 1 + -8. Let c be l(k). Let -40/9*i**5 - 16/3*i**3 + 4/9*i + 0 - 2/9*i**c + 86/9*i**4 = 0. Calculate i.
-1/4, 0, 2/5, 1
Let j(h) be the third derivative of -h**8/560 - 4*h**7/525 - h**6/100 + h**4/120 - 2*h**2. Solve j(n) = 0 for n.
-1, 0, 1/3
Let v(q) be the second derivative of q**4/18 - q**3/9 + 6*q. Find h such that v(h) = 0.
0, 1
Let h be 8/3*(-18)/(-8). Let r(l) be the third derivative of 0*l**3 + 0 + 1/12*l**4 + 2/15*l**5 - l**2 + 1/10*l**h + 4/105*l**7 + 0*l + 1/168*l**8. Factor r(y).
2*y*(y + 1)**4
Let u(l) be the third derivative of 0*l**5 + 2*l**2 + 0*l + 0 + 0*l**3 + 0*l**6 + 0*l**4 - 1/630*l**7. Suppose u(t) = 0. What is t?
0
Let d = 3225/11 - 293. Factor d*c**2 - 2/11*c + 0.
2*c*(c - 1)/11
Let g(m) = 5*m**4 - 4*m**3 + 5*m**2 + 3. Let s(w) = 15*w**4 - 13*w**3 + 14*w**2 + 8. Let b(j) = -8*g(j) + 3*s(j). Factor b(a).
a**2*(a - 1)*(5*a - 2)
Let c be 1/((-3)/(-2) - 1). Let w be 3/(-2 + 24/3). Factor 0*d + w*d**c + d**3 + 1/2*d**4 + 0.
d**2*(d + 1)**2/2
Factor 10/7*q**3 + 1/7*q**5 + 5/7*q - 5/7*q**4 - 10/7*q**2 - 1/7.
(q - 1)**5/7
Let y(w) = -8*w**2 + 28*w - 22. Let h(x) = -x**2 + 4*x - 3. Let a(g) = 44*h(g) - 6*y(g). Factor a(s).
4*s*(s + 2)
Let x(s) = -s**3 + 3*s - 1. Let h be x(2). Let p be (1/(-9))/(h/18). Find q such that p*q + 2*q**2 - 2/3*q**4 - 4/3 - 2/3*q**3 = 0.
-2, -1, 1
Factor 28*x**2 + 20*x**3 - 32*x**3 + 6*x - 7*x**2.
-3*x*(x - 2)*(4*x + 1)
Let g(o) be the second derivative of 16*o**7/189 - 8*o**6/135 - 23*o**5/90 + 7*o**4/54 + 7*o**3/27 + o**2/9 + 32*o. Determine a so that g(a) = 0.
-1, -1/4, 1
Let f(a) = -2*a**5 - 38*a**4 + 42*a**3 - 18*a**2. Let t(l) = l**5 + 13*l**4 - 14*l**3 + 6*l**2. Let m(u) = -3*f(u) - 8*t(u). Factor m(n).
-2*n**2*(n - 3)*(n - 1)**2
Let b be -2 + 42/12 + 0. Factor 1 + 1/2*x**2 + b*x.
(x + 1)*(x + 2)/2
Let u(z) = z + 16. Let v be u(-10). Suppose 0 = -2*y - 4*b + v + 14, -5*y + b = 5. Factor -1/2*a**3 + a**2 + y - 1/2*a.
-a*(a - 1)**2/2
Let f(i) = -i**2 - i + 1. Let w(a) = -a**4 + a**2 + 3*a + 8. Let x(u) = u**2 - 4*u - 1. Let n be x(-3). Let k(t) = n*f(t) - 4*w(t). Factor k(o).
4*(o - 3)*(o + 1)**3
Solve -4/3*d - 4/3 + 4/3*d**2 + 4/3*d**3 = 0 for d.
-1, 1
Let b(c) = c**3 - 43*c**2 - 187*c - 256. Let w = 25 - 31. Let s(x) = -2*x**3 + 42*x**2 + 186*x + 256. Let m(y) = w*b(y) - 5*s(y). Find p, given that m(p) = 0.
-4
Suppose 6*w - 2*w = 0. Suppose w = t + 4*t. Factor t*u**2 - 4/9*u**3 + 0 + 2/9*u + 2/9*u**5 + 0*u**4.
2*u*(u - 1)**2*(u + 1)**2/9
Let i(r) be the first derivative of -r**8/9240 - r**7/4620 - 4*r**3/3 + 8. Let p(f) be the third derivative of i(f). Factor p(g).
-2*g**3*(g + 1)/11
Let j be (-4)/(-6) - (-7)/3. Let l be 1 - ((-12)/j)/(-12). Solve -l*f + 10*f**2 - 4/3 = 0 for f.
-1/3, 2/5
Let j(r) be the second derivative of -r**4/6 + r**3 - 2*r**2 + 9*r. Let j(w) = 0. Calculate w.
1, 2
Let z(i) = i**3 + i**2 + 3*i - 5. Let q(k) = 6*k**3 + 4*k**2 + 16*k - 26. Let j(y) = 6*q(y) - 33*z(y). Factor j(w).
3*(w - 3)*(w - 1)*(w + 1)
Let q(x) be the third derivative of 0 + 1/210*x**5 + 5*x**2 + 0*x + 0*x**3 + 0*x**4. Factor q(l).
2*l**2/7
Suppose 24 = 3*n - 6. Let s = -17 + 19. Factor 2 - 33*i**3 - 26*i + 44*i**4 + 64*i**s - n*i**5 + 2 - 43*i**3.
-2*(i - 1)**4*(5*i - 2)
Let c(i) = i**4 + i**3 + i**2 - i + 1. Let p(x) = 2*x**5 - 9*x**4 + 19*x**3 + 15*x**2 - 21*x + 3. Let s(a) = -3*c(a) + p(a). Solve s(w) = 0.
-1, 0, 1, 3
Suppose -3*g = g + 384. Let y be (-2)/9 - g/189. Factor 0*h - y + 2/7*h**2.
2*(h - 1)*(h + 1)/7
Let y(j) = 12*j**3 - 4*j**2 - 12*j. Let i(q) = -q**4 - q**2 + q. Let s(z) = -4*i(z) + y(z). Factor s(k).
4*k*(k - 1)*(k + 2)**2
Let y be 1/((-6)/21)*2. Let c(w) = -13*w**3 - 24*w**2 - 30*w - 5. Let k(n) = 9*n**3 + 16*n**2 + 20*n + 3. Let a(b) = y*k(b) - 5*c(b). Factor a(z).
2*(z + 1)**2*(z + 2)
Let t(x) be the first derivative of 2*x**3/9 + 4*x**2/3 + 2*x - 4. Find w, given that t(w) = 0.
-3, -1
Let k(y) = 3*y**3 - y**2 - y + 2. Let n be k(2). Find c such that -10*c + n*c**2 + 7*c**3 - 13*c**3 + 4 - 8*c = 0.
1/3, 1, 2
Let p(a) = 3*a - 6. Let m be p(6). Suppose 3*i = -i + m. Solve i*j + 2 - j**2 - 3*j**2 + 5*j**2 = 0.
-2, -1
Let u(p) be the third derivative of 1/525*p**7 + 0 + 1/100*p**6 + 0*p**3 + 3*p**2 + 1/60*p**4 + 0*p + 1/50*p**5. Suppose u(j) = 0. What is j?
-1, 0
Let s(t) = 8*t**4 - 21*t**3 - 61*t**2 - 13. Let v(y) = 4*y**4 - 10*y**3 - 30*y**2 - 6. Let r(p) = -6*s(p) + 13*v(p). Factor r(z).
4*z**2*(z - 3)*(z + 2)
Let f(p) be the second derivative of -p**8/2800 + p**7/6300 + p**6/900 - 5*p**4/12 - 3*p. Let a(t) be the third derivative of f(t). Find r such that a(r) = 0.
-1/2, 0, 2/3
Let 8*g**5 - 4*g - g - 2*g**2 + 12*g**2 - 3*g**5 - 10*g**4 = 0. What is g?
-1, 0, 1
Factor 0*j**2 - 1/4*j**3 + 0 + 0*j.
-j**3/4
Let y(f) be the first derivative of 2*f**3/21 - 2*f**2/7 - 6*f/7 - 13. Factor y(h).
2*(h - 3)*(h + 1)/7
Let l be 0*(-4 + (-2 - -5)). Factor -7*s**2 - 4*s**3 + 6*s**2 + 4*s + l*s**2 + 1.
-(s - 1)*(s + 1)*(4*s + 1)
Solve 0*j**2 - 6/5 + 3/5*j**3 - 9/5*j = 0 for j.
-1, 2
Let k = 1/493 - -6893/4437. Suppose 2*g**2 - 10/9*g**3 + 2/9*g**4 - k*g + 4/9 = 0. What is g?
1, 2
Let v(g) = -162*g**4 - 563*g**3 - 548*g**2 - 163*g - 11. Let a(z) = 81*z**4 + 282*z**3 + 274*z**2 + 81*z + 5. Let u(y) = 5*a(y) + 3*v(y). Factor u(q).
-(q + 1)*(q + 2)*(9*q + 2)**2
Let v = -3 + 9. Let w be 0 + -1 - (-8)/v. Factor 1/3 - 2/3*a + w*a**2.
(a - 1)**2/3
Let n = -14 - -13. Let j(s) = -s**4 + s**2 - s + 1. Let w(u) = 3*u**4 - 4*u**3 + 4*u**2 - 2*u - 1. Let k(r) = n*w(r) - 2*j(r). Factor k(l).
-(l - 1)**4
Suppose 0 = 3*w + 4 - 13. Suppose -w*j - 6 = -5*j. Solve -2*r**2 + 2*r**j + 3*r - 2*r**2 - r = 0.
0, 1
Factor 3*z - 3 - 3/4*z**2.
-3*(z - 2)**2/4
Let t = 5 - 3. Factor 0 - 11*r - 2*r**2 + 0*r**t + 3*r - 8.
-2*(r + 2)**2
Let p(q) be the third derivative of 1/10*q**5 + 0 + 1/40*q**6 + 0*q + 0*q**3 + 1/8*q**4 - 3*q**2. Solve p(n) = 0 for n.
-1, 0
Let p(s) = s**3 + 5*s**2 - 4*s - 28. Let l be 