(-1)/3 + (-14)/(-6). Suppose 2*g - 3*p = w*p + 27, -2*g - 5*p = 3. Factor -3*n**5 - g*n**3 + 8*n**4 + n - 3*n + 3*n.
-n*(n - 1)**3*(3*n + 1)
Let d(l) be the third derivative of -2/105*l**7 - 10*l**2 + 0 + 1/15*l**5 - 1/30*l**6 + 0*l**4 + 1/84*l**8 + 0*l**3 + 0*l. Factor d(z).
4*z**2*(z - 1)**2*(z + 1)
Let w(g) = g**3 - 9*g**2 - 11*g + 15. Let v be w(10). Factor 3*o**3 - o**3 - v*o**2 + 2*o**2 + 5*o**2.
2*o**2*(o + 1)
Factor 0 + 3/5*r**2 + 6/5*r - 3/5*r**3.
-3*r*(r - 2)*(r + 1)/5
Determine v so that -5*v - v + v**2 - 4*v**2 + v**2 = 0.
-3, 0
Let j(d) be the third derivative of 2/35*d**7 + 1/112*d**8 + 0*d**3 - 6*d**2 + 1/8*d**4 + 0 + 3/20*d**6 + 0*d + 1/5*d**5. Factor j(z).
3*z*(z + 1)**4
Let r(z) = 5*z**4 + 5*z**3 + 4*z**2 - 7*z + 7. Let i(c) = -3*c**4 - 3*c**3 - 2*c**2 + 4*c - 4. Let n(t) = 7*i(t) + 4*r(t). Determine l so that n(l) = 0.
-2, 0, 1
Suppose -1/11*g**5 + 0 + 0*g**4 + 2/11*g**2 + 3/11*g**3 + 0*g = 0. Calculate g.
-1, 0, 2
Let h(s) be the first derivative of s**6/6 - 2*s**5/5 + 2*s**3/3 - s**2/2 - 10. Find a such that h(a) = 0.
-1, 0, 1
What is k in -3*k + 1/2*k**2 + 0 + 3/2*k**4 + 5*k**3 = 0?
-3, -1, 0, 2/3
Let m = 15 - 15. Let g(k) be the third derivative of 0*k**3 + 0*k + 1/15*k**7 + 1/12*k**6 - k**2 + 0*k**4 + m - 1/15*k**5. Factor g(x).
2*x**2*(x + 1)*(7*x - 2)
Let r(t) = 6*t**3 + 34*t**2 + 14. Let w(d) = -d**3 - 7*d**2 - 3. Let i(c) = -3*r(c) - 14*w(c). Solve i(y) = 0.
-1, 0
Let s(j) = 27*j + 1. Let k be s(1). Suppose k + 14 = 3*y. Factor 2*w**2 + y*w + 2 + 23*w**2 - w**2.
2*(3*w + 1)*(4*w + 1)
Let v(z) = -4*z**3 - 12*z**2 + 12*z + 12. Let w(x) = -3*x - 4. Let s be w(-4). Let f(u) = u**2 - u - 1. Let i(y) = s*f(y) + v(y). Factor i(k).
-4*(k - 1)*(k + 1)**2
Let b(k) = -9*k**2 + 15 + 29*k**2 - 19. Let x(p) = p**2 - p - 1. Let f(o) = b(o) - 4*x(o). Let f(q) = 0. Calculate q.
-1/4, 0
Let n(x) be the first derivative of -2*x**5/5 + 3*x**4/2 - 2*x**3/3 - 3*x**2 + 4*x - 2. Determine h so that n(h) = 0.
-1, 1, 2
Suppose -27/7*r**4 + 12/7 + 123/7*r**2 - 3*r**5 + 72/7*r + 57/7*r**3 = 0. What is r?
-1, -2/7, 2
Suppose -i - 5 = v, 11 - 1 = -i + 4*v. Let h be i/9*(-4 + 2). Let h + 2*u - 2/3*u**3 + 0*u**2 = 0. What is u?
-1, 2
Let i(b) = -4*b**4 - 8*b**2 + 6. Let d(c) = -5*c**4 - 9*c**2 + 7. Let n(r) = -6*d(r) + 7*i(r). Factor n(v).
2*v**2*(v - 1)*(v + 1)
Let n(a) = -3*a**3 - 3*a**2 - 5. Let t(c) = -5*c**3 - 5*c**2 - 8. Let o(d) = 8*n(d) - 5*t(d). Factor o(k).
k**2*(k + 1)
Let w(l) = -2*l**4 + 6*l**2 + 6*l. Let n(a) = a**2 + a. Let s be 0/(-2) + 7 + -5. Let p be -2 + (1 - (s - 2)). Let x(c) = p*w(c) + 6*n(c). Factor x(y).
2*y**4
Let p(s) = s + 4. Let j be p(-9). Let m be (8/j)/(8/(-20)). Factor 4*u**4 + 0*u**3 - 2*u**2 + 2*u**4 + m*u**3.
2*u**2*(u + 1)*(3*u - 1)
Let y = -6 - -13/2. Let i be (-33)/(-12) - 12/16. Factor -1 - y*m**i + 3/2*m.
-(m - 2)*(m - 1)/2
Suppose i + 2*b = -10, 28 = -0*i - 4*i - 2*b. Let k be -4*(-1 - 3/i). Factor c**4 - c**2 + 2*c**k - c**5 + c**3 - 2*c**2.
-c**2*(c - 1)**2*(c + 1)
Let g(f) be the first derivative of -f**6/30 - f**5/15 + 3*f**2/2 + 5. Let r(j) be the second derivative of g(j). Find a, given that r(a) = 0.
-1, 0
Solve -4/7*y**3 + 0 + 8/7*y - 4/7*y**2 = 0 for y.
-2, 0, 1
Let d(l) be the first derivative of -l**4/16 + l**3/3 + l**2/8 - l - 2. Factor d(x).
-(x - 4)*(x - 1)*(x + 1)/4
Let c(i) be the second derivative of i**4/6 + 2*i**3 + 8*i**2 - 10*i. What is w in c(w) = 0?
-4, -2
Suppose 2*y = 9*y - 21. Factor 0*d + 0 - 1/5*d**y + 3/5*d**2.
-d**2*(d - 3)/5
Let a(o) = -101*o**2 + 43*o. Let f(c) = c**2 + c + 1. Let q(p) = 2*a(p) - 6*f(p). Let i(k) = 69*k**2 - 27*k + 2. Let w(l) = 8*i(l) + 3*q(l). Factor w(h).
-2*(6*h - 1)**2
Let x(z) be the second derivative of 0*z**4 + 0*z**3 + 3/50*z**6 + 0 - 1/50*z**5 - z + 0*z**2 - 1/30*z**7. Factor x(c).
-c**3*(c - 1)*(7*c - 2)/5
Let y be (60/(-36))/(1/(-2)*5). Factor 4/3*o + 0 + y*o**2.
2*o*(o + 2)/3
Let q(f) = -f**3 + 7*f**2 + f - 1. Let i be q(7). Suppose i*r = 2*r + 8. Solve 6*x**4 - x**5 - x**3 - 5*x**3 + r*x**2 - x**5 = 0.
0, 1
Let u(m) = m + 13. Let k be u(-5). Let z be k/(-36)*-6 + 0. Factor 0 + 2/3*o**3 + 0*o - z*o**4 + 0*o**2 + 2/3*o**5.
2*o**3*(o - 1)**2/3
Let z(w) be the first derivative of -w**5/20 + w**4/8 - w**3/12 + 8. Find a, given that z(a) = 0.
0, 1
Suppose -i + 1 + 1 = 0. Let x be (-1)/5 + (-33)/(-15). Factor -i*w**2 - x*w + w - w.
-2*w*(w + 1)
Let l(d) be the second derivative of 0 + 0*d**2 - 1/6*d**3 + 1/12*d**4 + d. What is a in l(a) = 0?
0, 1
Let x = -3 - -7. Determine t, given that -6*t**2 + 6*t**3 - 2*t**x + 2*t + 8 - 18 + 10 = 0.
0, 1
Suppose 12*a - 17*a = -10. Let v(i) be the first derivative of -2/3*i**3 + a + 8/7*i + 12/7*i**2. Suppose v(m) = 0. What is m?
-2/7, 2
Let f(c) = -c**3 - c**2 + c + 1. Let i(g) = 18*g**3 + 16*g**2 - 4*g - 2. Let z be (-18)/14 + 10/35. Let t(v) = z*i(v) + 2*f(v). Factor t(p).
-2*(p + 1)*(2*p - 1)*(5*p + 2)
Find k such that 1/3*k + 0*k**2 - 1/3*k**3 + 0 = 0.
-1, 0, 1
Suppose -2*g + g = -2. Determine u, given that 5/2*u**2 + 3/2*u**3 - 3/2*u - 1/2 - g*u**4 = 0.
-1, -1/4, 1
Suppose 0 = h - 2*i - 2, 2*h - 18 + 0 = -3*i. Suppose 5*n = h + 4. Factor -2*x**2 + x**2 + 0*x - n*x - 1.
-(x + 1)**2
Let y = 760/1149 - -2/383. Factor -y*h**2 + 16/3*h - 32/3.
-2*(h - 4)**2/3
Let f(a) = a**2 - 7*a + 9. Let s be f(6). Solve -g**2 + 5*g**3 - g**4 - s*g**3 + 0*g**3 = 0 for g.
0, 1
Let i = 413/120 + -27/8. Let n(q) be the second derivative of -i*q**6 + q + 0*q**5 + 0*q**2 + 0 + 0*q**3 + 1/6*q**4. Suppose n(s) = 0. What is s?
-1, 0, 1
Factor 0*j + 0 + 0*j**2 + 1/2*j**3.
j**3/2
Suppose 12 = 4*f + 4*a - 2*a, 5*f - 6 = 2*a. Suppose -4*r + 0 + 4 = 0. Factor -5/2*h**f + 1/2*h + 3/2*h**4 + r - 1/2*h**3.
(h - 1)**2*(h + 1)*(3*h + 2)/2
Factor -4*w**2 - 40 + 40 + 24*w**4 - 2*w**3 + 8*w**3 + 14*w**5.
2*w**2*(w + 1)**2*(7*w - 2)
Find d such that 12/11*d - 25/11*d**4 - 1/11 + 60/11*d**3 - 46/11*d**2 = 0.
1/5, 1
Determine t, given that 0*t**3 - 1/4*t**2 + 0*t + 0 + 1/4*t**4 = 0.
-1, 0, 1
Suppose 10*f + 2*f = 48. Let p(x) be the first derivative of -f - 1/3*x**3 - 1/2*x**2 + 0*x. Factor p(q).
-q*(q + 1)
Let d(k) be the second derivative of -k**7/2520 - k**6/720 + k**5/60 + k**4/4 + k. Let r(f) be the third derivative of d(f). Factor r(t).
-(t - 1)*(t + 2)
Let a(z) = -z**3 + 6*z**2 + 2*z - 8. Suppose 0*c = -5*o - 5*c + 35, -5 = -5*c. Let h be a(o). Factor 0*d**2 - h*d**2 + 2*d**2.
-2*d**2
Let z(j) = j**5 - 7*j**4 - 12*j**3 - 9*j**2 - 5*j. Let k(u) = -4*u**4 - 6*u**3 - 4*u**2 - 2*u. Let v(p) = -5*k(p) + 2*z(p). Factor v(q).
2*q**2*(q + 1)**3
Let s(k) be the first derivative of 3*k**3 - 9/2*k**2 + 3*k - 3/4*k**4 - 1. Factor s(n).
-3*(n - 1)**3
Let h(i) = -i**3 + 3. Let j be h(0). Factor 6*a**2 - 2*a**2 + 0*a**2 + 6*a - 4*a + 2*a**j.
2*a*(a + 1)**2
Let o be (-10)/15*(0 - 3). Let c(h) = -h + h**3 + h**o + h + 1. Let t(z) = -4*z**3 - 8*z**2 - 8*z - 7. Let p(q) = 3*c(q) + t(q). Suppose p(v) = 0. Calculate v.
-2, -1
Let y = -235/3 - -79. Let m(w) be the first derivative of 3/2*w**4 + 0*w + 2/3*w**3 - 2/5*w**5 - y*w**6 + 3 - w**2. Determine i, given that m(i) = 0.
-1, 0, 1/2, 1
Let a(m) be the third derivative of -m**8/1680 + m**7/525 - m**5/150 + m**4/120 + 38*m**2. Let a(b) = 0. What is b?
-1, 0, 1
Let s(f) = -3*f**2 - f. Suppose 5*m + 0*z - 10 = 2*z, -4*m - 3*z = -31. Let b(q) = 8*q**2 + 3*q. Let o(w) = m*b(w) + 11*s(w). Factor o(p).
-p*(p - 1)
Let k(n) be the first derivative of n - 1/10*n**5 + 1/3*n**3 + 0*n**2 + 1/15*n**6 - 1 - 1/6*n**4. Let d(m) be the first derivative of k(m). Factor d(l).
2*l*(l - 1)**2*(l + 1)
Let d(w) be the second derivative of 0 + 8*w - 1/60*w**6 - 1/40*w**5 + 1/24*w**4 + 1/12*w**3 + 0*w**2. Solve d(j) = 0 for j.
-1, 0, 1
Let y(m) be the second derivative of -m**4/3 + 2*m**3/3 + 16*m. What is p in y(p) = 0?
0, 1
Let t(u) be the first derivative of u**6/18 + u**5/15 - u**4/4 - 5*u**3/9 - u**2/3 + 6. Factor t(o).
o*(o - 2)*(o + 1)**3/3
Let n be 4/18 + 455/(-63). Let w(x) = x**3 + 6*x**2 - 7*x + 4. Let i be w(n). Suppose 1/2*r**2 - 1/2*r**3 + 1/4*r - 1/4*r**i + 1/4*r**5 - 1/4 = 0. What is r?
-1, 1
Let z be -1 + -1 + (7 - 2). Factor -2*o**3 - 2*o**2 - z*o + 2*o**4 + 4 + 0*o**2 - 4*o**2 + 5*o.
2*(o - 2)*(o - 1)*(o + 1)**2
Let l(y) be the second derivative of y**7/11340 + y**6/1080 - y**4/4 - 9*y. Let u(i) be the third derivative