tor r(k).
-k*(k - 1)*(k + 1)*(3*k + 1)/2
Let j(q) be the first derivative of q**3/3 + q**2 + 1. Suppose 27 - 10 = t. Let w(h) = -3*h**2 - 6*h. Let u(g) = t*j(g) + 6*w(g). Factor u(y).
-y*(y + 2)
Let i(o) be the first derivative of 2*o**3/3 + 8*o**2 + 32*o + 7. Factor i(d).
2*(d + 4)**2
Let j(v) be the second derivative of -9*v**5/20 + v**4 + 13*v**3/2 + 9*v**2 + 11*v. Suppose j(t) = 0. What is t?
-1, -2/3, 3
Let l(d) be the second derivative of 0*d**2 + 0*d**4 + 0*d**3 + 1/60*d**5 + 2*d + 1/90*d**6 + 0. Solve l(u) = 0.
-1, 0
Let n(a) be the second derivative of -a**5/4 + 5*a**4/3 + 5*a**3/6 - 10*a**2 + 15*a. Factor n(z).
-5*(z - 4)*(z - 1)*(z + 1)
Find j such that 0 - 2/3*j**2 + 2/3*j = 0.
0, 1
Let i(t) = -3*t**2 + 3*t + 4. Let v(r) = -4*r**2 + 3*r + 5. Let x(h) = 5*i(h) - 4*v(h). Factor x(u).
u*(u + 3)
Suppose 0*p + 14 = 3*m + 2*p, p - 4 = 0. Let k = -1 - -3. Factor 2 + r + r + k*r**m + 2*r.
2*(r + 1)**2
Let 2/3*x - 2/9*x**3 - 4/9*x**2 + 0 = 0. What is x?
-3, 0, 1
Let b(o) be the second derivative of -o**6/120 + o**4/24 - o**2/2 + 4*o. Let i(a) be the first derivative of b(a). Factor i(y).
-y*(y - 1)*(y + 1)
Let g(q) be the first derivative of -2*q**3/27 - 2*q**2/9 - 2*q/9 + 34. Factor g(f).
-2*(f + 1)**2/9
Let i(k) be the first derivative of -k**4/4 - 2*k**3/3 + k**2/2 + 2*k + 13. Suppose i(d) = 0. Calculate d.
-2, -1, 1
Let x(o) = 4*o**2 - 1. Let h be x(-1). Factor -3*t**4 + 2*t**4 + h*t**4.
2*t**4
Find r, given that -6/7*r + 0 + 15/7*r**5 - 57/7*r**4 + 9*r**3 - 15/7*r**2 = 0.
-1/5, 0, 1, 2
Let z be (-6)/(-15)*5 - -4. Factor -z + 13*b + 44*b**2 + 14*b - 65*b**2.
-3*(b - 1)*(7*b - 2)
Let f(b) = -b**3 - 3*b**2 + 4*b + 3. Let l be f(-4). Factor 5*n**2 - 5*n**2 - 3 - l*n + 1 - n**2.
-(n + 1)*(n + 2)
Let w = 13 - 16. Let v be w/(-36)*(-2 - -5). Find f, given that v*f**3 + 0 - 1/4*f**2 - 1/4*f + 1/4*f**4 = 0.
-1, 0, 1
Let v = -14 + 12. Let g be (-5)/(-8)*v/(-5). Factor 0 + g*k**3 + 1/4*k - 1/2*k**2.
k*(k - 1)**2/4
Let t(g) be the second derivative of -3*g**5/70 - 4*g**4/21 - g**3/3 - 2*g**2/7 + 6*g. Find p, given that t(p) = 0.
-1, -2/3
Suppose 0 = -0*n - 4*n + 16. Solve 4*c**2 - 3 - c**2 - 5*c**2 + c**2 + n*c = 0 for c.
1, 3
Let i(n) be the first derivative of n**4/10 + 2. Factor i(y).
2*y**3/5
Solve 3/4*l**2 + 0 + 1/2*l + 1/4*l**3 = 0.
-2, -1, 0
Let z(v) be the first derivative of v**3/15 + v**2/10 - 19. Let z(o) = 0. What is o?
-1, 0
Let t = 3 - 0. What is c in -10*c**4 - c**3 + 3*c**3 + 8*c**5 + 0*c**t = 0?
0, 1/4, 1
Let l(h) = -h**2 + 7*h + 8. Let t(c) = -2*c**2 + 13*c + 15. Let a = -15 - -21. Let z(r) = a*t(r) - 11*l(r). Factor z(p).
-(p - 2)*(p + 1)
Let g be -2*((-1)/3)/((-20)/(-45)). Solve g*a + 1/2*a**3 + 1/2 + 3/2*a**2 = 0.
-1
Let s(f) = -f + 7 + 3*f + 6 - f. Let h be s(-11). Suppose 2/11 + 20/11*w**3 + 48/11*w**h - 50/11*w**4 - 20/11*w = 0. What is w?
-1, 1/5, 1
Let w(a) = 2*a**3 - 5*a**3 - 4 + 3*a**4 - 3*a**2 + 5*a + 2*a**3. Let u(l) = -7*l**4 + 3*l**3 + 6*l**2 - 11*l + 9. Let n(y) = 4*u(y) + 9*w(y). Factor n(s).
-s*(s - 1)**3
Let x(l) be the third derivative of l**6/780 - l**5/195 - 5*l**2. Factor x(w).
2*w**2*(w - 2)/13
Factor -1/8*n**3 - 3/2*n + 1 + 3/4*n**2.
-(n - 2)**3/8
Let j(a) be the second derivative of -a**6/15 - a**5/2 - 3*a**4/2 - 7*a**3/3 - 2*a**2 - 2*a. Factor j(k).
-2*(k + 1)**3*(k + 2)
Let 10*a**2 - 3*a + 3*a**2 + 10*a**3 + 8*a + 2*a**2 = 0. Calculate a.
-1, -1/2, 0
Let f(i) = -i - 4. Let n be f(-2). Let c be ((-2)/n)/((-1)/(-2)). Factor -4/9 - 2/3*s - 2/9*s**c.
-2*(s + 1)*(s + 2)/9
Let r(w) be the first derivative of w**6/21 + 2*w**5/35 - 3*w**4/14 - 10*w**3/21 - 2*w**2/7 - 15. Find p such that r(p) = 0.
-1, 0, 2
Let x be 1/3 - (-25)/(-3). Let f be ((-8)/6)/(x/12). Determine s so that 1 - 4*s + f*s**2 - 1 = 0.
0, 2
Let b(a) = -a**5 + a**4 - a**3 - a**2 - a - 1. Let y(d) = -9*d**5 + 48*d**4 + 18*d**3 - 15*d - 18. Let h(u) = 18*b(u) - y(u). Suppose h(w) = 0. Calculate w.
-1, -1/3, 0
Let a(w) be the third derivative of 1/32*w**4 - w**2 - 1/480*w**6 + 0 + 0*w**5 - 1/12*w**3 + 0*w. Factor a(v).
-(v - 1)**2*(v + 2)/4
Suppose -2*n + 13 = -5*c, -n - 2*n + 17 = -5*c. Let b(f) be the first derivative of -f**2 - 1/4*f**n - 12/5*f**5 + 3*f**3 + 0*f + 4. Factor b(v).
-v*(v + 1)*(3*v - 2)*(4*v - 1)
Let y(f) be the first derivative of 4*f**3/21 + 6*f**2/7 + 8*f/7 - 29. Factor y(c).
4*(c + 1)*(c + 2)/7
Let z be ((-78)/27 + 2)*-6 - 3. Factor 1/3 + 2/3*b + 4/3*b**3 - z*b**2.
(b - 1)**2*(4*b + 1)/3
Let x(f) be the third derivative of -f**9/3024 - f**8/1680 + f**7/840 + f**6/360 - 5*f**3/6 + 4*f**2. Let r(w) be the first derivative of x(w). Factor r(c).
-c**2*(c - 1)*(c + 1)**2
Let r = -1/32 - -35/96. Suppose 0 - 7/6*g**2 + r*g = 0. Calculate g.
0, 2/7
Let y(c) be the third derivative of c**6/24 - c**5/10 - 3*c**4/10 - 4*c**3/15 - 5*c**2. What is i in y(i) = 0?
-2/5, 2
Let z(o) be the second derivative of -o**7/2520 - o**6/1080 + o**5/180 - 7*o**3/6 + 7*o. Let f(h) be the second derivative of z(h). Factor f(j).
-j*(j - 1)*(j + 2)/3
Let c(j) = -j**2 + 2*j**2 - 4 - 6*j + 3*j. Let s(r) = 2*r**2 - 2*r - 4. Let w(p) = -4*c(p) + 3*s(p). Factor w(g).
2*(g + 1)*(g + 2)
Solve 4/3 + 1/3*u**2 + 5/3*u = 0.
-4, -1
Let t = -2 + 44. Let k be (9/t)/(3/16). Factor k*a - 2/7*a**2 - 8/7.
-2*(a - 2)**2/7
Factor -4*b - 957*b**5 + 2*b**3 + 6*b**4 + 959*b**5 + 0*b**4 - 6*b**2.
2*b*(b - 1)*(b + 1)**2*(b + 2)
Let k(p) = -p**3 + 8*p**2 + 21*p - 10. Let f be k(10). Let v(l) be the first derivative of -4 + f*l**2 - 2/3*l**3 + 2*l. Factor v(a).
-2*(a - 1)*(a + 1)
Let y(v) be the first derivative of 2*v**3/15 - 8*v**2/5 + 32*v/5 - 8. Let y(w) = 0. Calculate w.
4
Let p = -1 - -3. Determine y, given that 34*y**4 - y**3 + y**p + 40*y**5 - 5*y**2 - 9*y**3 = 0.
-1, -1/4, 0, 2/5
Let f(p) be the first derivative of p**3/6 + p**2/4 - 1. Factor f(k).
k*(k + 1)/2
Let x(v) be the first derivative of -v**6/3 + 2*v**5 - 5*v**4 + 20*v**3/3 - 5*v**2 + 2*v + 5. Factor x(i).
-2*(i - 1)**5
Let y(w) be the third derivative of 0*w + 0 - 1/40*w**5 + 0*w**4 + 1/160*w**6 + 0*w**3 + 3*w**2 + 1/280*w**7. Factor y(d).
3*d**2*(d - 1)*(d + 2)/4
Let h(u) be the third derivative of u**8/252 - u**7/70 + u**6/60 - u**5/180 + 4*u**2. Factor h(o).
o**2*(o - 1)**2*(4*o - 1)/3
Let x(m) be the third derivative of m**7/1260 + m**6/240 - m**5/60 - m**4/8 + 2*m**2. Let n(j) be the second derivative of x(j). Suppose n(l) = 0. Calculate l.
-2, 1/2
Let n(h) be the second derivative of h**8/12 - 6*h**7/35 + h**6/15 - h**2 - 7*h. Let q(m) be the first derivative of n(m). What is z in q(z) = 0?
0, 2/7, 1
Suppose -4 = -x - 1. Suppose -x*z + 10 = 2*z. Factor 2*w**2 + z*w**3 - 2*w**2 - 2*w.
2*w*(w - 1)*(w + 1)
Factor t**3 - 42*t**4 + 282*t**4 - 3 - 56*t**3 + 30*t - 5*t**3 + 192*t**5 - 75*t**2.
3*(t + 1)**2*(4*t - 1)**3
Let p be 2 + -4 + -1 + 5. What is s in 0*s**3 - s**3 + 0*s**p + 2*s**2 - s = 0?
0, 1
Factor 21/5*g + 8/5*g**2 + 1/5*g**3 + 18/5.
(g + 2)*(g + 3)**2/5
Suppose 2*y - 6 = -u, 28*y - 6 = 26*y + 4*u. Factor 2/5*l**2 - 2/5*l**y + 0*l + 0.
-2*l**2*(l - 1)/5
Let d = 29 - 3. Let h = d - 77/3. Suppose -1/3*v**2 - h + 2/3*v = 0. Calculate v.
1
Let g(t) be the first derivative of -t**4 + 4*t**3 - 4*t**2 + 1. Suppose g(q) = 0. What is q?
0, 1, 2
Suppose 0 = 4*z + 4*h - 8, -4*z + 4*h = -13 - 3. Let k = -149 - -153. Suppose -2/7*g**z + 8/7*g**k + 2/7*g + 0 - 8/7*g**2 = 0. Calculate g.
-1, 0, 1/4, 1
Let d be 55/(-10) - -8 - (-2)/(-4). Let 16/3*k - 4/3*k**d - 4 = 0. Calculate k.
1, 3
Let v(o) = -21*o**2 - 48*o - 39. Let i(b) = -5*b**2 - 12*b - 10. Suppose 4*y = -6 - 30. Let l(d) = y*i(d) + 2*v(d). Factor l(w).
3*(w + 2)**2
Let u(y) = -3*y**3 + 9*y**2 - 3*y + 3. Let t(o) = o + 1. Let f(j) = -3*t(j) + u(j). Determine b so that f(b) = 0.
0, 1, 2
Factor 2*w + 11*w**3 + 8*w**2 - 7*w**3 + 2*w.
4*w*(w + 1)**2
Let t(q) be the first derivative of -q**3/6 + 2*q**2 - 8*q + 6. Factor t(b).
-(b - 4)**2/2
Let s(u) be the first derivative of 3/4*u**4 - 1/3*u**6 + 0*u + 1/3*u**3 - 2 - 1/2*u**2 - 1/5*u**5. Find l, given that s(l) = 0.
-1, 0, 1/2, 1
Let r be ((-64)/90)/(-2) - 66/297. Let f(v) be the first derivative of 4 - 2/5*v - 1/10*v**2 + 1/20*v**4 + r*v**3. Factor f(o).
(o - 1)*(o + 1)*(o + 2)/5
Let o = 466/75 + -22/25. Let g = 1/456 - -7597/1368. Let -o*d**3 - g*d**5 - 8/9*d**2 - 10*d**4 + 0*d + 0 = 0. What is d?
-1, -2/5, 