tor -2*k**4 - 10*k + 9*k - 2*k**4 - 4*k**2 - 6*k**3 - k**o.
-k*(k + 1)**4
Factor -18/5 + 2/5*y**2 - 16/5*y.
2*(y - 9)*(y + 1)/5
Let z(w) be the first derivative of -w**4/20 + w**3/5 + 7. Factor z(l).
-l**2*(l - 3)/5
Let z = 3 + 0. Suppose -3*a - 2*l = -3 - 3, 17 = 5*a + l. Factor -2/9*i**2 - 2*i**5 + 0*i + 10/9*i**z - 2/3*i**a + 0.
-2*i**2*(i + 1)*(3*i - 1)**2/9
Let c = -6 - -10. Factor -5*z**2 - 2*z - 7*z**c + 2 + z - 10*z**2 + 0 - 19*z**3.
-(z + 1)**3*(7*z - 2)
Let x(f) be the first derivative of -4*f**4 - 20*f**3 + 8*f**2 + 50. Factor x(j).
-4*j*(j + 4)*(4*j - 1)
Factor 1/4*u**2 - 1/4*u - 3.
(u - 4)*(u + 3)/4
Let w(a) be the first derivative of -6*a**5/95 + 5*a**4/38 - 2*a**3/57 - a**2/19 - 9. Factor w(m).
-2*m*(m - 1)**2*(3*m + 1)/19
Solve -1/3*l**3 + 2/3 - 2/3*l**2 + 1/3*l = 0.
-2, -1, 1
Let u(m) be the third derivative of -m**8/84 - 4*m**7/105 + m**6/15 + 4*m**5/15 - m**4/6 - 4*m**3/3 - 19*m**2. Find n, given that u(n) = 0.
-2, -1, 1
Factor -4/7*r**2 + 6/7*r**4 - 2/7 - 6/7*r + 4/7*r**3 + 2/7*r**5.
2*(r - 1)*(r + 1)**4/7
Let j be 1/4 + 7/4. Suppose -k = z + 4, -j*z + 0*k + 4*k + 16 = 0. Factor -7*x**3 - 2*x**2 + 5*x**5 + 3*x**4 + 2*x - x**2 + 0*x + z*x**3.
x*(x - 1)*(x + 1)**2*(5*x - 2)
Let a(z) be the second derivative of -z**7/7 + 74*z**6/45 - 89*z**5/15 + 2*z**4 + 27*z**3 - 18*z**2 + 5*z + 6. What is p in a(p) = 0?
-1, 2/9, 3
Let r(y) = -y**5 - y**2. Let c(f) = 24*f - 3*f**5 - 15*f - f**2 + 4*f**3 - 11*f. Let z(w) = 2*c(w) - 2*r(w). Suppose z(u) = 0. What is u?
-1, 0, 1
Factor 0 - 10*v**5 + 5*v**5 - 10*v**4 + 0 + 10*v**2 + 5*v.
-5*v*(v - 1)*(v + 1)**3
Let l(r) = r**2 - 6*r - 11. Let d be l(8). Determine s so that d + 7*s + 0*s + 2*s**4 + s + 3 - 6*s**2 - 4*s**3 = 0.
-1, 2
Let m(d) = -d**2 - 3*d - 4. Let s(q) = 2*q**2 + 7*q + 9. Let c(t) = 9*m(t) + 4*s(t). Let g(v) = 5*v**2 + 4*v. Let n(i) = -2*c(i) + g(i). Factor n(r).
r*(7*r + 2)
Determine p so that 5*p**2 + 4*p**2 + 32*p - 5*p**2 + 64 = 0.
-4
What is j in 0*j**2 + 0 + 0*j - 1/3*j**3 = 0?
0
Let h(b) be the second derivative of -b**6/450 - b**5/200 + b**4/120 - 5*b**3/6 + 3*b. Let z(u) be the second derivative of h(u). Let z(w) = 0. Calculate w.
-1, 1/4
Factor 6*k**3 + 3*k + 2*k**5 - 12*k**3 + k**5.
3*k*(k - 1)**2*(k + 1)**2
Suppose 2*u - u = -3*r + 5, -5*u = -3*r + 11. Let l be (u + 0)/(4/(-16)). What is o in 6/5*o**3 + 6/5*o**2 + 2/5*o + 2/5*o**l + 0 = 0?
-1, 0
Let d = -7/3 - -8/3. Let w(z) be the first derivative of -3 - d*z**3 + z**2 - z. Factor w(o).
-(o - 1)**2
Factor -4/3*t**2 + 4 + 8/3*t.
-4*(t - 3)*(t + 1)/3
Let m(r) be the third derivative of r**7/315 - r**5/45 + r**3/9 + 27*r**2. Suppose m(k) = 0. Calculate k.
-1, 1
Suppose -2 = 2*f, 3*f + 9 - 2 = 2*j. Factor -1/2*s + 1/6*s**j + 1/3.
(s - 2)*(s - 1)/6
What is u in -3/2*u - 1/2*u**2 - 1 = 0?
-2, -1
Let q(y) = 4*y**2 + 0*y**2 + 3*y**2 + y**3 + 4*y + 0*y**3 - 8. Let z be q(-6). Solve 2*o + 2*o**z - 2*o + o**3 - 3*o**3 = 0 for o.
0, 1
Let x be ((-1)/5)/(3/5 - 1). Suppose -2*u**4 - 3*u**3 - 1/2*u**5 + 0 - x*u - 2*u**2 = 0. Calculate u.
-1, 0
Let p be (6 - 1 - -1) + -6. Factor 2/11*v**5 + 2/11*v**4 + 0*v + p - 2/11*v**3 - 2/11*v**2.
2*v**2*(v - 1)*(v + 1)**2/11
Let v(s) = s**2 - 13*s + 27. Let r be v(11). Suppose -6/5*o**r + 8/5*o - 4*o**4 + 36/5*o**2 - 16/5 - 2/5*o**3 = 0. Calculate o.
-2, -1, 2/3, 1
Let y(b) be the third derivative of -b**7/42 + b**6/24 + b**5/12 - 5*b**4/24 + 13*b**2. Suppose y(q) = 0. What is q?
-1, 0, 1
Suppose -3*m - 3 = -9. Let o(q) = -33 + 4 - 20*q**2 + 36*q - 12*q**m. Let l(t) = 11*t**2 - 12*t + 10. Let c(w) = 17*l(w) + 6*o(w). Solve c(a) = 0.
2/5, 2
Let d(c) = -c**3 + 4*c + 3. Let w(f) = f**3 - f**2 + f + 1. Let x be 7/(-14) + 14/4. Let b(z) = x*w(z) - d(z). Find l such that b(l) = 0.
-1/4, 0, 1
Suppose 21 = z + 19. Let n(m) be the third derivative of -2/105*m**7 + 0 + 0*m**4 + 0*m**3 + 2*m**z + 0*m + 1/60*m**5 + 1/40*m**6. Let n(y) = 0. What is y?
-1/4, 0, 1
Suppose -1/6*q**2 + 5/6*q + 0 = 0. Calculate q.
0, 5
Factor 4*d**4 + 53*d**2 + 11*d - 139*d - 32*d**3 + 64 + 43*d**2.
4*(d - 2)**4
Let o = -5/34 + 28/17. Let a(z) be the first derivative of o*z**2 - z**3 + 1/4*z**4 - 3 - z. Factor a(v).
(v - 1)**3
Let l(r) = r**2 + 10*r + 2. Let y be l(-10). Let 3*a - 3*a**3 + 3*a**4 + 2*a**2 + 0*a**y + a**2 - 6*a**2 = 0. Calculate a.
-1, 0, 1
Let a(z) be the third derivative of 0 + 0*z - 1/60*z**5 - 1/3*z**3 + z**2 - 1/8*z**4. Solve a(w) = 0 for w.
-2, -1
Let d(s) = -8*s. Let c(g) = -g**2 + 8*g - 1. Let h(u) = -4*c(u) - 3*d(u). Factor h(v).
4*(v - 1)**2
Let j(m) be the third derivative of m**5/150 + m**4/30 + m**3/15 + 8*m**2. Factor j(f).
2*(f + 1)**2/5
Let x(z) be the first derivative of -10*z**6/3 + 52*z**5/5 - 9*z**4 - 4*z**3/3 + 4*z**2 - 13. What is t in x(t) = 0?
-2/5, 0, 1
Let g be 3 - (0 + 20/12). Suppose 2/3*z**4 + 2/3 + 0*z**3 - g*z**2 + 0*z = 0. What is z?
-1, 1
Determine h, given that 2/7*h**4 + 8/7*h**3 + 10/7*h**2 + 0 + 4/7*h = 0.
-2, -1, 0
Suppose -127/4*y**4 + 5*y**5 - 87/4*y + 1/4*y**2 + 211/4*y**3 - 9/2 = 0. Calculate y.
-2/5, -1/4, 1, 3
Let a(n) be the third derivative of n**6/240 - n**5/30 - 11*n**4/48 - n**3/2 + 5*n**2. Find g, given that a(g) = 0.
-1, 6
Let r = 99 + -887/9. Let o = -10/63 + r. Find a such that -10/7*a**2 - 8/7 - 16/7*a - o*a**3 = 0.
-2, -1
Let j(h) be the second derivative of 1/3*h**3 + 1/720*h**6 + 0 + 0*h**4 + 0*h**2 - 1/240*h**5 - h. Let v(f) be the second derivative of j(f). Factor v(o).
o*(o - 1)/2
Let g(m) be the second derivative of -m**7/1960 - m**6/210 - 2*m**5/105 + m**4/3 - 7*m. Let c(p) be the third derivative of g(p). Find a, given that c(a) = 0.
-4/3
Solve -3/4*i**2 + 3/4*i**3 + 1/4*i - 1/4*i**4 + 0 = 0.
0, 1
Let w = 518 + -3604/7. Let w*l + 2*l**3 - 4/7 - 32/7*l**2 = 0. What is l?
2/7, 1
Suppose t - 3*t + 4 = 0. Factor -2*v**4 + 7 + t*v**2 - 7.
-2*v**2*(v - 1)*(v + 1)
Let k(s) = -69*s + 1. Let b be k(-1). Suppose -2*z + 3*z + 4*c + 6 = 0, -5*c - b = -5*z. Factor -3*m**3 - 2*m**2 - 2*m**3 - 4*m**4 + m**5 + 0*m**5 + z*m**3.
m**2*(m - 2)*(m - 1)**2
Let i = 853 - 851. Factor -2/7 - 2/7*f**i + 4/7*f.
-2*(f - 1)**2/7
Let f be (-1)/(-5)*((5 - -1) + -4). Factor -f*i**2 + 6/5*i - 4/5.
-2*(i - 2)*(i - 1)/5
Let y = 3886007 - 8490924411/2185. Let x = -2/437 + y. Determine r, given that 0*r + 0*r**3 + 0 + 2/5*r**2 - x*r**4 = 0.
-1, 0, 1
Let i(f) = -f**2 - 64*f + 137. Let t(m) = -16*m + 34. Let r(a) = 2*i(a) - 9*t(a). Solve r(o) = 0.
4
Suppose 0 = -5*b + 4*c - 2, b - 12 + 1 = -3*c. Factor 2 + 9*p**2 - 6*p**2 - 5*p**2 + b*p - 2*p**3.
-2*(p - 1)*(p + 1)**2
Let w(g) = -g**5 + 7*g**4 - 12*g**3 + 13*g**2 - 5*g - 1. Let x(y) = -y**4 - y**3 - y**2 + y + 1. Let z(a) = 2*w(a) + 2*x(a). Factor z(s).
-2*s*(s - 2)**2*(s - 1)**2
Let x = -1/391 - -1567/1173. Factor 2 + 2/9*s**2 - x*s.
2*(s - 3)**2/9
Let p(t) be the first derivative of t**4/2 + 10*t**3/3 + 8*t**2 + 8*t + 1. Factor p(n).
2*(n + 1)*(n + 2)**2
Let t(k) be the third derivative of 0*k + 4*k**2 + 0 + 0*k**3 - 1/10*k**5 + 1/8*k**4 + 1/40*k**6. Let t(i) = 0. What is i?
0, 1
Let s(a) be the first derivative of -5*a**6/6 + 5*a**4 + 10*a**3/3 - 15*a**2/2 - 10*a - 2. Suppose s(d) = 0. What is d?
-1, 1, 2
What is x in -30*x - 4*x**2 - 7*x**2 - 3*x**2 - 18 - 2*x**3 = 0?
-3, -1
Factor 4*g**2 - 8*g**3 + 11*g**3 - 2*g**2.
g**2*(3*g + 2)
Suppose -3*i - 3*h = -5*i + 8, 0 = 5*i - 2*h - 20. Factor -1/3*b**3 + 1/3*b + 1/3*b**2 + 0 - 1/3*b**i.
-b*(b - 1)*(b + 1)**2/3
Let y(n) be the first derivative of -4 - 1/6*n**6 - 2/3*n**3 + n + 1/2*n**4 - 1/2*n**2 + 1/5*n**5. Find x such that y(x) = 0.
-1, 1
Factor -5/3*b**3 + 1/3*b**4 + 0 + 8/3*b**2 - 4/3*b.
b*(b - 2)**2*(b - 1)/3
Suppose -2*n = -3*x - 223 + 750, 0 = -2*n - x - 507. Let j be 2/(-9) + n/(-504). Determine m so that -2/7 - 2/7*m + 2/7*m**2 + j*m**3 = 0.
-1, 1
Let z(p) = -p**2 + 12*p - 18. Let d be z(10). Factor -2/3*r**5 - 4/3*r**d + 0 + 4/3*r**4 + 2/3*r + 0*r**3.
-2*r*(r - 1)**3*(r + 1)/3
Suppose -882 + 857 = -5*y. Let h be 2 - ((0 - 0) + 0). Let -3*g**3 + 2*g**h + 0 + 2*g**4 - 1/2*g - 1/2*g**y = 0. What is g?
0, 1
Factor -9*t**2 - 4*t + 6*t + 3*t**3 + 4*t.
3*t*(t - 2)*(t - 1)
Let w(g) be the second derivative of -g**6/75 + g**5/50 + 2*g**4/15 - 4*g**3/15 + 10*g. Factor w(o).
-2*o*(o - 2)*(o - 1)*(o + 2)/5
Factor 5 + 40*f**2 - 40*f**3 + 0 - 20*f + 20*f**4 - 1 - 4*f**5.
-4*(f - 1)**5
Let 