actor x(c).
-2*c*(c + 3)**4/3
Let y be (-3)/(-9) + 5/(-15) - -3. Let t(a) be the third derivative of 0*a**6 + 0*a**y - 1/120*a**5 + 1/420*a**7 - 2*a**2 + 0*a**4 + 0*a + 0. Factor t(g).
g**2*(g - 1)*(g + 1)/2
Let q(b) be the first derivative of -b**4/28 + b**2/2 + 6*b/7 + 20. Factor q(x).
-(x - 3)*(x + 1)*(x + 2)/7
Suppose 0 = -l - 3*l + 16. Factor 3*o**3 - o**3 + 0 - l - 2*o + 4*o**2.
2*(o - 1)*(o + 1)*(o + 2)
Let j(x) = -60*x**5 - 45*x**4 + x**3 + 4*x**2 + 3*x. Let g(d) = -d**5 + d**3 - d. Let i(h) = 3*g(h) + j(h). Determine c so that i(c) = 0.
-2/3, -1/3, 0, 2/7
Let x(s) = 5*s**2 + 6*s + 13. Let b(u) = u**2 + 1. Let a(q) = 20*b(q) - 5*x(q). Factor a(c).
-5*(c + 3)**2
Let u(m) be the third derivative of -m**8/504 - m**7/315 + m**6/60 + m**5/90 - m**4/18 - 9*m**2. What is t in u(t) = 0?
-2, -1, 0, 1
Let m(p) be the first derivative of -p**4/4 + p**3/3 - 16. Factor m(z).
-z**2*(z - 1)
Let j(a) be the third derivative of -a**8/13440 + a**7/2520 - a**4/8 + 3*a**2. Let k(f) be the second derivative of j(f). Factor k(i).
-i**2*(i - 2)/2
Let p(x) be the third derivative of -5*x**8/336 + x**7/21 - x**5/6 + 5*x**4/24 - 20*x**2. Determine g so that p(g) = 0.
-1, 0, 1
Let m(b) be the third derivative of b**8/72 + 2*b**7/21 + 5*b**6/18 + 4*b**5/9 + 5*b**4/12 + 2*b**3/9 - 3*b**2. Determine g, given that m(g) = 0.
-1, -2/7
Let y(r) = -6*r + 2. Let q be y(-4). Let h be (-10)/(-35) - q/(-7). Factor -2*u**2 - 2*u - h*u + 2*u - 2.
-2*(u + 1)**2
Suppose 4/3*q + 0 + 2/3*q**2 = 0. Calculate q.
-2, 0
Let f be 0 + (9 + -9 - -3). Solve -3*n**f + 0 + 15/2*n**4 + 0*n**2 + 21/2*n**5 + 0*n = 0.
-1, 0, 2/7
Suppose 0 = -4*c - 16*c. Factor c - 3/4*b**2 - 1/4*b**4 + 1/4*b + 3/4*b**3.
-b*(b - 1)**3/4
Let w(c) be the first derivative of c**4/14 - 8*c**3/21 - 36. Factor w(n).
2*n**2*(n - 4)/7
Let s(f) be the first derivative of -f**5/90 - f**2 - 2. Let v(i) be the second derivative of s(i). Suppose v(z) = 0. Calculate z.
0
Factor -1/2*d**3 - 1/2 - 3/2*d - 3/2*d**2.
-(d + 1)**3/2
Let z = -119/4 + 603/20. Factor 2/5*b**3 - z*b + 0 + 0*b**2.
2*b*(b - 1)*(b + 1)/5
Let k = 22 - 21. Let p(j) be the first derivative of 0*j**2 + 0*j + k - 1/15*j**5 + 0*j**4 + 1/9*j**3. Suppose p(x) = 0. What is x?
-1, 0, 1
Let x be (-97)/(-42) + -1 + (-190)/1140. Factor 32/7*f + 10/7*f**3 + 34/7*f**2 + x.
2*(f + 1)*(f + 2)*(5*f + 2)/7
Let w = -9 + 9. Let t(r) be the third derivative of -1/15*r**5 + 1/3*r**3 + 1/105*r**7 + 0*r**4 + 0*r + 2*r**2 + 0 + w*r**6. Factor t(c).
2*(c - 1)**2*(c + 1)**2
Factor -11*i**2 + 15 + i**2 + 23*i**2 - 8*i**2 - 20*i.
5*(i - 3)*(i - 1)
Suppose 4*p - 2*p**3 + 8*p**3 - p**4 - 26 + 26 - 9*p**2 = 0. Calculate p.
0, 1, 4
Suppose -5 - 9*y**3 - 12*y + 0*y - 36*y**2 + 15*y**4 + 5 = 0. What is y?
-1, -2/5, 0, 2
Let v(f) = -3*f**5 + f**4 - f**3 + 16*f**2 - 3*f. Let k(r) = r**5 + r**3 - 8*r**2 + 2*r. Let o(c) = -5*k(c) - 2*v(c). Factor o(l).
l*(l - 2)*(l - 1)**2*(l + 2)
Factor 8788 + 3262*j + 4*j**3 - 1234*j + 490*j**2 - 334*j**2.
4*(j + 13)**3
Let d(t) be the first derivative of 3*t**3/5 + 3*t**2/2 + 6*t/5 - 25. Factor d(b).
3*(b + 1)*(3*b + 2)/5
Let f be 5/3*(-10)/(-25). Determine s, given that -f + 1/3*s - 1/3*s**3 + 2/3*s**2 = 0.
-1, 1, 2
Factor -28/3 - 4/3*d**3 + 28/3*d**2 + 4/3*d.
-4*(d - 7)*(d - 1)*(d + 1)/3
Suppose x = 3*v - 0*x - 7, 2*v - 2 = -2*x. Suppose 1 + 9*c - c**2 - 4*c + 5*c**v = 0. Calculate c.
-1, -1/4
Let s = -164 - -494/3. Let 0*b + 2/3 - s*b**2 = 0. Calculate b.
-1, 1
Let r(y) = 58*y**4 - 4*y**3 - 38*y**2 - 16*y. Let o(n) = 19*n**4 - n**3 - 13*n**2 - 5*n. Let m(s) = 10*o(s) - 3*r(s). Factor m(i).
2*i*(i - 1)*(i + 1)*(8*i + 1)
Factor 0 + 0*l - 1/5*l**2 + 1/5*l**3.
l**2*(l - 1)/5
Let i be (-134)/(-4) + (-1)/(-2). Let o be i/12 - (-1)/2. Factor 2*c + 4/3 - o*c**2.
-2*(c - 1)*(5*c + 2)/3
Factor -11*c - 6*c + 21*c + 8*c**2 + 6*c**2.
2*c*(7*c + 2)
Let q(z) be the second derivative of -7*z**6/60 - z**5/8 + z**4/12 + 11*z. Factor q(n).
-n**2*(n + 1)*(7*n - 2)/2
Let a be (-1)/1 - (-2 - -1). Determine b, given that 5*b**3 - 2*b**3 - 4*b**3 + a*b**3 + b**5 - b**4 + b**2 = 0.
-1, 0, 1
Let k = 1879/546 - 1/78. Factor -2/7*p**3 + 16/7 - k*p + 12/7*p**2.
-2*(p - 2)**3/7
Let v = 349/35 - 47/5. Suppose 4*u - 38 = -30. Factor -v*l - 2/7 - 2/7*l**u.
-2*(l + 1)**2/7
Let g(r) be the second derivative of -1/9*r**3 - 1/18*r**4 + 3*r + 1/30*r**5 + 1/45*r**6 + 0 + 0*r**2. Factor g(c).
2*c*(c - 1)*(c + 1)**2/3
Let j(u) be the first derivative of -u**6/30 - 2*u**5/25 - u**4/20 + 2. Factor j(t).
-t**3*(t + 1)**2/5
Let g(k) be the second derivative of 3*k**5/20 - k**3/2 - 8*k. Determine n, given that g(n) = 0.
-1, 0, 1
Suppose -10*i + 15*i - 6*i**2 + 6*i**4 - 2*i - 3*i**5 = 0. What is i?
-1, 0, 1
Suppose -1/7*a**3 - 3/7*a - 3/7*a**2 - 1/7 = 0. What is a?
-1
Factor 5 - 13*i**4 + 4*i**2 + 3*i**4 + 12*i**3 - 14*i + 2*i**5 + 1.
2*(i - 3)*(i - 1)**3*(i + 1)
Let s be ((-42)/63)/(7/9 - 1). Find f such that -1/3 - 5/3*f + 5/3*f**s + 4/3*f**4 - f**2 = 0.
-1, -1/4, 1
Find m such that 2/17*m**2 + 2/17 - 4/17*m = 0.
1
Let y be (-2)/(-5) - 62/5. Let n be 6*(-1 + y/(-9)). Find l such that -4*l**2 + 2*l**3 + 2 - l + 7*l + 2*l**5 - 6*l**3 + n*l**4 - 4*l = 0.
-1, 1
Let q(d) = -2*d**2 + 8*d - 11. Let s(l) = l**2 - 4*l + 5. Let h(p) = -2*q(p) - 5*s(p). Determine x, given that h(x) = 0.
1, 3
Let h(k) be the first derivative of k**6/30 - k**4/10 + k**2/10 + 32. Factor h(p).
p*(p - 1)**2*(p + 1)**2/5
Let z(l) be the first derivative of l**5/5 - 3*l**4/4 + l**3 - l**2/2 + 6. Let z(p) = 0. What is p?
0, 1
Solve 2/7*w**2 + 0 + 1/7*w**3 + 0*w - 1/7*w**4 = 0 for w.
-1, 0, 2
Let t be ((-6)/4)/(6/(-8)). Let f(o) = -o. Let x be f(-2). Determine q so that -16*q - 2 - 19*q**x - 16*q**t + 3*q**2 = 0.
-1/4
Let w(a) be the third derivative of -a**7/350 + a**6/40 - 9*a**5/100 + 7*a**4/40 - a**3/5 - 23*a**2. Factor w(b).
-3*(b - 2)*(b - 1)**3/5
Let h(j) be the second derivative of -3*j**5/70 + 5*j**4/42 - 2*j**3/21 + 4*j. Factor h(t).
-2*t*(t - 1)*(3*t - 2)/7
Let p(u) be the first derivative of -u**5 + 25*u**4/4 + 65*u**3/3 + 35*u**2/2 + 1. Factor p(s).
-5*s*(s - 7)*(s + 1)**2
Let j = 6 - 4. Suppose 2*y - 18 = 2*x, -3*y - y + j*x = -38. Factor -y*l**2 - 4*l - 4*l**3 + 0*l - 2*l**3.
-2*l*(l + 1)*(3*l + 2)
Let u(r) be the second derivative of r**7/14 + 2*r**6/15 - r**5/20 - r**4/6 + r. What is f in u(f) = 0?
-1, 0, 2/3
Let z(n) be the first derivative of -n**5/45 + 7*n**4/36 - 5*n**3/9 + 13*n**2/18 - 4*n/9 - 22. What is y in z(y) = 0?
1, 4
Let g(w) be the third derivative of -w**9/362880 + w**8/120960 - w**5/30 + 3*w**2. Let i(t) be the third derivative of g(t). Factor i(p).
-p**2*(p - 1)/6
Factor 2/5*y**2 + 0 + 1/5*y**3 - 3/5*y.
y*(y - 1)*(y + 3)/5
Let k(t) be the second derivative of t**7/63 - t**6/9 + t**5/3 - 5*t**4/9 + 5*t**3/9 - t**2/3 - 10*t. Factor k(p).
2*(p - 1)**5/3
Let w = 2329/5 + -464. Factor w*d + 0*d**2 - 3/5*d**3 - 6/5.
-3*(d - 1)**2*(d + 2)/5
Let l(q) be the third derivative of 1/60*q**6 + 0*q**4 + 0*q + 0 - 2*q**2 - 1/30*q**5 + 0*q**3. Determine f so that l(f) = 0.
0, 1
Let q(v) = -v**3 + 3*v**2 + v. Let d be q(3). Suppose -19 = 4*r + 1, -2*r - 13 = -m. Factor g**2 - 2*g**m + 3*g**3 - 2*g**d.
-g**2*(g - 1)
Factor -4*o**2 + 6*o + 4 - 3*o**2 + 9*o**2.
2*(o + 1)*(o + 2)
Let j(q) be the third derivative of 1/96*q**4 - q**2 + 0 + 1/240*q**5 + 1/1440*q**6 + 0*q + 1/6*q**3. Let s(v) be the first derivative of j(v). Factor s(x).
(x + 1)**2/4
Factor -18 - 14 + 2*a**2 - 4*a + 2*a**3 + 32.
2*a*(a - 1)*(a + 2)
Let w be (-1)/(-4) + 11/4. Suppose -w = -3*t + 6. Factor -2*l**t - 1 - 2*l**2 + 2*l + 2*l**2 + l**4.
(l - 1)**3*(l + 1)
Let w be 7/(-14) - 22/(-4). Factor 4*f**3 - 4*f**2 - 2*f**4 - 2/5 + 2/5*f**w + 2*f.
2*(f - 1)**5/5
Suppose -4 = t + 4. Let h(n) = 10*n**3 + 8*n + 8. Let z(d) = -d**3 - d - 1. Let j(o) = t*z(o) - h(o). Suppose j(y) = 0. What is y?
0
Let b(j) = 9*j**3 + 34*j**2 - 160. Let f(n) = 55*n**3 + 205*n**2 - 960. Let k(u) = 25*b(u) - 4*f(u). Factor k(i).
5*(i - 2)*(i + 4)**2
Let l(t) be the third derivative of 0*t + 0 + 4*t**2 - 3/28*t**4 - 2/105*t**5 - 2/21*t**3. What is r in l(r) = 0?
-2, -1/4
Let -c**4 + 13*c**2 - 3*c**3 + 3*c**3 - 2*c**3 - 10*c**2 = 0. Calculate c.
-3, 0, 1
Factor 0*r + 0 + 1/6*r**4 + 0*r**2 - 1/6*r**5 + 1/3*r**3.
-r**3*(r - 2)*(r + 1)/6
Let z(s) be the second derivative of -s**4/3 