6*f**2 + 23*f + 8. Let h(k) = -4*k**3 - 48*k**2 - 68*k - 24. Let t(i) = 3*h(i) + 8*u(i). Factor t(w).
-4*(w + 1)**2*(w + 2)
Suppose -2*a + 4 = -a. Suppose 0*j**a - 9/2*j**5 - 2*j + 13/2*j**3 + 0 + 0*j**2 = 0. What is j?
-1, -2/3, 0, 2/3, 1
Let w(m) be the second derivative of m**4/96 - m**3/48 + 8*m. Factor w(c).
c*(c - 1)/8
Let z be (45/198)/(15/12). Factor z + 0*n - 2/11*n**2.
-2*(n - 1)*(n + 1)/11
Suppose r - 8 = -3*r. Find i, given that -6*i**3 + 0*i**2 - r*i**4 - 8*i**3 + 2*i - 6*i**4 - 4*i**2 = 0.
-1, 0, 1/4
Factor 3*d**3 - 6*d**2 + 142 - 142.
3*d**2*(d - 2)
Factor 0 + 2*u + 1/2*u**5 - u**4 - 3/2*u**3 + 2*u**2.
u*(u - 2)**2*(u + 1)**2/2
Let w = 13 - 9. Factor 0*h + 2*h - 4*h - 6*h + w + 4*h**2.
4*(h - 1)**2
Suppose 27 = 14*g - 5*g. Factor 7/3*d**g - 16/3*d**2 + 11/3*d - 2/3.
(d - 1)**2*(7*d - 2)/3
Let o(f) be the third derivative of -f**9/5040 - f**8/1400 - f**7/1400 + 5*f**3/6 - 5*f**2. Let r(h) be the first derivative of o(h). Factor r(u).
-3*u**3*(u + 1)**2/5
Let q(w) be the first derivative of -2/3*w**3 + 1/6*w**4 + 2/5*w**5 + 0*w - 3 + 1/9*w**6 - 2/3*w**2. Determine r so that q(r) = 0.
-2, -1, 0, 1
Suppose 3*z + 6*z - 18 = 0. Let t(i) be the third derivative of -i**z - 13/60*i**6 - 7/12*i**4 + 1/3*i**3 + 1/2*i**5 + 0*i + 4/105*i**7 + 0. Factor t(a).
2*(a - 1)**3*(4*a - 1)
Let o(m) be the third derivative of -m**8/336 - 2*m**7/105 - m**6/24 - m**5/30 - 3*m**2. Factor o(w).
-w**2*(w + 1)**2*(w + 2)
Let h = -14 - -16. Let d(p) be the second derivative of 0*p**h - 1/30*p**3 + 0 + 2*p + 1/60*p**4. Factor d(b).
b*(b - 1)/5
Let r(k) be the second derivative of k**6/15 - 7*k**5/30 + k**4/6 + k**3/3 - 2*k**2/3 - 24*k. What is m in r(m) = 0?
-2/3, 1
Let x(m) = -2*m**2 - 6*m + 9. Suppose -b - 2*g = -12, -3*b + 7*g - 14 = 3*g. Let c(l) = l**2. Let t(h) = b*x(h) + 6*c(h). Factor t(u).
2*(u - 3)**2
Suppose 16 = d + 3*d - 4*a, 4*d - 2*a = 22. Factor -17*m**2 - 8*m - 8*m**4 - 12*m**2 + d*m**2 + 4*m - 26*m**3.
-2*m*(m + 1)*(m + 2)*(4*m + 1)
Let g(d) be the third derivative of -d**6/240 + d**4/16 - d**3/6 + 19*d**2. Solve g(t) = 0 for t.
-2, 1
Suppose -5*x = 5, x = -2*t - 0*x + 7. Let f = 8 - t. Factor 4*s**4 + f*s**3 + 0*s**4 - 2*s**4 + s**2 + s**2.
2*s**2*(s + 1)**2
Let s(u) be the second derivative of u**4/4 + u**3/6 + 2*u. Let w be s(-1). Factor k + 0*k**w + k**2 + k.
k*(k + 2)
Let g(b) be the first derivative of -b**6/12 - b**5/5 - b**4/8 + 1. Factor g(m).
-m**3*(m + 1)**2/2
Let k(s) = -17*s**2 + 9*s + 10. Let v(q) = 4*q - 6*q**2 - 5*q + 3 + 0*q + 4*q. Let d be (4/6)/((-2)/(-9)). Let b(a) = d*k(a) - 8*v(a). Factor b(x).
-3*(x - 2)*(x + 1)
Let s(c) = -c**4 + 7*c**3 - 6*c**2 - 6*c - 6. Let a(b) = 3*b**4 - 20*b**3 + 17*b**2 + 17*b + 17. Let y(w) = 6*a(w) + 17*s(w). Factor y(x).
x**3*(x - 1)
Let x be (-35)/(-15) - (10 + -8). Factor 0*r + 0 + x*r**2.
r**2/3
Let l = -2/11 - -28/33. Let d be 2/(-9)*(-84)/56. Find f, given that d*f**2 + 0 - l*f = 0.
0, 2
Let j be 1*12*(12/3)/12. Let x(i) be the third derivative of 0*i**j + 0*i**6 - 1/210*i**7 + 0 + 0*i**5 - 1/168*i**8 - 2*i**2 + 0*i**3 + 0*i. Factor x(a).
-a**4*(2*a + 1)
Let z(n) = -n**3 - 4*n**2 + 5*n + 2. Let h be z(-5). Let p be 8/6*(3 - 0). Factor 12*w**3 + 9*w**h + 0*w**2 + 5*w**p - 4*w + 6*w.
w*(w + 1)**2*(5*w + 2)
Suppose -4*x - 1 = 23. Let a be (-1 + -2)/(x/4). Solve -3 - 3/4*n**a + 3*n = 0.
2
Let w(o) be the second derivative of o**4/14 - o**3/21 + 3*o. Solve w(j) = 0 for j.
0, 1/3
Let h(g) = -3*g**3 + 4*g. Let y be h(-2). Let z be y/6*3/7. Find i, given that -8/7 - 90/7*i**5 + 82/7*i**3 + z*i - 106/7*i**4 + 114/7*i**2 = 0.
-1, -2/5, 2/9, 1
Let b(m) be the third derivative of -5*m**6/96 - m**5/24 + 13*m**4/96 - m**3/12 - 9*m**2. Let b(x) = 0. What is x?
-1, 1/5, 2/5
Let w(g) be the first derivative of 0*g + 1/60*g**5 + 1/480*g**6 - 1 + 5/96*g**4 + 1/12*g**3 - 1/2*g**2. Let j(s) be the second derivative of w(s). Factor j(m).
(m + 1)**2*(m + 2)/4
Let c(n) = 2*n**3 + n**2 + n - 1. Let p be c(1). Let i(s) be the second derivative of -1/4*s**2 - s + 1/24*s**4 + 0*s**p + 0. Let i(w) = 0. Calculate w.
-1, 1
Let q be -3*1*(-4 - -3). Let f(n) be the third derivative of 0 + 0*n + 0*n**q + 1/12*n**4 + 1/60*n**6 - 1/15*n**5 + 2*n**2. Solve f(r) = 0.
0, 1
Find f such that -2/9*f**3 - 8/9*f**2 - 4/9 - 10/9*f = 0.
-2, -1
Let u(x) be the third derivative of -x**6/240 - 11*x**5/120 - 35*x**4/48 - 25*x**3/12 + 62*x**2. Factor u(j).
-(j + 1)*(j + 5)**2/2
Factor 0 + l**2 + 1/3*l**4 + l**3 + 1/3*l.
l*(l + 1)**3/3
Let p(v) be the first derivative of 16*v**5/5 + 13*v**4 + 44*v**3/3 + 4*v**2 + 1. Factor p(m).
4*m*(m + 1)*(m + 2)*(4*m + 1)
Let c = 27 - 22. Let f(n) be the second derivative of -1/70*n**c + 0*n**2 + 1/21*n**3 + 4/105*n**6 + 0 - 2*n - 2/21*n**4. Let f(a) = 0. Calculate a.
-1, 0, 1/4, 1
Let g be 238/(-732)*-1*8. Let m = g + 4/61. Factor m*c**3 + 2/3 + 6*c**2 + 4*c.
2*(c + 1)**2*(4*c + 1)/3
Let f(y) = 3*y - 5. Let b be f(5). Suppose 3*c = -2*c + b. What is i in 2*i - 3*i + 0*i + i**c = 0?
0, 1
Factor -41*t**2 + 41*t**2 + 4*t**4.
4*t**4
Let n(m) be the third derivative of -m**7/525 - m**6/100 - m**5/50 - m**4/60 - 6*m**2. Factor n(r).
-2*r*(r + 1)**3/5
Let w = 467/1180 + 1/236. Find v, given that 0 + 0*v - 2/5*v**3 - w*v**2 = 0.
-1, 0
Let 3*s**2 + 3*s**4 + 0 + 3 - 9*s**2 = 0. Calculate s.
-1, 1
Solve -2/5 - 2/5*q**2 - 4/5*q = 0 for q.
-1
Factor 1/3*x**2 - x + 2/3.
(x - 2)*(x - 1)/3
Let s be 8/44 + 2/(-11). Let a(v) be the second derivative of 0 - v**2 - v + 2/3*v**3 + s*v**4 + 1/15*v**6 - 1/5*v**5. Solve a(q) = 0 for q.
-1, 1
Let q(n) be the second derivative of -5*n + 1/12*n**4 - 1/2*n**3 + 0 + n**2. Solve q(i) = 0 for i.
1, 2
Let a(s) be the third derivative of 0 - 1/24*s**5 - 1/16*s**4 + 0*s + 1/12*s**3 + 5*s**2 + 1/105*s**7 + 1/80*s**6. Let a(k) = 0. Calculate k.
-1, 1/4, 1
Let d(u) be the first derivative of u**3 + 3*u**2 + 3*u - 16. What is a in d(a) = 0?
-1
Let x be (-2)/(-3) + (-10)/15. Suppose 8 = -x*r + 2*r. Let 3*h**4 - r*h**3 - 2*h**3 + 6*h + 3*h**4 - 8*h**3 + 6*h**2 - 4 = 0. What is h?
-2/3, 1
Let u be 3311/1935 - (6/(-10))/(-1). Factor 2/9*b**4 - u*b - 2/3*b**2 + 2/9*b**3 - 4/9.
2*(b - 2)*(b + 1)**3/9
Suppose -6 + 0 = -3*r. Suppose -5*b + 3*b = 0. Factor 0 + 0*l**3 + 0*l - 2/11*l**4 + b*l**r.
-2*l**4/11
Let y(x) be the second derivative of -1/2*x**2 - 1/180*x**5 - 1/18*x**3 - 1/36*x**4 + 0 - 2*x. Let f(t) be the first derivative of y(t). Solve f(b) = 0 for b.
-1
Let d(r) be the second derivative of r**7/480 - r**6/288 - r**5/240 + r**3/3 + 2*r. Let w(t) be the second derivative of d(t). Suppose w(u) = 0. What is u?
-2/7, 0, 1
Suppose 36 - 27 = 3*y. Factor 1/2*a + 1/2*a**4 + 3/2*a**2 + 0 + 3/2*a**y.
a*(a + 1)**3/2
Let d(a) be the third derivative of 1/20*a**5 + 4*a**2 - 5/24*a**4 + 1/6*a**3 + 0*a + 0 + 1/24*a**6 - 2/105*a**7. Factor d(t).
-(t - 1)**2*(t + 1)*(4*t - 1)
Suppose 0 = -7*f - 3*f + 20. Solve -2/7*t**f + 8/7*t - 6/7 = 0.
1, 3
Let m(d) be the first derivative of -6*d**4 + 28*d**3/3 - 4*d - 7. Solve m(k) = 0 for k.
-1/3, 1/2, 1
Let y = -6 - -2. Let n be (12/(-15))/(y/10). Suppose -a - 2*a - 4*a**2 + n*a**2 + a = 0. Calculate a.
-1, 0
Let n(b) = -4*b**4 + 17*b**3 + 5*b**2 - 12*b + 4. Let y(q) = q**4 + q**3. Let m(r) = r - 8. Let s be m(7). Let v(h) = s*n(h) + 5*y(h). Factor v(z).
(z - 1)*(z + 1)*(3*z - 2)**2
Let o(i) be the third derivative of 1/36*i**4 - 4*i**2 + 0*i**3 + 0*i + 1/60*i**5 + 1/360*i**6 + 0. Factor o(c).
c*(c + 1)*(c + 2)/3
Let s(o) be the first derivative of -o**6/1260 - o**5/210 - o**4/84 + o**3 - 4. Let v(j) be the third derivative of s(j). Determine m, given that v(m) = 0.
-1
Let c be (254/(-10))/((-4)/(-5)). Let b = c - -32. Factor -1/4 - 1/4*l + b*l**3 + 1/4*l**2.
(l - 1)*(l + 1)**2/4
Let m(d) = -3*d - 6. Let w be m(-9). Factor 0 + 27*u**2 - 3 - 4 + w*u + 1.
3*(u + 1)*(9*u - 2)
Let p(r) = 3*r**5 - 8*r**4 - 3*r**3 + 8*r**2 + 5. Let q(u) = -3*u**5 + 9*u**4 + 3*u**3 - 9*u**2 - 6. Let i(o) = -6*p(o) - 5*q(o). Factor i(k).
-3*k**2*(k - 1)**2*(k + 1)
Factor -13*w**5 + 17*w**2 - 7*w**2 - 17*w**4 - 2*w**5 - 3*w**4 + 5*w**3.
-5*w**2*(w + 1)**2*(3*w - 2)
Let z(q) be the second derivative of 3*q**5/20 - q**4/6 + 9*q. Determine b so that z(b) = 0.
0, 2/3
Factor 1 + 2*a - 1 + 4*a + 3*a**2.
3*a*(a + 2)
Let m(l) be the third derivative of -l**6/240 + l**5/24 + l**4/6 - 4*l**3 +