actor 0 + b + 1/2*b**3 + 3/2*b**i.
b*(b + 1)*(b + 2)/2
Factor 0 - 1/3*s**2 - 2/3*s.
-s*(s + 2)/3
Let u(h) be the second derivative of -h**6/90 - h**3/6 + 10*h. Let n(f) be the second derivative of u(f). Solve n(i) = 0 for i.
0
Let g(t) = 6*t + 18. Let v be g(-3). Factor v - 2/3*o - 2/3*o**2.
-2*o*(o + 1)/3
Let p = -165 + 1817/11. Factor -p*g**5 - 2/11*g + 0 + 0*g**2 + 4/11*g**3 + 0*g**4.
-2*g*(g - 1)**2*(g + 1)**2/11
Factor 1/2*v + 3/4 - 1/4*v**2.
-(v - 3)*(v + 1)/4
Let u = 13/7 + -25/21. Factor 2/9*h**2 - u*h + 4/9.
2*(h - 2)*(h - 1)/9
Let d be -1 - ((-100)/(-36) + -4). Let 0 - d*s**2 - 4/9*s**3 + 0*s - 2/9*s**4 = 0. What is s?
-1, 0
Let t be (-1)/2 - 370/(-8). Let u = t - 42. Determine l so that 3/4*l**3 - u*l**2 - 3 + 6*l = 0.
1, 2
Determine c, given that 0*c + 0 + 4*c**4 + 2/5*c**2 + 13/5*c**3 + 9/5*c**5 = 0.
-1, -2/9, 0
Let i(v) = v**3 + v**2 - 2*v - 1. Let b be i(2). Factor -1 - 1 + 0*h**2 - 7*h**3 + 2*h**2 + b*h.
-(h - 1)*(h + 1)*(7*h - 2)
Let g(q) be the third derivative of 2*q**7/735 + q**6/70 - q**5/105 - q**4/14 + 32*q**2. Factor g(x).
4*x*(x - 1)*(x + 1)*(x + 3)/7
Let z(r) be the third derivative of 1/90*r**6 - 6*r**2 - 1/315*r**7 - 1/9*r**3 - 1/36*r**4 + 1/45*r**5 + 0*r - 1/504*r**8 + 0. Solve z(s) = 0 for s.
-1, 1
Let f(d) be the second derivative of -d**6/720 + d**5/60 - d**4/12 + d**3/3 - 2*d. Let k(i) be the second derivative of f(i). Factor k(b).
-(b - 2)**2/2
Let j(i) be the third derivative of -i**7/280 + i**6/120 + i**5/20 - 2*i**3/3 + 2*i**2. Let p(y) be the first derivative of j(y). What is h in p(h) = 0?
-1, 0, 2
Let f(g) = -9*g**3 + 12*g + 8. Let u(x) = 14*x**3 - 18*x - 12. Let w(i) = 8*f(i) + 5*u(i). Suppose w(v) = 0. Calculate v.
-1, 2
Suppose -4*c - k - 4 = 0, 19 = 2*c - 5*k - 1. Factor c*q**2 - 1/4*q**4 + 1/4*q**5 + 0*q**3 + 0*q + 0.
q**4*(q - 1)/4
Let i(r) be the second derivative of r**5/60 + r**4/6 + r**3/2 - 7*r. Factor i(w).
w*(w + 3)**2/3
Let y(c) = 3*c. Let i be y(1). Let x be 18/24 + 6/(-8). Solve x*j**2 - i*j**2 - 3 - j - 5*j = 0.
-1
Suppose -7*l = -3*l - 20. Let i be ((-1)/l)/(3/(-5)). Factor 0*z - i*z**4 - 1/3*z**2 + 2/3*z**3 + 0.
-z**2*(z - 1)**2/3
Let o(l) be the third derivative of -1/24*l**4 + 3*l**2 + 0*l + 0 + 1/12*l**3 + 1/120*l**5. Factor o(y).
(y - 1)**2/2
Suppose 3*a = -12, -2*o - 16 = -5*o + a. Let t(w) be the second derivative of -2*w + 1/18*w**o - 1/18*w**3 + 0*w**2 + 0. Factor t(l).
l*(2*l - 1)/3
Let s(b) be the second derivative of 0 - 1/6*b**3 + b + 1/20*b**5 - 1/12*b**4 + 1/2*b**2. Find r such that s(r) = 0.
-1, 1
Let d(f) be the third derivative of f**9/30240 - f**8/4032 + f**7/1260 - f**6/720 - f**5/10 + 2*f**2. Let g(l) be the third derivative of d(l). Factor g(m).
(m - 1)**2*(2*m - 1)
Suppose -6*a = -a + 4*g - 71, -2*a + 5*g = -2. Factor 11*w - 38*w + 14*w + a*w + 2*w**2.
2*w*(w - 1)
Suppose -2*q = -0*q. Factor -1/3*h**3 + h + 2/3 + q*h**2.
-(h - 2)*(h + 1)**2/3
Let w(y) = y**2 - 5*y - 20. Let k be w(8). Let d(s) be the third derivative of 0 + s**2 + 0*s**3 + 1/30*s**5 + 1/12*s**k + 0*s. Solve d(v) = 0.
-1, 0
Let g(j) be the third derivative of j**5/75 - j**4/10 - 8*j**3/15 + 2*j**2. Factor g(k).
4*(k - 4)*(k + 1)/5
Let y(p) be the first derivative of -p**3/9 - 5*p**2/3 + 42. Factor y(r).
-r*(r + 10)/3
Let c(w) be the third derivative of -w**8/448 + w**7/56 - 3*w**6/80 - w**5/20 + w**4/4 + 6*w**2. Factor c(o).
-3*o*(o - 2)**3*(o + 1)/4
Factor 0*m + 0*m**2 + 0*m**3 + 0 - 2/19*m**4.
-2*m**4/19
Let c(m) be the first derivative of -m**5/5 + m**4/4 + m**3/3 - m**2/2 - 7. Factor c(n).
-n*(n - 1)**2*(n + 1)
Let v(p) be the first derivative of -3/2*p**4 + 2*p + 1 + 8/5*p**5 + 3*p**2 - 10/3*p**3. Factor v(y).
2*(y - 1)**2*(y + 1)*(4*y + 1)
Let c be (-3)/7 + (-781)/(-924). Let n(d) be the second derivative of -1/6*d**4 + c*d**3 + 1/40*d**5 + 3*d - 1/2*d**2 + 0. Factor n(y).
(y - 2)*(y - 1)**2/2
Let o = 2 - 1. Factor -o + 3*v**4 - 18*v**3 + 27*v**2 + 3 - 2.
3*v**2*(v - 3)**2
Factor 8/7*t - 6/7 + 2/7*t**4 + 4/7*t**2 - 8/7*t**3.
2*(t - 3)*(t - 1)**2*(t + 1)/7
Let j(k) be the third derivative of 0*k - 1/120*k**5 + 1/48*k**4 + 0 + 0*k**3 + 2*k**2. Find s, given that j(s) = 0.
0, 1
Let y(w) be the first derivative of -4*w**3/3 - 3*w**2 + 1. Let q(n) = n**2 + n. Let j(v) = -6*q(v) - y(v). Determine x so that j(x) = 0.
0
Let y(v) be the second derivative of 3*v**5/100 + v**4/10 - 39*v. Factor y(a).
3*a**2*(a + 2)/5
Suppose 0 = -30*o + 31*o. Factor 1/4*j**2 + o + 1/2*j.
j*(j + 2)/4
Let b(r) be the second derivative of -r**5/40 + r**4/8 - r**2 + 4*r. Factor b(j).
-(j - 2)**2*(j + 1)/2
Factor 12/5 + 7/5*n**3 - 8*n - 9/5*n**2.
(n - 3)*(n + 2)*(7*n - 2)/5
Solve 7/3*k**2 - 4 + 8/3*k - 2/3*k**3 - 1/3*k**4 = 0.
-3, -2, 1, 2
Let t be ((-33)/5)/(-3) + -1. Let x be 3*2/(-30)*-3. Factor -x*a**2 + 0 - t*a.
-3*a*(a + 2)/5
Suppose -2*b + 5*f + 18 = 0, 3*b - f = -3*f + 27. Factor 2*p**2 + b - 41 + 16*p - 4*p**2.
-2*(p - 4)**2
Let s be (-3 + -2 - -4) + (-28)/(-8). Suppose n + 0 + s*n**2 = 0. Calculate n.
-2/5, 0
Let l(b) be the third derivative of -b**9/90720 + b**5/20 - 6*b**2. Let o(m) be the third derivative of l(m). Factor o(f).
-2*f**3/3
Let x be ((-1)/4)/(5/(-35)). Suppose p + 2*o + 0*o = 4, 2*o = -3*p + 4. Suppose -1/2*s + p + x*s**2 = 0. What is s?
0, 2/7
Let d be 2/(-9) - (-10)/45. Let k(p) be the first derivative of -4 + d*p - 2/15*p**3 + 1/5*p**2. Determine l so that k(l) = 0.
0, 1
Let m(q) be the third derivative of -q**5/360 + q**4/144 + q**3/18 - 10*q**2. Factor m(u).
-(u - 2)*(u + 1)/6
Let b(v) be the first derivative of v**4/4 - v**3/3 - 5*v**2/2 - 2*v - 2. Let c be b(4). Factor -c*t**4 - 30*t**3 - 2*t - 5*t**5 - 14*t**2 + 0*t - 3*t**5.
-2*t*(t + 1)**3*(4*t + 1)
Suppose 0 = -4*d - 5*o - 45, 34 = -5*d - 2*o - 1. Let f(n) = 4*n**2 - n + 7. Let k(w) = -3*w**2 + w - 5. Let i(r) = d*f(r) - 7*k(r). Factor i(l).
l*(l - 2)
Let x = -8 - -16. Suppose -2*h + x = 2*h. Factor -4 - 2*g - 7*g**4 + h*g**3 + 4 + 7*g**2.
-g*(g - 1)*(g + 1)*(7*g - 2)
Let v(k) be the second derivative of 0*k**3 + 3/20*k**5 + 0*k**4 + 7*k + 0 + 0*k**2 + 1/5*k**6 + 1/14*k**7. Factor v(g).
3*g**3*(g + 1)**2
Let h(q) be the third derivative of q**5/20 + q**4/4 + q**3/2 + 3*q**2. Factor h(o).
3*(o + 1)**2
Let f(v) be the third derivative of 0 + 7*v**2 + 0*v - 1/20*v**5 + 1/24*v**4 - 1/210*v**7 + 1/40*v**6 + 0*v**3. Factor f(s).
-s*(s - 1)**3
Let f be (685 - -2)*(-7)/(-63). Let d = 1021/12 - f. Factor d*m**4 - m**2 + 0 + 0*m + m**3.
m**2*(5*m + 2)*(7*m - 2)/4
Suppose -5*o + 10*o = 0. Let f be (-2)/10 - 69/(-45). Factor 0*n**2 - f*n**4 + n**5 + 0 + 1/3*n**3 + o*n.
n**3*(n - 1)*(3*n - 1)/3
Let p(c) = 6*c**5 - 24*c**4 + 28*c**3 - 12*c**2 + 2*c. Let u(m) = m**5 + m**4 - m**3 - m**2. Let x(w) = 2*p(w) + 2*u(w). Factor x(d).
2*d*(d - 1)**3*(7*d - 2)
Let k(v) be the first derivative of -2*v**5/55 - 3*v**4/11 - 26*v**3/33 - 12*v**2/11 - 8*v/11 - 3. Factor k(m).
-2*(m + 1)**2*(m + 2)**2/11
Let a = -655/9 - -73. Factor 4/9*c**2 - 2/9*c**3 + 0 - a*c.
-2*c*(c - 1)**2/9
Suppose -7*s + 9 = -4*s. Let z(i) be the third derivative of 0*i + 0*i**4 + 0 + 0*i**s + 1/30*i**5 + i**2. Factor z(j).
2*j**2
Let v be 6 + (-2)/3*3. Determine x, given that 9*x**5 + 3*x - 12*x**5 + 2*x**2 + 4*x**3 - 4*x - 2*x**v = 0.
-1, 0, 1/3, 1
Suppose -59*u = -64*u. Factor 0*p - 1/5*p**4 + 0*p**3 + u + 4/5*p**2.
-p**2*(p - 2)*(p + 2)/5
Let n be (-54)/(-4) - (-3)/6. Let o be 4/14 + 52/n. Find v, given that 2*v**4 - 4*v**5 + 2*v**5 - o*v**4 = 0.
-1, 0
Let c(r) = r**2 - 1. Let x(d) = -3*d**4 + 45*d**3 - 183*d**2 + 147*d - 6. Let s(a) = -6*c(a) + x(a). Let s(b) = 0. What is b?
0, 1, 7
Let u(s) = s**3 - 12*s**2 - s + 15. Let p be u(12). Factor 3*l**2 + 4*l**3 - 4*l**2 - 5*l**p.
-l**2*(l + 1)
Factor 4/3*c**4 + 8/3 + 20/3*c**3 + 12*c**2 + 28/3*c.
4*(c + 1)**3*(c + 2)/3
Let y = 3 + -4. Let g(s) = -s**4 - s**3 - s**2 + s - 1. Let n(i) = 2*i**5 - 6*i**4 - 2*i**3 - 3*i**2 + 3*i - 3. Let l(c) = y*n(c) + 3*g(c). Factor l(r).
-r**3*(r - 1)*(2*r - 1)
Find q, given that -2/5*q**2 + 0*q - 6/5*q**4 + 6/5*q**3 + 2/5*q**5 + 0 = 0.
0, 1
Suppose -5*w**3 - 42 + 3*w + 2*w + 32 + 10*w = 0. What is w?
-2, 1
Let k(n) be the third derivative of n**8/3360 - n**7/420 + n**6/180 - 5*n**4/24 - 3*n**2. Let y(c) be the second derivative of k(c). Factor y(a).
2*a*(a - 2)*(a - 1)
Let u(p) = -21*p**2 + 15*p + 24. Let 