rd derivative of -t**6/720 + t**4/144 + 5*t**2. Factor x(v).
-v*(v - 1)*(v + 1)/6
Let a(c) be the third derivative of c**6/40 - c**5/20 - c**4/4 + 2*c**2. Factor a(m).
3*m*(m - 2)*(m + 1)
Let c(l) be the first derivative of -l**7/42 + l**5/10 - l**3/6 - 2*l + 3. Let t(m) be the first derivative of c(m). Factor t(a).
-a*(a - 1)**2*(a + 1)**2
Let l(f) be the second derivative of f**4/3 - 2*f**3/3 - 4*f**2 - 20*f. Factor l(j).
4*(j - 2)*(j + 1)
Factor -9*v + 48*v - 6*v**2 - 6 - 24*v.
-3*(v - 2)*(2*v - 1)
Let f(i) be the first derivative of i**6/11 - 14*i**5/55 + 3*i**4/22 + 2*i**3/11 - 2*i**2/11 + 10. Factor f(g).
2*g*(g - 1)**3*(3*g + 2)/11
Let x(o) be the third derivative of 0*o + 3/112*o**8 + 0 + 3/35*o**7 + 1/9*o**3 + 1/20*o**6 - 4/45*o**5 - 5/72*o**4 - 2*o**2. What is z in x(z) = 0?
-1, -2/3, 1/3
Let v(h) be the third derivative of 5*h**8/336 + h**7/14 - h**6/24 - 7*h**5/12 + 10*h**3/3 + 49*h**2. Find k, given that v(k) = 0.
-2, -1, 1
Let i(s) be the first derivative of 0*s - 1/30*s**5 - 1/3*s**4 - 1 - 4/3*s**3 - s**2. Let l(v) be the second derivative of i(v). Factor l(p).
-2*(p + 2)**2
Let y be (-7)/(-4) + -3 + 2. Let d be (8/(-3))/((-6)/9). Suppose 3/4*x**d - 1/4*x**5 - 1/4 - 1/2*x**2 - 1/2*x**3 + y*x = 0. What is x?
-1, 1
Let t be 1/(-2) - 13/2. Let d be (-12)/8*(t - -1). Factor f**4 - d*f - f**2 + 9*f - f**3 + f**5.
f**2*(f - 1)*(f + 1)**2
Factor 6*n**2 - 3 - 12*n**2 + 7*n**2 + 2*n**2.
3*(n - 1)*(n + 1)
Let j(c) be the first derivative of c**6/6 - c**5/5 - c**4/4 + c**3/3 + 11. Let j(m) = 0. What is m?
-1, 0, 1
Let n = 4 + -3. Suppose n - 5 = -2*a. Factor r - 4 - 4*r - 6*r - 6*r**a - r.
-2*(r + 1)*(3*r + 2)
Factor 2*z**3 + 89*z - z**4 - 90*z + z**4 - z**5.
-z*(z - 1)**2*(z + 1)**2
Let d(q) be the second derivative of q**6/40 + q**5/15 + q**4/24 + q**2 + 2*q. Let p(b) be the first derivative of d(b). Factor p(c).
c*(c + 1)*(3*c + 1)
Let v(g) be the third derivative of -1/108*g**4 + 0 + 0*g - 5*g**2 - 1/270*g**5 + 1/27*g**3 + 1/540*g**6. Suppose v(y) = 0. Calculate y.
-1, 1
Let q(v) be the first derivative of 2*v**3/3 - 8*v - 11. Factor q(x).
2*(x - 2)*(x + 2)
Suppose 0 = -3*s, 4*s + 20 = 4*x - 0*s. Let 2/7*z**3 - 4/7*z**4 + 2/7*z**x + 0*z**2 + 0*z + 0 = 0. What is z?
0, 1
Let r(m) be the third derivative of m**10/604800 - m**9/120960 - m**5/30 + 3*m**2. Let u(y) be the third derivative of r(y). Factor u(b).
b**3*(b - 2)/4
Let c(y) be the third derivative of y**5/90 - y**4/18 + y**3/9 + 11*y**2. Determine b so that c(b) = 0.
1
Let y(r) be the second derivative of -2*r**6/135 + r**5/9 - 8*r**4/27 + 8*r**3/27 - 12*r - 1. Find t such that y(t) = 0.
0, 1, 2
Let r = -29 - -20. Let v(u) = -5*u**2 - 21*u + 8. Let s(q) = q**2 + 5*q - 2. Let d(w) = r*s(w) - 2*v(w). Let d(y) = 0. What is y?
1, 2
Let x(g) be the second derivative of g**6/30 + 4*g**5/15 + 5*g**4/6 + 4*g**3/3 + 5*g**2/2 - 7*g. Let p(i) be the first derivative of x(i). Factor p(j).
4*(j + 1)**2*(j + 2)
Let g(n) = 8*n**4 - 26*n**3 + 12*n + 20. Let p(m) = -5*m**3 + 4*m - 23 - 4*m**3 + 3*m**4 + 30. Let t(d) = -5*g(d) + 14*p(d). Determine z so that t(z) = 0.
-1, 1
Suppose 1 = -2*g + 11. Let d(b) = b - 3. Let h be d(g). Factor -3*v**h - 3*v**2 - 3*v + v + 7*v**2.
v*(v - 2)
Let x(b) = 4*b**3 + 6*b**2 + 2*b - 5. Let l = -11 + 16. Let t(c) = 3*c**3 + 6*c**2 + 3*c - 6. Let n(h) = l*t(h) - 6*x(h). Factor n(s).
-3*s*(s + 1)*(3*s - 1)
Let o be (6/(-4))/((-5)/10). Suppose -4*a + 2 + 6 = 0. Solve -5*z - 2*z**o + 3*z + 3*z**a + z**2 = 0 for z.
0, 1
Factor 3*w**3 - 4*w**2 + 0*w + 8*w - 8*w**2 + 4*w.
3*w*(w - 2)**2
Factor 2*r**4 - 47*r**3 - 2*r**2 + 47*r**3.
2*r**2*(r - 1)*(r + 1)
Suppose 0 = -6*p + 5*p - c, -2*c + 6 = 0. Let b = p - -5. Solve -b*t + 5 - 4*t - 1 + 2*t**2 = 0 for t.
1, 2
Find k, given that 3/2*k**4 + 5/2*k**2 + 1/2*k + 0 + 7/2*k**3 = 0.
-1, -1/3, 0
Let w be 4/(-1)*(-1)/(-2)*-2. Let t(b) be the second derivative of 0 - 1/60*b**w + 1/10*b**2 + 1/30*b**3 + 4*b - 1/100*b**5. Factor t(f).
-(f - 1)*(f + 1)**2/5
Let v(s) be the third derivative of 7*s**7/6 - 7*s**6 + 22*s**5/3 + 20*s**4 + 40*s**3/3 + 11*s**2. Determine p so that v(p) = 0.
-2/7, 2
Let t(f) = f**2 + 9*f - 10. Let s = -5 + -5. Let q be t(s). Factor -2*i**5 + 5*i**2 - i**2 - 6*i**4 + q*i**2 + 2*i + 2*i**4.
-2*i*(i - 1)*(i + 1)**3
Let a(s) be the second derivative of -s**7/105 + s**6/30 - s**5/30 - 3*s**2 - s. Let i(x) be the first derivative of a(x). Factor i(v).
-2*v**2*(v - 1)**2
Factor 1/3 - 1/2*r + 1/6*r**2.
(r - 2)*(r - 1)/6
Let x(d) be the third derivative of -d**6/40 + d**5/10 + 3*d**4/8 - 11*d**2. Factor x(p).
-3*p*(p - 3)*(p + 1)
Let g be (-16)/12 + 5 + (-212)/84. Factor -10/7*m**2 + 2/7*m**3 + 16/7*m - g.
2*(m - 2)**2*(m - 1)/7
Factor 32/3*a**3 - 10*a + 4/3 + 16*a**2.
2*(a + 2)*(4*a - 1)**2/3
Let d = 77 + -77. Let f(z) be the first derivative of 1/3*z - 1/9*z**3 + 1 + d*z**2. Factor f(q).
-(q - 1)*(q + 1)/3
Suppose -3*r = -2*r. Factor -3*c + 3*c + c**4 - c**2 + r*c**2.
c**2*(c - 1)*(c + 1)
Let c(i) = i**2 - 4*i + 8. Let z be c(2). Find b, given that 0*b - 1/2*b**z + 1/2*b**2 + 0 + 0*b**3 = 0.
-1, 0, 1
Suppose -11*d + 5*d = 0. Let x(g) be the third derivative of d*g + 0 - 2/3*g**3 + 1/4*g**4 - g**2 - 1/30*g**5. Determine k, given that x(k) = 0.
1, 2
Let n = 0 + -1. Let q be -3 - (3 + 2)/n. Factor q*k**5 - 5*k**5 + 2*k - 4*k**3 + 2*k**5 + 3*k**5.
2*k*(k - 1)**2*(k + 1)**2
Let g be (-2)/(-4)*4 - -3. Suppose -5*m = -3*u - 2 + 3, g*u - m - 9 = 0. Factor 2/9*j**u + 4/9 + 2/3*j.
2*(j + 1)*(j + 2)/9
Factor 18 + 5*g - 91*g**2 - 32*g - 4*g**4 - 3*g**4 - 6*g - 47*g**3.
-(g + 1)*(g + 3)**2*(7*g - 2)
Let x(d) be the third derivative of d**6/600 - d**5/100 - d**4/120 + d**3/10 + 2*d**2. Factor x(k).
(k - 3)*(k - 1)*(k + 1)/5
Let v = -196 + 196. Let j be ((-9)/(-12))/(1/2). Factor -1/2*t**5 + j*t**4 + v*t - 3/2*t**3 + 0 + 1/2*t**2.
-t**2*(t - 1)**3/2
Let f(y) = 11*y + 24. Let m be f(-2). Factor 1/4*u**5 + 1/2 + 7/2*u**3 + 4*u**m + 9/4*u + 3/2*u**4.
(u + 1)**4*(u + 2)/4
Let a(v) be the third derivative of -v**6/120 + v**5/15 - v**4/8 + v**3/3 - 2*v**2. Let q be a(3). Factor 2 + p**3 - q.
p**3
Let b(t) = -t**2 + 2. Let m(z) = 4*z**2 - 9. Let y be 86/(-10) - 6/15. Let q(g) = y*b(g) - 2*m(g). Factor q(p).
p**2
Let l be (-3)/5 - (-140)/25. Let f(a) = -a**3 + 6*a**2 - 6*a + 5. Let p be f(l). Factor -2/7*s**5 + 0*s + p*s**2 + 0 + 0*s**4 + 2/7*s**3.
-2*s**3*(s - 1)*(s + 1)/7
Let w be (3/(-12))/(1 - 11/8). Suppose 0*v + w*v**4 - 4/3*v**3 + 0 + 0*v**2 + 2/3*v**5 = 0. What is v?
-2, 0, 1
Let f be (-2)/(-5) + 294/15. Let s = -17 + f. Factor -s*q**4 + 36/5*q**3 + 0 - 27/5*q**2 + 6/5*q.
-3*q*(q - 1)**2*(5*q - 2)/5
Let k(s) = -4*s**2 + 2*s - 2. Let g(h) = 3*h**2 - h + 2. Let w(c) = 3*g(c) + 2*k(c). Let b be w(-1). Factor 2*d**3 - 2*d**4 + d**b + 1 + 1/2*d**5 - 5/2*d.
(d - 2)*(d - 1)**3*(d + 1)/2
Let l(j) be the first derivative of j**6/2 - 9*j**5/5 + 3*j**4/2 - 20. Solve l(k) = 0.
0, 1, 2
Let g be 4*(-1)/(-2) - 0. Find o, given that 4*o**2 + 2*o - 3 + 5 - 3*o**g - 1 = 0.
-1
Suppose 0 = 5*w + 20, -3*r + 2*r + 21 = -4*w. Let a be (-3 + 0)/((-1)/r). Let -9*m**2 + a*m**4 - 6*m + 35*m**4 + 57*m**2 - 2*m - 90*m**3 = 0. What is m?
0, 2/5, 1
Find l such that -1/5*l**4 + 0*l**2 - 2/5*l**5 + 0 + 1/5*l**3 + 0*l = 0.
-1, 0, 1/2
Let z(b) be the second derivative of -b**6/165 + b**5/55 - b**4/66 + 16*b. Factor z(d).
-2*d**2*(d - 1)**2/11
Suppose 0 = -5*w + 3*n - n - 1, -3*n = w - 10. Suppose -5*t + w = -9. Suppose -3*o**2 + o**t + o**2 + o = 0. What is o?
0, 1
Let o(j) be the third derivative of j**7/315 - j**5/90 - 2*j**2 - 58. Factor o(r).
2*r**2*(r - 1)*(r + 1)/3
Determine o so that 2*o**3 - 6*o**3 + 6*o**3 + 6*o**2 = 0.
-3, 0
Suppose -2*n - 9*n = -55. Let -50*g**n - 976/5*g**2 - 288/5*g - 210*g**4 - 32/5 - 304*g**3 = 0. What is g?
-2, -1, -2/5
Let t(o) be the first derivative of o**4/16 - o**3/8 - 3*o**2/4 - 3*o + 1. Let v(k) be the first derivative of t(k). Suppose v(x) = 0. What is x?
-1, 2
Let r(g) = -g**3 - 4*g**2 + 6*g + 7. Let p be r(-5). Determine l, given that 4*l**p + 128*l**4 - 33*l**3 + 15*l**2 - 63*l**3 - 2*l + 5*l**2 = 0.
0, 1/4
Let x(d) be the third derivative of -d**7/105 + d**5/30 + 6*d**2. Factor x(c).
-2*c**2*(c - 1)*(c + 1)
Let p(m) be the first derivative of 2*m**6/15 - 3*m**5/10 + m**4/48 + m**3/4 + m**2/8 + 3*m - 1. Let y(c) be the f