(g) be the second derivative of -g**6/55 - 6*g**5/55 - 3*g**4/11 - 4*g**3/11 - 3*g**2/11 - g. Factor h(j).
-6*(j + 1)**4/11
Let d(t) = -t**2 + 12*t + 1. Let m be d(15). Let b be m/(-30) + 4/(-5). Factor 0*r**2 - 2/3*r**3 + b*r + 0.
-2*r*(r - 1)*(r + 1)/3
Factor 0*n + 0*n**2 + 4/5*n**3 + 4/5*n**4 + 0.
4*n**3*(n + 1)/5
Suppose -5*x + 16 = -x. Let r = 4 - x. Solve 3*j**4 + r*j**4 + 4*j**2 - 5*j**4 - 2 = 0.
-1, 1
Suppose l - 3*p - 4 = 0, 4*l - 2*p - 19 = l. Factor 2*u**2 - l*u**2 + 4*u - 2 + 2*u**2 + 3*u.
-(u - 2)*(3*u - 1)
Factor 0 + 2/7*h**3 + 0*h + 2/7*h**2 - 2/7*h**4 - 2/7*h**5.
-2*h**2*(h - 1)*(h + 1)**2/7
Factor 0*k**2 - k + 1/3*k**3 - 2/3.
(k - 2)*(k + 1)**2/3
Let b(g) be the third derivative of 5/9*g**4 - 13/90*g**5 + 0 - 1/15*g**6 + 2*g**2 + 0*g - 4/9*g**3. Solve b(m) = 0 for m.
-2, 1/4, 2/3
Let j be -3 + 0 + (4 - (-15)/(-20)). Solve -1/4*a - 1/4*a**2 + 1/4*a**4 + 0 + j*a**3 = 0 for a.
-1, 0, 1
Factor 33/2*q**3 - 6*q**4 - 18*q**2 + 27/4*q + 3/4*q**5 + 0.
3*q*(q - 3)**2*(q - 1)**2/4
Let o(m) be the first derivative of -m**6/8 - 3*m**5/10 + m**3/2 + 3*m**2/8 + 9. Let o(w) = 0. Calculate w.
-1, 0, 1
Let t(q) be the third derivative of -1/30*q**5 + 0 + 0*q + 2*q**2 + 0*q**3 - 1/120*q**6 - 1/24*q**4. Determine b so that t(b) = 0.
-1, 0
Let u be 66/10 + (-15)/25. Let s be ((-12)/(-8))/(u/8). Factor -1/2 - 3/2*v + s*v**3 + 0*v**2.
(v - 1)*(2*v + 1)**2/2
Let m(w) be the first derivative of 3/2*w**2 + 4 + 0*w - 2*w**3 + 3/4*w**4. Let m(s) = 0. Calculate s.
0, 1
Let q be (-2 - 25/(-8))/(9/6). Factor q*v**2 + 0 + 3/4*v.
3*v*(v + 1)/4
Let o be 2/(-15)*3/36*-10. Let b(r) be the first derivative of o*r**3 + 0*r - 3 + 1/3*r**2. Determine a so that b(a) = 0.
-2, 0
Suppose 165 = 3*j + 2*j. Let w(r) = -81*r**2 - 15*r + 63. Let a(z) = 5*z**2 + z - 4. Let t(n) = j*a(n) + 2*w(n). Solve t(d) = 0.
-2, 1
Factor -5/4 - 1/4*j**2 - 3/2*j.
-(j + 1)*(j + 5)/4
Factor 0*i - 2/3*i**3 + 0 + 2/3*i**2.
-2*i**2*(i - 1)/3
Let q(k) be the second derivative of -7*k**8/360 - k**7/45 - k**6/135 - k**3/6 + k. Let m(h) be the second derivative of q(h). Find d, given that m(d) = 0.
-2/7, 0
Solve 0 - 3/2*t**2 - 15/2*t = 0.
-5, 0
Let b(n) be the first derivative of -1/15*n**3 - 1 + 1/5*n - 1/20*n**4 + 1/10*n**2. Factor b(t).
-(t - 1)*(t + 1)**2/5
Let j be (-2)/6 + 6/18. Factor -2/7*t**3 + 0*t**4 + j + 2/7*t**5 + 0*t**2 + 0*t.
2*t**3*(t - 1)*(t + 1)/7
Let h(m) = -6*m**2 + 7*m + 12. Let o(b) = -b**2 + b + 2. Let s(c) = 6*h(c) - 39*o(c). Solve s(r) = 0.
-2, 1
Let s = 153/286 - 5/143. Factor 0 + 1/2*g**2 - s*g.
g*(g - 1)/2
Suppose -2*g = 3*g - 20. Factor 0*q**2 - 8*q**2 - 5*q**3 + 0*q**g - q**4 - 4*q.
-q*(q + 1)*(q + 2)**2
Solve -3*u**3 - 33*u**2 + 14*u + 30*u**2 - 2*u + 12 = 0 for u.
-2, -1, 2
Let f(w) = -230*w**3 - 110*w**2 + 210*w + 155. Let l(r) = -21*r**3 - 10*r**2 + 19*r + 14. Let k(u) = -6*f(u) + 65*l(u). Factor k(p).
5*(p + 1)**2*(3*p - 4)
Let r(j) be the second derivative of 0*j**2 + 1/42*j**7 + 0 + 1/20*j**6 + 0*j**3 + 0*j**5 - 1/24*j**4 - 7*j. Find v such that r(v) = 0.
-1, 0, 1/2
Let v(l) be the first derivative of -l**4/12 - 4*l**3/9 - 5*l**2/6 - 2*l/3 - 27. Factor v(b).
-(b + 1)**2*(b + 2)/3
Let f(i) = -i**4 - 1. Let d(y) = 4*y**5 - 2*y**4 - 8*y**3 + 8*y**2 + 4*y - 2. Let n(r) = d(r) + 2*f(r). Factor n(b).
4*(b - 1)**3*(b + 1)**2
Let w(m) be the first derivative of -4*m**3/15 + 6*m**2/5 - 8*m/5 - 8. Find p, given that w(p) = 0.
1, 2
Suppose 0*h - 2*t - 14 = -2*h, 3*t + 1 = -h. Factor 1/2*x - 1/2*x**4 + 1/2*x**h - x**3 - 1/2 + x**2.
(x - 1)**3*(x + 1)**2/2
Let x(d) = -d**2 - 11*d - 10. Let h be x(-6). Suppose -17*n + h*n - 9 = 0. Factor -1/2*f**n + 1 + 3/2*f + 0*f**2.
-(f - 2)*(f + 1)**2/2
Suppose -w**2 + 13*w + 3*w**2 - 20 + 7*w - 7*w**2 = 0. What is w?
2
Find c such that 26/9*c**3 + 4/3*c**4 + 8/9*c + 0 + 8/3*c**2 + 2/9*c**5 = 0.
-2, -1, 0
Let k = -195/8 + 1007/40. Factor -2/5*a - k + 2/5*a**2.
2*(a - 2)*(a + 1)/5
Let o(d) be the second derivative of -d**6/6 + 5*d**4/4 + 5*d**3/3 - 2*d. Factor o(v).
-5*v*(v - 2)*(v + 1)**2
Let g(v) be the first derivative of 2*v**5/45 - 7*v**4/18 + 4*v**3/3 - 20*v**2/9 + 16*v/9 - 2. Factor g(l).
2*(l - 2)**3*(l - 1)/9
Let r(f) be the first derivative of -16/7*f**2 - 8/7*f - 10/7*f**3 - 2. Determine t, given that r(t) = 0.
-2/3, -2/5
Suppose 75*t = -4*t + 11*t. Let -2/17*s**3 - 2/17*s + t - 4/17*s**2 = 0. What is s?
-1, 0
Let u(i) = -3*i**3 + 13*i**2 + 15*i + 9. Let t(a) = 5*a**3 - 20*a**2 - 23*a - 14. Let p(g) = 5*t(g) + 8*u(g). Let p(z) = 0. Calculate z.
-2, -1
Let p(j) be the second derivative of -11*j + 0 + 0*j**2 - 1/3*j**4 + 1/5*j**5 + 0*j**3. Factor p(t).
4*t**2*(t - 1)
Let k = 55 + -55. Solve k + 2/3*a + 2/3*a**2 = 0.
-1, 0
Let s(n) be the first derivative of 9*n**6/8 - 36*n**5/5 + 219*n**4/16 - 3*n**3/2 - 27*n**2/2 - 6*n - 3. Factor s(y).
3*(y - 2)**3*(3*y + 1)**2/4
Let k = -11 - -13. Factor 3*z**3 + 4 + 13*z**k + 4*z**2 + 16*z + 2*z**3.
(z + 1)*(z + 2)*(5*z + 2)
Let s(q) be the first derivative of q**8/336 + q**7/210 - q**6/60 - 7*q**2/2 + 1. Let u(v) be the second derivative of s(v). Let u(y) = 0. Calculate y.
-2, 0, 1
Let h(z) be the first derivative of 1/5*z**5 + 0*z**2 + 2 + 0*z**3 + 0*z - 1/4*z**4. Factor h(f).
f**3*(f - 1)
Let g**2 - 8*g**2 + 4*g**2 - 3*g**3 = 0. What is g?
-1, 0
Factor 9/7*u**2 + 24/7*u + 12/7.
3*(u + 2)*(3*u + 2)/7
Let k(j) = -j**3 - 10*j**2 - j - 12. Let m be k(-10). Let g(d) = -2*d - 2. Let x be g(m). Factor -3*b**3 - 1/2*b**5 - 1/2*b + x*b**2 + 0 + 2*b**4.
-b*(b - 1)**4/2
Let w(t) = t**3 - 4*t**2 + 2*t + 3. Suppose -5*u = -8 - 7. Let y be w(u). Suppose -1/5*d + y*d**3 + 1/5*d**5 - 2/5*d**2 + 0 + 2/5*d**4 = 0. Calculate d.
-1, 0, 1
Let r(k) = 4*k**4 + 21*k**3 + 9*k**2 - 25*k - 9. Let y(x) = x**4 + 5*x**3 + 2*x**2 - 6*x - 2. Let a(v) = -4*r(v) + 18*y(v). Factor a(u).
2*u*(u - 1)*(u + 2)**2
Let n(m) be the third derivative of -m**7/7560 - m**6/720 - m**5/180 + m**4/8 + 2*m**2. Let k(g) be the second derivative of n(g). Factor k(v).
-(v + 1)*(v + 2)/3
Let y(c) be the second derivative of 0 + 2/9*c**3 + 1/18*c**4 + c + 1/3*c**2. Factor y(b).
2*(b + 1)**2/3
Let i(v) be the third derivative of v**8/84 - 2*v**7/21 + v**6/10 + 3*v**5/5 + 27*v**2. Let i(f) = 0. What is f?
-1, 0, 3
Factor 0 - 2*r**2 + 2/3*r**3 + 0*r.
2*r**2*(r - 3)/3
Let u be 9/(-18)*(1 - 1). Let o(v) be the third derivative of -1/12*v**4 + u - 2/3*v**3 + 1/30*v**5 + 0*v + 2*v**2. Factor o(s).
2*(s - 2)*(s + 1)
Let -6/7*t**2 + 2*t**3 + 4/7 - 6/7*t - 6/7*t**4 = 0. Calculate t.
-2/3, 1
Let l be (-2)/17 + 210/51. Solve 32*x - 13 - 28*x**3 + 3 + 20*x**l - 4*x**2 - 3 - 3 - 4*x**5 = 0 for x.
-1, 1, 2
Let u(o) be the third derivative of -o**5/240 - 4*o**2 - 2*o. Factor u(z).
-z**2/4
Let h(u) = -12*u**5 + 3*u**3 - 9*u**2 - 9. Let y(m) = 3*m**5 - m**3 + 2*m**2 + 2. Let v(j) = -2*h(j) - 9*y(j). What is w in v(w) = 0?
-1, 0, 1
Suppose 4*c - v = -37 + 10, -4*v + 6 = c. Let k be ((-2)/c)/((-4)/(-12)). Factor -3 + n**2 + k - 2*n**2 - 3*n.
-(n + 1)*(n + 2)
Suppose 17*u = -7*u. Factor o**2 - 1/2*o - 1/2*o**3 + u.
-o*(o - 1)**2/2
Let x(z) = 4*z**2 + 10*z + 1. Let m = -20 + 13. Let n(t) = -8*t**2 - 21*t - 3. Let r(w) = m*x(w) - 3*n(w). Factor r(b).
-(b + 2)*(4*b - 1)
Solve -2*u**4 - 6*u + 13 + 7*u**3 - u**3 - 9 - 2*u**2 = 0 for u.
-1, 1, 2
Let -676/5 + 104/5*j - 4/5*j**2 = 0. Calculate j.
13
Let w be 2/(-15)*42/12. Let m = 11/5 - w. Let 16/3*v**2 + 2/3 + m*v**3 + 10/3*v = 0. What is v?
-1, -1/2
Let j be (-3)/15 + (129/45 - 2). Suppose -j*w**2 + 0*w + w**3 + 5/3*w**4 + 0 = 0. Calculate w.
-1, 0, 2/5
Let a(r) be the third derivative of r**7/1050 + r**6/200 + r**5/100 + r**4/120 - 5*r**2. Solve a(l) = 0.
-1, 0
Solve -4/7*g**3 + 2/7*g**2 + 0*g + 0 - 2/7*g**4 + 4/7*g**5 = 0 for g.
-1, 0, 1/2, 1
Suppose 5 - 26 = 3*p. Let g(m) = m**3 + 7*m**2 + 2. Let q be g(p). Suppose 0 - 9/5*x**3 + 0*x**q + 12/5*x - 3/5*x**4 = 0. Calculate x.
-2, 0, 1
Let t(c) be the first derivative of -2 - 1/12*c**3 + 3/8*c**2 - 3/16*c**4 + 1/4*c. Factor t(k).
-(k - 1)*(k + 1)*(3*k + 1)/4
Let u(q) = 5*q**2 + 3*q - 17. Let o(g) = 15*g**2 + 8*g - 52. Let w(m) = -3*o(m) + 8*u(m). Solve w(c) = 0 for c.
-2, 2
Let s be 33/77 - (-15)/63. Determine g so that 5/3*g**3 + 7/3*g + 3*g**2 + s + 1/3*g**4 = 0.
-2, -1
Let w(u) be the second derivative of u**7/210 - u**6/75 + u**5/100 - 25*u. Factor w(c).
c**3*(