t**5/30 - t**4/3 + 4*t**3/3 + 3*t**2/2 + 3. Let y(v) be the second derivative of s(v). Suppose y(o) = 0. Calculate o.
2
Let k be (-3 - (-1 - -1))*-1. Let b = k - 1. Suppose 2/7*u - 2/7*u**b + 2/7 - 2/7*u**3 = 0. What is u?
-1, 1
Let g(c) be the second derivative of c**6/40 - 3*c**5/40 + c**4/16 + 6*c. Factor g(j).
3*j**2*(j - 1)**2/4
Let q(s) be the first derivative of 0*s**5 + 0*s**3 - 1/120*s**6 - 1/210*s**7 + 0*s**4 - 1 + 0*s + s**2. Let h(m) be the second derivative of q(m). Factor h(j).
-j**3*(j + 1)
Let f(p) = -2*p**3 + 23*p**2 - 29*p - 7. Let u be f(10). Factor 21/2*k**u + 3/4*k**5 - 3/2 + 27/4*k - 9/2*k**4 - 12*k**2.
3*(k - 2)*(k - 1)**4/4
Let o = -163/3 - -55. Factor -4*f**2 - o*f**4 - 8/3*f**3 - 8/3*f - 2/3.
-2*(f + 1)**4/3
Let z(g) be the third derivative of g**5/120 + g**4/16 + g**3/6 + 26*g**2. Factor z(u).
(u + 1)*(u + 2)/2
Let m = -12 + 16. Factor 6*g**3 - g**4 - g**4 - 8*g**m + 7*g**4.
-3*g**3*(g - 2)
Let c(o) be the third derivative of o**8/1344 + o**7/210 + o**6/120 - 7*o**2. Factor c(a).
a**3*(a + 2)**2/4
Suppose 15 = -5*m + 10*m. Suppose -4 = m*l - 13. Find z, given that -2/3*z**2 + 0 - 2/3*z**4 - 4/3*z**l + 0*z = 0.
-1, 0
Let b(u) = u**2 + u + 1. Let l(x) = 14*x**2 + 16*x + 12. Let c(r) = -12*b(r) + l(r). Factor c(q).
2*q*(q + 2)
Let v(d) = -2*d**2 + 4*d + 2. Let a be 2/(-4) - 6/12. Suppose i = -3 - 1. Let o(y) = -y. Let m(z) = a*v(z) + i*o(z). Determine j so that m(j) = 0.
-1, 1
Let l(p) = -p**2 + 2*p + 3. Let j be l(5). Let c be 6/20*(-10)/j. Solve 0*y - y**3 + c*y**2 + 0 = 0 for y.
0, 1/4
Let l be (-549)/(-30) + (-3)/2. Let 12/5*v + 0 + 15*v**5 + 42*v**4 + l*v**2 + 207/5*v**3 = 0. Calculate v.
-1, -2/5, 0
Let w be (-1 - -3)/(1/2). Let s = -1 + 3. Find r, given that w*r - r**s + 0*r**2 - 3*r = 0.
0, 1
Suppose f + 5*f = 18. Factor -1/4*m + 1/4 + 1/4*m**4 - 1/2*m**2 - 1/4*m**5 + 1/2*m**f.
-(m - 1)**3*(m + 1)**2/4
Factor 4/9*j**3 - 2/9*j + 0 - 2/9*j**5 + 0*j**4 + 0*j**2.
-2*j*(j - 1)**2*(j + 1)**2/9
Factor 0 - 42/5*x - 3/5*x**2.
-3*x*(x + 14)/5
Let v = 0 + 1. Let x be 4 + (v - -2) + -4. Solve 14/3*d - 4/3 + 10/3*d**2 - 8/3*d**x = 0.
-1, 1/4, 2
Let m(r) be the first derivative of r**5/50 + 3*r**4/40 + r**3/10 + r**2/20 + 3. Factor m(w).
w*(w + 1)**3/10
Suppose -4*f - 846 = -7*f. Let i = f + -2534/9. Factor -2*a**4 - 8/3*a**3 - 2/9 + 8/9*a + i*a**2.
-2*(a + 1)**2*(3*a - 1)**2/9
Factor -5 + 5 - 3*t**2 - 9 - 14*t + 2*t.
-3*(t + 1)*(t + 3)
Suppose -5*x + 5 = 5. Factor x + 1/2*q**2 - q.
q*(q - 2)/2
Let v be 2 + (-3 + 4)*-31. Let w = -115/4 - v. Factor 0 + w*o**2 + 0*o.
o**2/4
Let f(g) be the second derivative of 0 + 0*g**3 + 1/18*g**4 + 1/90*g**6 + 4*g + 0*g**2 + 1/20*g**5. Factor f(s).
s**2*(s + 1)*(s + 2)/3
Let u = 631/117 + -21/13. Let z = u - 22/9. Factor -2/3*w**4 - z*w**3 + 0*w + 0 - 2/3*w**2.
-2*w**2*(w + 1)**2/3
Let s(o) be the second derivative of -o**4/3 - 4*o**3/3 - 7*o. Determine p, given that s(p) = 0.
-2, 0
Factor -12/5*z**5 - 21/5*z**4 + 0 + 3/5*z**2 + 0*z - 6/5*z**3.
-3*z**2*(z + 1)**2*(4*z - 1)/5
Let q(a) be the third derivative of -a**9/8064 - a**8/6720 + a**7/672 + a**6/240 - a**5/60 + 5*a**2. Let m(i) be the third derivative of q(i). Factor m(j).
-3*(j - 1)*(j + 1)*(5*j + 2)/2
Let i(c) = 4*c**2 + 2*c**4 - 4 + c - c - 2*c**2. Let v(b) = 5*b**4 + 7*b**2 - 12. Let o(a) = 17*i(a) - 6*v(a). What is p in o(p) = 0?
-1, 1
Let v(i) be the first derivative of 8*i**5/15 + i**4/2 - 2*i**3 + 2*i**2/3 - 18. Determine n, given that v(n) = 0.
-2, 0, 1/4, 1
Let k(i) be the first derivative of 1/16*i**4 + 0*i**3 + 1 - 1/20*i**5 + 0*i + 0*i**2. Suppose k(v) = 0. Calculate v.
0, 1
Let i be (2 + -7)*-1*1. Suppose i*k + 5*d - 70 = 0, 6 + 3 = 3*d. Determine x, given that 9*x + 12*x**3 - k*x - 10*x + 9*x**4 - 4 - 5*x**2 = 0.
-1, -2/3, 1
Suppose -2 = k + 2. Let r(c) = -c**3 - 3*c**2 + 4*c + 2. Let p be r(k). Factor g**2 + 4*g**4 + 2*g - 5*g**2 + 0*g**p - 2*g**5.
-2*g*(g - 1)**3*(g + 1)
Determine i so that 0 + 1/5*i**2 - 1/5*i = 0.
0, 1
Factor 3*z**4 + 0*z**2 - 8*z**2 + 3*z**5 + 5*z**2 - 3*z**3.
3*z**2*(z - 1)*(z + 1)**2
Let z(s) = -s**3 - 11*s**2 + 10*s - 8. Let a be z(-12). Solve -11*x - 8 - a*x**2 - 2*x - 3*x + 26*x**2 = 0.
-2/5, 2
Let u be (-14)/(-3) + 100/(-25). Solve 4/3*l + 0 + u*l**2 = 0.
-2, 0
Let n(w) be the second derivative of 3*w**5/140 - w**4/28 + 3*w. Determine h, given that n(h) = 0.
0, 1
Factor 12*q**2 + 13*q**4 - 8*q**4 - 4*q**4 - 14*q**2 + q**3.
q**2*(q - 1)*(q + 2)
Let p(a) = a**3 + a**2 - 2*a - 4. Let n(i) = 3*i**3 + i**2 - 5*i - 8. Let m(v) = -2*n(v) + 5*p(v). Factor m(b).
-(b - 2)**2*(b + 1)
Let g(n) = -n**4 + n**3 - n**2 - n - 1. Let u(x) = x**4 + 49*x**3 - 169*x**2 + 171*x - 64. Let o(y) = -4*g(y) + u(y). Factor o(k).
5*(k - 1)**3*(k + 12)
Let f = 79/448 - -7/64. Factor 2*i**2 - 6/7*i - 10/7*i**3 + 0 + f*i**4.
2*i*(i - 3)*(i - 1)**2/7
Let r = -2 + 5. Suppose -19 = -5*m + 6, 4*p - m = r. Factor 2 + 4*a**5 + 3*a**5 - 6*a**5 + 4*a**3 - 5*a + p*a**2 - 4*a**4.
(a - 2)*(a - 1)**3*(a + 1)
Factor 5*r**4 - 20*r**2 + r**3 + 23*r + 4*r**3 - 3*r - 10*r**3.
5*r*(r - 2)*(r - 1)*(r + 2)
Let s(v) = v**2 + 10*v - 4 + 3 + 5. Let j(l) = 21*l - 2*l**2 + 3*l**2 + 8 + l**2. Let i(f) = 6*j(f) - 13*s(f). Factor i(p).
-(p + 2)**2
Let j(n) be the first derivative of n**7/420 - n**6/240 + n**2/2 + 7. Let r(s) be the second derivative of j(s). Solve r(m) = 0 for m.
0, 1
Suppose 6 = -3*l + 4*l. Let z(s) be the third derivative of -1/8*s**4 + 2*s**2 + 0*s + 0 + 1/6*s**3 + 1/20*s**5 - 1/120*s**l. Find a, given that z(a) = 0.
1
Factor 3/4*w**4 - 3/4*w**2 + 0 - 1/4*w**3 + 1/4*w.
w*(w - 1)*(w + 1)*(3*w - 1)/4
Let i(s) be the first derivative of 2*s**5/45 + s**4/18 - 2*s**3/27 - s**2/9 - 16. Factor i(v).
2*v*(v - 1)*(v + 1)**2/9
Let i be 1*2 + 5 + -5. Suppose 0 = -5*d + d + 20. Factor -16*j**d - i + 8*j + 40*j**4 - 5*j**2 - 25*j**3 - 3*j + 3.
-(j - 1)**3*(4*j + 1)**2
Let v(w) = -2*w**2 + 2*w. Let k(x) = -x**2 + x. Let t(r) = 5*k(r) - 3*v(r). Let t(j) = 0. What is j?
0, 1
Let v(j) be the third derivative of -j**6/40 - j**5/10 - j**4/8 + 10*j**2. Factor v(l).
-3*l*(l + 1)**2
Let -14/9*u + 10/3*u**2 - 26/9*u**3 + 2/9 + 8/9*u**4 = 0. Calculate u.
1/4, 1
Factor -8/9 + 0*o + 2/9*o**2.
2*(o - 2)*(o + 2)/9
Let p(d) be the second derivative of d**6/15 + d**5/5 - 2*d**4/3 - 8*d**3/3 + 6*d. Factor p(o).
2*o*(o - 2)*(o + 2)**2
Let d(f) be the third derivative of -f**8/224 + f**7/420 + f**6/120 - 8*f**2. Factor d(q).
-q**3*(q - 1)*(3*q + 2)/2
Let z(x) be the second derivative of 0 + 1/70*x**5 + 1/42*x**4 - 1/21*x**3 - x - 1/105*x**6 + 0*x**2. Solve z(y) = 0 for y.
-1, 0, 1
Let z = 13 + -11. Find m, given that 2*m**4 - 2 - 6*m**3 - 2 + 6*m**2 - 2*m**2 - z*m**2 + 6*m = 0.
-1, 1, 2
Let y(h) = h**2 - 2*h + 7. Let l(x) = -x**2 + x - 7. Let v(a) = 6*l(a) + 7*y(a). Suppose v(o) = 0. Calculate o.
1, 7
Suppose 4*k = -2*k + 54. Let w be (-18)/(-24)*4/k. Factor 8/3 - w*r**3 - 4*r + 2*r**2.
-(r - 2)**3/3
Factor -28/5*l + 48/5 + 4/5*l**2.
4*(l - 4)*(l - 3)/5
Let d(b) be the first derivative of -b**6/30 + b**4/12 - 2*b - 3. Let a(t) be the first derivative of d(t). Let a(r) = 0. What is r?
-1, 0, 1
Let d be ((-1)/10)/(24/(-60)). What is q in d*q**3 - 9/4*q**2 + 27/4*q - 27/4 = 0?
3
Factor 35*h**3 + 0*h + 5*h + 29*h**3 - 69*h**3.
-5*h*(h - 1)*(h + 1)
Let q(r) be the second derivative of -r**6/45 - r**5/30 + r**4/18 + r**3/9 + 4*r. Let q(n) = 0. What is n?
-1, 0, 1
Let t(v) be the second derivative of -v**3/2 - 7*v**2/2 + v. Let i be t(-5). Determine c, given that -2*c**3 + i*c**3 - 2*c + c**3 + 9*c**2 + 4*c = 0.
-1, -2/7, 0
Suppose -3*p + 4 = -v, -2*p - v - 12 = 2*v. Suppose -6/7*f**2 + 4/7*f**3 + 6/7*f**4 - 4/7*f + p = 0. Calculate f.
-1, -2/3, 0, 1
Let s(h) = -3*h**4 - 3*h**3 + 4*h**2 - h - 1. Let k(w) = w**4 + w**3 + w + 1. Let r(i) = -k(i) - s(i). Factor r(z).
2*z**2*(z - 1)*(z + 2)
Factor -2/7*f**2 + 0 + 10/7*f.
-2*f*(f - 5)/7
Let d(o) = -o**3 - 3*o**2 + 3*o. Let q(b) = -3*b**3 - 9*b**2 + 8*b. Let v(x) = -8*d(x) + 3*q(x). Determine h, given that v(h) = 0.
-3, 0
Let c(k) be the first derivative of -25*k**6/18 - 19*k**5/3 - 19*k**4/2 - 52*k**3/9 - 4*k**2/3 + 13. Solve c(n) = 0 for n.
-2, -1, -2/5, 0
Let x = 1/3 + 1/15. Let x*m**2 + 4/5 - 6/5*m = 0. Calculate m.
1, 2
Let b(m) be the first derivative of 7*m**4/22 - 6*m**3/11 + 2*m**2/11 - 6. Factor b(t).
2*t*(t - 1)*