359*s**2 + 1. What is v in q(v) = 0?
-12, -1, 1
Let t(f) be the third derivative of f**6/120 - f**5/5 - 13*f**4/24 + 4*f**3/3 - f**2. Let i be t(13). Factor -i*h - h**2 + 6*h + 1 + 2*h.
-(h - 1)*(h + 1)
Determine h, given that -2/11*h**3 + 18/11*h + 0 - 16/11*h**2 = 0.
-9, 0, 1
Let l(a) be the third derivative of a**7/315 + a**6/20 - a**5/30 - 29*a**4/36 - 2*a**3 + 137*a**2. Factor l(f).
2*(f - 2)*(f + 1)**2*(f + 9)/3
Let b be (-2)/(-4) + 45/10. Factor -b*o + 8*o + 4 - 9*o + 2*o**2.
2*(o - 2)*(o - 1)
Let f(h) = -7*h**4 + 41*h**3 + 78*h**2 + h - 113. Let i(t) = -3*t**4 + 20*t**3 + 39*t**2 - 56. Let p(b) = 4*f(b) - 9*i(b). Determine o so that p(o) = 0.
-13, -2, 1
Suppose -54 = -13*g + 15*g. Let h = 29 + g. Factor 0 + 3/2*l**h - 3*l.
3*l*(l - 2)/2
Let d(h) = -h**2 + 2*h + 8. Let z be d(4). Suppose -4*n - 3*v + 126 = 0, z = 5*n - 0*n + 5*v - 160. Factor -f**3 + 0 - 28*f**4 - f**5 + 0 + n*f**4.
-f**3*(f - 1)**2
Suppose -34 = -3*j - 19. Let u(v) be the third derivative of -1/60*v**j + 0*v + 0 - 1/240*v**6 + 0*v**3 + 4*v**2 + 0*v**4. Solve u(t) = 0.
-2, 0
Let i = -9487/6 + 3165/2. Factor 4*n**2 - 4*n + i - 4/3*n**3.
-4*(n - 1)**3/3
Suppose 11 + 15 = -2*u. Let i(n) = 2*n**2 + 8*n + 6. Let x(a) = -4*a**2 - 17*a - 13. Let m(b) = u*i(b) - 6*x(b). Find r, given that m(r) = 0.
-1, 0
Let m(t) = -2*t**3 - 2*t**2 - 4*t - 5. Let r be m(-2). Factor -16*x**4 + 13*x**2 + 7*x**5 + 17*x**2 - 32*x**2 + r*x**3.
x**2*(x - 1)**2*(7*x - 2)
Suppose 28/11 + 36/11*n**4 + 114/11*n + 16*n**2 + 2/11*n**5 + 124/11*n**3 = 0. Calculate n.
-14, -1
Let f(y) = -5*y**4 - 38*y**3 - 425*y**2 - 1288*y - 1152. Let u(s) = 4*s**4 + 38*s**3 + 426*s**2 + 1289*s + 1153. Let l(b) = -3*f(b) - 4*u(b). Factor l(z).
-(z + 2)**2*(z + 17)**2
Suppose 0 = -11*g - g + 840. Let p be (-6)/(-14) - 2/g. Factor 1/5 - 3/5*r**2 - p*r.
-(r + 1)*(3*r - 1)/5
Let q(t) = -3*t**3 - 74*t**2 - 70*t - 54. Let a(y) = -y**3 - 26*y**2 - 23*y - 18. Let x(u) = 11*a(u) - 4*q(u). Factor x(l).
(l + 1)*(l + 3)*(l + 6)
Find x, given that -64*x**3 - 4*x**4 + 21*x**2 - 54*x**2 + 240 - 11*x**2 + 256*x = 0.
-15, -2, -1, 2
Let b = 10/3 - 44/15. Factor -b*a**3 - 8/5*a**2 - 6/5*a + 0.
-2*a*(a + 1)*(a + 3)/5
Let v be ((-1)/(-6))/((-3)/(-9)) - 0. Suppose 0 = -14*k + 25 + 3. Factor -1/2*c**k + 0 + v*c.
-c*(c - 1)/2
Let a(i) = -64*i**2 - 2182*i - 204. Let q be a(-34). Find r, given that -8/5*r**2 + 6/5*r**3 + 0*r + 2/5*r**4 + q = 0.
-4, 0, 1
Find b such that 37/3*b - 1369/6 - 1/6*b**2 = 0.
37
Let k(h) = -2*h**2 - 11*h + 8. Let j(d) = d**3 + 7*d**2 + 5*d - 12. Let p be j(-6). Let x be k(p). Factor 8/9 + 8/9*o + 2/9*o**x.
2*(o + 2)**2/9
Factor -1/6*r**2 - 22/3 + 5/2*r.
-(r - 11)*(r - 4)/6
Let s(i) be the second derivative of 0 + 5*i - 3/40*i**5 + 0*i**2 - 1/18*i**3 - 1/252*i**7 - 7/72*i**4 - 1/36*i**6. Determine p, given that s(p) = 0.
-2, -1, 0
Let c(u) = -3 - 3*u**2 + 5*u - 4*u**2 + 2*u - u. Let v(r) = -6*r**2 + 6*r - 4. Let l(d) = 5*c(d) - 6*v(d). Suppose l(o) = 0. What is o?
3
Let 22*m - 2/3*m**2 - 64/3 = 0. Calculate m.
1, 32
Factor -19*h**3 + 2020 + 25*h**2 - 2040 + 20*h + 4*h**3.
-5*(h - 2)*(h + 1)*(3*h - 2)
Solve 0*c + 1/3*c**3 + 10/3*c**2 + 0 = 0.
-10, 0
Let a(h) = 2*h**2 + 68*h - 219. Let f be a(3). Factor -1/5*v**5 - 4/5 + 1/5*v**4 + v**f - 1/5*v**2 - 8/5*v.
-(v - 2)**2*(v + 1)**3/5
Let g(u) be the first derivative of 512*u**6/3 + 1152*u**5/5 + 33*u**4 + 4*u**3/3 + 282. Factor g(c).
4*c**2*(c + 1)*(16*c + 1)**2
Let s(a) = a**3 + 7*a**2 + 3*a - 2. Let k be s(-6). Suppose k*f + 17*f - 22*f**2 - 4 - 7*f + 0*f = 0. Calculate f.
2/11, 1
Factor -14/11*s**3 + 16/11 - 40/11*s - 52/11*s**2.
-2*(s + 2)**2*(7*s - 2)/11
Let z be (-1)/(7/(-28)) - 4. Let o(g) be the second derivative of 3/40*g**5 + 1/60*g**6 - 1/2*g**2 - 1/4*g**3 - 4*g + 1/24*g**4 + z. Factor o(h).
(h - 1)*(h + 1)**2*(h + 2)/2
Let d(q) be the second derivative of q**7/525 - q**6/75 + q**5/25 - q**4/15 + q**3/15 + 6*q**2 + 10*q. Let g(z) be the first derivative of d(z). Factor g(l).
2*(l - 1)**4/5
Let u(f) be the first derivative of f**5/6 - 5*f**4/24 - 5*f**3/6 - 2*f**2 - 8. Let g(k) be the second derivative of u(k). Factor g(p).
5*(p - 1)*(2*p + 1)
Let s(y) be the second derivative of -2/9*y**3 - 1/45*y**6 + 0 - 2/15*y**5 - 5/18*y**4 + 0*y**2 - 9*y. Factor s(i).
-2*i*(i + 1)**2*(i + 2)/3
Let h be (-10)/(-5) + (6/21 - 66/35). Factor 0*g - 2/5*g**4 + h*g**2 - 2/5*g**5 + 0 + 2/5*g**3.
-2*g**2*(g - 1)*(g + 1)**2/5
Solve 0 - 2/5*d**3 - 8/5*d + 8/5*d**2 = 0 for d.
0, 2
Let r(w) be the first derivative of w**6/30 - w**4/20 + 302. Factor r(d).
d**3*(d - 1)*(d + 1)/5
Factor -140*k + 70 - 143 + 203*k**2 - 198*k**2 - 72.
5*(k - 29)*(k + 1)
Let k(a) be the first derivative of 72*a - 5*a**4 + 22 + 60*a**2 + 2/5*a**5 + 26/3*a**3. Factor k(u).
2*(u - 6)**2*(u + 1)**2
Let g = -11 + 16. Let x(m) be the first derivative of -2 + 4/5*m**g + 0*m**2 + 0*m + m**4 + 0*m**3. Determine r so that x(r) = 0.
-1, 0
Let u(y) be the second derivative of -5*y**4/4 - 4*y**3 + 3*y + 5. What is v in u(v) = 0?
-8/5, 0
Find k, given that 194/5*k**3 - 322/5*k**4 + 0*k - 28/5*k**2 + 0 - 24/5*k**5 = 0.
-14, 0, 1/4, 1/3
Factor 30*s - 16*s + 4*s**3 - 28*s**2 - 36 + 6*s + 40*s.
4*(s - 3)**2*(s - 1)
Let x(i) be the first derivative of 4/9*i + 6 - 4/27*i**3 + 5/9*i**2 - 5/18*i**4. Solve x(m) = 0 for m.
-1, -2/5, 1
Let n be 30/(-20)*48/(-30). Suppose -6/5*l - 3*l**2 - 3/5*l**4 - n*l**3 + 0 = 0. What is l?
-2, -1, 0
Let p be ((-72)/78)/(10/(-13)). Let b = -207 - -1038/5. Find u, given that -b - 3/5*u**2 - p*u = 0.
-1
Let s(t) = -19*t**2 - 80*t - 82. Let y be s(-2). Find n such that -2/3 - n**y - 5/3*n = 0.
-1, -2/3
Let j(u) = -1 + 0*u - 10*u - 2 + 2. Let y be j(-1). Factor -3*q**5 + 2*q**4 - y*q**3 + 15*q**4 + 3*q**2 - 8*q**4.
-3*q**2*(q - 1)**3
Suppose -38*b + 29*b - 9 = 0. Let t be (-25)/(-7) - (b - (-8 + 4)). Factor -1/7*o**4 + t - 4/7*o + 4/7*o**3 - 3/7*o**2.
-(o - 2)**2*(o - 1)*(o + 1)/7
Let n(z) be the second derivative of z**6/45 + 4*z**5/15 + 7*z**4/6 + 2*z**3 - z + 8. Factor n(j).
2*j*(j + 2)*(j + 3)**2/3
Let 34/9*v - 14/9*v**2 - 2 - 2/9*v**3 = 0. What is v?
-9, 1
Let x(q) = -2*q**2 + 16*q + 28. Suppose 24 = -4*b - 2*f, b = 3*b - 5*f - 12. Let s(v) = -3*v**2 + 32*v + 57. Let g(c) = b*s(c) + 7*x(c). Factor g(r).
-2*(r + 4)**2
Let j(n) be the third derivative of -n**6/180 + n**5/15 - 11*n**4/36 + 2*n**3/3 + 23*n**2 + 2*n. Factor j(s).
-2*(s - 3)*(s - 2)*(s - 1)/3
Suppose -5*k = -2*z + 58, 2*z + 3*z - 112 = -4*k. Solve -r**5 - 2*r**5 - z*r**3 - 21*r**4 + 4*r**2 + 44*r**2 = 0.
-4, 0, 1
Let y be ((-91)/14 + 6)*12/(-2). Factor -192*t + 6*t**3 - 7*t**y - 23*t**3 - 36 + 140*t**2.
-4*(t - 3)**2*(6*t + 1)
Factor 2/21*q**3 - 8/7*q**2 - 20/7 - 86/21*q.
2*(q - 15)*(q + 1)*(q + 2)/21
Let u(l) = l**2 + 9*l + 10. Let w(z) = -z**2 - 10*z - 9. Let s(q) = 4*u(q) + 5*w(q). Let p(n) = -15*n - 5. Let j(c) = 4*p(c) - 5*s(c). Factor j(o).
5*(o + 1)**2
Let f(r) be the third derivative of r**8/20160 - r**7/20160 + r**5/30 + 3*r**2. Let q(a) be the third derivative of f(a). Factor q(p).
p*(4*p - 1)/4
Factor 0 + 3/4*o**4 - 27/4*o**3 + 9/2*o**2 + 12*o.
3*o*(o - 8)*(o - 2)*(o + 1)/4
Let -3*c**3 + 23*c**2 + 16*c**2 - 39*c**2 = 0. Calculate c.
0
Suppose 11*r = 10*r + 2. Let q(c) = c**3 + 6*c**2 - c. Let l(j) = j**3 + 5*j**2. Let w(a) = r*q(a) - 3*l(a). Factor w(m).
-m*(m + 1)*(m + 2)
Let k(m) be the third derivative of -m**8/1512 + m**7/315 - m**6/270 - m**5/135 + m**4/36 - m**3/27 - 2*m**2 - 17. What is y in k(y) = 0?
-1, 1
Factor -62*u + 4*u**4 - 24*u**3 - u**4 - 31*u**3 - 418*u + 306*u**2 + 128.
(u - 8)**2*(u - 2)*(3*u - 1)
Suppose 4*f - 16 = -r, -5*r - 5 + 37 = 4*f. Suppose 5*k - 17 = -2*m, k - 4*k = -3*m - 6. Factor -6*x**k - 2*x**2 + 9*x**4 - x - 4*x**5 + 2*x**r + 3*x - x**4.
-2*x*(x - 1)**3*(2*x + 1)
Factor 98/5 + 28/5*b + 2/5*b**2.
2*(b + 7)**2/5
Let m(z) be the second derivative of z**5/12 - 5*z**4/24 - z**2 + 26*z. Let g(f) be the first derivative of m(f). Suppose g(r) = 0. Calculate r.
0, 1
Factor -144/7 - 51/7*s**2 + 3/7*s**3 + 192/7*s.
3*(s - 12)*(s - 4)*(s - 1)/7
Let c(b) = 8*b**4 + 22*b**3 - 58*b**2 + 12*b + 84. Let m(f) = -9*f**4 - 24*f**3 + 57*f**2 - 12*f - 84. Let g(l) = 6*c(l) + 5*m(l). Find h such that g(h) = 0.
-7, -1, 2
Let d(q) = 6*q**2 + 18*q + 3. Let v = -105 + 109. Let m(y) = 7*y**2 + 19*y + 4. Let s(a) = v*d(a) -