(h) = -f(h) + 15*m(h). Find k, given that y(k) = 0.
0, 1
Let y = 2108/9 - 234. Suppose 2/9*v**2 + 0 + y*v = 0. Calculate v.
-1, 0
Let j be -3*2/(-6) + -1. Factor -2/5*r**4 - 2/5*r**5 + 0*r**3 + 0 + j*r**2 + 0*r.
-2*r**4*(r + 1)/5
Let q(n) = 5*n**4 + 15*n**3 - 75*n**2 + 80*n - 25. Let g(t) = -5*t**4 - 15*t**3 + 75*t**2 - 79*t + 24. Let w(b) = 5*g(b) + 6*q(b). Factor w(h).
5*(h - 1)**3*(h + 6)
Suppose -15/7*h - 9/7 + 2/7*h**2 + 1/7*h**5 + h**4 + 2*h**3 = 0. What is h?
-3, -1, 1
Suppose 0 = -3*b - 2*b. Let t(o) be the third derivative of b*o - 1/20*o**5 + 0 - 2*o**2 - 1/12*o**4 + 0*o**3 - 1/120*o**6. Factor t(w).
-w*(w + 1)*(w + 2)
Let l(a) be the first derivative of a**6/120 - a**5/60 - 7*a**2/2 - 5. Let m(p) be the second derivative of l(p). Determine u so that m(u) = 0.
0, 1
Let q(c) be the first derivative of -2*c**5/15 + 5*c**4/6 + 2*c**3/9 - 5*c**2/3 + 9. Factor q(u).
-2*u*(u - 5)*(u - 1)*(u + 1)/3
Suppose -1 = 5*w + 14. Let i be 0*(0 + w)/6. Factor i + 2/9*y - 2/9*y**3 + 0*y**2.
-2*y*(y - 1)*(y + 1)/9
Let v(k) be the third derivative of -k**5/45 - k**4/6 - 4*k**3/9 - 31*k**2. Determine m, given that v(m) = 0.
-2, -1
Suppose -3 = -o + 3*w + 11, 3*o + 10 = -4*w. Factor 2/7*q**4 + 2/7*q - 2/7*q**3 + 0 - 2/7*q**o.
2*q*(q - 1)**2*(q + 1)/7
Let q(g) = 5*g**2 + 5*g - 3. Let k be (-1)/((-21)/9 - -2). Let r(u) = 11*u**2 + 11*u - 7. Let p(l) = k*r(l) - 7*q(l). Factor p(h).
-2*h*(h + 1)
Let h(u) be the first derivative of -2*u**7/525 + u**6/150 + u**5/75 - u**4/30 + 2*u**2 - 7. Let y(d) be the second derivative of h(d). Factor y(m).
-4*m*(m - 1)**2*(m + 1)/5
Let q(h) be the first derivative of h**3 + 2*h**2 + 2 - 2*h + 1/6*h**4. Let m(r) be the first derivative of q(r). Factor m(b).
2*(b + 1)*(b + 2)
Suppose -5*r + 16 = -4*v, -4*v - 3*r = -0*r - 16. Let d be v/1 - (1 - 0). Factor 1/3*s**4 + 0*s**2 + 0*s**3 + d + 0*s.
s**4/3
Let q(w) be the first derivative of -w**6/1260 + w**5/420 - 4*w**3/3 - 4. Let n(p) be the third derivative of q(p). Let n(c) = 0. Calculate c.
0, 1
Let n(c) be the third derivative of -3/8*c**4 + 0*c + 2*c**2 + 0 + 1/5*c**5 - 1/24*c**6 + 1/3*c**3. Let n(x) = 0. Calculate x.
2/5, 1
Let u(p) be the second derivative of -p**6/75 - 6*p**5/25 - 7*p**4/6 + 4*p**3/5 + 36*p**2/5 + 25*p. Find b such that u(b) = 0.
-6, -1, 1
Let p(h) = 2*h**2. Let x be p(1). Let t(j) be the third derivative of 0*j + 1/30*j**5 + 1/3*j**4 + 0 + 4/3*j**3 + x*j**2. Factor t(d).
2*(d + 2)**2
Let k(q) be the second derivative of -3*q**4 + 0 - 3/4*q**5 + 3*q - 9/2*q**3 - 3*q**2. Factor k(l).
-3*(l + 1)**2*(5*l + 2)
Let t(d) be the second derivative of d**5/30 - d**4/6 + d**3/3 - 3*d**2/2 + 7*d. Let m(x) be the first derivative of t(x). Solve m(j) = 0 for j.
1
Let s(j) = 6*j**2 + 12*j - 1. Let z(p) = 3*p**2 + 6*p - 1. Let w(i) = 4*s(i) - 7*z(i). Find r such that w(r) = 0.
-1
Let j(q) be the second derivative of -q**4/30 - 2*q**3/5 - 9*q**2/5 - 13*q. Factor j(a).
-2*(a + 3)**2/5
Let r(n) = n - 3. Let y be r(4). Let v be y/6*2*21. Determine f, given that -3*f + 8*f**2 + 4*f - v*f**2 = 0.
-1, 0
Let a = 4 - 0. Factor -2*z**4 - 2*z**3 + z**3 + a*z + 2 - 3*z**3.
-2*(z - 1)*(z + 1)**3
Factor -23*x**3 + 4*x**3 + 3*x**3 + x - 16*x**2 + 1.
-(x + 1)*(4*x - 1)*(4*x + 1)
Suppose 25 = -y + 9. Let p be (y/24)/(4/(-30)). Let 8/5*j**p + 2/5 + 16/5*j**4 + 2/5*j**3 - 2*j**2 - 2/5*j = 0. Calculate j.
-1, 1/2
Let y(w) = 3*w**3 - w**2 + 2*w - 1. Let b be y(1). Factor 2*r**b + 4*r - 10*r**2 - 2*r + 6*r**3.
2*r*(r - 1)*(4*r - 1)
Let z(l) = l**2 + l + 1. Let a(n) = -20*n**2 - 15*n - 20. Let j(m) = -a(m) - 25*z(m). Factor j(p).
-5*(p + 1)**2
Let q = -761/3 - -254. Determine y, given that 0*y + 0 + 5/6*y**4 - q*y**3 + 0*y**2 = 0.
0, 2/5
Let g = 149/335 - 3/67. Let t = -14 + 18. What is u in -1/5*u**5 + 0*u**t - 3/5*u - g*u**2 + 2/5 + 4/5*u**3 = 0?
-2, -1, 1
Suppose -7*m + 11*m = 0. Let v(b) be the third derivative of m*b - 1/20*b**5 + b**3 + 1/8*b**4 - 3*b**2 + 0. Factor v(n).
-3*(n - 2)*(n + 1)
Find g such that -10*g**4 + 10*g**3 + 25*g**4 - 10*g**5 + 24*g - 24*g = 0.
-1/2, 0, 2
Let a be (-6)/8*18/(-27). Let -1/2*k**2 + a + 0*k = 0. Calculate k.
-1, 1
Let z be 15/(-60)*(-2)/40. Let a(y) be the third derivative of 0*y + 0*y**3 - 1/16*y**4 + 0 + y**2 - z*y**5. Factor a(l).
-3*l*(l + 2)/4
Let z(p) = 2*p**2 + p - 4. Let j be z(-2). Suppose -2*l**5 + 0*l**j + 2*l**2 + 8*l**3 - 1 - 3 + 2*l**2 - 6*l = 0. What is l?
-1, 1, 2
Let m(x) be the second derivative of -3*x**5/100 + 7*x**4/20 - 11*x**3/10 + 3*x**2/2 + 12*x. Factor m(u).
-3*(u - 5)*(u - 1)**2/5
Let i be (-28)/(-6) + 60/45. Determine f, given that -f**3 - i*f + 14*f - 4*f**4 + 8*f**2 - 5*f**3 + 2*f**5 = 0.
-1, 0, 2
Factor -7/3 + 1/3*u**2 - 2*u.
(u - 7)*(u + 1)/3
Let w(h) be the third derivative of -h**5/120 - h**4/48 - 4*h**2. Factor w(a).
-a*(a + 1)/2
Let 0 - 3/2*v**3 + v**2 - 1/4*v**5 - 1/4*v + v**4 = 0. What is v?
0, 1
Let g = 323/5295 - -2/353. Let j(x) be the second derivative of 0*x**2 - g*x**4 + x + 0 - 1/15*x**3 - 1/50*x**5. Factor j(k).
-2*k*(k + 1)**2/5
Let n(t) be the first derivative of -3*t**4/8 - 21*t**3/2 - 297*t**2/4 + 363*t/2 - 62. Factor n(b).
-3*(b - 1)*(b + 11)**2/2
Suppose 2/7 + 6/7*h - 6/7*h**3 - 2/7*h**2 = 0. What is h?
-1, -1/3, 1
Suppose v = -v + 6. Suppose i**2 - 12*i**4 - 4*i**2 - 5*i**v + 6*i**2 - 4*i**3 = 0. What is i?
-1, 0, 1/4
Suppose 0 = 4*g - 4*o + 36, 5*g + 21 + 12 = o. Let w be 4/g*(-12)/20. Factor 0 - 2/5*i**5 - 4/5*i**4 + 0*i**2 - w*i**3 + 0*i.
-2*i**3*(i + 1)**2/5
Let p(i) be the second derivative of -i**7/105 + i**6/45 + 7*i**5/150 - 7*i**4/30 + 16*i**3/45 - 4*i**2/15 + 3*i. Let p(o) = 0. What is o?
-2, 2/3, 1
Factor -3/7*q**4 + 6/7*q**3 + 3/7*q**2 + 0 - 6/7*q.
-3*q*(q - 2)*(q - 1)*(q + 1)/7
Let u(z) = -3*z**4 - 3*z**3 + 4*z**2 - 4. Let f(j) = -j**4 - j**3 + j**2 - 1. Let w(n) = -12*f(n) + 3*u(n). Suppose w(v) = 0. What is v?
-1, 0
Let x(r) be the third derivative of 1/240*r**5 + 0 - 4*r**2 + 1/32*r**4 + 0*r + 1/12*r**3. Factor x(y).
(y + 1)*(y + 2)/4
Let i(c) = -c**3 - 11*c**2 - 27*c - 22. Let x be i(-8). Suppose -2/5 + 12/5*s**4 - x*s**2 + s**5 - 9/5*s + 4/5*s**3 = 0. What is s?
-1, -2/5, 1
Let m = 558/5 + -111. Factor 6/5*l - m*l**2 + 0.
-3*l*(l - 2)/5
Solve -4/11*d**2 + 0 + 0*d**3 + 2/11*d**5 - 2/11*d + 4/11*d**4 = 0.
-1, 0, 1
Let a(u) = -2*u**4 + 12*u**3 - 14*u**2 + 6*u + 2. Let d(n) = 3*n**4 - 24*n**3 + 29*n**2 - 13*n - 5. Let f(r) = 5*a(r) + 2*d(r). Factor f(g).
-4*g*(g - 1)**3
Let k(h) be the second derivative of 0*h**2 - 1/6*h**3 + 1/120*h**5 - 1/180*h**6 + 0 - 2*h + 0*h**4. Let i(s) be the second derivative of k(s). Factor i(m).
-m*(2*m - 1)
Suppose 0 + 1/5*x**2 - 1/5*x = 0. Calculate x.
0, 1
Solve 0 - 2/3*y**2 - 2/9*y**4 - 2/3*y**3 - 2/9*y = 0.
-1, 0
Let g(j) = -j**3 - 7*j**2 - 17*j - 119. Let i be g(-7). Solve i*z - 2/5*z**2 + 0 = 0 for z.
0
Let c(n) = -10*n**4 - 16*n**3 - 4*n**2 + 9*n - 7. Let y(l) = -3*l**4 - 5*l**3 - l**2 + 3*l - 2. Let q(g) = -2*c(g) + 7*y(g). Factor q(s).
-s*(s - 1)*(s + 1)*(s + 3)
Let a be (-1)/(-3) - (-2 + (-5)/(-3)). Factor -a*i**5 + 0 - 4/3*i**2 - 8/3*i**4 - 10/3*i**3 + 0*i.
-2*i**2*(i + 1)**2*(i + 2)/3
Let k(b) be the first derivative of -b**6/2 + 6*b**5/5 + 9*b**4/4 - 4*b**3 - 6*b**2 - 12. Find r, given that k(r) = 0.
-1, 0, 2
Let k(u) be the third derivative of -5*u**6/48 + 13*u**5/30 - 29*u**4/48 + u**3/6 - 22*u**2. Factor k(x).
-(x - 1)**2*(25*x - 2)/2
Suppose 4*d = -16, -t + 3*d = 5*d + 6. Factor 3 - 6*x + 3*x - 3*x + 3*x**t + 0*x.
3*(x - 1)**2
Let l(v) be the first derivative of -2*v**3/3 + v**2/5 + 10. Factor l(c).
-2*c*(5*c - 1)/5
Let o = 18 - 24. Let n be (2/o)/(2/(-18)). Determine w so that 2*w**n - 2/3*w**4 - 2*w**2 + 0 + 2/3*w = 0.
0, 1
Let k(m) be the third derivative of 1/24*m**4 + 0 + 1/15*m**5 + 2/105*m**7 + 2*m**2 + 1/336*m**8 + 1/20*m**6 + 0*m**3 + 0*m. Find j, given that k(j) = 0.
-1, 0
Let m(w) be the first derivative of 5 + 0*w**2 - 1/4*w**4 + 0*w + 1/3*w**3. Factor m(j).
-j**2*(j - 1)
Let i(v) be the third derivative of 1/525*v**7 + 4/75*v**5 + 0*v**3 + 1/60*v**6 - v**2 + 1/15*v**4 + 0*v + 0. Find a, given that i(a) = 0.
-2, -1, 0
Let n be (-3 - -15)*(-2)/(-8). Factor -1/2*g - 1/2*g**5 + g**n + 0 + 0*g**2 + 0*g**4.
-g*(g - 1)**2*(g + 1)**2/2
Let a(k) be the first derivative of -3*k**5 - 25*k**4/4 + 5*k**3/3 + 25*k**2/2 + 10*k + 39. Solve