 Let g(h) be the first derivative of 13/7*h**2 - l + 9/14*h**4 + 4/7*h + 16/7*h**3. Find k such that g(k) = 0.
-2, -1/3
Suppose -171*t**4 + 4*t**3 + 22*t - 8 - 5*t**3 - 18*t**2 + 3*t**3 + 173*t**4 = 0. Calculate t.
-4, 1
Let w be (-9)/6*8/(-6). Let h(d) = 2*d. Let m be h(w). Factor o**4 + 4 + o**3 - m.
o**3*(o + 1)
Let a(x) be the third derivative of -x**9/211680 - x**8/70560 + x**5/60 - x**2. Let i(m) be the third derivative of a(m). Find t, given that i(t) = 0.
-1, 0
Let n(r) be the third derivative of 5*r**5/96 - 5*r**4/32 + 3*r**3/16 + 2*r**2. Factor n(p).
(5*p - 3)**2/8
Find t, given that -10*t**2 + 6*t - 8 - 12*t - 3*t**3 - 10*t + t**3 = 0.
-2, -1
Let p(o) be the second derivative of -o**6/120 + o**5/30 - o**2/2 - 3*o. Let n(q) be the first derivative of p(q). Solve n(s) = 0.
0, 2
Factor -j + j**2 - j - 6*j - 3*j**2 - 6.
-2*(j + 1)*(j + 3)
Let s be (-3)/(6 - 3) - -1. Let w(j) be the third derivative of 1/24*j**3 + 0 + 1/48*j**4 + 1/240*j**5 + s*j + j**2. Find v, given that w(v) = 0.
-1
Let g(w) = 6*w**4 - 5*w**3 - 13*w**2 + 8*w - 5. Suppose -c = -4*c - 12. Let v(b) = 6*b**4 - 6*b**3 - 12*b**2 + 8*b - 4. Let a(y) = c*g(y) + 5*v(y). Factor a(i).
2*i*(i - 2)*(i + 1)*(3*i - 2)
Let y(r) = -r**3 - r**2 - r - 1. Let o(s) = 4*s**4 - 19*s**3 + 53*s**2 + s - 11. Let x(l) = -2*o(l) - 14*y(l). Find b, given that x(b) = 0.
-1/2, 1, 3
Let k be 1/(-2 + 33/15). Factor 57*d**4 - 1 + 15*d**k - 15*d**3 + 42*d**2 + 93*d**3 + 3*d - 2.
3*(d + 1)**4*(5*d - 1)
Factor 12/5*z**3 - 44/5*z**2 + 4*z + 12/5.
4*(z - 3)*(z - 1)*(3*z + 1)/5
Suppose -d = 28*b - 25*b, -2 = d + 5*b. Factor -9/2*i**2 - 9/4*i**4 + 0 + 33/4*i**d + 0*i.
-3*i**2*(i - 3)*(3*i - 2)/4
Find k, given that -15/2*k + 11/6 + 2/3*k**2 = 0.
1/4, 11
Let w(c) be the second derivative of c**4/12 - 2*c**3 + 11*c**2/2 + 36*c. Factor w(u).
(u - 11)*(u - 1)
Let k(q) = -4*q**2 - 2*q - 2. Let u(f) = -f**3 + 3*f**2 + 3*f + 3. Let b(a) = 3*k(a) + 2*u(a). Factor b(g).
-2*g**2*(g + 3)
Let v(h) be the second derivative of h**4/30 - 8*h**3/15 + 7*h**2/5 + 14*h. What is w in v(w) = 0?
1, 7
Let b be (0 - 2) + 2 - -27. Let n = -19 + b. What is s in -12*s**4 + n*s**3 - 2*s**2 + s**3 + 0*s**2 + 5*s**5 = 0?
0, 2/5, 1
Let w(x) = x**3 - x**2 + 2*x - 2. Let f(l) = 3*l**3 - 4*l**2 + 7*l - 6. Let o(q) = 2*f(q) - 7*w(q). Let a be o(0). Solve -11 - a*k - 6*k - 2*k**2 + 3 = 0.
-2
Let v be (6/2 - (-6 - -3)) + -4. Let -1/4 - 3/2*t - 9/4*t**v - t**3 = 0. What is t?
-1, -1/4
Let r be 44/8 + -2 + 2 + -5. Let 1/2*z**4 - r*z + 1/2*z**3 + 0 - 1/2*z**2 = 0. Calculate z.
-1, 0, 1
Let i = -1/30 + 7/10. Determine p so that -2/3 - i*p**4 - 2/3*p**5 - 2/3*p + 4/3*p**2 + 4/3*p**3 = 0.
-1, 1
Let l be 3/9 - (-4)/(-3). Let t be 1 + 0 - (l - -2). Factor 1/3*g + 0 + t*g**3 - 1/3*g**5 - 2/3*g**4 + 2/3*g**2.
-g*(g - 1)*(g + 1)**3/3
Factor -2/5 + 4/5*a - 2/5*a**2.
-2*(a - 1)**2/5
Let w = -12 - -12. Let i = -3 - -6. Let -4*h**2 - 2*h**4 - 2*h**i + 8*h**3 + w*h**4 = 0. What is h?
0, 1, 2
Let t(r) be the first derivative of r**5 - 5*r**4/4 - 5*r**3/3 + 5*r**2/2 - 63. Factor t(s).
5*s*(s - 1)**2*(s + 1)
Let c(z) = -3*z - 12. Let q be c(-5). Suppose 2*s + 5*d = 3*s - 20, 2*d = -q*s - 8. Find b such that s*b**2 - 1/3*b**3 + 2/3 + b = 0.
-1, 2
Suppose u - 2*u = 2*g - 11, 4*g - 32 = -4*u. Suppose -f + 3*f - 13 = a, -36 = -u*f - a. Factor h**2 + f*h - 3*h - 2*h - h.
h*(h + 1)
Let p(x) be the third derivative of -x**6/20 - 11*x**5/140 - x**4/28 - 3*x**2. Factor p(z).
-3*z*(2*z + 1)*(7*z + 2)/7
Let b(c) be the second derivative of c**5/40 - c**4/16 - c**3/2 + 3*c**2/2 - 5*c. Let i(k) be the first derivative of b(k). Factor i(z).
3*(z - 2)*(z + 1)/2
Suppose -2*q = 10 - 4. Let j be (-16)/18*q/6. Factor -j*n + 0 + 2/9*n**2.
2*n*(n - 2)/9
Determine p, given that 120*p + 35*p**4 + 150*p**3 + 105*p**2 + 20 + 50*p**2 + 60*p**2 = 0.
-2, -1, -2/7
Let f(n) = 4*n - 9. Let b be f(3). Let v(x) be the first derivative of 1/5*x**5 + 3 + x**2 + 0*x**b - x - 1/2*x**4. Find w, given that v(w) = 0.
-1, 1
Let t = -3/32 - 67/480. Let q = 1/10 - t. Let -q*d**2 - 1/3*d**3 + 0 + 0*d = 0. Calculate d.
-1, 0
Let r = -663575/163 - -4071. Let y = 316/815 - r. Determine l, given that 2/5*l**2 + y*l - 2/5*l**3 - 2/5 = 0.
-1, 1
Suppose h + 2 - 26 = -4*v, 2*h = -5*v + 48. Suppose h*r**3 - 52*r**2 + 3 - 4*r**4 - 9 + 5 - 15 + 48*r = 0. Calculate r.
1, 2
Let u(a) be the first derivative of a**3/3 - 2*a**2 - 2. Factor u(s).
s*(s - 4)
Let 36*v**4 - 144 - 292*v**2 - 6*v**3 - 6*v**3 + 110*v - 494*v - 2*v**5 - 2*v**5 = 0. Calculate v.
-1, 6
Let n(m) be the first derivative of m**6/300 - m**5/150 - m**2/2 - 4. Let o(u) be the second derivative of n(u). Factor o(i).
2*i**2*(i - 1)/5
Let r be ((-12)/14)/((-22)/126). Let k = r + -183/44. Factor 5/4*a**2 + k*a - 1/2.
(a + 1)*(5*a - 2)/4
Let o(u) = u**3 - 3*u**2. Let d(v) = -v**2. Let y(q) = -q - 14. Let l be y(-11). Let i(g) = l*o(g) + 7*d(g). Factor i(t).
-t**2*(3*t - 2)
Let z(v) be the first derivative of -v**3/15 - v**2/10 + 2*v/5 - 10. Let z(m) = 0. Calculate m.
-2, 1
Let m = 20 - 12. Suppose -x**2 - m*x**4 - 8*x**4 - 1 + 6*x - 23*x**3 - x**3 = 0. What is x?
-1, 1/4
Factor 2/11*x + 2/11*x**2 + 0.
2*x*(x + 1)/11
Let g(y) be the first derivative of -y**6/1260 + y**5/210 - y**3 + 5. Let h(p) be the third derivative of g(p). Solve h(z) = 0.
0, 2
Let z be (107/(-105) + 1)/(336/(-196)). Let u(y) be the second derivative of 1/36*y**4 - y + 1/60*y**5 + 0*y**2 - z*y**6 + 0 + 0*y**3 - 1/126*y**7. Factor u(s).
-s**2*(s - 1)*(s + 1)**2/3
Suppose 5*a + s = 33, 5*a - 15 = 5*s - 0. Suppose -5*u + c = -4*u - 6, -3*u - a = 3*c. Factor 2/3*p**3 - 2/3*p**4 + 0 - 2/3*p**5 + 0*p + 2/3*p**u.
-2*p**2*(p - 1)*(p + 1)**2/3
Let z = 175/3 - 58. Factor -1/3*f**2 - 1/3*f**3 + 1/3*f + z*f**4 + 0.
f*(f - 1)**2*(f + 1)/3
Factor -4/3*t + 4/3*t**4 - 8/3*t**2 + 8/3*t**3 - 4/3*t**5 + 4/3.
-4*(t - 1)**3*(t + 1)**2/3
Let w(a) be the third derivative of a**7/70 - a**6/10 - 11*a**5/20 - 3*a**4/4 - 21*a**2. Factor w(k).
3*k*(k - 6)*(k + 1)**2
Let b(o) be the second derivative of -2*o**6/5 + 8*o**5/5 - 7*o**4/3 + 4*o**3/3 - 5*o. Factor b(n).
-4*n*(n - 1)**2*(3*n - 2)
Let j(s) = s**2 - 1. Let c(x) = x**3 - 3*x**2 - x + 3. Let u(h) = 5*c(h) + 5*j(h). Factor u(o).
5*(o - 2)*(o - 1)*(o + 1)
Let s = -99 - -101. Let u(b) be the second derivative of 0*b**3 - 1/4*b**4 - 2*b + 0 + 3/2*b**s. Find x, given that u(x) = 0.
-1, 1
Let m(r) be the third derivative of r**8/40320 - r**7/5040 + r**6/1440 - r**5/60 - 2*r**2. Let w(u) be the third derivative of m(u). Find a such that w(a) = 0.
1
Let a(h) be the second derivative of 6*h + 0*h**3 + 1/126*h**7 - 1/90*h**6 + 0 + 0*h**2 + 1/36*h**4 - 1/60*h**5. Factor a(n).
n**2*(n - 1)**2*(n + 1)/3
Factor -75*y**2 - 71*y**2 + 40*y**3 + 141*y**2.
5*y**2*(8*y - 1)
Suppose -5 = -3*i + 1. Factor 3*d - d - 4*d**3 + 14*d**4 - 7*d**i - 2*d**4 - 3*d**3.
d*(d - 1)*(3*d + 2)*(4*d - 1)
Let j = -8/83 - -763/166. Factor 3*p + 33/4*p**2 - 3 - j*p**3 - 27/4*p**4.
-3*(p + 1)**2*(3*p - 2)**2/4
Let t be -1 + -1 + 2 + 4. Factor -b**2 - t*b - 4 + 3 - 2*b**2.
-(b + 1)*(3*b + 1)
Factor 8/5*q**2 + 12/5*q**3 + 0 + 2/5*q**5 - 2*q**4 - 16/5*q.
2*q*(q - 2)**3*(q + 1)/5
Let q = -55 + 60. Let z(s) be the first derivative of 5/4*s**q - 2 + 0*s - 4/3*s**3 - 5/16*s**4 - 1/2*s**2. Suppose z(i) = 0. What is i?
-2/5, 0, 1
Let a be ((-26)/65)/(1/(-15)). Let l(v) be the third derivative of -v**2 - 1/2*v**5 - 4/3*v**3 + 0 + 0*v + 7/120*v**a + 3/2*v**4. Factor l(y).
(y - 2)**2*(7*y - 2)
Let j(i) = -36*i**2 - 8*i + 12. Let d(y) = -y**2 + y. Let o(n) = -24*d(n) + j(n). Factor o(v).
-4*(v + 3)*(3*v - 1)
Let 5*k**2 - 9*k + 45 - 15*k - 26*k = 0. What is k?
1, 9
Let y(l) be the third derivative of -5*l**8/336 + 2*l**7/21 - l**6/24 - 5*l**5/6 + 5*l**4/6 + 20*l**3/3 - 11*l**2. Factor y(w).
-5*(w - 2)**3*(w + 1)**2
Factor 4*t - 7*t - 3*t - 3*t**2.
-3*t*(t + 2)
Let h = 5 + -9/2. Factor 3/4*c + h + 1/4*c**2.
(c + 1)*(c + 2)/4
Let g(j) be the second derivative of 0 + 1/2*j**3 - 3/2*j**2 + j - 3/20*j**5 + 1/4*j**4. Let g(f) = 0. Calculate f.
-1, 1
Let k(q) = -q**2 - 2. Let g(p) = -2*p**2 + 3*p - 4. Let h(f) = -3*f**2 + 5*f - 6. Let m(d) = -8*g(d) + 5*h(d). Let x(l) = 4*k(l) + 3*m(l). Factor x(j).
-(j - 2)*(j - 1)
Let r = 9426/13 + -724. Let s = r - 16/39. Factor 8/3 + s*h**2 - 8/3*h.
2*(h - 2)**2/3
Let p(r) be the thi