. Calculate k.
-1/4, 0, 1
Suppose -5*x - 5*s = -35, 0*x - 2*s = 5*x - 35. Suppose 5*y - 3 - 7 = 0. Factor 2 + x*u - 9*u**2 - 2*u + y*u.
-(u - 1)*(9*u + 2)
Factor 0 - 8/3*z**2 + 4/3*z + 5/3*z**3 - 1/3*z**4.
-z*(z - 2)**2*(z - 1)/3
Let q = 3/19 - 41/380. Let o(z) be the second derivative of -1/12*z**3 + 5/24*z**4 - 1/2*z**2 + 1/40*z**5 + 2*z - q*z**6 + 0. Suppose o(y) = 0. Calculate y.
-1, -2/3, 1
Suppose -9*q = -12*q. Let s(l) be the third derivative of -1/540*l**6 + 1/27*l**3 + 1/108*l**4 + 2*l**2 - 1/270*l**5 + q + 0*l. Factor s(h).
-2*(h - 1)*(h + 1)**2/9
Let g(b) be the second derivative of -b**5/240 + b**4/96 - 2*b**2 - 3*b. Let o(q) be the first derivative of g(q). Suppose o(h) = 0. What is h?
0, 1
Let j = 37 - 52. Let a be 5/(j/(-6)) - 2. Factor a - 4/5*i**4 - 2/5*i**3 - 2/5*i**5 + 0*i + 0*i**2.
-2*i**3*(i + 1)**2/5
Suppose -5/2*o - 1/2*o**2 + 0 = 0. Calculate o.
-5, 0
Let d(j) = -j**2 - 20*j - 200. Let l(r) = -r**2 - 18*r - 201. Let o(x) = -5*d(x) + 4*l(x). Factor o(m).
(m + 14)**2
Let q(f) be the first derivative of -f**6/6 - 6*f**5/5 - 3*f**4 - 10*f**3/3 - 3*f**2/2 - 12. Factor q(k).
-k*(k + 1)**3*(k + 3)
Let b(c) be the first derivative of -2*c**5/15 + 2*c**3/3 + 2*c**2/3 + 17. Let b(p) = 0. What is p?
-1, 0, 2
Let v(n) be the third derivative of 7*n**6/6 - 74*n**5/15 + 2*n**4/3 + 16*n**3/3 - 37*n**2. Determine z, given that v(z) = 0.
-2/7, 2/5, 2
Let m(r) = -3*r**2 + 5*r - 4. Let y(n) = 7*n**2 - 11*n + 9. Suppose -5*g - 3*q - 14 = 0, 0*g - g - 6 = -q. Let d(t) = g*y(t) - 10*m(t). Factor d(a).
2*(a - 2)*(a - 1)
Let k = -4 + 6. Let f(u) = -2*u**2 + 5*u**2 + 6*u**k + 1. Let n(r) = -14*r**2 - 2. Let t(y) = -8*f(y) - 5*n(y). Let t(g) = 0. Calculate g.
-1, 1
Let z(m) be the first derivative of m**6/1260 + m**5/420 + m**3/3 - 1. Let r(t) be the third derivative of z(t). Let r(h) = 0. What is h?
-1, 0
Let h be 1/2 - (-27)/18. Factor 1/5*p**5 - 1/5*p**h + 0*p + 3/5*p**3 + 0 - 3/5*p**4.
p**2*(p - 1)**3/5
Solve -15*r**2 - 3/2*r**5 - 3/2 - 15/2*r**4 - 15*r**3 - 15/2*r = 0.
-1
Let j(o) be the third derivative of o**5/30 + o**4/14 - o**3/21 + o**2 + 23. Factor j(c).
2*(c + 1)*(7*c - 1)/7
Let l(v) be the second derivative of -v**8/26880 + v**7/3360 - v**6/960 + v**5/480 - 5*v**4/12 + 3*v. Let r(a) be the third derivative of l(a). Factor r(j).
-(j - 1)**3/4
Suppose 4*v - 24 = m + 3*m, -5*m = 5*v. Let r(s) be the second derivative of s**v - 2*s + 0 + s**2 - 11/24*s**4 + 5/12*s**6 - 3/4*s**5. Solve r(j) = 0 for j.
-2/5, 1
Let l(y) be the first derivative of y**7/1260 - y**6/180 + y**5/60 - y**4/36 + 2*y**3/3 - 2. Let h(w) be the third derivative of l(w). Factor h(t).
2*(t - 1)**3/3
Let z(h) = -2*h**2 - 31*h - 12. Let i be z(-15). Find u, given that -2*u**2 - 2/3 - 2*u - 2/3*u**i = 0.
-1
Let w be 3939/(-105) + 24/30. Let r = 37 + w. Let -2/7*u + 0 + r*u**2 = 0. Calculate u.
0, 1
Let h(a) be the first derivative of a**5/5 + a**4 - a**3/3 - 2*a**2 - 12. Factor h(z).
z*(z - 1)*(z + 1)*(z + 4)
Let s(v) be the second derivative of v**7/14 - v**6/2 + 3*v**5/2 - 5*v**4/2 + 5*v**3/2 - 3*v**2/2 - 2*v. What is z in s(z) = 0?
1
Let j be 2 + 28/(-12) + (-11)/(-15). Factor 0*m**3 + 6/5*m**2 + 0 - j*m**4 + 4/5*m.
-2*m*(m - 2)*(m + 1)**2/5
Let g = -11 - -6. Let v = -5 - g. Find b, given that v*b + 3*b - 5*b + 2*b**2 - 4 = 0.
-1, 2
Let v(p) be the second derivative of -p**7/525 + p**6/100 - p**5/50 + p**4/60 - p**2/2 + p. Let h(f) be the first derivative of v(f). Factor h(r).
-2*r*(r - 1)**3/5
Let t(l) = l**2 - 7*l + 4. Let a be t(7). Suppose -2*z = -7*z + 4*b + 19, 0 = -a*z + 3*b + 15. Factor 1/2 + 2*y**z - 1/2*y**2 - 2*y.
(y - 1)*(y + 1)*(4*y - 1)/2
Let b be (-264)/(-110)*(-10)/(-4). Determine i so that -9/2*i**4 + 3/2 + b*i**3 - 6*i + 3*i**2 = 0.
-1, 1/3, 1
Let i(p) = p**2 + p + 1. Let k be i(-2). Suppose 6*w = w + 20, -j - 7 = -k*w. Determine g, given that -4/9*g**4 + 0*g**3 + 2/9*g + 0 + 4/9*g**2 - 2/9*g**j = 0.
-1, 0, 1
Let g(l) be the second derivative of 3*l**5/10 - 5*l**4/4 + l**3/2 + 3*l**2 - 7*l - 3. Factor g(s).
3*(s - 2)*(s - 1)*(2*s + 1)
Let b(d) be the third derivative of -d**6/40 + 11*d**5/20 - 5*d**4 + 24*d**3 - 4*d**2. Factor b(k).
-3*(k - 4)**2*(k - 3)
Let w(j) be the third derivative of j**6/300 + j**5/150 - j**4/60 - j**3/15 + 3*j**2. Factor w(q).
2*(q - 1)*(q + 1)**2/5
Let u(z) be the first derivative of 1 - 1/10*z**4 + 0*z**2 - 4/15*z**3 + 0*z. Let u(j) = 0. Calculate j.
-2, 0
Let o = 11 + -9. Determine z so that -2/11*z**5 + 2/11*z**3 - 2/11*z**o + 2/11*z**4 + 0 + 0*z = 0.
-1, 0, 1
Let k(l) be the third derivative of l**4 + 0 + 0*l - 5*l**2 + 6*l**3 + 1/15*l**5. What is h in k(h) = 0?
-3
Suppose s + 2 = 4. Let l(v) be the second derivative of -1/6*v**3 + 0 + 0*v**2 - s*v + 1/12*v**4. Solve l(z) = 0 for z.
0, 1
Let q(r) = r. Let d = 11 + -8. Let i(x) = -5*x**2 - d*x**2 - 6*x + 6*x**2. Let s(w) = i(w) + 6*q(w). Factor s(y).
-2*y**2
Let u(h) be the third derivative of h**6/30 + h**5/15 + 3*h**2. Determine y so that u(y) = 0.
-1, 0
Let h(g) be the second derivative of -g**7/14 - g**6/10 - 4*g. Factor h(y).
-3*y**4*(y + 1)
Let f = -935/3 - -312. Factor f*z + 0*z**3 + 2/3*z**4 + 0 - 2/3*z**2 - 1/3*z**5.
-z*(z - 1)**3*(z + 1)/3
Factor 0*u + 0 + 0*u**2 + 0*u**4 - 2/3*u**5 + 2/3*u**3.
-2*u**3*(u - 1)*(u + 1)/3
Let d(p) be the first derivative of 2*p**5/15 - 2*p**3/9 - 6. What is b in d(b) = 0?
-1, 0, 1
Let r(k) be the first derivative of 12*k**5/5 - 4*k**4 - 20*k**3/3 + 4*k**2 + 6. Factor r(w).
4*w*(w - 2)*(w + 1)*(3*w - 1)
Let k(x) be the first derivative of -x + 2 + 0*x**2 + 1/36*x**4 + 1/9*x**3. Let h(w) be the first derivative of k(w). Factor h(i).
i*(i + 2)/3
Let g(k) be the third derivative of k**8/280 + 2*k**7/525 - k**6/75 - k**5/75 + k**4/60 + 18*k**2. What is v in g(v) = 0?
-1, 0, 1/3, 1
Let m(y) = -3*y + 3. Let g be m(0). Factor 0*v**g + v**4 - v**2 + 1/2*v - 1/2*v**5 + 0.
-v*(v - 1)**3*(v + 1)/2
Let j(y) be the second derivative of y**6/30 - y**5/10 + y**4/12 - 10*y. Solve j(c) = 0 for c.
0, 1
Let l be 2/(-3)*54/(-12). Let w(s) be the third derivative of 0*s**l + 1/60*s**5 + 1/120*s**6 - 1/210*s**7 - 1/24*s**4 + 0*s + 3*s**2 + 0. Factor w(t).
-t*(t - 1)**2*(t + 1)
Solve -3*l**2 + 0 + 0 - 3*l**3 - l - l**4 + 0*l = 0.
-1, 0
Find d such that -1/2*d**2 - 2 - 2*d = 0.
-2
Let m = 23 + -551/24. Let s(d) be the second derivative of 0*d**2 - m*d**4 + 0*d**3 + 0 + 2*d. Determine k so that s(k) = 0.
0
Let u(f) = -7 + 2 - 6*f + 2. Let o be u(-1). Factor -2/3*w**o - 2/3 - 2*w - 2*w**2.
-2*(w + 1)**3/3
Let g be 2 + 74/(-25) + 1. Let p(s) be the first derivative of -1/5*s - g*s**5 - 2 + 0*s**2 + 2/15*s**3 + 0*s**4. Factor p(d).
-(d - 1)**2*(d + 1)**2/5
What is j in 0 + 66/7*j**4 - 99/7*j**3 - 15/7*j**5 - 12/7*j + 60/7*j**2 = 0?
0, 2/5, 1, 2
Let z(b) be the first derivative of b**4/12 - 5*b**3/9 + 7*b**2/6 - b + 2. Factor z(p).
(p - 3)*(p - 1)**2/3
Let o(v) be the third derivative of 5*v**8/336 + v**7/21 - v**6/6 - v**5/6 + 5*v**4/8 - 64*v**2. What is u in o(u) = 0?
-3, -1, 0, 1
Factor 16 - 63*s**2 + 16*s**4 + 65*s + 139*s**2 + 28*s**3 + 2*s**5 + 22*s**3 - 9*s.
2*(s + 1)**2*(s + 2)**3
Let g(j) = 4*j - 3. Let x be g(2). Suppose 4*i + m - 43 = 0, -2*m - 39 = -x*i + 31. Solve 2*w**2 - 12*w**2 - 6*w**4 - 2 + 20*w**3 - 14*w**2 + i*w = 0 for w.
1/3, 1
Let z(f) be the first derivative of 1/6*f**2 - 3 - 1/12*f**4 + 2/3*f - 2/9*f**3. Factor z(q).
-(q - 1)*(q + 1)*(q + 2)/3
Let o(s) be the second derivative of 1/63*s**7 + 0 - 2/3*s**2 - s - 2/15*s**5 + 1/3*s**3 + 0*s**6 + 1/9*s**4. Find d, given that o(d) = 0.
-2, -1, 1
Factor -2/7*r + 2/7*r**3 + 2/7*r**4 - 6/7*r**2 + 4/7.
2*(r - 1)**2*(r + 1)*(r + 2)/7
Let j(g) be the second derivative of -g**5/50 + g**4/15 - g**3/15 - 9*g. Solve j(u) = 0 for u.
0, 1
Factor 6/5*u + 4/5 + 2/5*u**2.
2*(u + 1)*(u + 2)/5
Let m(t) be the first derivative of -t**4/38 + 2*t**3/19 + 9*t**2/19 + 10*t/19 - 27. Suppose m(c) = 0. Calculate c.
-1, 5
Factor 8*d - 3*d**2 - 2*d**3 + 4*d**4 + 35 - 3*d**4 - 39.
(d - 2)*(d - 1)**2*(d + 2)
Let m = -161334/7 + 22966. Let v = m - -82. Suppose 0*x**2 - v*x**4 + 0*x**3 + 0 + 0*x = 0. Calculate x.
0
Factor 5*b**5 - 86*b**2 + 31*b**2 + 31*b - b**3 - 20 - 4*b**3 - 91*b + 15*b**4.
5*(b - 2)*(b + 1)**3*(b + 2)
Let k be 2 - (-4 + -3 + 4). Let i(d) be the second derivative of 3*d - 5/42*d**4 + 1/70*d**k + 0