irst derivative of -n**7/168 - n**6/120 + n**5/80 + n**4/48 - n - 4. Let w(x) be the first derivative of b(x). Suppose w(f) = 0. What is f?
-1, 0, 1
Let y(s) be the third derivative of s**7/1260 - s**6/180 - s**4/8 - 6*s**2. Let p(q) be the second derivative of y(q). Find j, given that p(j) = 0.
0, 2
Let q(d) be the third derivative of -1/350*d**7 + 0*d**4 + 0 - 9/100*d**5 + 0*d**3 + 3/100*d**6 - 4*d**2 + 0*d. Factor q(t).
-3*t**2*(t - 3)**2/5
Let k(r) be the first derivative of r**3/6 + r**2/4 - r - 4. Solve k(g) = 0 for g.
-2, 1
Let 8/3*m - 2 - 2/3*m**2 = 0. What is m?
1, 3
Let k(n) = 2*n**5 - 26*n**4 - 12*n**3 + 20*n**2 + 26*n + 14. Let g(m) = m**5 - 9*m**4 - 4*m**3 + 7*m**2 + 9*m + 5. Let f(r) = -8*g(r) + 3*k(r). Factor f(h).
-2*(h - 1)*(h + 1)**4
Let d(v) = -v**2 + 4*v + 2. Let x = 0 - -4. Let f be d(x). What is m in 7*m**4 - 5*m**4 + m**2 + 4*m**3 + m**f = 0?
-1, 0
Factor 1/3 + 0*d - 1/3*d**2.
-(d - 1)*(d + 1)/3
Let u(l) be the first derivative of 2*l**3/3 - 12. Factor u(s).
2*s**2
Let z(x) be the third derivative of -x**7/735 + x**6/140 + x**5/30 - 5*x**4/28 - 6*x**3/7 - 46*x**2. Solve z(v) = 0 for v.
-2, -1, 3
Let f(q) be the third derivative of -q**7/70 + q**6/10 - 3*q**5/20 + 28*q**2. Find y such that f(y) = 0.
0, 1, 3
Let u(q) be the second derivative of -q**5/70 - q**4/21 + q**3/21 + 2*q**2/7 + 21*q. Factor u(z).
-2*(z - 1)*(z + 1)*(z + 2)/7
Let g(o) be the third derivative of o**6/120 - o**5/60 - o**4/24 + o**3/6 - 21*o**2. Let g(w) = 0. What is w?
-1, 1
Let k(s) = -12*s**2 + 6*s - 4. Let n(t) = t**2. Let w(v) = k(v) + 10*n(v). Let w(i) = 0. What is i?
1, 2
Let j(t) = 2*t**2 - t + 1. Let a(h) = -79 + 42 + h + 38. Let n(m) = 4*a(m) - j(m). Factor n(u).
-(u - 3)*(2*u + 1)
Let t(j) be the second derivative of j**4/3 + 4*j**3/3 + 2*j**2 - 7*j. Determine m, given that t(m) = 0.
-1
Suppose -2*s + 70 = -2*q - 2*q, -4*s + q = -119. Suppose 15*w**2 - 12*w**2 - 18*w + s - 2 = 0. What is w?
3
Factor -23*o + 28*o**4 + 36*o**3 + 2*o**2 - 50*o**2 + 7*o.
4*o*(o - 1)*(o + 2)*(7*o + 2)
Let b(k) be the first derivative of -k**5/5 + k**4/2 - k**2 + k - 5. Factor b(f).
-(f - 1)**3*(f + 1)
Factor -1/3*o**2 + 2/9*o + 0 + 1/9*o**3.
o*(o - 2)*(o - 1)/9
Let s(t) be the third derivative of t**8/10080 + t**7/1260 + t**6/360 - t**5/15 - 4*t**2. Let r(z) be the third derivative of s(z). Solve r(p) = 0 for p.
-1
Let s(k) = -13*k**4 + 7*k**3 - 4*k**2 - 5. Let o(m) = 7*m**4 - 3*m**3 + 2*m**2 + 3. Let l(h) = -5*o(h) - 3*s(h). Factor l(a).
2*a**2*(a - 1)*(2*a - 1)
Let a(w) = w - 1. Let x(q) = -2*q**2 + 9*q - 9. Let l be (-6)/(-2) + -1 + -1. Let p(n) = l*a(n) - x(n). Factor p(s).
2*(s - 2)**2
Let i = 15 - 15. Factor 1/4*d**2 + i*d - 1.
(d - 2)*(d + 2)/4
Let j(o) = 2*o**2 - 5*o + 2. Let i be j(3). Suppose 5*s - 15 = 0, 4*f + i*s - 18 = 5. Determine l, given that -l**f + 0*l**2 - l**3 + 2*l**2 = 0.
0, 1
Let t(s) = -2*s**3 + 2*s**2 + 3*s + 1. Let q be t(-1). Determine o so that 2*o**2 - 4*o**q - 2*o + 2*o**3 + 0*o**2 + 2*o**4 = 0.
-1, 0, 1
Suppose m - 4 = 4*g, 0*m + 2*g = m - 4. Let 8*r - 2*r**2 + 0*r - m - 2*r + 0*r**2 = 0. Calculate r.
1, 2
Let a(d) be the first derivative of -d**3/12 + d/4 + 6. What is p in a(p) = 0?
-1, 1
Let f be 5/2 - (-36)/72. Suppose 5 = 4*y - 3. Factor -1/2*l**4 + 2*l - 3/2*l**2 - 2*l**f + y.
-(l - 1)*(l + 1)*(l + 2)**2/2
Suppose z - 1 = 3. Find a such that 2/3 + a**2 - 7/3*a - 5/3*a**z + 7/3*a**3 = 0.
-1, 2/5, 1
Let u(c) = -2*c**2 - 4*c + 2. Let w(i) = -i + 1. Let t(x) = -2*u(x) + 4*w(x). Let t(k) = 0. Calculate k.
-1, 0
Let y = -751/8 - -94. Factor -y*b**2 + 1/2 + 0*b.
-(b - 2)*(b + 2)/8
Factor 0 + 3/4*t**3 + 0*t + 0*t**4 - 3/4*t**5 + 0*t**2.
-3*t**3*(t - 1)*(t + 1)/4
Let r(p) be the third derivative of p**6/600 + p**5/150 - 16*p**2. Determine n, given that r(n) = 0.
-2, 0
Let r(w) be the third derivative of w**7/42 + w**6/12 - w**5/12 - 5*w**4/12 + w**2. Determine q, given that r(q) = 0.
-2, -1, 0, 1
Let n = -1688/7 + 455767/1890. Let r(y) be the third derivative of 0*y - 1/270*y**6 + 3*y**2 + 1/945*y**7 + 0*y**3 + n*y**5 + 0*y**4 + 0. Factor r(x).
2*x**2*(x - 1)**2/9
Suppose 0 = 2*g - 0 - 4. Factor -8*s**2 - 9 - g*s**2 + 7*s**2 - 12*s.
-3*(s + 1)*(s + 3)
Let w(u) = u**4 + u**3 + u - 1. Let i(z) = -10*z**4 - 12*z**3 - 2*z**2 - 11*z + 11. Let r(c) = 2*i(c) + 22*w(c). Suppose r(l) = 0. What is l?
-1, 0, 2
Let g(z) be the second derivative of -z**3/6 - z**2/2 + z. Let a(x) = x**2 + 2*x + 1. Let d be 12/((-6)/2)*1. Let o(v) = d*a(v) - 6*g(v). Factor o(f).
-2*(f + 1)*(2*f - 1)
Let j be (5/15)/(0 - 1/(-6)). Suppose 2/7*m**j + 4/7 - 6/7*m = 0. What is m?
1, 2
Factor -91*l**2 - 2*l + 2*l**3 + 2*l**3 + 88*l**2 - 5*l**3.
-l*(l + 1)*(l + 2)
Let y(r) = -r**3 - 6*r**2 - r - 2. Let z be y(-6). Suppose d - z = -d. Factor -h**d + 1 + 0*h - 4*h + h - 3.
-(h + 1)*(h + 2)
Let l(o) be the second derivative of -o**7/10080 - o**6/960 - o**5/240 + 5*o**4/12 - 2*o. Let k(d) be the third derivative of l(d). Suppose k(s) = 0. What is s?
-2, -1
Let w = -85/231 + 23/21. Let g be (-12)/22 - (-56)/22. Factor 6/11*d**g - 2/11*d + w*d**3 + 0.
2*d*(d + 1)*(4*d - 1)/11
Let i(b) = 10*b**4 + 8*b**3 - 3*b**2 - 4*b - 11. Let a(v) = v**4 + v**3 - v - 1. Let f(p) = -18*a(p) + 2*i(p). What is r in f(r) = 0?
-2, 1
Suppose 5*x - 5 = 5. Find r, given that -6 + 4 + r**x - 3*r + 4 = 0.
1, 2
Factor -49*w**2 - w + 7 - 6*w - 1.
-(7*w - 2)*(7*w + 3)
Suppose 0 = 2*o - o - 3. Let 0 + 2/5*x**o + 0*x**2 - 2/5*x = 0. What is x?
-1, 0, 1
Let a(g) = -g**4. Let r(c) = 8*c**4 - 4*c**3 - 4*c**2 + 4*c. Let x(k) = 4*a(k) + r(k). Factor x(j).
4*j*(j - 1)**2*(j + 1)
Suppose 4*j - 5*r = -34 - 340, 2*r = -j - 87. Let u = 281/3 + j. Factor 0*y + 2*y**2 - u - 2/3*y**3.
-2*(y - 2)**2*(y + 1)/3
Let h(g) be the first derivative of 5 + 0*g - 1/18*g**4 - 2/45*g**5 + 1/9*g**2 + 2/27*g**3. Factor h(l).
-2*l*(l - 1)*(l + 1)**2/9
Let o(c) be the third derivative of 7*c**2 + 0*c + 1/225*c**5 + 1/900*c**6 + 0 + 0*c**3 + 0*c**4. Factor o(x).
2*x**2*(x + 2)/15
Factor 15/4 - 35/4*y + 25/4*y**2 - 5/4*y**3.
-5*(y - 3)*(y - 1)**2/4
Let b(i) be the first derivative of 1/10*i**5 + 0*i + 5 + 3/8*i**4 + 0*i**2 + 1/3*i**3. Factor b(v).
v**2*(v + 1)*(v + 2)/2
Let a(j) be the second derivative of 1/9*j**3 + 4/15*j**5 + 0 - 4/45*j**6 + 0*j**2 - 3*j - 5/18*j**4. Solve a(c) = 0 for c.
0, 1/2, 1
Solve 4/3 - 1/3*s**2 + s = 0 for s.
-1, 4
Factor 0 - 5/4*m**2 + 1/2*m - 1/2*m**3 + 5/4*m**4.
m*(m - 1)*(m + 1)*(5*m - 2)/4
Solve -8/3*v - 8/3 + 2/3*v**2 + 2/3*v**3 = 0.
-2, -1, 2
Let i(a) be the first derivative of -a**4 - 4*a**3 - 4*a**2 - 3. Factor i(g).
-4*g*(g + 1)*(g + 2)
Factor 1/2*p**2 + 1/4*p**5 - 3/4 + 5/4*p - 3/2*p**3 + 1/4*p**4.
(p - 1)**3*(p + 1)*(p + 3)/4
Factor j**3 - j - 2*j**2 + j + 0*j**2.
j**2*(j - 2)
Let m(a) be the first derivative of a**6/180 - a**3/3 - 1. Let t(i) be the third derivative of m(i). Suppose t(s) = 0. What is s?
0
Let m(i) be the second derivative of 5*i + 1/105*i**7 + 28/15*i**3 + 1/2*i**5 + 8/75*i**6 + 0 + 8/5*i**2 + 19/15*i**4. Factor m(h).
2*(h + 1)**2*(h + 2)**3/5
Suppose a - 4*s = s - 24, 0 = -2*s + 10. Let q be a + (-2)/6*-3. Let 4*b**2 + 2*b**q - 4*b**2 - 2 = 0. Calculate b.
-1, 1
Solve 0*x**3 + 13*x**5 + 6*x**4 - 3*x**3 - 16*x**5 = 0.
0, 1
Suppose -3*i + 2*k + 14 = 0, -i + 4*i - 5*k - 26 = 0. Factor -4*x**i - x**2 + 0*x**2 + 2*x**2.
-3*x**2
Factor 0 + 1/4*v**2 + 0*v.
v**2/4
Let d(m) be the first derivative of 27*m**6/200 - 9*m**5/50 + m**4/10 + m**3 - 1. Let s(j) be the third derivative of d(j). Factor s(h).
3*(9*h - 2)**2/5
Let m be ((-2)/(-3))/((-2)/(-72)). Factor 9*x**3 + 12*x**5 - 10*x + m*x**2 - 3*x**3 - x - 27*x**4 - 7*x + 3.
3*(x - 1)**3*(x + 1)*(4*x - 1)
Let q(m) be the third derivative of -m**4/12 - 5*m**3/6 + 2*m**2. Let n be q(-4). What is s in s**n + 0*s**4 + 0*s**4 - s**4 = 0?
0, 1
Suppose -2 = n, -2*c - 2*c + 46 = n. Let b be (-18)/(-8) + (-3)/c. Factor w**2 - 2*w - b*w**4 + 3*w**2 - 2*w**2 + 2*w**3.
-2*w*(w - 1)**2*(w + 1)
Solve 8/13 + 88/13*d + 242/13*d**2 = 0.
-2/11
Let g(c) be the second derivative of c**6/15 + c**5/10 - c**4/6 - c**3/3 - 4*c. Factor g(k).
2*k*(k - 1)*(k + 1)**2
Let w(i) be the third derivative of i**8/80640 - i**5/15 + 5*i**2. Let g(b) be the third derivative of w(b). Suppose g(v) = 0. What is v?
0
Suppose -2*k = -j + 3*j, 4*k + j = 9. Factor 2/9*g**4 + 2/9*g