 the third derivative of -z**6/200 - z**5/50 - z**4/40 + 7*z**2. Factor x(g).
-3*g*(g + 1)**2/5
Suppose -1/4*p**4 + 0*p - p**3 + 1/4*p**2 + p**5 + 0 = 0. Calculate p.
-1, 0, 1/4, 1
What is t in -10/3*t**3 + 0 + 32/3*t**2 - 32/3*t + 1/3*t**4 = 0?
0, 2, 4
Let a(q) = 3*q**3 + 12*q**2 + 6*q. Let b(n) = 8*n + 3*n**3 - 3*n - 1 + 8*n**2 + 6*n**2 - n**2. Let m(u) = -4*a(u) + 3*b(u). Determine d, given that m(d) = 0.
-1
Suppose -w - 6 = -4*w. Factor -w*t**3 + t - 2*t - 3*t + 6*t**2.
-2*t*(t - 2)*(t - 1)
Let m = 2 - -2. Let o = 8 - m. Solve -2*x**3 - 2*x**o + 4*x**3 + 4*x**2 + 0*x**4 = 0 for x.
-1, 0, 2
Let l(s) be the first derivative of -9*s**3 + 18*s**2 - 12*s - 8. Suppose l(u) = 0. Calculate u.
2/3
Suppose 10 = r + 17. Let d be (1 - -2) + 19/r. Suppose 2/7 + 0*v - 4/7*v**2 + d*v**4 + 0*v**3 = 0. What is v?
-1, 1
Let h(m) = 10*m**2 + 31*m. Let a(j) = 2*j**2 + 6*j. Let f(b) = -22*a(b) + 4*h(b). Suppose f(s) = 0. Calculate s.
-2, 0
Factor 2*r**3 - 5*r**2 + 16*r + 3*r**3 - 26*r.
5*r*(r - 2)*(r + 1)
Let p be (-1)/(-4 + 5/2). Let c(v) be the first derivative of 4 - 8/3*v**3 - v**4 + 0*v**2 + p*v**6 + 6/5*v**5 + 2*v. Factor c(j).
2*(j - 1)*(j + 1)**3*(2*j - 1)
Suppose 0 = 4*k + 5*h + 43, 4*k = -k - 4*h - 56. Let c = 16 + k. Factor -3/2*x**2 - 5/6*x**c + 0 + 2*x**3 + 1/3*x.
-x*(x - 1)**2*(5*x - 2)/6
Let h(j) be the second derivative of -1/100*j**5 + 0 - 2/15*j**3 + 0*j**2 + j - 1/15*j**4. Let h(k) = 0. Calculate k.
-2, 0
Factor 36 - 14*j**2 + 11*j**2 - 10*j - 3*j + j.
-3*(j - 2)*(j + 6)
Let z = 29 + -201/7. Factor -6/7*b**4 - 6/7*b**3 - z*b**2 + 0*b + 0 - 2/7*b**5.
-2*b**2*(b + 1)**3/7
Let n(i) = 5*i**3 + 2*i + 2. Let u be n(-2). Let x be 3*(122/u - -3). Factor 2/7*k + 2/7*k**2 - x - 2/7*k**3.
-2*(k - 1)**2*(k + 1)/7
Let h = 10 + 0. Let d(s) = -s**3 + 10*s**2 - s + 13. Let w be d(h). Factor -1/4*u**w + 0*u + 0 - 1/4*u**2.
-u**2*(u + 1)/4
Let o(n) = -n**2 - 5*n - 2*n + 3*n - 6 - 3*n. Let q be o(-6). Factor -2/9*p**2 + 2/9 + q*p.
-2*(p - 1)*(p + 1)/9
Let q(u) be the second derivative of 3*u**7/14 - 113*u**6/10 + 4099*u**5/20 - 4615*u**4/4 - 4056*u**3 - 4394*u**2 - 9*u. Determine d, given that q(d) = 0.
-2/3, 13
Let d(f) be the second derivative of -f**7/8820 + f**6/1260 - f**5/420 + f**4/2 + 6*f. Let y(q) be the third derivative of d(q). Factor y(g).
-2*(g - 1)**2/7
Let a(m) be the second derivative of -1/75*m**6 - 1/50*m**5 + 1/105*m**7 + 0*m**2 + 0 + 1/30*m**4 + 0*m**3 + 5*m. Factor a(s).
2*s**2*(s - 1)**2*(s + 1)/5
Let r(f) = f**3 + f**2 - f - 1. Let z(p) = -6*p**3 - 5*p**2 + 6*p + 5. Let d = 9 + -4. Let n(s) = d*r(s) + z(s). Factor n(g).
-g*(g - 1)*(g + 1)
Let s(c) be the first derivative of -2*c**5/45 - 5*c**4/18 - 2*c**3/3 - 7*c**2/9 - 4*c/9 - 6. Suppose s(b) = 0. What is b?
-2, -1
Let g(u) be the second derivative of u**7/28 - 3*u**6/10 + 3*u**5/5 + 3*u**4/4 - 9*u**3/4 + 2*u. Determine q, given that g(q) = 0.
-1, 0, 1, 3
Let l(m) be the first derivative of -m**8/4200 + m**7/700 - m**6/300 + m**5/300 + m**3/3 + 4. Let p(q) be the third derivative of l(q). Factor p(d).
-2*d*(d - 1)**3/5
Determine u so that 2 + 0 + 7*u - 10*u + u**2 = 0.
1, 2
Factor c**3 + c**4 - 6*c**2 - c**4 - c - c**4 + 7*c**2.
-c*(c - 1)**2*(c + 1)
Factor -w**4 + 3*w**4 + w - 4*w**5 - 7*w**5 + 10*w**5 - 2*w**2.
-w*(w - 1)**3*(w + 1)
Solve 17/2*u**4 - 45*u**3 + 108*u - 1/2*u**5 + 54*u**2 + 0 = 0.
-1, 0, 6
Let r(c) be the second derivative of 2*c**7/21 + 4*c**6/15 - c**5/5 - 2*c**4/3 - 23*c. Factor r(l).
4*l**2*(l - 1)*(l + 1)*(l + 2)
Let h(j) = j**3 + 3*j**2 - j. Let f be h(-3). Let v(s) = s**3 + 6*s**2 - s - 3. Let c be v(-6). Let -c*k**3 - 2*k**2 - 2*k**2 + 5*k**f = 0. Calculate k.
0, 2
Let c = 711/10 + -71. Let l(z) be the third derivative of 0 - 1/2*z**3 + 0*z + 1/2*z**4 + c*z**6 - 1/70*z**7 - 2*z**2 - 3/10*z**5. Factor l(r).
-3*(r - 1)**4
Let g(u) = 3*u + 6. Let w be g(-5). Let x(r) = 10*r**3 - 23*r**2 + 4*r - 9. Let q(h) = 5*h**3 - 11*h**2 + 2*h - 4. Let l(n) = w*q(n) + 4*x(n). Factor l(v).
-v*(v - 1)*(5*v - 2)
Let g(v) be the third derivative of -v**8/252 - v**7/210 + 13*v**6/360 + v**5/180 - v**4/8 + v**3/9 + 13*v**2. Let g(s) = 0. Calculate s.
-2, -1, 1/4, 1
Let z(u) = u**4 - u**3 - u**2 + u - 1. Let m(h) = -5*h**4 + 5*h**3 + 5*h**2 - 5*h + 1. Let w(x) = m(x) + z(x). Factor w(a).
-4*a*(a - 1)**2*(a + 1)
Suppose -3*z + 18 = 6. Let f(m) be the second derivative of 0*m**5 + 0 + 0*m**2 - 1/30*m**6 + 0*m**z + m + 1/42*m**7 + 0*m**3. Solve f(q) = 0 for q.
0, 1
Let l(u) be the first derivative of 3*u**2/2 + 1. Let z(f) = -f**2 + 5*f. Suppose -y - 82 = -87. Let m(b) = y*l(b) - 3*z(b). Determine h so that m(h) = 0.
0
Let d(t) be the second derivative of t**5/20 + 7*t**4/12 + 7*t**3/6 + 9*t**2/2 - 2*t. Let c be d(-6). Factor -1 + 7/2*j**4 + 19/2*j**c + 1/2*j + 15/2*j**2.
(j + 1)**3*(7*j - 2)/2
Let d(m) be the first derivative of -m**4/12 + m**3/6 + m**2 - 7*m - 4. Let n(o) be the first derivative of d(o). Factor n(r).
-(r - 2)*(r + 1)
Let x(c) = -2*c**3 + 1 + c**2 + 2*c + 4*c**3 - c - 3*c**3. Let w(v) = 9*v**4 - 23*v**3 + 22*v - 6. Let p(a) = w(a) - 2*x(a). Factor p(u).
(u - 2)*(u + 1)*(3*u - 2)**2
Let o(s) be the second derivative of s - 2*s**2 - 1/15*s**6 + 0 - 3/2*s**4 - 7/3*s**3 - 1/2*s**5. Let o(r) = 0. What is r?
-2, -1
Determine a, given that 4/5*a**3 - 6/5*a**2 + 2/5*a + 0 = 0.
0, 1/2, 1
Let y(k) = -4*k**5 + 7*k**3 - 7*k**2 + 7. Let w(c) = -2*c**5 + 3*c**3 - 3*c**2 + 3. Let r(s) = -7*w(s) + 3*y(s). Find o, given that r(o) = 0.
0
Suppose 6 = 4*x - 2*o, -x + 3*o - 9 = 6*o. Let -3/2*k**5 + 3/2*k**2 - 9/2*k**3 + x*k + 9/2*k**4 + 0 = 0. What is k?
0, 1
Let n(m) be the second derivative of m**7/7 - m**6/2 + 3*m**5/5 - m**4/4 - 7*m. Factor n(l).
3*l**2*(l - 1)**2*(2*l - 1)
Let z(l) be the first derivative of l**3 + 3*l**2/2 - 10. Suppose z(p) = 0. Calculate p.
-1, 0
Let w be (-14)/(-6) - (-2)/(-6). Let l(b) = b**3 - 11*b**2 + 7. Let x be l(11). Factor m**3 - 8*m + 12*m**2 + 2*m**4 + 2 - x*m**3 - w*m**3.
2*(m - 1)**4
Suppose -4 - 25 = q - 5*c, -3*c + 3 = 3*q. Let x be q/18 - (-40)/18. Find d such that x*d**4 - 4*d**4 - d**3 + d**4 = 0.
-1, 0
Let h(k) be the first derivative of -2*k**3/15 - 2*k**2/5 + 6*k/5 - 9. Factor h(d).
-2*(d - 1)*(d + 3)/5
Let a = 1599/1496 + 3/136. Factor 18/11 + 2/11*t**2 + a*t.
2*(t + 3)**2/11
Let s(a) = 9*a - 1 + 1 - 2 - 3 + a**2. Let d(n) = -4*n + 2. Suppose -o = o - 4. Let y(x) = o*s(x) + 5*d(x). Factor y(c).
2*c*(c - 1)
Suppose 8*z = 4*z. Factor 1/3*g**4 + 8/3*g**2 + z + 5/3*g**3 + 4/3*g.
g*(g + 1)*(g + 2)**2/3
Suppose 4*x - 2 = -5*v, x + v + 2 = 3. Let c(f) be the third derivative of 0*f**5 + 1/60*f**6 + 0 - 3*f**2 + 0*f**x + 0*f + 0*f**4. Factor c(m).
2*m**3
Let y = 14 - 69/5. Let o(p) be the second derivative of 1/3*p**3 + 3*p + 2/3*p**4 - 4/15*p**6 + y*p**5 - 1/7*p**7 + 0 + 0*p**2. Let o(k) = 0. Calculate k.
-1, -1/3, 0, 1
Let u(i) be the second derivative of i**4/12 - 4*i**3 + 72*i**2 - 35*i. Factor u(h).
(h - 12)**2
Suppose 5 = -5*u - 5. Let t be (u/(-42))/((-4)/(-24)). Factor 2/7*v**3 - 2/7*v**4 + 0 - 2/7*v + t*v**2.
-2*v*(v - 1)**2*(v + 1)/7
Let a(z) be the second derivative of z**8/4480 + z**7/840 + z**6/480 + 7*z**4/12 + z. Let l(h) be the third derivative of a(h). Find c, given that l(c) = 0.
-1, 0
Let m(v) be the second derivative of v**6/140 - v**5/280 - v**4/56 - v**3/3 - 3*v. Let y(p) be the second derivative of m(p). Let y(j) = 0. Calculate j.
-1/3, 1/2
Let v(k) = -23*k**3 - 40*k**2 - 21*k + 1. Let x(u) = -22*u**3 - 40*u**2 - 22*u. Let m(f) = -4*v(f) + 5*x(f). Factor m(c).
-2*(c + 1)**2*(9*c + 2)
Let c(d) be the first derivative of d**3/3 - 3*d**2 + 9*d + 22. Let c(k) = 0. Calculate k.
3
Determine m, given that -4*m**2 + 4*m**2 + 5*m - 10 + 2*m**2 + 3*m**2 = 0.
-2, 1
Let h(o) be the third derivative of -o**8/112 - o**7/35 + o**5/10 + o**4/8 - 8*o**2. Factor h(d).
-3*d*(d - 1)*(d + 1)**3
Let s(w) = -26*w**4 - 12*w**3 - 3*w**2 - 17. Let o(q) = 9*q**4 + 4*q**3 + q**2 + 6. Let n(m) = 17*o(m) + 6*s(m). Solve n(u) = 0.
-1, -1/3, 0
Let a be 5/(-14)*(-496)/310. Factor -5/7*w**3 - 8/7*w**2 - 1/7*w**4 + 0 - a*w.
-w*(w + 1)*(w + 2)**2/7
Let c = 45 - 20. Solve 8*b**4 - 8*b**4 + 16*b**2 - c*b**4 + 5*b**3 + 4*b = 0.
-2/5, 0, 1
Let y be (-4)/8*(6 - 7 - -1). What is f in y*f - 2/3*f**2 - 2/9*f**3 + 8/9 = 0?
-2, 1
Let u = 5 - 4. Suppose -2*l - 5*z + 3 = 