4. Let k be w(-7). Let r(p) = 2 - 4*p + p + 4*p**2 + p**2. Let z(v) = 4*v**2 - 3*v + 2. Let b(n) = k*z(n) - 3*r(n). Factor b(q).
(q - 2)*(q - 1)
Factor -2/3*g**3 + 0 + 2/3*g - 1/3*g**4 + 1/3*g**2.
-g*(g - 1)*(g + 1)*(g + 2)/3
Let g(t) be the third derivative of t**7/1155 - t**6/660 - 4*t**2. Suppose g(j) = 0. What is j?
0, 1
Let z be (8/6)/((-5)/(-15)). Suppose -2*n**2 + 2*n**5 - 12*n**4 - 2*n**3 + 10*n**4 + z*n**2 = 0. Calculate n.
-1, 0, 1
Let q(s) be the third derivative of -2*s**2 + 1/144*s**4 + 0*s - 1/360*s**5 + 1/18*s**3 + 0. Suppose q(t) = 0. What is t?
-1, 2
Let v(y) = -4*y - 1. Let o be v(-1). Factor 5*t**2 + o*t - 4*t**2 + 2*t**2.
3*t*(t + 1)
Factor 0*n**2 + 0 - 2/5*n**3 + 0*n.
-2*n**3/5
Let u(l) = -l**2 - 11*l - 4. Let j(b) = -15*b - 4*b - 12*b - 7 - b**2 + 8*b. Let a(k) = 2*j(k) - 5*u(k). Find h such that a(h) = 0.
-2, -1
Suppose 3*h - 3 - 6 = 0. Let y(v) be the first derivative of h + v**3 + 3/4*v**2 + 0*v. Factor y(t).
3*t*(2*t + 1)/2
Suppose 4*a - 1 = -1. Let s(w) be the first derivative of a*w**2 + 0*w + 3 - 2/9*w**3. Factor s(m).
-2*m**2/3
Let n(a) be the first derivative of -a**6/1440 - 2*a**3/3 - 1. Let u(z) be the third derivative of n(z). Factor u(b).
-b**2/4
Suppose -3/2 - 11/2*s - 3/2*s**4 - 1/6*s**5 - 5*s**3 - 23/3*s**2 = 0. Calculate s.
-3, -1
Find f, given that -1/6*f + 1/2*f**3 + 0 - 1/3*f**2 = 0.
-1/3, 0, 1
Let g be 5/7 - 2/(-7). Let i(u) be the first derivative of -1/8*u**4 - 1/2*u - g + 1/6*u**3 + 1/4*u**2. Factor i(j).
-(j - 1)**2*(j + 1)/2
Let b(l) be the first derivative of l**4/6 - l**3/3 + l/3 + 2. What is f in b(f) = 0?
-1/2, 1
Let y = -2094261/490 - -4274. Let g = y - -1969/4410. Factor -2/9*h**2 - g + 2/3*h.
-2*(h - 2)*(h - 1)/9
Let u(l) be the third derivative of -l**8/840 + l**7/350 + l**6/600 - l**5/100 + l**4/120 + 7*l**2. Suppose u(d) = 0. Calculate d.
-1, 0, 1/2, 1
Factor 20 - 220*g**2 + 20*g + 12*g**3 - 32*g**3 + 205*g**2 - 5*g**4.
-5*(g - 1)*(g + 1)*(g + 2)**2
Let u(l) = -2*l - 37. Let i be u(-21). Find r, given that 0*r + 4*r**i + 5/3*r**4 + 1/3*r**2 + 0 - 2*r**3 = 0.
-1, 0, 1/4, 1/3
Let k(u) = u**2 - 26*u + 105. Let s be k(21). Suppose 1/6*d**2 + 1/6*d**3 + s + 0*d = 0. What is d?
-1, 0
Let z(m) be the second derivative of m**5/20 + m**4/3 - m**3/6 - 2*m**2 + 17*m. Find x, given that z(x) = 0.
-4, -1, 1
Suppose -j = q + 1, -3*j + 4*q - q + 15 = 0. Solve -13*u + 18*u**3 + 12*u**j + 18*u**3 - 19*u - 16 = 0.
-2/3, 1
Let a = 11 - 9. Factor a*f**3 - 4*f**3 - f**4 + 3*f**4 + 0*f**3.
2*f**3*(f - 1)
Suppose 2*c - 3 = 53. Let f be -2 + 92/c - 1. Suppose -26/7*d**2 - 2/7 - 2*d + 4*d**4 - f*d**3 + 16/7*d**5 = 0. What is d?
-1, -1/2, -1/4, 1
Let l(s) = s**2 + 3*s - 5. Let o be l(-4). Let b be 10*o/(1 + -3). Factor -b*c**2 - 7 + 3*c**2 + 7 + c**4 - c**3.
c**2*(c - 2)*(c + 1)
Let k(g) = 2*g**2 - g + 3. Let y(i) = -7*i**2 + 4*i - 11. Let n(v) = -22*k(v) - 6*y(v). Factor n(x).
-2*x*(x + 1)
Let m(u) be the second derivative of -u**5/4 - 5*u**4/3 - 5*u**3/2 + 60*u. Factor m(a).
-5*a*(a + 1)*(a + 3)
Factor 1/6*o**2 - 1/6 - 1/3*o + 1/3*o**3.
(o - 1)*(o + 1)*(2*o + 1)/6
Let o be 1/1 + (2 - 4). Let y(l) = l**4 + l**2 + l - 1. Let u(w) = -w**3 + w**2 + w - 1. Let f(s) = o*y(s) + u(s). Solve f(h) = 0 for h.
-1, 0
Let j(o) = -o**3 + o + 1. Let y(u) = 4*u**3 + 14*u**2 + 7*u - 1. Let x(g) = -5*j(g) - 5*y(g). Factor x(v).
-5*v*(v + 4)*(3*v + 2)
Let y = 274/1395 - -4/155. Determine q so that 2/9*q**5 + 2/3*q**3 + y*q**2 + 2/3*q**4 + 0 + 0*q = 0.
-1, 0
Suppose 3*a = -2*p + 8, a = -4*p - 4*a + 16. Factor 3*d + p + d + 0*d + 2*d**2 - 2.
2*(d + 1)**2
Factor 45*r + 21*r**2 + 27 + 3*r**3 + 7*r - 7*r.
3*(r + 1)*(r + 3)**2
What is j in 0*j**2 + 2/9*j**4 - 4/3*j**3 + 64/9*j + 0 = 0?
-2, 0, 4
Let d(n) be the third derivative of -n**5/160 - n**4/4 - 4*n**3 - 19*n**2. Let d(w) = 0. Calculate w.
-8
Let u(s) be the third derivative of s**8/672 + s**7/420 - s**6/240 - s**5/120 + 16*s**2. Solve u(d) = 0 for d.
-1, 0, 1
Suppose -w = 0, -2*f + w + 4*w = 18. Let r = f - -37/4. Factor 1/4 - 1/2*s**3 + 0*s**2 + 1/2*s - r*s**4.
-(s - 1)*(s + 1)**3/4
Let f(s) be the first derivative of -1/9*s**4 + 2/27*s**3 + 0*s**2 + 2/45*s**5 + 0*s - 5. What is m in f(m) = 0?
0, 1
Let o(r) be the third derivative of -r**8/462 - 19*r**7/1155 - 9*r**6/220 - 4*r**5/165 + r**4/33 - 16*r**2. Determine n, given that o(n) = 0.
-2, -1, 0, 1/4
Let t(h) be the second derivative of -h**6/480 + h**5/240 + h**4/96 - h**3/24 - 3*h**2/2 - 2*h. Let b(k) be the first derivative of t(k). Solve b(d) = 0.
-1, 1
Let m = -3 - -3. Let l be ((3/(-3))/1)/((-12)/60). Factor -2/5*i**l + 2/5*i + m*i**3 + 0 - 4/5*i**2 + 4/5*i**4.
-2*i*(i - 1)**3*(i + 1)/5
Let j(y) = 104*y**2 + 36*y + 3. Let u(l) = l**2. Let v(i) = -j(i) - 4*u(i). Suppose v(f) = 0. Calculate f.
-1/6
Suppose -3*i + 16 = -2*c, -30 = -2*i - 3*i + 4*c. Let l(f) be the second derivative of f + 1/6*f**4 + 0*f**3 + 1/10*f**5 + 0 + 0*f**i. Let l(p) = 0. What is p?
-1, 0
Let f be 8/(-5 - -3) - (-660)/154. Factor 4/7*l + 2/7*l**2 + f.
2*(l + 1)**2/7
Factor -4 + 2*w + 2*w + 7*w**2 + 0 - 8*w**2.
-(w - 2)**2
Suppose -6*n = 2*p - n - 1, -5*p - n + 14 = 0. Factor -p*r**2 + 6 + 4*r**2 + 8*r + r**2.
2*(r + 1)*(r + 3)
Let m(u) = u**3 + 9*u**2 + 13*u - 5. Let c be m(-7). Let o(k) be the third derivative of k**c + 0 + 0*k**4 + 0*k**3 + 1/120*k**6 + 0*k + 0*k**5. Factor o(b).
b**3
Let x(n) be the third derivative of -3*n**2 + 1/45*n**5 - 1/180*n**6 + 0*n**3 + 0 - 1/36*n**4 + 0*n. Factor x(p).
-2*p*(p - 1)**2/3
Let r(w) = 4*w**2 + 3*w + 1. Let a(t) = -t**2 - 1. Let n(d) = -a(d) - r(d). Suppose n(c) = 0. What is c?
-1, 0
Let n(g) = g**3 + g + 1. Let u(f) = 10*f**3 - f**2 + 6. Let p be (10/4)/((-9)/18). Let l(v) = p*n(v) + u(v). Find b, given that l(b) = 0.
-1, 1/5, 1
Suppose 0 + 3 = n. Factor -i**2 + i**2 - i**4 + n*i**2 - 2*i**4.
-3*i**2*(i - 1)*(i + 1)
Let g(s) be the first derivative of 27*s**5/5 - 45*s**4/2 + 4*s**3 + 21*s**2 + 9*s - 29. Solve g(p) = 0 for p.
-1/3, 1, 3
Factor 12/5*m + 2/5*m**2 + 18/5.
2*(m + 3)**2/5
Let s(y) be the third derivative of 0*y + 0 + 5*y**2 + 0*y**5 + 0*y**4 - 1/90*y**6 + 0*y**3 + 2/315*y**7. Factor s(z).
4*z**3*(z - 1)/3
Let k = 255 - 255. Factor 0*g**2 + 0*g**4 + 0*g + 1/4*g**5 + k - 1/4*g**3.
g**3*(g - 1)*(g + 1)/4
Let l = 42 + -39. Solve 5/2*v + 1 - 1/2*v**4 - 1/2*v**l + 3/2*v**2 = 0 for v.
-1, 2
Let j be ((-6)/8)/((-396)/24). Let h(r) be the first derivative of -4/55*r**5 - 3 - 1/33*r**6 - j*r**4 + 0*r**3 + 0*r + 0*r**2. What is a in h(a) = 0?
-1, 0
Let g = -92 - -94. Let c(b) be the second derivative of -2*b**g + 1/2*b**4 - b - 5/3*b**3 + 0. Factor c(q).
2*(q - 2)*(3*q + 1)
Let r(h) be the second derivative of -h**8/8400 - h**7/12600 - 5*h**4/12 - 3*h. Let f(q) be the third derivative of r(q). Determine i so that f(i) = 0.
-1/4, 0
Let n(i) = -i**2 - i - 7*i**4 + 4*i**4 + 4*i**4. Let v(d) = -d**5 - 2*d**4 - 5*d**3 + 8*d**2 + 6*d. Let a(t) = -6*n(t) - v(t). Find m, given that a(m) = 0.
0, 1, 2
Factor -19/3*d + 40/3*d**2 + 2/3 + 25/3*d**3.
(d + 2)*(5*d - 1)**2/3
Let c(k) be the second derivative of -1/9*k**3 + 1/9*k**4 + 1/30*k**5 + 0 - 2/3*k**2 - 3*k. Factor c(f).
2*(f - 1)*(f + 1)*(f + 2)/3
Suppose 2*i = -5 + 11. Let d(k) be the second derivative of -2*k - 1/9*k**4 + 0*k**i + 0 + 1/3*k**2 + 0*k**5 + 1/45*k**6. Find l, given that d(l) = 0.
-1, 1
Let v(f) be the first derivative of -3*f**4/4 - 8*f**3 - 39*f**2/2 - 18*f + 60. Determine r so that v(r) = 0.
-6, -1
Let -1/2*b**3 - 1/2*b**2 + 1/2*b + 1/2 = 0. What is b?
-1, 1
Let z(t) be the second derivative of -1/2*t**2 + 0 - 1/108*t**4 + 9*t - 1/9*t**3. Factor z(f).
-(f + 3)**2/9
Suppose b - 5*o = -0*b - 2, 4*o - 10 = -2*b. Factor r**2 - 19*r**4 + 21*r**4 - b*r**2.
2*r**2*(r - 1)*(r + 1)
Let l(k) be the second derivative of -8*k + 0 + 14/5*k**5 + 2/21*k**7 - 16/3*k**4 - 4/5*k**6 - 4*k**2 + 6*k**3. Factor l(p).
4*(p - 2)*(p - 1)**4
Factor -3*z**2 - 3*z + z - z.
-3*z*(z + 1)
Let v(h) = -10*h**2 - 12*h - 2. Let n(m) = m**3 - 39*m**2 - 49*m - 9. Let i(b) = 2*n(b) - 9*v(b). Factor i(z).
2*z*(z + 1)*(z + 5)
Let m(r) = -5*r**4 - 3*r**3 - 5*r**2 + 21*r + 1. Let o(y) = -y**4 - y**3 - y**2 + 5*y. Let b(q) = 4*m(q) - 18*o(q). Factor b(n).
-2*(n - 2)*(n - 1)**2*(n + 1)
Let x = 49 - 145/3. Factor -r**2 + 1/3 + x*r.
-(r - 1)*(3*r + 1)/3
Let q(g) be the second derivative o