 4. Factor 4*k**4 + 8*k**2 + 7*k**3 - k - 6*k**2 + d*k**2.
k*(k + 1)**2*(4*k - 1)
Let j(t) be the second derivative of 6/5*t**2 - 9*t + 1/20*t**4 + 0 - 1/2*t**3. What is h in j(h) = 0?
1, 4
Let r(f) = -f. Let t be r(0). Factor -z**2 - 3*z**3 + 3*z**2 + t*z**3 + 2*z**3.
-z**2*(z - 2)
Let b(h) = 9*h**5 + 4*h**3 - 13*h**2 - 13. Let g(v) = 4*v**5 + 2*v**3 - 6*v**2 - 6. Let p(k) = 6*b(k) - 13*g(k). Find a such that p(a) = 0.
-1, 0, 1
Let v be (-1)/(-5) + (-56)/(-20). Let s(l) be the second derivative of 0 + l - 1/54*l**4 - 1/90*l**5 + 1/9*l**2 + 1/27*l**v. Factor s(q).
-2*(q - 1)*(q + 1)**2/9
Let a = -4139/36 - -115. Let v(h) be the third derivative of -h**2 + 0 - 1/24*h**4 - a*h**5 + 1/9*h**3 + 0*h. Determine z so that v(z) = 0.
-1, 2/5
Suppose -2*p + p = 4*p. Let a(h) be the second derivative of p + 1/42*h**4 + 0*h**5 + 0*h**2 - 3*h - 1/105*h**6 + 0*h**3. Determine d, given that a(d) = 0.
-1, 0, 1
Suppose -6*l - 2325 = -l. Let o = l + 1409/3. Let 4/3 - o*z**3 + 14/3*z + 2*z**2 - 10/3*z**4 = 0. Calculate z.
-1, -2/5, 1
Solve -2*p**3 + 6*p + p**4 - 1 + 4*p - 8*p = 0.
-1, 1
Let i(b) be the first derivative of 1/15*b**3 - 1/20*b**4 + 3 + 0*b + 0*b**2. Factor i(c).
-c**2*(c - 1)/5
What is t in -53*t**4 - 33*t - 6 - 9*t**2 + 65*t**4 - 27*t**2 + 3*t**3 = 0?
-1, -1/4, 2
Find k such that 8/7*k**3 + 2/7*k + 10/7*k**2 + 0 = 0.
-1, -1/4, 0
Let h(k) be the third derivative of k**5/20 - 5*k**4/4 + 25*k**3/2 + 11*k**2. Factor h(o).
3*(o - 5)**2
Let x(p) = 3*p**3 + p**2 + p - 1. Let o be x(1). Let n be o/22 + 174/132. Determine l so that 3/2*l**2 - n*l - 1/2*l**3 + 1/2 = 0.
1
Suppose 5*z - 48 = -5*k - 18, -3*k + 9 = 0. Let x(b) be the first derivative of 2 + 1/10*b**4 + 0*b**z - 4/5*b - 3/5*b**2. Factor x(v).
2*(v - 2)*(v + 1)**2/5
Suppose n = -n + 12. Suppose 0 = 4*c - n*k + k + 8, -c = k - 7. Factor 8/3*t**2 - 2*t**c - 2/3*t + 0.
-2*t*(t - 1)*(3*t - 1)/3
Let t be (-9)/(54/(-4))*1. Let n(f) be the first derivative of 1 + 2*f - t*f**3 + 0*f**2. What is j in n(j) = 0?
-1, 1
Let t(k) = 7*k**2 - k + 4. Let p(r) = 10*r**2 - 2*r + 6. Let w(i) = -5*p(i) + 7*t(i). Find d such that w(d) = 0.
1, 2
Let u(h) be the second derivative of h**4/4 - 2*h**3 + h. Factor u(q).
3*q*(q - 4)
Suppose -5*u + 15 = -5*a - 25, 4*u = 5*a + 36. What is l in 2*l + 2*l + 4*l**2 - u - 5*l**2 = 0?
2
Let t(a) = -9*a**2 - a. Suppose -12 = -4*s, 7*s = -3*u + 2*s + 30. Let f(i) = -i**2 - i. Let c(m) = u*f(m) - t(m). Factor c(y).
4*y*(y - 1)
Let u(f) be the third derivative of f**7/280 - f**5/20 + 7*f**2. Factor u(k).
3*k**2*(k - 2)*(k + 2)/4
Let z(m) be the second derivative of 1/6*m**4 - 3*m - 1/3*m**3 - 1/15*m**6 + 0 + 0*m**2 + 1/10*m**5. Suppose z(f) = 0. What is f?
-1, 0, 1
Factor 1 + 7/4*t**2 + 4*t.
(t + 2)*(7*t + 2)/4
Let d(n) = -3*n**4 + 7*n**3 - 2*n**2 - 4. Let t(u) = -u**4 + u**3 - u**2 - 1. Let j(w) = -d(w) + 4*t(w). Factor j(v).
-v**2*(v + 1)*(v + 2)
Suppose -4*q = -3*s + 24, 3*s - 30 = 5*q - 3. Factor s*z**5 + z**3 - 4*z**3 + z**3 - 5*z**5 + 3*z**4.
-z**3*(z - 2)*(z - 1)
Let d = 43/48 - 9/16. Let p(s) be the first derivative of 0*s**2 + d*s - 3 - 1/9*s**3. Solve p(o) = 0.
-1, 1
Let r(j) = -20*j**3 - 16*j**2 - 22*j - 2. Let q(g) = -g**3 - g. Let h(v) = 12*q(v) - r(v). Suppose h(z) = 0. Calculate z.
-1, -1/2
Let f(k) be the second derivative of k**6/40 + 3*k**5/16 + 9*k**4/16 + 7*k**3/8 + 3*k**2/4 - 28*k. Factor f(j).
3*(j + 1)**3*(j + 2)/4
Let b(m) be the third derivative of 1/210*m**5 + m**2 + 0*m**4 + 0*m**3 + 0 + 0*m. Factor b(f).
2*f**2/7
Let n = 19 + -17. Factor 0 + 2/3*o**n - 2*o**3 + 2*o**4 - 2/3*o**5 + 0*o.
-2*o**2*(o - 1)**3/3
Let b(o) be the second derivative of o**5/15 + o**4/4 + o**3/3 + o**2/6 + o. What is h in b(h) = 0?
-1, -1/4
Let c be (-1)/(-3)*(1 + 2). Let f = 3 - c. Factor 3*q - 5*q - 2*q - 6*q**2 - f*q**3.
-2*q*(q + 1)*(q + 2)
Let h = 4/27 - -5/27. Suppose 4*u + 0*u = -u. Find q such that u*q + h*q**2 - 1/3 = 0.
-1, 1
Let f(z) be the second derivative of z**2 - 1/40*z**5 + 1/4*z**3 + 0*z**4 + z + 0. Let a(d) be the first derivative of f(d). Suppose a(r) = 0. What is r?
-1, 1
Let z(t) = t**2 + 5*t + 4. Let x(o) = 3*o**2 + 14*o + 11. Let y(f) = 4*x(f) - 11*z(f). Factor y(a).
a*(a + 1)
Let x = 6 - 4. Suppose 4 = 2*p - x. Find i such that 3*i + 2*i**2 + 0*i**2 + i**p - 2*i = 0.
-1, 0
Let p(b) be the first derivative of -25*b**4/24 - 10*b**3/3 + 43*b**2/12 - b + 47. Factor p(y).
-(y + 3)*(5*y - 2)*(5*y - 1)/6
Suppose 8*w = 12*w. Let i(l) be the second derivative of 0 + w*l**2 - 1/3*l**3 - 1/6*l**4 - l. Factor i(j).
-2*j*(j + 1)
Let o(v) be the first derivative of v**4/5 - 6*v**2/5 - 8*v/5 + 14. Determine k so that o(k) = 0.
-1, 2
Solve 0 + 3*r**2 - 6/5*r + 6/5*r**3 - 3*r**4 = 0 for r.
-1, 0, 2/5, 1
Let u = 28 - 26. Determine j so that -2/11*j**u - 4/11 - 6/11*j = 0.
-2, -1
Suppose -5*p + 4 = -1. Suppose -t = -3 + p. Let 0*y**t + 1/4*y**3 + 0*y + y**4 + 0 = 0. What is y?
-1/4, 0
Let t(p) = 131*p**2 - 106*p + 20. Let r(a) = 392*a**2 - 317*a + 60. Let h(k) = -6*r(k) + 17*t(k). Factor h(u).
-5*(5*u - 2)**2
Let r(c) = -c**3 - 5*c**2 + 5*c - 4. Let y be r(-6). Let i(t) = 2*t - 1. Let j be i(y). Factor 3*z - 2*z**j - 1 + 4*z**3 - 3*z**2 - z**3.
(z - 1)**3
Let f(v) be the second derivative of -v**8/168 + v**6/60 - 4*v**2 - 3*v. Let n(b) be the first derivative of f(b). Solve n(j) = 0 for j.
-1, 0, 1
Let r(g) be the first derivative of -1/3*g**3 + 3 + 0*g + 1/180*g**6 + 0*g**2 + 0*g**5 - 1/12*g**4. Let n(d) be the third derivative of r(d). Factor n(a).
2*(a - 1)*(a + 1)
Let j(a) = a - 4. Let i be j(8). Suppose 0*g - i*g = -12. Let 4 - 4*x**3 + 6*x**3 + 8*x**g + 2*x - 16*x**2 = 0. What is x?
-2/5, 1
Let a(q) = -10*q**3 + q**2 + 7*q + 2. Let j(b) = -b**3 + b**2 + 11*b - 11*b. Let i(o) = 2*a(o) - 6*j(o). Solve i(k) = 0.
-1, -2/7, 1
Suppose -4*n + 11 = -9. Find c, given that 2*c**2 + 0*c - 12*c - n - 1 + 24 = 0.
3
Let b(t) be the second derivative of t**7/63 - t**6/45 - t**5/10 + 5*t**4/18 - 2*t**3/9 - 35*t. Solve b(r) = 0 for r.
-2, 0, 1
Find c such that 3/5*c - 6/5 + 3/5*c**2 = 0.
-2, 1
Let o(m) be the first derivative of -2*m**5/35 + m**4/14 + 2*m**3/21 - m**2/7 + 8. Solve o(s) = 0 for s.
-1, 0, 1
Let c(g) be the third derivative of -g**7/21 - g**6/24 + 5*g**5/12 - 5*g**4/12 - 23*g**2. Suppose c(m) = 0. Calculate m.
-2, 0, 1/2, 1
Factor 31*a**4 + 10*a**2 + 25*a**3 + 5*a**5 + 27*a**4 - 38*a**4.
5*a**2*(a + 1)**2*(a + 2)
Let q(j) be the third derivative of -j**6/180 + j**5/90 - 10*j**2. Solve q(x) = 0.
0, 1
Suppose -4*s + 2 = -18. Let g be 1 + (-5)/5*1. Factor g*h + 0*h**4 - 2/7*h**3 + 0 + 0*h**2 + 2/7*h**s.
2*h**3*(h - 1)*(h + 1)/7
Let r(g) be the third derivative of g**5/120 - g**4/12 + g**3/3 + 2*g**2 - 3*g. Factor r(u).
(u - 2)**2/2
Let h(k) be the second derivative of -k**6/6 + 7*k**5/4 - 25*k**4/4 + 15*k**3/2 + k. Determine i so that h(i) = 0.
0, 1, 3
Let p(j) be the first derivative of -2/9*j**2 - 2/27*j**3 + 4 + 1/18*j**4 + 0*j. Find u, given that p(u) = 0.
-1, 0, 2
Let a(r) be the third derivative of r**6/240 + r**5/40 + r**4/24 - 7*r**2. Find d, given that a(d) = 0.
-2, -1, 0
Suppose 0 = y - 3 - 1. Let l(a) be the third derivative of -1/8*a**y - 1/30*a**5 - 1/6*a**3 - 2*a**2 + 0 + 0*a. Factor l(o).
-(o + 1)*(2*o + 1)
Let o(w) = -9*w**3 + 3*w**2 + 7*w. Let t(m) = 4*m**3 - 2*m**2 - 4*m. Let g(j) = -2*o(j) - 5*t(j). Solve g(q) = 0.
-1, 0, 3
Let g(s) = -s**4 + s**3 + s**2 - s + 1. Let q(i) = -90*i**4 - 130*i**3 + 134*i**2 - 22*i - 10. Let d(a) = 10*g(a) + q(a). Factor d(h).
-4*h*(h + 2)*(5*h - 2)**2
Let i(f) be the third derivative of f**7/4200 + f**6/1200 - f**5/100 - f**4/8 + f**2. Let p(b) be the second derivative of i(b). Suppose p(v) = 0. What is v?
-2, 1
Let a(q) be the second derivative of 3/2*q**2 + 1/12*q**4 - q + 0 + 1/6*q**3 + 1/60*q**5. Let h(z) be the first derivative of a(z). Find b such that h(b) = 0.
-1
Let f be (-2)/1 - 36/(-14). Let n = -14 - -14. Suppose 2/7 + 2/7*q**4 + n*q + 0*q**3 - f*q**2 = 0. What is q?
-1, 1
Suppose -b = b + 14. Let n be (-14)/4*4/b. Factor -18/5*q**3 - 4/5*q**n - 14/5*q**4 + 0 + 0*q.
-2*q**2*(q + 1)*(7*q + 2)/5
Let b(s) be the first derivative of s**4/2 - 4*s**3/3 + s**2 - 17. Determine w so that b(w) = 0.
0, 1
Let q(t) be the third derivative of t**9/30240 - t**7/5040 + t**4/12 - 2*t**2. Let y(a) be the second derivative of q(a). 