. Factor -27*n**2 - 46*n**3 + 28*n**2 - 14*n**4 - k*n**2 - 8*n.
-2*n*(n + 1)*(n + 2)*(7*n + 2)
Suppose 0 = 969*f - 975*f. Factor -1/4*o - 1/8*o**3 + f - 3/8*o**2.
-o*(o + 1)*(o + 2)/8
Factor -14*n**4 - 13*n + 12*n**4 + n**2 + n**2 + 12*n**2 + n.
-2*n*(n - 2)*(n - 1)*(n + 3)
Factor -60*x - 68*x**2 + 35*x**3 - 67*x**2 + 155*x**2 + 5*x**4.
5*x*(x - 1)*(x + 2)*(x + 6)
Suppose 3*o + 3*x = -x + 7, -2*x - 4 = 0. Suppose 7 + o = 2*p. Factor -3*t**2 + 0*t**2 - p - 12*t + 5*t - 2*t.
-3*(t + 1)*(t + 2)
Let h be 3/12 + 9/12. Factor -3 + h - 28*z**3 - 20*z - 30*z**4 + 22*z**4 - 36*z**2 - 2.
-4*(z + 1)**3*(2*z + 1)
Let d(i) be the first derivative of i**5/12 + 5*i**4/6 - 47*i**2/2 + 14. Let y(v) be the second derivative of d(v). Factor y(c).
5*c*(c + 4)
Suppose -30 = 69*h - 84*h. What is z in -20/7*z + 30/7*z**h - 6/7*z**5 + 10/7*z**4 + 50/7*z**3 - 16/7 = 0?
-1, 2/3, 4
Suppose -37 = 8*a - 125. Let 135 - 2*n**2 - 7*n**2 - 7 + a*n**2 + 32*n = 0. Calculate n.
-8
Let g = 270 - 238. Let v be (1 + 15/(-6))*g/(-54). Factor -4/3*i**2 - v*i + 2/9*i**4 + 16/9 + 2/9*i**3.
2*(i - 2)*(i - 1)*(i + 2)**2/9
Factor 15*s**2 + s**4 - 5*s**5 + 41*s**3 - 80*s**2 - s**3 + 5*s**2 + 4*s**4.
-5*s**2*(s - 2)**2*(s + 3)
Let q = 21221/33 - 643. Let d(h) be the third derivative of -1/44*h**4 + 0 + 0*h - q*h**3 + 3/110*h**5 + 5*h**2. Factor d(a).
2*(3*a - 2)*(3*a + 1)/11
Factor -2052/5*z + 263169/5*z**2 + 4/5.
(513*z - 2)**2/5
Let w(r) be the first derivative of -r**3/3 + r**2 - r - 3. Factor w(g).
-(g - 1)**2
Let i = 2/311 + 227/13062. Let f(s) be the third derivative of 0*s - 1/420*s**6 + 1/7*s**3 + i*s**5 + 0 - 1/12*s**4 - 2*s**2. Factor f(d).
-2*(d - 3)*(d - 1)**2/7
Determine x so that 75/2*x**2 - 69/2*x - 3 = 0.
-2/25, 1
Let c(u) = -11*u**5 + 20*u**4 + 25*u**3 + 12*u**2 + 9*u - 9. Let x(v) = 5*v**5 - 9*v**4 - 13*v**3 - 7*v**2 - 4*v + 4. Let f(b) = 4*c(b) + 9*x(b). Factor f(s).
s**2*(s - 5)*(s + 1)*(s + 3)
Let y(a) be the first derivative of 5*a**4/4 - 25*a**3 - 165*a**2/2 - 85*a - 101. Find n, given that y(n) = 0.
-1, 17
Let p be 6/(-112) - (-50)/525. Let t(z) be the second derivative of 1/6*z**3 - 4*z + p*z**4 - 3/40*z**5 + 0*z**2 + 0. Factor t(r).
-r*(r - 1)*(3*r + 2)/2
Suppose 180*s = 166*s. Let w(q) be the second derivative of s - 2/21*q**3 - 5*q + 0*q**2 - 1/42*q**4. Find r, given that w(r) = 0.
-2, 0
Let v = 115867/42 + -16549/6. Factor 8/7*m + 20/7*m**2 + 0 + v*m**4 + 16/7*m**3.
4*m*(m + 1)**2*(m + 2)/7
Let b be 3 - -4*(-3)/(-6). Find t such that 35*t**4 + 80*t + 23*t**3 + 188 + 72*t**3 + b*t**5 - 168 + 125*t**2 = 0.
-2, -1
Let u(y) be the second derivative of -y**5/5 - y**4/3 + 6*y**3 + 18*y**2 + 21*y. Factor u(l).
-4*(l - 3)*(l + 1)*(l + 3)
Suppose 19*v - 14*v = 485. Let o = 681/7 - v. Determine b, given that -4/7*b**3 + o*b**2 + 0*b + 2/7*b**4 + 0 = 0.
0, 1
Let l(j) be the third derivative of -j**6/24 + j**5/6 + 25*j**4/24 - 5*j**3 - 2*j**2. Factor l(o).
-5*(o - 3)*(o - 1)*(o + 2)
Let r(h) be the third derivative of -h**7/105 - 4*h**6/15 - 2*h**5 + 16*h**4/3 + 256*h**3/3 + 5*h**2 + 40. Factor r(y).
-2*(y - 2)*(y + 2)*(y + 8)**2
Suppose -3*o + 5*o - 520 = 5*s, 4*o + 4*s = 1012. Factor 5*r**3 - 320 + 98*r**2 - o*r**2 + 240*r + 97*r**2.
5*(r - 4)**3
Let c(i) be the first derivative of 0*i**2 - 14/5*i**5 - 8*i**4 + 0*i - 8/3*i**3 - 12. Factor c(x).
-2*x**2*(x + 2)*(7*x + 2)
Let i be 6 - (2 + -1 + -7 + 7). Suppose -38*b**4 + 88*b**4 + 6*b**3 - 8*b - 8*b**2 - 2*b**i - 46*b**4 = 0. Calculate b.
-1, 0, 2
Let h(c) be the third derivative of 0*c**3 + 0 + 0*c**5 + 0*c - 7*c**2 + 1/8*c**4 - 1/40*c**6. Suppose h(f) = 0. Calculate f.
-1, 0, 1
Let j(v) be the third derivative of -v**5/390 - 41*v**4/78 - 1681*v**3/39 - 13*v**2 - v. Factor j(z).
-2*(z + 41)**2/13
Let x(z) = -14*z**2 - 993*z - 49005. Let k(g) = -25*g**2 - 1985*g - 98010. Let m(p) = -3*k(p) + 5*x(p). Factor m(b).
5*(b + 99)**2
Suppose 94*z = 90*z. Let g(a) be the second derivative of -6*a + 1/7*a**3 - 1/28*a**4 + z*a**2 + 0. Solve g(v) = 0 for v.
0, 2
Let x(p) be the first derivative of 3/11*p**4 - 6/11*p - 10 - 9/11*p**2 + 1/11*p**6 - 4/11*p**3 + 18/55*p**5. Determine h, given that x(h) = 0.
-1, 1
Determine t, given that -8*t - 11 + 80*t + 2*t**2 - 17 + 28 = 0.
-36, 0
Let t(z) = -3*z**3 - z**2 - z. Let c be t(-1). Let y = 5 + 1. Solve 0 - 6*l + y - c*l + 3*l**2 = 0.
1, 2
Let x = 14 - 12. What is y in -2*y + 9*y**2 + 4 - 1 - 10*y**x = 0?
-3, 1
Let u(w) be the first derivative of 8/3*w**3 + w - 1/3*w**4 + 1 - 8*w**2. Let k(r) be the first derivative of u(r). Solve k(v) = 0 for v.
2
Find f, given that 48*f + 64/7*f**3 + 3/7*f**4 + 232/7*f**2 - 1/7*f**5 + 176/7 = 0.
-2, 11
Let i(k) be the second derivative of k**4/12 - 10*k**3/3 + 19*k**2/2 + 18*k + 9. Factor i(u).
(u - 19)*(u - 1)
Factor -1/2*l**5 + 97/2*l**2 - 36*l - 59/2*l**3 + 10 + 15/2*l**4.
-(l - 10)*(l - 2)*(l - 1)**3/2
Let j(c) be the first derivative of -c**6/69 - 2*c**5/115 + 3*c**4/46 + 10*c**3/69 + 2*c**2/23 - 5. Suppose j(o) = 0. Calculate o.
-1, 0, 2
Let d(j) = 2*j**3 + 18*j**2 - 20*j + 2. Let p be d(-10). Let t(z) be the first derivative of -8 - 3/8*z**4 + 0*z + 2*z**3 - 3*z**p. Find s, given that t(s) = 0.
0, 2
Let o(h) be the first derivative of h**4/40 - 17*h**3/30 + 11*h**2/5 - 14*h/5 + 502. Let o(p) = 0. What is p?
1, 2, 14
Let k(o) = -85*o**2 - 12*o - 9. Let i(s) = -85*s**2 - 13*s - 6. Let t(j) = 3*i(j) - 2*k(j). Factor t(w).
-5*w*(17*w + 3)
Let c = -78 + 83. Let s(w) be the second derivative of -3/8*w**c - w + 0*w**2 + 1/4*w**4 + 1/5*w**6 + 0 + 0*w**3 - 1/28*w**7. What is i in s(i) = 0?
0, 1, 2
Let m = 343/282 + 40/141. Factor -v + 0 - 1/2*v**3 + m*v**2.
-v*(v - 2)*(v - 1)/2
Let t(m) = -m**3 + 82*m**2 - 84*m + 3. Let g be t(1). Find v, given that 6/5*v**2 + g + 2/5*v**3 + 4/5*v = 0.
-2, -1, 0
Let l be (-3)/(18/(-48)) + (-532)/70. Factor -l*g**2 + 4/5*g**3 + 0 - 2/5*g**4 + 0*g.
-2*g**2*(g - 1)**2/5
Solve 3/2*p**3 + 0*p + 0 - 3/2*p**2 = 0.
0, 1
Let i(t) be the first derivative of -5*t**3/3 - 25*t**2/2 - 30*t - 122. Suppose i(o) = 0. What is o?
-3, -2
Let s = 129164 - 47015613/364. Let z = s + 2/91. Factor z*p**2 - 3/4*p + 1/2.
(p - 2)*(p - 1)/4
Let l = -2000 - -22016/11. Suppose 2/11*r + 32/11*r**3 + 0 - l*r**2 = 0. What is r?
0, 1/4
Let a = -212 - -211. Let z(t) = 3*t**2 - 10*t - 10. Let s be z(a). Factor 1/3*r**5 - 1/6 - 1/3*r**s + 2/3*r**2 + 0*r - 1/2*r**4.
(r - 1)**3*(r + 1)*(2*r + 1)/6
Factor -1/6*y**2 - 3/2*y**4 + y**3 + 0 + 0*y.
-y**2*(3*y - 1)**2/6
Let a(f) = 40*f**4 + 60*f**3 - 215*f**2 + 125*f - 10. Let v(i) = -i**5 - i**4 + i**3 - i + 2. Let k(w) = -a(w) - 5*v(w). Factor k(y).
5*y*(y - 8)*(y - 1)**2*(y + 3)
Let x(r) = -r**3 + 15*r**2 + 32*r - 641. Let z be x(14). Find w, given that 3/5*w**z + 0*w + 6/5*w**4 - 3/5*w**5 - 6/5*w**2 + 0 = 0.
-1, 0, 1, 2
Let v(i) = -i**5 + 10*i**4 + 20*i**3 - 12*i**2 - 17*i. Let j(g) = 9*g**4 + 21*g**3 - 12*g**2 - 18*g. Let l(f) = -2*j(f) + 3*v(f). Solve l(y) = 0 for y.
-1, 0, 1, 5
Let v(r) = 58*r**2 + 23*r - 5. Let p(t) = -35*t**2 - 11*t + 3. Let s(j) = -5*p(j) - 3*v(j). Factor s(f).
f*(f - 14)
Let h(d) = -68*d**4 + 36*d**3 + 144*d**2 + 56*d + 8. Let y(k) = 23*k**4 - 12*k**3 - 48*k**2 - 19*k - 3. Let c(u) = -3*h(u) - 8*y(u). Let c(t) = 0. What is t?
-1, -2/5, 0, 2
Find i such that 410*i**2 - 419*i**2 - 88 - 74 + 249*i = 0.
2/3, 27
Let j(u) = 12*u**2 + 18*u - 42. Let v(y) = y**3 + 50*y**2 + 71*y - 166. Let s(i) = -11*j(i) + 3*v(i). Solve s(m) = 0 for m.
-4, -3, 1
Let i(a) be the third derivative of -1/30*a**5 - 10*a**2 + 0*a**3 + 0*a + 0 + 1/6*a**4. What is r in i(r) = 0?
0, 2
Let m(y) = -y**3 - y**2 - 2*y. Let i(p) = 31*p**3 - 2*p**2 - 22*p + 9. Let v(n) = -i(n) - m(n). Suppose v(w) = 0. What is w?
-1, 1/2, 3/5
Let f(l) be the first derivative of -l**3/9 - 11*l**2/3 - 85*l/3 + 57. Determine i, given that f(i) = 0.
-17, -5
Let x(h) = -13*h**2 - 35*h. Let f(j) = -2*j**2 - j. Let g(w) = 6*f(w) - x(w). Let g(l) = 0. What is l?
-29, 0
Let d be 1 - -1 - (-40)/4. Let k = d + 2. Find m such that k*m - 8*m + 3 - 9*m + 3*m**3 - 3*m**2 = 0.
-1, 1
Let c(r) = 20*r**3 - 65*r**2 - 675*r. Let v(j) = -5*j**3 + 16*j**2 + 169*j. Let q(p) = -6*c(p) - 25*v(p). Factor q(b).
5*b*(b - 7)*(b + 5)
Let o be 195/45 + (-2)/6. Suppose 16*p - o*p - 6 + 2*p**2 - 4*p**3 - 4 + 1 - p**4 = 0. What is p?
-3, 1
Let g(l) be the first derivative of l*