- 2. Factor p(n).
-4*(n + 2)**2
Let c(b) = b**3 - 10*b**2 + 10*b - 9. Let l be c(9). Factor 3*j**4 + 12*j + l*j**4 + 1 + 12*j**3 + 1 + 18*j**2 + 1.
3*(j + 1)**4
Let q(f) be the third derivative of f**7/3360 - f**6/1440 - f**5/480 + f**4/96 - f**3/3 + 7*f**2. Let c(w) be the first derivative of q(w). Factor c(j).
(j - 1)**2*(j + 1)/4
Let g(s) be the first derivative of s**6/36 + s**5/6 + s**4/3 + 2*s**3/9 + 1. Determine r, given that g(r) = 0.
-2, -1, 0
Suppose 145*k - 145*k + 4*k**3 = 0. Calculate k.
0
Let y be -2*(-4)/(-24)*0. Let z = -253/35 + 52/7. Factor y + 1/5*l + z*l**3 + 2/5*l**2.
l*(l + 1)**2/5
Find y such that 0 + 0*y - 1/4*y**2 - 1/8*y**3 + 1/4*y**4 + 1/8*y**5 = 0.
-2, -1, 0, 1
Let y(v) be the third derivative of 0 + 4*v**2 + 0*v**4 + 0*v + 0*v**5 + 0*v**3 - 1/20*v**6 - 3/70*v**7 - 1/112*v**8. Suppose y(m) = 0. Calculate m.
-2, -1, 0
Factor 6*f**4 + 4*f**4 - 3*f**4 - 5*f**4 - 2*f**3.
2*f**3*(f - 1)
Let 0 - 4/3*z**4 + 4/3*z**2 - 2/3*z**5 + 0*z**3 + 2/3*z = 0. What is z?
-1, 0, 1
Let f(c) be the third derivative of -c**7/14 + 9*c**6/20 - 6*c**5/5 + 7*c**4/4 - 3*c**3/2 + 13*c**2. Factor f(u).
-3*(u - 1)**3*(5*u - 3)
Let q(h) = h**3 - h**2 - 1. Let j be q(2). Factor -6*y**4 - j*y**3 + 6*y**3 - 4*y**4 + 3*y**5 + 4*y**4.
3*y**3*(y - 1)**2
Let w = -34 + 36. Factor -w*l**2 + 4/3*l + 2/3.
-2*(l - 1)*(3*l + 1)/3
Suppose 0 = -21*u + 30 + 75. Suppose 16/5*o**2 - 56/5*o**3 + 28/5*o + 28/5*o**u - 8/5*o**4 - 8/5 = 0. What is o?
-1, 2/7, 1
Let k(u) be the third derivative of 0 + 1/90*u**5 - 1/9*u**3 - 1/360*u**6 + 0*u + 4*u**2 + 1/72*u**4. Let k(o) = 0. What is o?
-1, 1, 2
Determine o so that -2*o**2 + 2*o**4 + 0*o**4 + 2*o + 0*o - 2*o**3 = 0.
-1, 0, 1
Let h(w) be the first derivative of w**5/20 + w**4/30 - 8*w - 6. Let z(n) be the first derivative of h(n). Factor z(d).
d**2*(5*d + 2)/5
Let w(x) be the third derivative of x**5/66 - 7*x**4/132 + 2*x**3/33 - 6*x**2. Factor w(p).
2*(p - 1)*(5*p - 2)/11
Determine q so that 0*q + 10*q**5 + 8/5*q**3 - 8*q**4 + 0*q**2 + 0 = 0.
0, 2/5
Let q = -447 - -1815/4. Let y(w) be the first derivative of -9/2*w**2 - w - 2 - q*w**3. Factor y(j).
-(9*j + 2)**2/4
Let s(j) = j**3 - j**2 - j. Let z be s(2). What is x in 2*x**5 + 2*x**4 + 3*x**3 - 4*x**2 - 5*x**3 + 2*x**z = 0?
-1, 0, 1
Let c(w) be the first derivative of -3/5*w**5 + 4 + w**3 + 3/4*w**4 + 0*w - 3/2*w**2. Factor c(n).
-3*n*(n - 1)**2*(n + 1)
Let w(v) = -v**3 - v - 1. Let y(q) = 2*q**5 + 2*q**3 - 4*q**2 + 8*q + 8. Let m(r) = -8*w(r) - y(r). Factor m(g).
-2*g**2*(g - 2)*(g + 1)**2
Let l(x) be the first derivative of -x**5/25 + x**4/20 + x**3/15 - x**2/10 + 44. Factor l(r).
-r*(r - 1)**2*(r + 1)/5
Let p be 0 + 12/7 + -1. Let j = 11/14 + p. Factor -1 - 1/2*m**2 - j*m.
-(m + 1)*(m + 2)/2
Let h(q) be the first derivative of -3*q**4/28 + 5*q**3/7 - 12*q**2/7 + 12*q/7 - 23. Factor h(v).
-3*(v - 2)**2*(v - 1)/7
Let l = 1 - -2. Let r be ((-1)/l)/((-4)/24). Factor k**r + 3*k**4 + k**5 - 4*k**4 + 0*k**2 - k**3.
k**2*(k - 1)**2*(k + 1)
Let i be ((-16)/10)/((-4)/10). Suppose i = 4*r - 8. Determine y, given that 0*y - 2/5*y**2 + 2/5*y**r + 0 = 0.
0, 1
Let m(d) be the third derivative of d**6/720 - d**2. Determine o, given that m(o) = 0.
0
Factor 0*k**3 + 0*k - 2/11*k**4 - 2/11 + 4/11*k**2.
-2*(k - 1)**2*(k + 1)**2/11
Let z = 11 + -9. Let x be 1 - 3/9*3. Let x - 2/7*d**z - 2/7*d = 0. Calculate d.
-1, 0
Let 15*n**4 - 2*n**5 + 2*n - 19*n**4 - 3*n**2 + 7*n**2 = 0. What is n?
-1, 0, 1
Let x = 19 + -11. Let h(j) be the third derivative of -1/84*j**4 + 0 + 0*j + 0*j**3 + 1/210*j**6 + 0*j**7 - 1/1176*j**x + j**2 + 0*j**5. Factor h(i).
-2*i*(i - 1)**2*(i + 1)**2/7
Let c = -1/203 - -205/406. Factor 0*u**4 + 3/4*u - 1/2*u**2 + c + 1/4*u**5 - u**3.
(u - 2)*(u - 1)*(u + 1)**3/4
Let w(n) = 2*n**2 + 83*n + 225. Let a(i) = -i**2 - 55*i - 150. Let u(c) = -7*a(c) - 5*w(c). Factor u(v).
-3*(v + 5)**2
Let q(k) = -6*k**4 + 3*k**3 - 23*k**2 + 11*k - 5. Let p(v) = -v**4 - v**3 - v**2 - v. Let y(f) = 10*p(f) - 2*q(f). Factor y(z).
2*(z - 5)*(z - 1)**3
Factor 0*f**2 + 4/5*f**3 + 0 + 0*f.
4*f**3/5
Suppose n + 16 = 3*n. Suppose 0 = -4*v - n, -2*i - v + 2*v = -2. Factor 2/7*a**3 + i + 0*a**2 - 2/7*a.
2*a*(a - 1)*(a + 1)/7
Let k(l) be the second derivative of 0 - 1/16*l**2 + 1/48*l**3 + 3*l - 1/160*l**5 + 1/96*l**4. Factor k(j).
-(j - 1)**2*(j + 1)/8
Let r(k) = -4*k**2 + 8. Let p(o) = -8*o**2 + 15. Let w(i) = 4*p(i) - 7*r(i). Factor w(z).
-4*(z - 1)*(z + 1)
Let c = -66 + 68. Factor -z**c + 1/2*z**3 + 0 + 1/2*z.
z*(z - 1)**2/2
Let w(o) be the first derivative of -o**6/6 - 3*o**5/5 - o**4/2 - 4. Solve w(l) = 0 for l.
-2, -1, 0
Let j(o) = -5*o**3 + 8*o**2 + 5*o - 8. Suppose 4*d + 15 + 17 = 0. Let k(r) = -3*r**3 + 5*r**2 + 3*r - 5. Let b(x) = d*k(x) + 5*j(x). Factor b(w).
-w*(w - 1)*(w + 1)
Let u(y) be the third derivative of -1/210*y**7 + 0*y**3 - 1/48*y**4 - y**2 + 1/672*y**8 + 0 + 0*y**6 + 0*y + 1/60*y**5. Factor u(k).
k*(k - 1)**3*(k + 1)/2
Suppose 4*b - 1 = -x, 7*b - 3*b + 2 = 2*x. Let a(d) be the second derivative of 1/45*d**5 - 1/54*d**4 + 4*d + 0 + b*d**3 + 0*d**2. Solve a(s) = 0 for s.
0, 1/2
Let s(l) = 12*l**2 + 16*l - 21. Let k(i) = -36*i**2 - 48*i + 62. Let v(b) = 5*k(b) + 14*s(b). Factor v(g).
-4*(g + 2)*(3*g - 2)
Let g = 5 - 9. Let r be g/((-12)/(-9)) - -3. Factor r + 0*q + 1/4*q**2 - 1/4*q**3.
-q**2*(q - 1)/4
Let c(n) be the first derivative of -n**5/60 + n**4/24 - n**2/2 + 3. Let d(t) be the second derivative of c(t). Factor d(j).
-j*(j - 1)
Factor 16/3 - 28/3*r + 2*r**2.
2*(r - 4)*(3*r - 2)/3
Let p be (-90)/(-4) + (-22)/(-11). Let -54*j + 84*j**2 + 8 + p*j**3 = 0. What is j?
-4, 2/7
Let r(s) be the first derivative of 2/3*s**3 + 1/2*s**2 - s - 1/2*s**4 + 1/6*s**6 + 2 - 1/5*s**5. Factor r(b).
(b - 1)**3*(b + 1)**2
Let r(h) be the second derivative of 1/2*h**3 - h - 1/24*h**4 - 9/4*h**2 + 0. Factor r(c).
-(c - 3)**2/2
Let p = -210233/180 - -1168. Let u(k) be the third derivative of -1/45*k**5 - p*k**6 + k**2 + 0*k + 7/36*k**4 + 2/9*k**3 + 0. Factor u(g).
-2*(g - 1)*(g + 1)*(7*g + 2)/3
Factor 36 + 4*n**3 - 4*n**2 + 17*n**2 + 60*n + 15*n**2.
4*(n + 1)*(n + 3)**2
Let u(y) = 3*y**2 - 6*y - 14. Let v(k) = 15*k**2 - 30*k - 69. Let n(b) = -24*u(b) + 5*v(b). Factor n(f).
3*(f - 3)*(f + 1)
Let 0 - 4/5*a**4 - 8/5*a**3 + 0*a - 4/5*a**2 = 0. What is a?
-1, 0
Let z(a) = -17*a**3 - 40*a**2 - 73*a - 41. Let w(p) = 4*p**3 + 10*p**2 + 18*p + 10. Let k(y) = 9*w(y) + 2*z(y). Factor k(g).
2*(g + 1)*(g + 2)**2
Let x = -66 - -69. Let y(a) be the first derivative of -4 + a**2 + 2/3*a**x + 1/6*a**4 + 2/3*a. Suppose y(g) = 0. What is g?
-1
Let h be 0 - -1 - (-6)/(-9). Let s(y) be the second derivative of 0*y**2 + 0 - 1/6*y**4 + h*y**3 + 2*y. Factor s(i).
-2*i*(i - 1)
Let j(g) = -g**2 + 15*g + 18. Let l be j(16). Let p(f) be the first derivative of f - 1/3*f**3 + 1/4*f**4 + l - 1/2*f**2. Solve p(t) = 0 for t.
-1, 1
Let n(g) be the third derivative of -1/270*g**6 + 0*g**3 + 1/270*g**5 + 0*g + 0 + 0*g**4 + 1/945*g**7 + 4*g**2. Factor n(u).
2*u**2*(u - 1)**2/9
Let v = -20 - -22. Factor 20*n**2 - v*n**3 - 12*n - 3*n**3 + 2*n**3 - n**3 - 36.
-4*(n - 3)**2*(n + 1)
Let u(o) = 7*o**2 + 7*o - 2. Let r be 46/12 + (-5)/(-30). Let g(s) = -s**2 - s - 1. Let z(l) = r*g(l) + u(l). Factor z(v).
3*(v - 1)*(v + 2)
Let u be 15/2*(-4)/(-6). Let o = u + -2. Determine h, given that 2*h**3 + 4*h**2 + 0*h**o - 2*h + 4*h = 0.
-1, 0
Let b(y) = y**3 - 20*y**2 - 43*y - 22. Let d be b(22). Factor 0*m + 3/5*m**3 + d*m**2 + 0.
3*m**3/5
Let d(h) be the third derivative of -h**5/210 - h**4/84 + 2*h**3/21 + 3*h**2. What is v in d(v) = 0?
-2, 1
Let w(p) be the second derivative of -p**7/42 + p**5/10 - p**3/6 - 11*p. What is j in w(j) = 0?
-1, 0, 1
Let c(u) be the first derivative of u**4/5 + 10. Factor c(m).
4*m**3/5
Factor -11*o**2 - o**2 + 285*o - 4 - 2*o**3 - 2*o**3 - 297*o.
-4*(o + 1)**3
Suppose 0*w**3 + 0 + 0*w - 7/3*w**4 + 4/3*w**2 - w**5 = 0. What is w?
-2, -1, 0, 2/3
Let y(l) be the third derivative of -l**8/50400 + l**6/1800 + l**5/60 - 2*l**2. Let s(x) be the third derivative of y(x). Factor s(q).
-2*(q - 1)*(q + 1)/5
Let n be 0*3/(-9) - -1*3. Determine x, given that 9/2*x - 3*x**2 + 1/2*x**n + 0 = 0.
0, 3
Let o(v) be the second derivative of -2*v**6/15 - 4*v**5/5 - 5*v**4/3 - 4*v**3/3 - 2*v. What is u in o(u) = 0?
-2, -1, 0
Let w(m) b