1. Let k(n) = x*b(n) + 3*u(n). Let m(r) = -6*k(r) - z(r). Factor m(f).
-f*(f - 2)
Factor -54*t**5 + 10*t**3 + 6*t**3 + 6*t**2 - 2*t**2 + 2*t**3.
-2*t**2*(3*t - 2)*(3*t + 1)**2
Let m = -2 + 4. Suppose 3*d = 2*x + 2*d - 1, 3*d = -x + 11. Factor -m*p**x - 1/2*p**3 - 5/2*p - 1.
-(p + 1)**2*(p + 2)/2
Let b(y) be the second derivative of y**4/20 - 14*y**3/5 + 294*y**2/5 - 29*y. Factor b(g).
3*(g - 14)**2/5
Let z = 948 + -948. Factor 0*m + 0 + z*m**2 + 0*m**4 - 4/7*m**5 + 4/7*m**3.
-4*m**3*(m - 1)*(m + 1)/7
Let q(r) be the first derivative of -2*r**3/3 - 4*r**2 + 10*r + 22. Find j such that q(j) = 0.
-5, 1
Suppose -3*y - 2*y = x - 103, -3*y = 5*x - 75. Suppose -13*f**4 + 18*f**3 + f**5 + 10*f - y*f**2 + 11*f**4 - 5*f**4 - 2*f = 0. Calculate f.
0, 1, 2
Let h be (-20)/(-450)*99 - (0 - -4). Find t, given that -h*t**2 + 0*t + 2/5 = 0.
-1, 1
Let t = 122 + -1097/9. Let k(b) be the third derivative of -3*b**2 + t*b**3 + 1/12*b**4 + 0*b + 0 + 1/45*b**5. Factor k(q).
2*(q + 1)*(2*q + 1)/3
Let b(o) = o**3 + 13*o**2 - 2*o - 5. Let z be b(-13). Let k be (-76)/(-21) - 6/z. Factor 0 + 4*a**3 + a**5 + 1/3*a - k*a**4 - 2*a**2.
a*(a - 1)**3*(3*a - 1)/3
Let h(x) be the first derivative of 1/9*x**6 - 1/6*x**4 + 2 + 0*x**5 + 0*x**3 + 0*x + 0*x**2. What is j in h(j) = 0?
-1, 0, 1
Suppose -29 - 47 = -38*v. Factor -2/7*z**v - 4/7*z - 2/7.
-2*(z + 1)**2/7
Let j(i) be the second derivative of -i**5/20 - i**4/3 - 5*i**3/6 - i**2 - i - 7. What is d in j(d) = 0?
-2, -1
Let v(b) be the second derivative of -1000*b**7/3 + 820*b**6/3 + 257*b**5/4 - 565*b**4/6 - 10*b**3/3 + 20*b**2 + 12*b. Suppose v(u) = 0. What is u?
-1/4, 2/7, 2/5
Let i(w) be the second derivative of -17/2*w**4 - 1/2*w**3 + 3*w + 21/20*w**5 + 3*w**2 + 41/5*w**6 + 0 - 4*w**7. Let i(n) = 0. What is n?
-1/2, -2/7, 1/4, 1
Let g(h) = -h**2 - 8*h + 4. Let y be g(-8). Determine w so that 0*w**2 + y*w - 4*w**3 + 8*w**2 + 0*w**2 + 8*w**3 = 0.
-1, 0
Suppose 0 = -4*o + 3*o. Let k(p) be the second derivative of -3*p - 1/6*p**6 + o + 0*p**2 - 1/14*p**7 + 0*p**4 + 1/10*p**5 + 0*p**3. Factor k(l).
-l**3*(l + 2)*(3*l - 1)
Let k(b) = -4*b**2 - 3*b + 1. Let l(j) = 2*j**2 + j - 1. Let p(v) = -2*k(v) - 5*l(v). Factor p(h).
-(h + 1)*(2*h - 3)
Factor 2/7*k**3 + 6/7*k + 18/7 - 10/7*k**2.
2*(k - 3)**2*(k + 1)/7
Let d(g) be the third derivative of g**5/3 + g**4/6 + g**2. Suppose d(a) = 0. What is a?
-1/5, 0
Let w be 2/1 - 12/7. Let r = 1 - -2. Suppose -20/7*p**r - 20/7*p**2 - 2/7 - 10/7*p**4 - w*p**5 - 10/7*p = 0. Calculate p.
-1
Let z = 40 - 20. Let k be (4/10)/(4/z). Factor 2/7*b + 4/7*b**k + 0 + 2/7*b**3.
2*b*(b + 1)**2/7
Let w(h) = h**3 + 9*h**2 + 8*h - 3. Let b(s) = 2*s**3 + 10*s**2 + 8*s - 2. Let r(m) = -3*b(m) + 2*w(m). Factor r(u).
-4*u*(u + 1)*(u + 2)
Let u(p) be the first derivative of -5*p**4/4 + 5*p**3 + 10*p**2 + 20. Find c such that u(c) = 0.
-1, 0, 4
Let p(v) be the third derivative of -3*v**2 - 1/390*v**5 - 2/39*v**3 + 0 - 1/52*v**4 + 0*v. Factor p(b).
-2*(b + 1)*(b + 2)/13
Let t(i) = i**2 - 9*i + 4. Let y(j) be the third derivative of j**5/10 - 21*j**4/8 + 9*j**3/2 - j**2. Let z(l) = 15*t(l) - 2*y(l). Factor z(w).
3*(w - 2)*(w - 1)
Let y(x) be the third derivative of x**8/112 - x**7/140 - x**6/24 + x**5/20 + x**3/3 + 7*x**2. Let d(z) be the first derivative of y(z). Factor d(p).
3*p*(p - 1)*(p + 1)*(5*p - 2)
Suppose -2 = -38*b + 74. Factor -1 - 1/4*t**b - t.
-(t + 2)**2/4
Factor 2*u + 5*u**2 + u**2 + 2*u - 5*u**3 + 7*u**3.
2*u*(u + 1)*(u + 2)
Let p(b) be the first derivative of -2/15*b**5 - 10/27*b**3 - 5 + 0*b - 1/9*b**2 - 7/18*b**4. Factor p(x).
-2*x*(x + 1)**2*(3*x + 1)/9
Let f(a) be the third derivative of 1/2*a**3 - 1/12*a**4 + 1/180*a**5 + 0*a + 2*a**2 + 0. What is z in f(z) = 0?
3
Let l(h) be the first derivative of -1/6*h**4 - 11/30*h**5 - 2/3*h**3 + 0*h**2 + 1 + 0*h - 121/360*h**6. Let o(b) be the third derivative of l(b). Factor o(j).
-(11*j + 2)**2
Let x(o) = -2*o**2 - 5*o + 4. Let r be x(-5). Let t be (-30)/(-56) + 6/r. Find j such that -3/4*j**3 - 1/4*j + 3/4*j**2 + 0 + t*j**4 = 0.
0, 1
Let q(c) be the first derivative of c**4/4 + 4*c**3/3 + 5*c**2/2 + 2*c - 35. Factor q(b).
(b + 1)**2*(b + 2)
Let t = -86 - -88. Solve 1/2*c**t + 0 - c = 0 for c.
0, 2
Let h(m) = -m**5 + m**4 - m**3 + m**2 - m + 1. Suppose 2 + 4 = 3*o. Let l(y) = -y**5 - 2*y**3 + 4*y**2 - 3*y + 2. Let g(x) = o*h(x) - l(x). Factor g(s).
-s*(s - 1)**3*(s + 1)
Suppose -5*y**2 + 9*y**2 + 2*y**3 - 2*y + 2*y + 2*y = 0. Calculate y.
-1, 0
Let l(a) be the third derivative of a**6/30 + a**5/15 + 5*a**2. Solve l(o) = 0.
-1, 0
Let g(u) = -9*u - 49. Let s be g(-6). Determine a, given that 0*a**2 + 0 + 2/5*a**3 + 0*a + 0*a**4 - 2/5*a**s = 0.
-1, 0, 1
Let b be (14/(-63))/((-5)/30). Let 0*c - 2*c**4 + 0 + b*c**3 + 2/3*c**5 + 0*c**2 = 0. Calculate c.
0, 1, 2
Let z(u) be the second derivative of -7*u**6/6 - 3*u**5 - 5*u**4/4 + 5*u**3/3 + 4*u. Factor z(j).
-5*j*(j + 1)**2*(7*j - 2)
Factor -3*a**3 - 8*a**3 + 9*a**3.
-2*a**3
Let a(m) be the second derivative of -m**8/560 + m**7/280 + m**6/120 - m**5/40 - 5*m**3/6 - m. Let p(w) be the second derivative of a(w). Factor p(s).
-3*s*(s - 1)**2*(s + 1)
Let j(o) be the second derivative of o**4/15 - 56*o**3/15 + 392*o**2/5 + 14*o. Factor j(m).
4*(m - 14)**2/5
Suppose 3*d + 2*h = 8 + 4, 5*h = 0. Suppose 0 = -0*c + 2*c. Factor -1 + 2*n**2 + 0 + c + 0 - n**d.
-(n - 1)**2*(n + 1)**2
Suppose 5*v = -536 - 2499. Let o = 4273/7 + v. Determine n, given that -o*n + 8/7 + 10/7*n**2 = 0.
2/5, 2
Factor 16*o - 7 + 28*o**2 - 8*o + 7.
4*o*(7*o + 2)
Determine r so that 2*r**2 + 5*r - 2*r - r**2 = 0.
-3, 0
Let l be (0*2/8)/(-2). Factor 1/4*z**2 + 1/2*z + l.
z*(z + 2)/4
Let r(n) be the third derivative of 5*n**2 + 1/20*n**6 - 1/20*n**5 - 1/4*n**4 + 0*n + 0*n**3 + 1/70*n**7 + 0. Determine w so that r(w) = 0.
-2, -1, 0, 1
Let s(k) be the first derivative of -4*k**5/5 - 2*k**4 - 4*k**3/3 - 2. Factor s(c).
-4*c**2*(c + 1)**2
Let q(h) be the second derivative of 2*h - 1/30*h**4 - 2/5*h**2 - 1/5*h**3 + 0. Solve q(m) = 0.
-2, -1
Suppose 5 = -7*z + 8*z. Let w be 16/(-60) - (-3)/z. Let p**2 + 0 + p**3 + w*p**4 + 1/3*p = 0. Calculate p.
-1, 0
Let k be ((-13)/26)/((-1)/56). Factor 76*r**3 - 100*r**2 - 23 + 7 - k*r**4 - 2*r**5 + 6*r**5 + 64*r.
4*(r - 2)**2*(r - 1)**3
Factor 1/6*o**3 + 1/3*o**2 + 0 - 1/2*o.
o*(o - 1)*(o + 3)/6
Let z(v) = -7*v**2 + 5*v + 4. Let g(p) = -3*p**2 - 3 - 3*p + 4*p**2 + 4*p + 2. Let y(i) = 2*g(i) - z(i). Find k, given that y(k) = 0.
-2/3, 1
Let b(m) be the second derivative of 0*m**5 + 0*m**4 - 1/480*m**6 + m + 0*m**3 - m**2 + 0. Let u(h) be the first derivative of b(h). Find k such that u(k) = 0.
0
Let z be (-4 - -5) + -5 + 7. Factor -t + 1/3 + 2/3*t**2 + 1/3*t**5 + 2/3*t**z - t**4.
(t - 1)**4*(t + 1)/3
What is t in 31 - 25 - 3*t - t**2 - 5*t**2 - 6*t - 3*t**5 + 12*t**3 = 0?
-2, -1, 1
Let v(t) be the second derivative of t**5/70 - t**4/14 - 3*t**3/7 + 27*t**2/7 - 4*t. Factor v(h).
2*(h - 3)**2*(h + 3)/7
Factor -12/7*f - 2/7*f**2 - 18/7.
-2*(f + 3)**2/7
Suppose 0 = -0*u - 2*u + 4. Factor -2*g**2 + 3*g**3 - 6*g**u - 3*g**3 - 2*g**3 - 6*g.
-2*g*(g + 1)*(g + 3)
Let z(c) = 7*c**2 - 6*c - 1. Let r = 15 + -14. Let h(f) = f**2 - f. Let a(y) = r*z(y) - 4*h(y). Find j, given that a(j) = 0.
-1/3, 1
Factor 0*q**2 + 0*q + 17*q**4 + 0 - 7/4*q**5 + 5*q**3.
-q**3*(q - 10)*(7*q + 2)/4
Let v = -1/60 + 23/30. Solve v*u**2 + 1/2 - 5/4*u = 0 for u.
2/3, 1
Suppose 4*b + 11 = -1. Let n be ((-3)/(-14))/(b/(-8)). Solve 2/7*m**2 + 2/7 + n*m = 0.
-1
Let d(w) be the first derivative of -w**5/60 - w**4/9 + 3*w + 7. Let l(r) be the first derivative of d(r). Factor l(n).
-n**2*(n + 4)/3
Let j(r) be the first derivative of r**6/18 + 7*r**5/15 + 5*r**4/12 - 7*r**3/9 - r**2 - 28. Determine i so that j(i) = 0.
-6, -1, 0, 1
Let l = -376 - -27073/72. Let h(k) be the third derivative of 0*k - l*k**4 + 0*k**3 + 1/180*k**5 + 0 - k**2. Factor h(f).
f*(f - 1)/3
Let w = -22/3 - -8. Let x(n) be the first derivative of w*n**3 + 0*n + 3 + n**2. Factor x(z).
2*z*(z + 1)
Let d = 140/93 - 26/31. Factor 2/3*i**4 - 2/3*i**2 - 2/3*i**3 + 0 + d*i.
2*i*(i - 1)**2*(i + 1)/3
Let j(o) be the third derivative of -1/270*o**5 + 1/945*o**7 - o**2 + 0*o**3 + 0*o + 1/540*o**6 - 1/108*o**4 + 0. Factor j(t).
2*t*(t - 1)*(t + 1)**2/9
Let l(y) be the first derivative of -2*y**3/15 - 6*