2
Let v(s) be the first derivative of s**5/120 - s**4/32 - s**3/12 + 2*s**2 - 2. Let q(h) be the second derivative of v(h). Factor q(k).
(k - 2)*(2*k + 1)/4
Let s(r) be the first derivative of -r**5/60 - r**2 + 3. Let z(t) be the second derivative of s(t). Factor z(x).
-x**2
Suppose -2*c = c. Factor c*f**2 - 2*f**3 - 2*f**2 + 23*f - 23*f.
-2*f**2*(f + 1)
Let q be 6/1 - (-10 - -13). Suppose 0 = q*d + d - 16. Factor 1/5*z**2 - 1/5*z**d + 0 + 1/5*z - 1/5*z**3.
-z*(z - 1)*(z + 1)**2/5
Let o be (-6)/45 + (-2560)/(-75). Let d = o - 32. Factor -1/2*i**4 + 0*i - 1/4*i**5 - 1/4*i**3 + 0 + 0*i**d.
-i**3*(i + 1)**2/4
Let r(f) = f**3 - f**2 - 9*f. Let m(u) = u. Let s(w) = 21*m(w) + 3*r(w). What is j in s(j) = 0?
-1, 0, 2
Let o(x) = x**3 - 18*x**2 - 54*x - 54. Let s(v) = v**3 - 36*v**2 - 108*v - 108. Let r(f) = 5*o(f) - 3*s(f). Factor r(d).
2*(d + 3)**3
Suppose -2*p - 4*s + 12 = 0, 13 = p - 5*s - 28. Let b be (-5)/20*p/(-14). Factor 0*i + b - 2/7*i**2.
-2*(i - 1)*(i + 1)/7
Factor -74*b - 17 + 173*b - 64*b + b**3 - 19*b**2.
(b - 17)*(b - 1)**2
Let v = -998 + 1997/2. Factor -5*i**3 - 5/2*i**4 - 1/2 - 5/2*i - v*i**5 - 5*i**2.
-(i + 1)**5/2
Let p be (-4)/42*-3 + 0. Factor 16/7*l**2 - 32/7*l**3 + p + 2*l.
-2*(l - 1)*(4*l + 1)**2/7
Factor -12*k**5 - k + 4*k + 24*k**5 - 9*k**5 - 6*k**3.
3*k*(k - 1)**2*(k + 1)**2
Let m be (-1477)/45 - (-8)/36. Let w = m + 33. Factor 0*y**4 - w*y**3 + 0*y**2 + 0 + 1/5*y**5 + 1/5*y.
y*(y - 1)**2*(y + 1)**2/5
Let h be (-4 - -3) + 15/3. Let g(d) be the second derivative of -d - 1/6*d**h + 0*d**2 + 0 - 1/45*d**6 + 1/9*d**3 + 1/10*d**5. Determine f so that g(f) = 0.
0, 1
What is l in 25*l**2 - 79/3*l**4 + 20*l**5 - 28/3*l**3 + 4/3 - 32/3*l = 0?
-1, 1/4, 2/5, 2/3, 1
Let p(l) be the first derivative of l**7/28 - 3*l**6/20 + 9*l**5/40 - l**4/8 - 2*l + 4. Let u(n) be the first derivative of p(n). Factor u(q).
3*q**2*(q - 1)**3/2
Let q(k) = 3*k**2 - 3. Let y(h) = h**3 + h**2 + 1. Let v(r) = -q(r) - 3*y(r). Factor v(o).
-3*o**2*(o + 2)
Let w(h) be the first derivative of 3*h**4/4 + 5*h**3 + 6*h**2 + 8. Factor w(c).
3*c*(c + 1)*(c + 4)
Suppose -5*r + 8 = 2*n - 4, 5*r - 2*n - 28 = 0. What is j in 0*j**2 - 2*j**5 + 2*j - 4*j**2 + j**4 + 3*j**r = 0?
-1, 0, 1
Let l(t) = 48*t**4 - 68*t**3 - t**2 + 14*t + 3. Let q(h) = 336*h**4 - 477*h**3 - 6*h**2 + 99*h + 21. Let i(s) = 27*l(s) - 4*q(s). Factor i(g).
-3*(g - 1)**2*(4*g + 1)**2
Let x(s) = -2*s**3 + 7*s**2 - 5*s - 3. Let t be 4/2 + (-5)/1. Let c(m) = -6*m**3 + 22*m**2 - 16*m - 10. Let h(v) = t*c(v) + 10*x(v). Find f such that h(f) = 0.
0, 1
Suppose 2/9 - 2/9*i - 2/9*i**2 + 2/9*i**3 = 0. Calculate i.
-1, 1
Find s, given that 1/5*s**3 + 0 + 0*s + 1/5*s**2 = 0.
-1, 0
Suppose -2*g = 3*y - 4*y - 3, 2*y = 2. Factor 1/2*u - 1/4 - 1/4*u**g.
-(u - 1)**2/4
Let p(t) be the second derivative of -t**7/98 - t**6/70 + 6*t. Solve p(d) = 0.
-1, 0
Let w(a) be the first derivative of 2*a**5/55 - a**4/11 + 8. Factor w(h).
2*h**3*(h - 2)/11
Let s = 86 - 254/3. Solve -2/3*o**2 - 2/3 - s*o = 0 for o.
-1
Factor -1/3 - 1/3*p + 1/3*p**3 + 1/3*p**2.
(p - 1)*(p + 1)**2/3
Let i be -1 + 1 + (-3)/(-1). Let t(x) be the second derivative of -2*x + 1/24*x**i + 0*x**2 + 0 + 1/48*x**4. Factor t(p).
p*(p + 1)/4
Let c(f) = f**3 + 5*f**2 - 5*f + 8. Let g be c(-6). Suppose 0*z**g - 1 + 3/2*z - 1/2*z**3 = 0. Calculate z.
-2, 1
Suppose 0 = 3*m + 5*n - 12, m + 4*n = 18 - 14. Factor 0 - 1/2*h**2 + 0*h + 0*h**3 + 1/2*h**m.
h**2*(h - 1)*(h + 1)/2
Let d be (8 - 8)/(-1 - -4). Let t(b) be the second derivative of 0*b**2 - 1/45*b**5 + 0*b**4 + 1/189*b**7 + d*b**6 - b + 1/27*b**3 + 0. Factor t(u).
2*u*(u - 1)**2*(u + 1)**2/9
Suppose 32 = -4*n + 4*k, 11 - 3 = 4*k. Let x be (9/42)/(n/(-8)). Factor -2/7*y**3 - 2/7*y**2 + x*y + 2/7.
-2*(y - 1)*(y + 1)**2/7
Let m = -1/60 + 4/15. Find y such that 0 + 1/2*y - m*y**2 = 0.
0, 2
Let w be (-1 + 3/(-2))*40/(-25). Let h(y) be the first derivative of 0*y + w - 1/3*y**3 + 1/4*y**2 + 1/8*y**4. Factor h(l).
l*(l - 1)**2/2
Let i(q) be the first derivative of -2*q**5/25 - q**4/10 + 2*q**3/5 + q**2 + 4*q/5 + 13. What is c in i(c) = 0?
-1, 2
Find h, given that 0 - 1/6*h - 1/2*h**2 = 0.
-1/3, 0
Suppose 5*r = 3*g + 7*r - 10, -3*g - 4*r + 14 = 0. Let 2/5*f**g - 2/5*f**4 + 2/5*f + 0 - 2/5*f**3 = 0. What is f?
-1, 0, 1
Let o(t) = -t**3 + 3*t**2 + 5*t - 1. Let w be o(4). Suppose -5 + 14 = w*u. Factor k**5 - 2*k**3 + k + u - 3.
k*(k - 1)**2*(k + 1)**2
Let z be (-27)/(-15) - (-8)/40. Solve 0 + 2/7*u**z - 2/7*u + 2/7*u**3 - 2/7*u**4 = 0 for u.
-1, 0, 1
Let m(n) be the second derivative of -n**7/210 - n**6/75 + n**5/100 + n**4/30 - 9*n. Find c such that m(c) = 0.
-2, -1, 0, 1
Suppose -h - 3*h + 26 = 2*l, 2*h - l - 3 = 0. Determine f so that 6*f**3 + 6*f**2 + 6*f**h - 3*f**4 - 3*f**2 = 0.
-1, 0
Let h(l) be the second derivative of -1/16*l**5 + 0 - 1/5*l**6 + 3*l + 0*l**3 + 1/24*l**4 + 0*l**2 + 3/8*l**7. Factor h(g).
g**2*(3*g - 1)**2*(7*g + 2)/4
Let b(p) be the third derivative of p**8/50400 + p**7/3150 + p**6/450 + p**5/12 + 2*p**2. Let d(y) be the third derivative of b(y). Solve d(r) = 0 for r.
-2
Let y be 6/5*20/12. Solve -18/5*c**y - 36/5*c - 24/5 - 3/5*c**3 = 0 for c.
-2
Let y(q) = -2*q**5 + 5*q**4 + 7*q**3 + 10*q**2 + 2*q - 2. Let a(j) = 3*j**5 - 10*j**4 - 15*j**3 - 20*j**2 - 5*j + 3. Let k(b) = -6*a(b) - 10*y(b). Factor k(m).
2*(m + 1)**5
Let p(q) be the first derivative of -2*q**3/3 - 22*q**2 - 242*q + 36. Factor p(h).
-2*(h + 11)**2
Let p be (2 - (3 + -1))/(-2). Let s = p - -3. Suppose 2*b**5 - 3*b - 5*b**s + b**3 + 5*b = 0. Calculate b.
-1, 0, 1
Factor -26/5*p**2 + 24/5*p**3 - 2/5 + 12/5*p - 8/5*p**4.
-2*(p - 1)**2*(2*p - 1)**2/5
Let y(f) be the third derivative of 1/540*f**6 + 0 + 0*f**3 + 8*f**2 + 1/270*f**5 + 0*f - 1/54*f**4. Factor y(b).
2*b*(b - 1)*(b + 2)/9
Let n = 30 - 30. Let y be 0/(n - 3 - -5). Factor y*i - 2/13*i**3 + 0 + 2/13*i**2.
-2*i**2*(i - 1)/13
What is r in 36*r**2 - 43*r**3 + 61*r**3 + 3*r**4 + 10*r + 9 + 20*r = 0?
-3, -1
Factor -5*g**2 - 26 + 5*g**3 + 26.
5*g**2*(g - 1)
Let k(p) = p**2 - p + 2. Let q(u) = -u**2 - u - 1. Let a(h) = -3*k(h) - 6*q(h). Factor a(x).
3*x*(x + 3)
Let u(h) = -h + 15. Let y be u(13). Determine b, given that -4*b + 4*b**y + 0*b**2 - 2 - 2*b**2 + 4 = 0.
1
Let d(x) be the third derivative of x**5/60 - x**4/4 + 3*x**3/2 + 20*x**2. Factor d(n).
(n - 3)**2
Let z = 2082 - 437219/210. Let t(i) be the third derivative of 1/60*i**6 + 0*i - 1/12*i**4 + 0 - 1/6*i**3 - 4*i**2 + 0*i**5 + z*i**7. Factor t(y).
(y - 1)*(y + 1)**3
Let r(z) be the third derivative of 0 - 1/75*z**5 + 0*z - z**2 - 1/60*z**4 + 0*z**3 - 1/300*z**6. What is j in r(j) = 0?
-1, 0
Let r = -2 + 8. Let a = r + -4. Determine c so that -6 + 5*c**3 + 16*c + 5*c - 2*c**3 - 24*c**3 + 6*c**a = 0.
-1, 2/7, 1
Let s(u) be the third derivative of 0 - 1/1365*u**7 + 0*u**6 + 0*u + 1/13*u**3 + 6*u**2 + 2/39*u**4 + 1/65*u**5. Determine a, given that s(a) = 0.
-1, 3
Suppose -s = 3*s + 2*l + 36, -5*s + 3*l = 45. Let n be s/6*1/(-3). Let -1/2*h**3 - 1/4*h**2 + n*h + 1/4 = 0. What is h?
-1, -1/2, 1
Suppose -8 = -10*x + 32. Factor -1/5*q**3 + 1/5*q**2 + 0*q + 0 + 1/5*q**5 - 1/5*q**x.
q**2*(q - 1)**2*(q + 1)/5
Let h(z) be the first derivative of -1/18*z**6 - 1/9*z**3 - 4/3*z + 1/3*z**5 + 1 - 7/12*z**4 + 4/3*z**2. What is d in h(d) = 0?
-1, 1, 2
Let s(g) be the second derivative of g**8/26880 - g**7/1120 + 3*g**6/320 - 9*g**5/160 + g**4/12 + g. Let l(w) be the third derivative of s(w). Factor l(n).
(n - 3)**3/4
Factor 9/4*d - 9/2*d**4 - 15/2*d**2 + 0 + 9*d**3 + 3/4*d**5.
3*d*(d - 3)*(d - 1)**3/4
Determine m so that -8/3*m**4 - 2/3*m - 8/3*m**2 + 0 - 2/3*m**5 - 4*m**3 = 0.
-1, 0
Let n(c) be the third derivative of c**4/24 + 2*c**3 + c**2. Let u be n(-9). Suppose -u - 4*k + 7*k**3 + 5 - 3*k**3 - 2*k**4 = 0. What is k?
-1, 1
Let d(u) = -2*u + 7. Let j(w) = -3*w + 13. Let x(r) = 11*d(r) - 6*j(r). Let s be x(-1). What is a in -2*a**4 + 7*a**5 + a**s + a**3 - 7*a**4 + 0*a**3 = 0?
0, 2/7, 1
Let m(n) = 2*n**2 + 16*n + 2. Let p(o) = -2*o**2 - 17*o - 3. Let v(x) = 3*m(x) + 2*p(x). Factor v(l).
2*l*(l + 7)
Factor -2/3*d**4 + d**2 + 1 + d**3 - 7/3*d.
-(d - 1)**3*(2*d + 3)/3
Let h(v) = -v**2 + v. Let i(r) = 2*r. Let f(t) = -3*h(t) + 2*i(t). What is x in f(x) = 0?
-1/3, 0
Let j(c) be the first derivative of 2*c**5/5 + 4*c**4/5 + 2*c**3/15 - 2*c**2/5 - 