1
Let j(s) be the second derivative of -s**4/48 + s**3/12 - s**2/8 + 12*s. Factor j(h).
-(h - 1)**2/4
Let s be 20/50*5*1. Factor -6*y**4 - 1 - y**5 + 2*y**3 + s*y**2 - y**4 + 6*y**4 - y.
-(y - 1)**2*(y + 1)**3
Suppose 6*n - 5*n = 0. Suppose -2*b = b - 9. Determine o so that 2/3*o**2 + 0*o + 1/3*o**b + n = 0.
-2, 0
Let s(h) be the third derivative of h**6/1200 - h**4/240 + 4*h**2 + 2. What is t in s(t) = 0?
-1, 0, 1
Let x(h) be the first derivative of 0*h**2 + 0*h**4 - 1 - 1/980*h**7 + 0*h + 0*h**5 + 1/1260*h**6 + h**3. Let b(t) be the third derivative of x(t). Factor b(c).
-2*c**2*(3*c - 1)/7
Suppose 4*i**3 + 0*i**3 - 8*i**2 - 2*i + 6*i = 0. Calculate i.
0, 1
Let b = 32 - 21. Let m = b - 7. Factor -j**4 - 3*j**5 + 0*j**m + 2*j**5.
-j**4*(j + 1)
Suppose -28 = -4*x - 4*f, 3*x + 3*f = x + 19. Let q(w) be the first derivative of 0*w**2 - 1/15*w**5 + 0*w + 1/9*w**3 + x + 0*w**4. Factor q(s).
-s**2*(s - 1)*(s + 1)/3
Suppose 0 = 5*l + t + 3*t - 42, 0 = 4*l + 5*t - 39. Let n be (-2)/(-15) + l/30. Factor 1/3*d**2 - n*d**4 + 1/3*d + 0 - 1/3*d**3.
-d*(d - 1)*(d + 1)**2/3
Let s(h) be the third derivative of -h**6/200 + h**5/50 + 10*h**2. Let s(y) = 0. What is y?
0, 2
Find y such that -y**5 + 4/5*y**2 - y + 2*y**3 - 2/5*y**4 - 2/5 = 0.
-1, -2/5, 1
Let i be 1/5 - 27/(-15). Suppose 4*g + 5*d - 30 = i, 5*g = d + 11. What is c in 0*c**2 + 1/2*c**4 + 0 + 1/4*c**5 + 0*c + 1/4*c**g = 0?
-1, 0
Let r(a) be the third derivative of 0*a + 0 - 1/84*a**4 + 1/420*a**6 - 2/21*a**3 + a**2 + 1/105*a**5. Determine p, given that r(p) = 0.
-2, -1, 1
Let q(y) be the first derivative of -y**4/2 + 4*y**2 + 10. Suppose q(g) = 0. Calculate g.
-2, 0, 2
What is k in 0 + 132*k + 4*k**2 - 124*k + 0 = 0?
-2, 0
Let z(q) = q + 8. Let t be z(-6). Determine j so that -3*j**5 + 4*j - 6*j + 4*j**4 + 5*j + t*j**4 - 6*j**2 = 0.
-1, 0, 1
Let r(c) = c + 1. Let g be 1 + -2*2 - -2. Let d(i) = 2*i**5 + 8*i**4 + 12*i**3 + 8*i**2 - 4*i - 6. Let z(b) = g*d(b) - 6*r(b). Factor z(k).
-2*k*(k + 1)**4
Let w(u) be the third derivative of u**8/40320 - u**6/1440 + u**5/6 + 2*u**2. Let d(j) be the third derivative of w(j). Factor d(o).
(o - 1)*(o + 1)/2
Suppose 9 = 3*q, -2*n = -q + 3 - 0. Let d be 3/(-45) + (-2)/(-5). Let n + d*r**2 + 1/3*r = 0. What is r?
-1, 0
Let p be ((-6)/1 - -4)/((-24)/3). Factor -1/2*b + 1/4*b**4 + 0*b**2 + 1/2*b**3 - p.
(b - 1)*(b + 1)**3/4
Factor -2*x**2 + x + 0*x - x**5 + 4*x**2 - 2*x**4 + 0*x**2.
-x*(x - 1)*(x + 1)**3
Let o(l) be the first derivative of l**7/63 - l**6/15 + l**5/15 + l**4/9 - l**3/3 + l**2/3 - l - 3. Let a(k) be the first derivative of o(k). Factor a(p).
2*(p - 1)**4*(p + 1)/3
Let z(k) be the first derivative of 4*k**5/35 - 2*k**4/7 - 4*k**3/7 - 4. Suppose z(t) = 0. What is t?
-1, 0, 3
Let m(g) = 11*g**2 - 11*g - 6. Let b(y) = 10*y**2 - 10*y - 5. Let h(z) = -6*b(z) + 5*m(z). Find x, given that h(x) = 0.
0, 1
What is c in c**5 + c**5 + 4 + 2*c - 8*c**2 - 559*c**4 + 563*c**4 - 4*c**3 = 0?
-2, -1, 1
Let j(a) = -a**3 + 3*a**2 - 2*a + 2. Let l be j(2). Factor 0*x + 0 + 1/2*x**l.
x**2/2
Let w(d) = d**3 - 2*d + 2. Let k be w(2). Suppose -2 - 3*l**2 + k*l**2 - l + 5 - 5*l = 0. What is l?
1
Let j be 18/8 + (-20)/80. Suppose 0 = -p + j. Factor 3/2*f**4 + 0*f - 5/2*f**3 + f**p + 0.
f**2*(f - 1)*(3*f - 2)/2
Let b be (-1)/((-2)/3 + 1). Let c = 6 + b. Solve -v**3 - 8*v + v**2 + 9*v**2 - 3*v**c + 2 = 0.
1/2, 1
Let j = 5 + -12. Let v(k) = -k**2 - 7*k + 3. Let a be v(j). Suppose -1/3*h**2 + 0*h**a + 0*h + 1/3*h**4 + 0 = 0. What is h?
-1, 0, 1
Let o be (-1 + 1 + 0)*-1. Let c(a) be the first derivative of 1/12*a**4 + 0*a**2 + o*a + 0*a**3 + 1. Factor c(s).
s**3/3
Let w = -16 + 18. Factor 10*s**2 + 12*s**w - 10*s**2 - 8*s**3 - 16 + 16*s - 4*s**4.
-4*(s - 1)**2*(s + 2)**2
Let t(p) be the third derivative of 2*p**7/105 + p**5/20 + p**2. Suppose v + 1 = -21. Let f(q) = -15*q**4 - 11*q**2. Let b(o) = v*t(o) - 6*f(o). Factor b(g).
2*g**4
Determine w, given that 9/5*w + 12/5 - 3/5*w**2 = 0.
-1, 4
Let s(f) be the first derivative of 2/3*f - 1/6*f**4 + 1/3*f**2 - 2/9*f**3 + 2. Let s(r) = 0. What is r?
-1, 1
Let l = -30359/60 + 506. Let w(a) be the second derivative of 0*a**3 + a + 0 + l*a**6 + 1/24*a**4 - 1/20*a**5 + 0*a**2. Let w(h) = 0. What is h?
0, 1
Let p be 1*3/(-108)*(-9)/30. Let x(g) be the third derivative of 1/12*g**3 + 1/24*g**4 + 0 + 2*g**2 + 0*g + p*g**5. Let x(w) = 0. What is w?
-1
Let h(r) be the third derivative of 0*r - r**2 + 0*r**3 - 1/40*r**6 + 0*r**5 + 1/8*r**4 + 0. Factor h(m).
-3*m*(m - 1)*(m + 1)
Let l = 24 - 24. Let s(m) be the third derivative of 0*m - 11/84*m**4 + l - 8/105*m**5 - 1/60*m**6 - 2/21*m**3 - m**2. Factor s(g).
-2*(g + 1)**2*(7*g + 2)/7
Let i(q) be the third derivative of q**5/24 + q**4/4 + q**3/3 - 16*q**2. Factor i(l).
(l + 2)*(5*l + 2)/2
Let j(o) be the first derivative of -o**6/3 - 13. Factor j(r).
-2*r**5
Let j(d) be the second derivative of d**7/420 + d**6/120 + d**5/120 + 2*d**2 - d. Let v(f) be the first derivative of j(f). Factor v(g).
g**2*(g + 1)**2/2
Let r(u) be the third derivative of u**7/105 + u**6/60 - u**5/30 - u**4/12 + 2*u**2. Find x, given that r(x) = 0.
-1, 0, 1
Suppose -3*k - 12 = 3*v, 5*k = -5*v + 2*v - 22. Factor v + 1 + 3*z**2 + z - 2.
z*(3*z + 1)
Find f, given that -3/2*f**3 + 9/2*f**2 + 15/2 + 27/2*f = 0.
-1, 5
Factor 18*q**2 - 19*q**2 + 17*q**2 - 36 - 36*q.
4*(q - 3)*(4*q + 3)
Let m(q) be the second derivative of -q**4/12 - 3*q**3 - 81*q**2/2 + 38*q + 2. Factor m(x).
-(x + 9)**2
Suppose 2*z + 0*z + 8 = -4*j, -5*j - 20 = 0. Factor -2*v**4 + 12*v**3 + 4*v - z*v**2 - 5*v**4 + 3*v**4 - 8*v**2.
-4*v*(v - 1)**3
Let v be ((-1)/11)/((-6)/1902). Let l = 29 - v. Factor l*c**4 - 2/11*c**2 + 0 + 2/11*c**3 - 2/11*c.
2*c*(c - 1)*(c + 1)**2/11
Let w(j) = -j. Let z(u) = u + 1. Let b be z(-7). Suppose -3*a + k = 0, 4*a = k + k - 2. Let q(x) = -3*x**3 - 3*x**2. Let i(c) = a*q(c) + b*w(c). Factor i(p).
-3*p*(p - 1)*(p + 2)
Let r(v) be the first derivative of v**4/2 - 5*v**3/6 + v**2/2 - v + 3. Let a(p) be the first derivative of r(p). Suppose a(g) = 0. What is g?
1/3, 1/2
Let g(t) = -t**2 - t + 1. Let m(o) = 5*o**2 + 2*o + 1. Let a(i) = -1. Let k(l) = -2*a(l) - m(l). Let v(w) = g(w) - k(w). Factor v(d).
d*(4*d + 1)
Let w(j) be the third derivative of j**5/120 - 5*j**4/24 - 11*j**3/12 - j**2 - 15. Factor w(i).
(i - 11)*(i + 1)/2
Let n(g) be the second derivative of -g**5/40 + g**4/24 + g**3/12 - g**2/4 + 15*g. Let n(q) = 0. What is q?
-1, 1
Suppose 5*b + 9 - 39 = 0. Let l(k) be the third derivative of 0 - 1/42*k**4 + 0*k + k**2 + 1/21*k**3 + 0*k**5 + 1/210*k**b - 1/735*k**7. Factor l(c).
-2*(c - 1)**3*(c + 1)/7
Let q(u) be the first derivative of -u**9/5040 - u**8/2800 + u**7/700 - 5*u**3/3 + 4. Let m(c) be the third derivative of q(c). Factor m(g).
-3*g**3*(g - 1)*(g + 2)/5
Factor -6/7*l**3 + 0 - 2/7*l**4 + 8/7*l**2 + 0*l.
-2*l**2*(l - 1)*(l + 4)/7
Let p = -45487 - -319033/7. Factor -32/7 + 256/7*b + 64*b**3 - 14*b**4 - p*b**2.
-2*(b - 2)**2*(7*b - 2)**2/7
Let j(l) = l + 13. Let z be j(-13). Factor -2/3*n**3 + z*n**2 - n**4 + 0*n + 0.
-n**3*(3*n + 2)/3
Solve 7*g**4 + 3*g**5 - 61*g + 56*g + 5 + 2*g**3 - 6 - 6*g**2 = 0 for g.
-1, -1/3, 1
Let -4*t**2 + 4*t + 5*t**2 + 3*t**2 = 0. Calculate t.
-1, 0
Determine p, given that 0*p**4 - 1/4*p**3 + 0*p**2 + 0*p + 0 + 1/4*p**5 = 0.
-1, 0, 1
Let o(f) be the second derivative of -2*f**6/3 - 7*f**5 - 365*f**4/12 - 70*f**3 - 90*f**2 + 37*f + 1. Factor o(t).
-5*(t + 2)**2*(2*t + 3)**2
Let o be (4 - 2)/1 + -2. Suppose o = p - 4*p. Solve 2/3*s**2 + s**4 + 5/3*s**3 + 0 + p*s = 0.
-1, -2/3, 0
Let w be (5/(-2) - -2)/(-1). Let t(q) be the first derivative of -w*q**4 + 0*q**2 + 0*q - 3 - 2/3*q**3. Factor t(i).
-2*i**2*(i + 1)
Let j(h) be the second derivative of -h**5/120 + h**4/24 - h**3/12 + h**2/12 - 8*h. Solve j(x) = 0 for x.
1
Let i(k) be the first derivative of -k**5/5 + 4*k**4 - 32*k**3 + 128*k**2 + 4*k - 3. Let c(m) be the first derivative of i(m). Factor c(s).
-4*(s - 4)**3
Let z(v) be the third derivative of 1/24*v**4 + 0*v**5 + 0 - v**2 + 0*v**3 - 1/60*v**6 + 1/336*v**8 + 0*v**7 + 0*v. Factor z(c).
c*(c - 1)**2*(c + 1)**2
Let k(u) be the first derivative of 1/2*u**2 + 2 + 1/20*u**5 + 1/3*u**3 + 7/24*u**4 + 0*u. Let v(q) be the second derivative of k(q). Solve v(t) = 0.
-2, -1/3
Let q(n) be the second deri