-9*m**3 + 9*m**2 + 21*m + 9. Let u(g) = g**4 - g**3 - g - 1. Let c(x) = 3*u(x) - z(x). Factor c(y).
3*(y - 2)*(y + 1)**2*(y + 2)
Let h(z) be the first derivative of 2*z**3/21 + 2*z**2/7 + 33. Let h(b) = 0. What is b?
-2, 0
Let g = 48371/70 + -691. Let v(y) be the third derivative of -g*y**5 + 0*y + 1/84*y**4 + 0 - 4*y**2 + 0*y**3. Factor v(c).
-2*c*(3*c - 1)/7
Let d(o) be the third derivative of -o**8/168 + 2*o**7/105 + o**6/20 - 2*o**5/15 - o**4/3 - 8*o**2. Suppose d(m) = 0. Calculate m.
-1, 0, 2
Find m, given that 0*m**2 + 8/3*m**3 + 0*m + 4/3*m**4 + 0 = 0.
-2, 0
Let s = -191/2 + 96. Let s*y**2 - 1/2 + 1/2*y - 1/2*y**3 = 0. What is y?
-1, 1
Factor -3/2*t**5 + 0 - 6*t**2 + 3*t**4 - 6*t + 9/2*t**3.
-3*t*(t - 2)**2*(t + 1)**2/2
Let q(d) be the first derivative of 3*d**4/4 - 2*d**3/3 - d**2/2 + 1. Let a(v) = 2*v**3 - v**2 - v. Let h(m) = 10*a(m) - 6*q(m). Factor h(j).
2*j*(j - 1)*(j + 2)
Let b(u) be the second derivative of -1/27*u**3 - 4*u - 1/54*u**4 + 1/90*u**5 + 0 + 1/9*u**2. Suppose b(q) = 0. Calculate q.
-1, 1
Let y(f) = 8*f**3 + 20*f**2 + 31*f + 13. Let k(s) = 18*s**3 + 39*s**2 + 62*s + 27. Let x(w) = -3*k(w) + 7*y(w). Determine r so that x(r) = 0.
-10, -1, -1/2
Let w(g) = g**2 - 2*g - 4. Let i be w(4). Factor -6*o**3 + 3*o**5 + 4*o**3 - 6*o**i + 0*o**3 + 5*o**5.
2*o**3*(o - 1)*(4*o + 1)
Factor 105 - u + 22*u**2 - 7*u - u**5 + 8*u**4 - 105 - 21*u**3.
-u*(u - 4)*(u - 2)*(u - 1)**2
Let h = 42 - 40. Solve 0 - 7/4*y**4 + 0*y**h + 0*y + 1/2*y**3 = 0.
0, 2/7
Let i(m) be the third derivative of 0*m + 1/80*m**5 - 1/840*m**7 + 3*m**2 - 1/6*m**3 + 1/240*m**6 - 1/24*m**4 + 0. Factor i(a).
-(a - 2)**2*(a + 1)**2/4
Factor 16 + 3*q**2 - 6*q**2 - 3*q - 3*q**2 + 2.
-3*(q + 2)*(2*q - 3)
Let j(v) be the third derivative of -v**5/120 + 11*v**4/24 - 121*v**3/12 - 2*v**2. Solve j(y) = 0.
11
Let t(y) = -2*y**3 + y**2 - 2*y + 3. Let b be -7 + (-4)/8*-2. Let i(k) = -9*k**3 - 9*k + 13 + k**2 + 7*k**2 - 3*k**2. Let c(g) = b*i(g) + 26*t(g). Factor c(n).
2*n*(n - 1)**2
Let k(x) be the second derivative of -x**5/16 - 5*x**4/24 - 5*x**3/24 + 20*x. Factor k(o).
-5*o*(o + 1)**2/4
Determine l so that -2/11*l + 0 + 0*l**2 + 2/11*l**3 = 0.
-1, 0, 1
Find j such that 1/2*j**2 - 1/2 + 0*j = 0.
-1, 1
Let r(f) = 4*f. Let b be r(1). Suppose b = 3*o - 2. Factor -1/5 + 0*q + 2/5*q**5 - 2/5*q**3 + 4/5*q**o - 3/5*q**4.
(q - 1)**3*(q + 1)*(2*q + 1)/5
Let i(m) = -m**3 + 4*m**2 - 2*m - 2. Let b be i(2). Suppose 6 = b*t + 2*s - 2, 0 = -2*t + 5*s + 15. Factor -j + 2 + 4*j**2 - t*j**2 + 2*j.
-(j - 2)*(j + 1)
Let n(f) = 5*f**2 + 2*f + 1. Let w be n(-1). Determine g so that 0*g + g + 3*g**3 - g**2 - 2*g**2 - g**w = 0.
0, 1
Suppose 2/3 + 122/3*i**2 + 56*i**3 + 24*i**4 + 28/3*i = 0. Calculate i.
-1, -1/6
Solve 6*c - 6*c**2 + 3*c**2 - 2*c**2 + 9 + 2*c**2 = 0 for c.
-1, 3
Let y be (-54 + 52)*((-10)/12)/5. Factor -y*g**3 + 1/3*g + 0 + 0*g**2.
-g*(g - 1)*(g + 1)/3
Let r(x) be the first derivative of 3*x**6/10 + 69*x**5/25 + 51*x**4/5 + 96*x**3/5 + 96*x**2/5 + 48*x/5 - 14. Solve r(m) = 0 for m.
-2, -1, -2/3
Let v(t) = -t**3 + 7*t**2 + t - 4. Let x be v(7). Suppose -x*n = -2*n - 3. Suppose 2/9 - 2/9*j**n - 2/3*j + 2/3*j**2 = 0. Calculate j.
1
Let g be 2/76*(28 - 1). Let m = g + -4/19. Determine t, given that 0 - m*t**3 + t**2 - 1/2*t = 0.
0, 1
Find a such that -16/7*a + 0*a**3 + 2/7*a**4 - 12/7*a**2 - 6/7 = 0.
-1, 3
Suppose 52 = -4*s - 76. Let q be s/130 + 40/100. Factor -q*c**2 + 0*c + 0.
-2*c**2/13
Let p(c) be the first derivative of -3*c**4/8 + 5*c**3/6 - c**2/4 - c/2 + 3. Solve p(l) = 0.
-1/3, 1
Let k be ((-6)/(-45))/2*(-130)/(-39). Factor 0*t - 2/9 + k*t**2.
2*(t - 1)*(t + 1)/9
Suppose -2*s + 3*q = 34, -37 = 2*s + q - 11. Let j be ((-4)/7)/(4/s). Determine m so that -4*m**3 + 2*m**4 - 2*m**j - 6*m + 6*m + 0*m**5 + 4*m**5 = 0.
-1, -1/2, 0, 1
Factor -4/9*f**2 + 10/9*f**4 + 0*f - 2/3*f**3 + 0.
2*f**2*(f - 1)*(5*f + 2)/9
Let y(w) be the second derivative of -w**5/150 - w**4/18 - w**3/15 + 3*w**2/5 - 39*w. Factor y(i).
-2*(i - 1)*(i + 3)**2/15
Suppose 5*j - k - 2*k = 14, 4*k = 5*j - 17. Let r = 1 + j. Let 0*h**5 - 6*h**4 + 8*h**r + 0*h**5 + 2*h**5 = 0. What is h?
-1, 0, 2
What is i in 0*i + 0 - 4/7*i**2 + 4/7*i**3 = 0?
0, 1
Let m(o) be the first derivative of o**5/6 - 5*o**4/8 + 5*o**3/9 - 28. Find a such that m(a) = 0.
0, 1, 2
Let z(i) be the third derivative of -i**4/24 + 2*i**3/3 + 5*i**2. Let m be z(0). Find a such that 0*a**2 + 0 - 49/4*a**5 - a**3 - 7*a**m + 0*a = 0.
-2/7, 0
Suppose -5*v - 8 = -9*v. Factor -3/2*q**v - 3*q - 3/2.
-3*(q + 1)**2/2
Let d be 2 + (1 - (236/60 + -1)). Let f(m) be the second derivative of d*m**6 - 3*m + 0 + 0*m**2 - 3/10*m**5 + 1/3*m**4 + 0*m**3. Factor f(x).
2*x**2*(x - 2)*(x - 1)
Let y be (6/(-4))/((-45)/(4 + 1)). Let k(m) be the first derivative of 0*m**2 - 4 + y*m**4 + 1/9*m**3 + 0*m + 1/15*m**5. Solve k(h) = 0 for h.
-1, 0
Suppose 0 = -w - 2*g - 8, -5*g - 7 = -3*w + 13. Suppose 0 = -3*x + 4*x - 3. Factor 1/3*t**x + w + 1/3*t + 2/3*t**2.
t*(t + 1)**2/3
Determine c so that -5*c**4 + 23*c**2 + 20*c**3 + 24*c**2 - 42*c**2 - 20*c = 0.
-1, 0, 1, 4
Suppose 3*c - s - 12 = 0, 0 = -c - 63*s + 62*s + 4. Suppose 0 + 6/13*z**c + 0*z**3 - 8/13*z**2 - 2/13*z**5 + 0*z = 0. What is z?
-1, 0, 2
Find x, given that -4/5*x - 6/5*x**2 + 0 + 0*x**3 + 2/5*x**4 = 0.
-1, 0, 2
Factor 1/4 + 1/2*w + 1/4*w**2.
(w + 1)**2/4
Suppose 2*z + 3*u - 4 = -3*z, -6 = 3*u. Let k be z/7 + 60/35. Factor 3/2*w**3 - 2*w + 1/2*w**4 + 0 + 0*w**k.
w*(w - 1)*(w + 2)**2/2
Suppose 21 = 4*w + 5. Suppose 0*y**3 + 2/5*y**2 + 0*y - 2/5*y**w + 0 = 0. Calculate y.
-1, 0, 1
Let d(q) = 8*q**3 + 8*q**2 - 32*q + 28. Let i(h) = -h**3 + h**2 - 1. Let l(f) = -d(f) - 12*i(f). What is n in l(n) = 0?
1, 2
Suppose 21 = 4*h - p - 12, 0 = 3*p - 9. Factor 0*d - 7*d**3 - 4 + h*d**3 - 6*d.
2*(d - 2)*(d + 1)**2
Factor -4/11*f**2 + 0*f + 2/11*f**3 + 0.
2*f**2*(f - 2)/11
Let x(u) be the second derivative of u**4/48 + u**3/8 - 3*u. Factor x(a).
a*(a + 3)/4
Find m such that 68*m**4 + 8*m + 3*m**3 - 134*m**4 + m**3 + 68*m**4 - 14*m**2 = 0.
-4, 0, 1
Let z(r) = 8*r**3 - 16*r**2 + 12*r - 4. Let m(g) = -g**3 + g**2. Let l(x) = 4*m(x) + z(x). Factor l(d).
4*(d - 1)**3
Let j(m) be the second derivative of m**5/60 + m**4/9 + 5*m**3/18 + m**2/3 - 9*m. Factor j(y).
(y + 1)**2*(y + 2)/3
Let s(u) = 2*u**2 + 14*u + 8. Let y(o) = o**2 + 15*o + 8. Let q(p) = 3*s(p) - 2*y(p). Let q(l) = 0. Calculate l.
-2, -1
Determine a so that 10*a - 11*a**2 + 2*a + 5*a**2 - 9*a = 0.
0, 1/2
Factor -4/9*z**3 + 2/9*z**2 + 2/9*z**4 + 0*z + 0.
2*z**2*(z - 1)**2/9
Let g(h) be the first derivative of -4*h**3/3 + 4*h**2 - 4*h - 10. Factor g(y).
-4*(y - 1)**2
Suppose -5*v - 9 + 19 = 0. Find g such that -6*g - 4/3 + 20/3*g**4 + 6*g**3 - 16/3*g**v = 0.
-1, -1/2, -2/5, 1
Let p = 10 - 6. Let i(y) = -9*y**2 + 5*y + 7. Let c(q) = 5*q**2 - 3*q - 4. Let m = -1 - -8. Let o(x) = m*c(x) + p*i(x). Solve o(w) = 0 for w.
-1, 0
Let l = 99 - 19. Factor -a**5 - 31*a**3 - 20*a**3 + 10*a**4 + 11*a**3 - 80*a + 32 + l*a**2.
-(a - 2)**5
Let j = 16 - 12. Find n such that -6*n**3 - 28*n - 8 + j*n**2 + 4*n**2 + 34*n**3 = 0.
-1, -2/7, 1
Let k be ((-2)/(-12))/((-6)/14). Let f = k - -8/9. Determine w so that -9/4*w - 7/4*w**2 - f + 9/4*w**4 + 9/4*w**3 = 0.
-1, -2/3, -1/3, 1
Let t(x) = 10*x**2 + 5*x + 10. Let d(u) = -9*u**2 - 6*u - 9. Let w(z) = -5*d(z) - 4*t(z). Let w(n) = 0. What is n?
-1
Suppose -5*t = b - 4*b - 65, -3*t = -4*b - 94. Let i be 15/b*35/(-6). Suppose 0 + a + 5/2*a**2 - i*a**3 = 0. What is a?
-2/7, 0, 1
Let z be -4 - (-3 + 3) - -9. Let x(q) be the third derivative of 0 + q**2 + 0*q + 0*q**4 + 0*q**3 + 1/240*q**z. Solve x(s) = 0.
0
Solve 3/2 - 1/4*k**2 + 5/4*k = 0.
-1, 6
Let b(f) be the first derivative of -f**2 + 0*f**3 - 3 + 0*f + 1/2*f**4. Factor b(p).
2*p*(p - 1)*(p + 1)
Let w(s) be the third derivative of -3*s**6/160 + s**5/12 - s**4/24 + 7*s**2. Factor w(m).
-m*(m - 2)*(9*m - 2)/4
Let f(o) be the first derivative of -27*o - 22*o**3 - 3/5*o**5 - 6*o**4 - 36*o**2 - 3. Find n, given that f(n) = 0.
-3, -1
Let k(j) be the second derivative of -j**7/231 - j**6/55 - j**5/55 + j**4/33 + j**3/11 + j**2/11 - 6*j. Factor k(x).
-2*(x - 1)*(x + 1)**4/11
Let l be (-6)/375*5*-10. Suppose 4*h = 4*k - 16, 4*h + 10 = 2*k - 0*h. Solve -l*b**2 + 0 - 2/5*b**k - 2/5*b = 0 for b.
-1, 0
Suppose 2*l = 3 