4
Let x(a) = -a**2 + 8*a + 6. Let f be x(8). Let z = f - 4. Suppose 3*q**3 + z*q**4 + q**3 + 0*q**3 - 2*q**3 = 0. What is q?
-1, 0
Let k be (-3 - -2)*(0 - 5). Let g(a) be the second derivative of 0*a**4 + 1/20*a**k - 1/30*a**6 - a + 0 + 0*a**3 + 0*a**2. Determine f, given that g(f) = 0.
0, 1
Factor 1/2*r**2 - 2/5*r**3 + 0 + 1/10*r**4 - 1/5*r.
r*(r - 2)*(r - 1)**2/10
Let s(c) = 15*c**5 + 30*c**4 - 35*c**3 - 65*c**2 + 55*c. Let y(o) = 22*o**5 + 45*o**4 - 52*o**3 - 98*o**2 + 83*o. Let n(w) = -7*s(w) + 5*y(w). Factor n(q).
5*q*(q - 1)**2*(q + 2)*(q + 3)
Suppose -5*b = -0*w + 4*w - 21, -2*w = -8. Let f(o) = -10*o**3 + 16*o**2 - 4*o. Let n(y) = -y**3. Let j(l) = b*f(l) - 3*n(l). Factor j(p).
-p*(p - 2)*(7*p - 2)
Suppose 529 = 19*p + 491. Let -6*n - 3/2*n**p + 0 = 0. What is n?
-4, 0
Let x(g) be the third derivative of -g**5/30 + 2*g**4/3 - 16*g**3/3 + 44*g**2. Solve x(c) = 0 for c.
4
Suppose 0 = -3*s + 48 + 15. Let t be s/36 + 2/(-6). Determine z so that 3/4*z**4 + 1/2 - 5/4*z**2 - t*z**3 + 1/4*z = 0.
-1, -2/3, 1
Let f be ((-8)/1)/(4/(-2)). Factor -f - 7*v**2 + 9*v + v**2 + v.
-2*(v - 1)*(3*v - 2)
Suppose -5*d = 4*r - 2, -r + 4*r = -4*d + 1. Factor 2/3*s + 0 - 2/3*s**4 - 2/3*s**r + 2/3*s**2.
-2*s*(s - 1)*(s + 1)**2/3
Let i = 22 - 10. Let d be i/9 + (-8)/(-12). Find y such that -y**3 + 1/2*y - 1/4 + 1/2*y**d - 1/4*y**4 + 1/2*y**5 = 0.
-1, 1/2, 1
Find i, given that 6*i**3 - 32*i**2 + 0*i**5 - 4*i**5 - 24*i**4 + 8*i**5 + 42*i**3 = 0.
0, 2
Let i(n) be the third derivative of -1/60*n**4 - 1/300*n**5 + 0 - 3*n**2 + 0*n - 1/30*n**3. Solve i(w) = 0 for w.
-1
Let m(h) = -h**2 - h. Let a be (-1 + -2 - -2)*1. Let r(v) be the first derivative of -v**2 - 2*v - 1. Let o(q) = a*r(q) - 2*m(q). Factor o(x).
2*(x + 1)**2
Let b be 2/6 - (-80)/12. Solve -3 - 8*z + b*z + 7*z - 3*z**2 = 0.
1
Let y be (-15)/108 + (-4)/(-16). Let f(l) be the second derivative of 0*l**2 - 1/9*l**4 + y*l**3 + 1/30*l**5 + 0 - 2*l. Factor f(n).
2*n*(n - 1)**2/3
Let f(q) be the first derivative of -3*q**5/5 - 3*q**4/2 + 3. Factor f(p).
-3*p**3*(p + 2)
Let l(r) be the second derivative of 3/80*r**5 + 0 + 0*r**4 + 6*r + 3/4*r**2 - 3/8*r**3. Factor l(a).
3*(a - 1)**2*(a + 2)/4
Let q be (3 - 1)*2/8. Let x = 23/6 - 10/3. Let 0 - 1/2*g - x*g**2 + 1/2*g**4 + q*g**3 = 0. What is g?
-1, 0, 1
Let i(d) = d + 5. Let m be i(4). Let j = m - 5. Solve 19*l**2 + 3*l**j - 22*l**2 - 3*l**5 - 5*l**3 + 8*l**3 = 0.
-1, 0, 1
Let w(d) = -d + 19. Let a be w(17). Let h(t) be the third derivative of -a*t**2 + 0 + 0*t**4 - 1/12*t**3 + 1/120*t**5 + 0*t. Let h(q) = 0. What is q?
-1, 1
Let -343*j**5 + 8 + 19*j**2 - 23*j + 94*j**2 + 21*j**2 + 161*j**3 - 392*j**4 - 45*j = 0. What is j?
-1, 2/7
Let s = -2 - -10. Suppose 4*i = s*i - 8. Solve -2 - 2 - 49*h**i - 32*h**2 - 36*h = 0.
-2/9
Let m(o) be the second derivative of o**7/42 - o**6/15 - o**5/10 + o**4/3 + o**3/6 - o**2 - 8*o. Determine g so that m(g) = 0.
-1, 1, 2
Let r be (-2)/(-3)*(-2)/(-4). Find n such that 1/3*n**3 + n**5 + 0 - r*n**2 + 0*n + 5/3*n**4 = 0.
-1, 0, 1/3
Let n be (-9)/(-2) - 2/(-4). Suppose 14 = n*l + 4. Let -10*c**3 + 8*c**l + c + 5*c**4 - 3*c - c**4 = 0. Calculate c.
0, 1/2, 1
Let y(m) = 34*m**4 + 16*m**3 - 63*m**2 - 27*m + 29. Let t(r) = -11*r**4 - 5*r**3 + 21*r**2 + 9*r - 10. Let v(i) = 11*t(i) + 4*y(i). Solve v(k) = 0.
-1, 2/5, 1
Let k(l) be the first derivative of l**6/60 - l**5/40 - l**4/24 + l**3/12 + 6*l - 1. Let x(z) be the first derivative of k(z). Factor x(c).
c*(c - 1)**2*(c + 1)/2
Let o(i) = 13 + 6 + 12*i - 5*i**2 + 0 - 4. Let s(n) = n**2 - n - 1. Let a(j) = -o(j) - 6*s(j). Solve a(v) = 0.
-3
Let u = 6 + -4. Factor h - 2*h**2 - 2*h + 3*h**3 - u*h**3 + 2*h**4.
h*(h - 1)*(h + 1)*(2*h + 1)
Suppose -3*y - 6 = -5*y. Suppose 3*x**3 - 7 - 3*x - 7 - y*x**2 + 17 = 0. Calculate x.
-1, 1
Let g = -367/3 + 124. Determine x so that 0 - 2/3*x**2 - 2/3*x**5 + g*x**3 - 1/3*x**4 + 0*x = 0.
-2, 0, 1/2, 1
Factor 2*k - 5*k - 5*k - 6*k**2 - 2.
-2*(k + 1)*(3*k + 1)
Find y, given that 0 - 3/4*y**3 + 3*y**2 + 0*y = 0.
0, 4
Let q = 235 + -233. Find y, given that 3/2*y**q + 27/4*y**5 + 3/4 - 9/4*y**4 + 15/4*y - 21/2*y**3 = 0.
-1, -1/3, 1
Factor 2/3*s**3 - 2/3*s + 0 + 0*s**2.
2*s*(s - 1)*(s + 1)/3
Let b = -12 - -19. Let v be -3*(b/(-15) + 0). Determine f, given that -2/5 - v*f + 9/5*f**2 = 0.
-2/9, 1
Let z(k) be the first derivative of -k**6/6 - 2*k**5/5 - k**4/4 + 5. Factor z(x).
-x**3*(x + 1)**2
Let 0*r**2 + 0 + 2/17*r**3 + 0*r = 0. Calculate r.
0
Let b be 70/66*3 - 3. Factor 0*v + b*v**5 + 2/11*v**2 + 6/11*v**4 + 6/11*v**3 + 0.
2*v**2*(v + 1)**3/11
Suppose 0 = 2*f - 5 + 1. Let p(u) be the third derivative of 0 + 0*u**4 - 1/840*u**7 + 0*u + 0*u**3 - 1/240*u**5 - 1/240*u**6 - u**f. Factor p(a).
-a**2*(a + 1)**2/4
Let l(k) = k**2 - 1. Suppose 5*a - 5*f = 15, 7 = 5*a - 4*f - 4. Let z be l(a). Factor 3*p**3 - 3*p**4 + 0 + z.
-3*p**3*(p - 1)
Let d be -1 + (2 - (-1)/1). Let y(b) = 3*b + 17. Let f be y(-5). Factor -d*k + 1 - 1 + 4*k - k**f - 1.
-(k - 1)**2
Suppose -k = -5, -4*k = -v - 2*v + 4. Suppose -a = -3*a + v. Let -a*c + 6*c**3 + c + 2*c**5 - c**5 - 4*c**5 = 0. What is c?
-1, 0, 1
Let a(m) be the third derivative of -m**6/1080 + m**5/180 - m**4/72 + m**3/54 - 4*m**2. Factor a(y).
-(y - 1)**3/9
Let i(o) = 2*o**2 + 2*o - 2. Suppose 5*f + 4 = -6. Let u be i(f). What is d in -5/2*d**3 - 1/2*d**5 + 0*d + 2*d**4 + d**u + 0 = 0?
0, 1, 2
Let j(l) be the first derivative of 8 + 1/20*l**4 + 2/15*l**3 + 0*l + 1/10*l**2. Factor j(f).
f*(f + 1)**2/5
Let l(a) = a**2 + a + 1. Let v(t) = 0 - 6 + 4 + 4*t**2 + 14*t. Suppose -2*j = 2*j + 4. Let r(x) = j*v(x) + 6*l(x). Factor r(p).
2*(p - 2)**2
Suppose 6 = 3*h + 2*k, -5*h = 13*k - 10*k - 11. Suppose -3/7*l**5 - 3/7*l**h + 6/7*l**2 - 3/7*l + 6/7*l**3 - 3/7 = 0. Calculate l.
-1, 1
Let i(q) be the second derivative of q**7/735 + q**6/140 + q**5/70 + q**4/84 + q**2 - 5*q. Let a(x) be the first derivative of i(x). Factor a(d).
2*d*(d + 1)**3/7
Factor 829 + 5*h**2 - 30*h - 420 - 409.
5*h*(h - 6)
Let n(s) = 2*s**2 + 8*s - 2. Let b be n(-4). Let o be ((-2)/6)/(b/12). Factor 0 - 2/9*t**3 + 2/9*t + 0*t**o.
-2*t*(t - 1)*(t + 1)/9
Let a(l) be the second derivative of -3*l**5/130 - 2*l**4/39 - l**3/39 + 3*l + 4. Factor a(p).
-2*p*(p + 1)*(3*p + 1)/13
Let j be (-13)/78 - 7/(-30). Let w(u) be the second derivative of u - 1/5*u**2 - 1/75*u**6 + 0*u**3 + j*u**4 + 0 + 0*u**5. Suppose w(y) = 0. Calculate y.
-1, 1
Let c = -79 - -83. Let w(k) be the third derivative of 0 + 1/72*k**c + 0*k - 3*k**2 - 1/90*k**5 + 1/360*k**6 + 0*k**3. Factor w(f).
f*(f - 1)**2/3
Let r = 56 - 53. Let 4/3*w - 6*w**2 + 10*w**r - 22/3*w**4 + 0 + 2*w**5 = 0. Calculate w.
0, 2/3, 1
Suppose 5*y - 57 = -2. Suppose -5*f = -4 - y. Suppose 1/3*a**f + 0*a - 1/3*a**2 + 0 = 0. Calculate a.
0, 1
Let s(c) = -c. Let y(l) = 2*l**3 - 2*l**2 + 2. Let q(h) = -4*s(h) - 2*y(h). Factor q(m).
-4*(m - 1)**2*(m + 1)
Let q(x) = -4*x**3 + 12*x**2 + 16*x + 4. Let v(g) = -4*g**3 + 13*g**2 + 17*g + 5. Let k(p) = -5*q(p) + 4*v(p). Determine b so that k(b) = 0.
-1, 0, 3
Let a(q) be the second derivative of -3*q**5/140 - q**4/7 - 2*q**3/7 - 7*q. Determine t so that a(t) = 0.
-2, 0
Suppose -g + 0*g = -2. Factor 3*a**3 - 5*a**2 - 7*a**3 + g*a**4 + 4*a**2 + 3*a**2.
2*a**2*(a - 1)**2
Let d(r) be the second derivative of r**6/360 - r**3/2 + 3*r. Let y(z) be the second derivative of d(z). Factor y(o).
o**2
Let k(v) = -12*v**3 - 4*v**2 - 6*v - 8. Let q(x) = -x**3 - x**2 - 1. Let i(z) = -k(z) + 10*q(z). Factor i(y).
2*(y - 1)**3
Let s(u) = -2*u**2 + 11*u + 4. Let y(c) = -c. Let i(a) = 2*s(a) + 18*y(a). Factor i(m).
-4*(m - 2)*(m + 1)
Let q(k) = 3*k**4 + k**3 + k**2 - k + 4. Suppose 0*x = x + 5. Let g(h) = 4*h**4 + h**3 + h**2 - h + 5. Let l(c) = x*q(c) + 4*g(c). Factor l(r).
r*(r - 1)**2*(r + 1)
Let h be (-84)/5*(-11)/44. Factor 12/5*b**2 - 6/5 - h*b.
3*(b - 2)*(4*b + 1)/5
Suppose -4*x = -g - 2 - 8, 2*x + 2*g = 0. Suppose 4*q - 3*o + 2*o = 10, -3*q - 3*o = -15. Determine y, given that y**3 + x*y**4 + y**2 - y**q - 3*y**2 = 0.
-1, 0, 1
What is t in 18/7*t**2 - 108/7*t + 216/7 - 1/7*t**3 = 0?
6
Factor -4/11*t**2 - 2/11*t**3 + 2/11*t + 4/11.
-2*(t - 1)*(t + 1)*(t + 2)/11
Let x(p) = -7*p**5 + 9*p**4 - 7*p**3 - 13*p**2 + 10*p. Let r(i) = 13*i**5 - 18*i**4 + 13*i**3 + 25*i**2 - 19*i. Let f(v) = -4*r(v) - 7*x(v). Solve f(b) 