et m be r(-6). Factor 4*x**m + 3*x**3 - x**3 - 2*x**2.
2*x**2*(x + 1)
Let g(n) be the second derivative of -n**4/96 + n**2/4 + 7*n. Factor g(a).
-(a - 2)*(a + 2)/8
Let k(c) be the third derivative of -c**5/210 - 5*c**4/21 - 100*c**3/21 + 5*c**2 + 3*c. Solve k(v) = 0.
-10
Let i = 1 - -3. Factor 5*o**2 - 19*o**2 + 4*o**3 + 4*o - 8*o**4 + 2*o**i + 12*o**3.
-2*o*(o - 1)**2*(3*o - 2)
Let x = 10 - 10. Let y be (x + -2)*(-3)/2. Factor 3 - 7*w**3 - 6 + 9*w - y + 4*w**3.
-3*(w - 1)**2*(w + 2)
Let c(i) be the first derivative of 6/55*i**5 - 3/11*i**2 - 4/11*i + 3 + 2/11*i**3 + 7/22*i**4. Determine s, given that c(s) = 0.
-1, 2/3
Factor 2*i - 94*i**4 - 2*i**3 + 92*i**4 + 6*i**2 + 0*i**3 - 4.
-2*(i - 1)**2*(i + 1)*(i + 2)
Find f such that 0 + 4/7*f**2 + 12/7*f = 0.
-3, 0
Suppose 0 - 3/7*g**4 + 3/7*g**3 - 3/7*g + 3/7*g**2 = 0. What is g?
-1, 0, 1
Let p(l) = -l**3 - 12*l**2 - 13*l - 7. Let h be p(-11). Solve -3*q**3 + h*q + 4*q**4 + 36*q**2 + 21*q**3 + 2*q**3 + 8 + 13*q = 0 for q.
-2, -1
Let j(k) = -3*k - 2. Let r be j(1). Let n = 9 + r. Factor -f - 1/2 + f**3 + 0*f**2 + 1/2*f**n.
(f - 1)*(f + 1)**3/2
Let r be (-3 + 2)*(-2 - 0). Let o(g) be the first derivative of -1 + 0*g - 1/16*g**4 + 0*g**r - 1/6*g**3. Factor o(x).
-x**2*(x + 2)/4
Let v be 0 - (1 - 2)*-1. Let m be ((-1)/(-6))/(v/(-2)). Solve -2/3*p + m*p**2 + 0 = 0 for p.
0, 2
Let z be (-12)/(-6) - (1 + -2). What is b in 27/2*b**z + 7/2*b**5 + 0 + 23/2*b**4 + 13/2*b**2 + b = 0?
-1, -2/7, 0
Factor 25/3*g**2 + 20/3*g**3 + 0 + 5/3*g**4 + 10/3*g.
5*g*(g + 1)**2*(g + 2)/3
Let y(g) be the third derivative of 0 + 1/42*g**4 - 1/21*g**3 + 2*g**2 + 0*g - 1/210*g**5. Suppose y(m) = 0. Calculate m.
1
Factor 36*j**3 + 2*j**4 + 5*j**2 - 30*j**3 - j**2.
2*j**2*(j + 1)*(j + 2)
Factor -8/7 + 2/7*u**2 + 0*u.
2*(u - 2)*(u + 2)/7
Let h = 14 + -10. Factor 6 - 9*o**3 - 5*o**4 - 4*o**4 + 2*o**4 + 4*o**h + 9*o - 3*o**2.
-3*(o - 1)*(o + 1)**2*(o + 2)
Suppose -11*d + 7*d + 32 = 0. Suppose 5*m + 5*z + 10 = 0, -m - 5*z = -z + d. Solve -3/2*c**3 + m - 3/2*c**2 + c - 3/2*c**5 + 7/2*c**4 = 0.
-2/3, 0, 1
Let d be 207/15 - 2/(-10). Let m be -6*(0 - d/6). Determine q, given that 2*q**3 - 2*q - 14 + m = 0.
-1, 0, 1
Factor 9/7*k**2 + 6/7 - 3*k.
3*(k - 2)*(3*k - 1)/7
Let v = -1/734 + 6611/3670. Factor 12/5*r + 3/5*r**2 + v.
3*(r + 1)*(r + 3)/5
Let f be 21/(-27) + (-4)/18. Let p(q) = -30*q**2 - 78*q - 81. Let a(y) = y**3 - y**2 + y. Let m(j) = f*p(j) + 3*a(j). Suppose m(v) = 0. What is v?
-3
Let b be 0 - (-10 + 6 - (-1 - 3)). Factor 2/7*c**2 + b + 2/7*c.
2*c*(c + 1)/7
Let x(u) be the first derivative of -u**4/34 - 8*u**3/51 - 5*u**2/17 - 4*u/17 - 7. Factor x(t).
-2*(t + 1)**2*(t + 2)/17
Let h(k) = -2*k**4 + 9*k**3 - 24*k**2 + 23*k - 6. Let n(p) = -6*p**4 + 26*p**3 - 72*p**2 + 70*p - 18. Let w(q) = 10*h(q) - 3*n(q). Factor w(g).
-2*(g - 3)*(g - 1)**3
Suppose 5*g - g = 12. Factor 9*m**g - 15*m**3 - 2*m + m**4 - 1 + 8*m**3.
(m - 1)*(m + 1)**3
Let y(i) be the second derivative of -i**4/9 - 8*i**3/9 - 8*i**2/3 + 2*i. Let y(a) = 0. What is a?
-2
Let x(b) be the third derivative of 0 + 1/150*b**6 - 1/15*b**3 + 1/525*b**7 + 0*b**5 - 1/30*b**4 + 0*b - b**2. Factor x(u).
2*(u - 1)*(u + 1)**3/5
Let f(j) = -3*j - 5. Let k be f(-3). Factor -2/9*w**k - 2/9*w**3 + 0*w**2 + 0 + 0*w.
-2*w**3*(w + 1)/9
Let u(p) be the third derivative of p**5/120 - p**4/24 + p**3/12 - 8*p**2. Let u(y) = 0. What is y?
1
Factor -24*f + 28*f + 8*f**3 + 0*f**3 - 14*f**2 + 2.
2*(f - 1)**2*(4*f + 1)
Let g(f) be the third derivative of f**8/336 - f**7/210 - f**6/60 + f**5/30 + f**4/24 - f**3/6 - 6*f**2. Factor g(a).
(a - 1)**3*(a + 1)**2
Let a(y) be the third derivative of y**7/1260 + y**6/270 + y**5/180 + 2*y**3/3 - y**2. Let o(f) be the first derivative of a(f). Factor o(u).
2*u*(u + 1)**2/3
Factor 3*h + h + 3*h**2 - h**2 - 4*h**2.
-2*h*(h - 2)
Let f(h) be the first derivative of -h**5/60 - h**4/18 - h**3/18 - 4*h + 7. Let n(g) be the first derivative of f(g). Factor n(t).
-t*(t + 1)**2/3
Let n(f) be the second derivative of f**6/105 + f**5/35 + f**4/42 + 27*f. Factor n(l).
2*l**2*(l + 1)**2/7
Let r(a) be the third derivative of -1/60*a**6 + 0*a + 0*a**3 - 2*a**2 + 1/12*a**4 + 0 - 1/105*a**7 + 1/30*a**5. Factor r(t).
-2*t*(t - 1)*(t + 1)**2
Let w be -6 + (-2)/4*-8. Let o be ((-5)/w)/((-10)/(-8)). Determine q, given that 1/3 + 0*q - 1/3*q**o = 0.
-1, 1
Let f(k) be the second derivative of -10*k**4 + 0 + 24*k**2 + k - 3/2*k**6 + 0*k**3 - 6*k**5 - 1/7*k**7. Solve f(q) = 0.
-2, 1/2
Let o = 7 + -3. Factor 5*x**4 - 2*x**o - 5*x**2 + 1 - x**2 + 2.
3*(x - 1)**2*(x + 1)**2
Let h(q) be the second derivative of -q**4/30 - 4*q**3/15 - 13*q. Determine i so that h(i) = 0.
-4, 0
Let z(n) be the second derivative of 5*n**7/84 + n**6/6 - 5*n**4/12 - 5*n**3/12 + 5*n. Factor z(d).
5*d*(d - 1)*(d + 1)**3/2
Suppose 5 = s + 1. Let c(g) be the second derivative of 0*g**2 + 0*g**3 + 8/15*g**6 + 1/12*g**s - 2/5*g**5 + 0 - g. Factor c(x).
x**2*(4*x - 1)**2
Let i(q) be the second derivative of 3*q + 4/39*q**3 + 5/78*q**4 + 0*q**2 + 0 + 1/130*q**5. Factor i(f).
2*f*(f + 1)*(f + 4)/13
Let q(s) = 22*s**3 + 4*s**2 - 38*s - 4. Let n(d) = -15*d**3 - 3*d**2 + 25*d + 3. Let h be 0/(9/3) + -5. Let r(g) = h*q(g) - 8*n(g). Factor r(p).
2*(p - 1)*(p + 1)*(5*p + 2)
Suppose -4*l = -2*l + 14. Let r = l + 10. Suppose 2*y**4 + 32/5*y**2 + 8/5*y + 34/5*y**r + 0 = 0. Calculate y.
-2, -1, -2/5, 0
Let s(x) = -7 + 0 + x**2 - 3*x**2 + x**2 + 8*x. Let o be s(6). Factor 2*l**3 + l**o + 0*l**5 - 4*l**3 + l**3.
l**3*(l - 1)*(l + 1)
Let h(m) be the second derivative of -3*m**4/4 + 2*m**3 - 3*m**2/2 + 21*m. Factor h(s).
-3*(s - 1)*(3*s - 1)
Let q(u) be the third derivative of -1/504*u**8 + 0*u + 0*u**3 + 8*u**2 + 0 + 0*u**4 + 0*u**5 - 2/315*u**7 - 1/180*u**6. Factor q(p).
-2*p**3*(p + 1)**2/3
Let y(n) = n**3 - n**2 - 10*n - 2. Let k(f) = f**3 - f**2 - 11*f - 3. Let o(d) = -6*k(d) + 7*y(d). Factor o(v).
(v - 2)*(v - 1)*(v + 2)
Let q(y) = y**3 - y**2 - y + 1. Let j be q(2). Let f = j - 8/3. Suppose 0 + 1/3*o**2 - f*o**4 - 1/3*o**3 + 0*o + 1/3*o**5 = 0. What is o?
-1, 0, 1
Let a(d) = -22 - d**2 - 20*d - d + 43. Let b(j) = -j**2 - 31*j + 31. Let h(k) = 7*a(k) - 5*b(k). Determine x, given that h(x) = 0.
2
Let q(a) be the third derivative of a**7/700 + a**6/600 + a**3/2 + a**2. Let v(d) be the first derivative of q(d). Factor v(x).
3*x**2*(2*x + 1)/5
Factor -17*k + 6 - 17*k + 25*k + 3*k**2.
3*(k - 2)*(k - 1)
Suppose 0 = q - 0*q - 12. Determine y, given that -4*y**4 + 5*y + q*y**2 + 3*y + 0*y = 0.
-1, 0, 2
Find b such that -6*b**2 + 2*b**2 + 20*b + 7*b**2 + 2*b**2 = 0.
-4, 0
Let f be -5 + 7 - (-2 - 0). Suppose 0 = -8*j + f*j + 12. Suppose -8/7*h - 8/7*h**j - 2/7*h**4 - 12/7*h**2 - 2/7 = 0. What is h?
-1
Let v be ((-3)/(-2))/((-9)/876). Let t = v + 736/5. Factor -2/5*j**5 + 0 - t*j**3 + 2/5*j**2 + 0*j + 6/5*j**4.
-2*j**2*(j - 1)**3/5
Suppose -42 + 7 = -5*v. Let z be (-6)/(-21) - (-2)/v. What is t in 4/7*t**2 + 2/7*t + 0 - z*t**4 + 0*t**3 - 2/7*t**5 = 0?
-1, 0, 1
Let n(h) be the second derivative of -3*h**5/100 + h**4/60 + h**3/10 - h**2/10 + 7*h. What is s in n(s) = 0?
-1, 1/3, 1
Let b(m) = m**2. Let a(s) = 2*s**2 - 4*s - 8. Let r(q) = -4*q**2 + 8*q + 17. Let y(z) = -9*a(z) - 4*r(z). Let i(o) = -3*b(o) - y(o). Factor i(p).
-(p + 2)**2
Let g(y) be the third derivative of 0*y + 11*y**2 + 1/20*y**5 + 0 + 0*y**3 - 1/8*y**4. Factor g(h).
3*h*(h - 1)
Let g(l) = -2*l**2 + 8. Let t(j) = -15*j**2 + 65. Let o(q) = 25*g(q) - 3*t(q). Factor o(r).
-5*(r - 1)*(r + 1)
Suppose 3*d = -d + 60. Let m(r) = -r**2 - r - 1. Let b(u) = 4*u**2 + 3*u + 4. Let p(q) = d*m(q) + 3*b(q). Factor p(n).
-3*(n + 1)**2
Let n(m) be the first derivative of m**4/24 - m**3/9 - m**2/12 + m/3 - 2. Factor n(l).
(l - 2)*(l - 1)*(l + 1)/6
Let w be (-12)/(-78) - (-31)/52. Find r such that 9/4*r + w*r**3 - 1/2 - 5/2*r**2 = 0.
1/3, 1, 2
Let u be 66/24 + 2/8. Find v, given that 0*v**u + v - 5*v**3 - 2*v + 4*v**3 - 2*v**2 = 0.
-1, 0
Let d(h) be the first derivative of h**5/15 + h**4/8 + h**3/18 + 2. Factor d(y).
y**2*(y + 1)*(2*y + 1)/6
Let u(b) be the first derivative of 4*b**5/5 + 2*b**4/3 + b**3/6 - 5*b + 5. Let c(d) be the first derivative of u(d). Factor c(w).
w*(4*w + 1)**2
Let n(w) = 5*w**3 - 40*w**2 + 103*w - 88. Let b(d) = -25*d**3 + 200*d**2 - 514*d + 439. Let i(z) = 2*b(z) + 1