4*(x - 1)*(x + 1)
Let y(p) be the third derivative of p**7/70 - p**6/40 - p**5/20 + p**4/8 - 2*p**2. Solve y(u) = 0 for u.
-1, 0, 1
Factor 31*c**5 - 26*c**5 + 0*c**3 - 10*c**3 + 5*c.
5*c*(c - 1)**2*(c + 1)**2
Let f(d) be the first derivative of -4*d - 1/3*d**3 + 2*d**2 - 3. Suppose f(l) = 0. What is l?
2
Let r(j) = -j**2 + 7*j + 13. Let f be r(8). Factor 0 - 9/5*a**3 - 9/5*a**4 + 0*a - 3/5*a**2 - 3/5*a**f.
-3*a**2*(a + 1)**3/5
Let u = 81/316 - 1/158. Factor u*i**3 + i - i**2 + 0.
i*(i - 2)**2/4
Let t = -115 + 115. Determine i so that 2/11*i**2 + 0*i**3 + t + 0*i - 2/11*i**4 = 0.
-1, 0, 1
Let f(l) = l**2 - 16*l + 23. Let q(w) = -8*w + 11. Let d(k) = -3*f(k) + 7*q(k). Let g(i) = -i**2. Let s(m) = -d(m) + 5*g(m). Factor s(j).
-2*(j - 2)**2
Let n(m) = -m**2 + 2*m + 5. Let x(b) = -4*b**2 + 6*b + 14. Let u(o) = 8*n(o) - 3*x(o). Suppose u(c) = 0. Calculate c.
-1/2, 1
Find x, given that -25/6*x - 15/2*x**2 + 125/3 + 13/6*x**3 - 1/6*x**4 = 0.
-2, 5
Let h(a) = a + 6. Let w be h(-2). Factor -2*f**2 - 4/3*f**w + 2/3 + 10/3*f**3 - 2/3*f.
-2*(f - 1)**3*(2*f + 1)/3
Let s be 3 + (2 + -7 - -4). Let m(i) = 7*i**2 + 4*i - 2. Let o(g) = g**2. Let q(v) = s*m(v) - 18*o(v). Find d, given that q(d) = 0.
1
Let x(j) = 8*j**2 - 53*j. Let n(c) = 20*c**2 - 132*c. Let f(s) = 5*n(s) - 12*x(s). Suppose f(q) = 0. What is q?
0, 6
Let a(j) = -j**3 - j + 3. Let l be a(0). Let v = -4/19 + 58/95. Factor 2/5*r**2 - v*r**4 + 2/5*r - 2/5*r**l + 0.
-2*r*(r - 1)*(r + 1)**2/5
Suppose -m + 10 = 4*m. Suppose 0 = -5*d + m*w, d + w = 4*w. Determine t, given that -2/7*t**2 + 2/7*t + d = 0.
0, 1
Let h(m) be the second derivative of -1/6*m**4 - 1/21*m**7 + 2*m - 3/10*m**5 + 0 + 0*m**2 + 0*m**3 - 1/5*m**6. Factor h(a).
-2*a**2*(a + 1)**3
Let c(i) be the first derivative of 5*i**3/3 + 25*i**2 + 125*i + 12. Factor c(q).
5*(q + 5)**2
Let x(o) = -o**2 + o + 2. Let q(z) = 5*z**2 - 5*z - 9. Suppose -3*p + 0*p - 12 = 0. Let a(v) = p*q(v) - 18*x(v). Solve a(t) = 0 for t.
0, 1
Factor -22 - 75*k**3 + 35*k**3 - 160*k - 58 - 120*k**2 - 5*k**4.
-5*(k + 2)**4
Let u(m) = -2*m. Let x be u(-1). Let s(p) be the first derivative of -4/7*p**6 - 4/21*p**3 - x + 2/5*p**5 + 0*p**2 + 1/2*p**4 + 0*p. Let s(c) = 0. Calculate c.
-2/3, 0, 1/4, 1
Let n(v) be the second derivative of v**6/165 + v**5/55 - 16*v. Factor n(r).
2*r**3*(r + 2)/11
Let g be 8/(-12)*-3 - -1. Factor 3*h**g - 2*h**5 - 3*h**5 - 2*h**3 + 4*h**5.
-h**3*(h - 1)*(h + 1)
Factor 16*y**2 - 1/4*y**5 + 0 + 17/4*y**4 + 0*y - 20*y**3.
-y**2*(y - 8)**2*(y - 1)/4
Let b(d) be the third derivative of 1/3*d**3 + 0*d - 1/1620*d**6 + 2*d**2 - 1/270*d**5 - 1/108*d**4 + 0. Let r(h) be the first derivative of b(h). Factor r(c).
-2*(c + 1)**2/9
Solve 0 - 2/19*m**4 + 6/19*m + 10/19*m**3 - 14/19*m**2 = 0.
0, 1, 3
Suppose 2*i = -b - 3, 5*b = 3*i + 3*b - 6. Determine p so that i*p**2 - p**2 + 3*p**2 - 8*p + 2 + 4 = 0.
1, 3
Let r(g) be the second derivative of -g**5/50 - g**4/30 + 2*g. Factor r(u).
-2*u**2*(u + 1)/5
Let m(q) = -10*q**4 - 2*q**3 + 14*q**2 + 12*q. Let y(j) = 29*j**4 + 5*j**3 - 43*j**2 - 36*j. Let o(a) = 17*m(a) + 6*y(a). Factor o(g).
4*g*(g - 3)*(g + 1)**2
Factor -16/9*a + 32/9 + 2/9*a**2.
2*(a - 4)**2/9
Let y(k) be the third derivative of -k**6/120 + k**5/60 + 4*k**2. Suppose y(w) = 0. Calculate w.
0, 1
Suppose -2*m = -2 - 0, -2*t + 3*m + 9 = 0. Let i be t/(-8) - (-44)/16. Factor 0 + 10/7*v**i + 8/7*v**3 + 2/7*v.
2*v*(v + 1)*(4*v + 1)/7
Let n(g) = -4*g**2 + 10*g - 6. Let j(c) = -11*c**2 + 29*c - 18. Let a(f) = -6*j(f) + 17*n(f). Factor a(r).
-2*(r - 1)*(r + 3)
Let u(s) = 11*s**2 - 60*s + 145. Let y(z) = 6*z**2 - 30*z + 72. Let b(r) = 3*u(r) - 5*y(r). Factor b(l).
3*(l - 5)**2
Let t(w) = w**2. Let y(x) = 3*x**2 - 15*x - 6. Suppose 5*p + 2 = -3. Let g(z) = p*y(z) - 18*t(z). Factor g(q).
-3*(q - 1)*(7*q + 2)
Suppose s + 1 = -r - r, 5*s = 3*r - 31. Factor 0 - 2 + 7*d**4 + 1 - 6*d**2 + r*d**3 + 3*d**5 - 5*d.
(d - 1)*(d + 1)**3*(3*d + 1)
Let c(y) = 16*y**4 + 4*y**3 + 12*y**2. Let i(v) = -v**4 + v**3 - v**2. Let z(f) = c(f) + 12*i(f). Factor z(j).
4*j**3*(j + 4)
Solve -1/3*a**3 - 2/3*a + 0 - a**2 = 0 for a.
-2, -1, 0
Suppose 15 = 4*b + b. Let v be 16/(-70) + b/7. Suppose 0*w + 1/5*w**2 - v = 0. What is w?
-1, 1
Let c = -252 + 254. Factor -2/5*d - 2/5 + 2/5*d**c + 2/5*d**3.
2*(d - 1)*(d + 1)**2/5
Let r(c) be the third derivative of 0*c - 1/24*c**4 + 1/60*c**5 + 0*c**3 + 2*c**2 + 0. Factor r(f).
f*(f - 1)
Let o = 74 + -74. Let t(q) be the first derivative of 2/9*q**3 + o*q**2 - 1/12*q**4 + 0*q - 1/5*q**5 + 2. Solve t(j) = 0 for j.
-1, 0, 2/3
Let i be (0 - 3) + -2 + 8. Suppose 3 = d - i. Solve 2*f + 6*f**3 + f**4 + f**4 + 0*f**3 + d*f**2 = 0 for f.
-1, 0
Factor -2/3*o**2 + 4/9 + 2/9*o.
-2*(o - 1)*(3*o + 2)/9
Suppose -5*f = -23 - 2. Suppose 8 = -q - 3*o, -5 = f*o + 15. Solve m**3 - 4*m**2 - 6*m**5 + m**3 + 0*m**3 + 4*m**q + 4*m**4 = 0 for m.
-2/3, 0, 1
Let w(p) be the first derivative of -1/4*p**3 - 1/4*p - 3 + 1/16*p**4 + 3/8*p**2. Find s, given that w(s) = 0.
1
Let z(a) = 8*a**2 + 3*a - 5. Let g(n) = -9*n**2 - 4*n + 6. Let j(k) = 5*g(k) + 6*z(k). Factor j(d).
d*(3*d - 2)
Let r(x) be the second derivative of -1/50*x**6 - 1/5*x**3 + 3/50*x**5 + 7*x + 0 + 1/20*x**4 + 0*x**2. Find y such that r(y) = 0.
-1, 0, 1, 2
Suppose 0 = -5*a + 5*t + 35, 2*t + 3*t + 30 = 4*a. Suppose 0 = 5*j + 3*f - 18, -a*j + 2*f + 37 = -1. Factor j*q**2 - 3*q + q**3 + 7*q + q**3.
2*q*(q + 1)*(q + 2)
Let x = 1561/15 - 104. Let a(w) be the second derivative of 0 + 0*w**4 - 3*w + x*w**6 + 0*w**2 + 0*w**3 - 1/21*w**7 + 0*w**5. Factor a(f).
-2*f**4*(f - 1)
Let b be (-2)/8 - (-58)/8. Determine y, given that 1 + 7*y**2 - b*y**2 + 2*y + y**2 = 0.
-1
Suppose -5*o = 45 - 15. Let j be 14/21 - (-2)/o. Factor -j*u**2 + 0 + 0*u.
-u**2/3
Factor 3/4*z**2 + 3/4*z + 1/4 + 1/4*z**3.
(z + 1)**3/4
Let t = -6 + 9. Determine x, given that 4*x**3 - 1 - x**2 + 3*x**t + 2*x**4 - 3*x + 2*x**3 - 6*x**3 = 0.
-1, -1/2, 1
Let a(u) be the second derivative of 2/13*u**2 - 1/39*u**3 + 0 - 1/91*u**7 + 5*u + 2/65*u**5 + 4/195*u**6 - 1/13*u**4. Solve a(s) = 0.
-1, -2/3, 1
Suppose 3*a = 4*a - 2. Factor -3*g - 10 + 3*g**3 + 0*g + 12 - 3*g**2 - g**4 + 2*g**a.
-(g - 2)*(g - 1)**2*(g + 1)
Factor -4/7*w + 0 - 2/7*w**2.
-2*w*(w + 2)/7
Let i be ((-89)/90 - -1) + 0/3. Let w(f) be the third derivative of 0 - i*f**5 + 0*f**4 + 0*f**3 - f**2 + 0*f. Find a, given that w(a) = 0.
0
Factor -3*k**4 + 8*k - 4*k**2 - 6*k**3 - 5*k**4 + 13*k**4 - k**5.
-k*(k - 2)**3*(k + 1)
Let o(k) be the first derivative of -7*k**5/10 + 23*k**4/8 - 9*k**3/2 + 13*k**2/4 - k + 1. Factor o(c).
-(c - 1)**3*(7*c - 2)/2
Let b(l) = 2*l**3 - 2*l**2 + 4*l - 4. Let i(p) = -p**3 + p**2 + 1. Let u(v) = b(v) + 4*i(v). Let u(z) = 0. What is z?
-1, 0, 2
Let n(w) = 4*w**2 - 5*w + 6. Let f(b) = 2*b + 5*b**2 - 3*b - 5*b + 7. Let y = 2 + -7. Let t(x) = y*f(x) + 6*n(x). What is g in t(g) = 0?
-1, 1
Let s(p) = -3*p**2 - p + 3. Let h(n) = -n**4 - n**3 + 1. Let y be 6/(-4) - (-7)/(-14). Let q(r) = y*h(r) + 2*s(r). Factor q(u).
2*(u - 1)**2*(u + 1)*(u + 2)
Let c = 76/21 + -10/3. Factor -c*f**2 + 0*f + 2/7*f**5 + 6/7*f**3 - 6/7*f**4 + 0.
2*f**2*(f - 1)**3/7
Suppose 0 = -2*a + 2*w, 5*a = 2*w - 6 + 18. Factor 5*k**4 + 11*k**4 + 5*k**a + 9*k**5 + 15*k**3 + 3*k**2.
3*k**2*(k + 1)**2*(3*k + 1)
Let z(h) = h**3 + h + 1. Let u(t) = 4*t**2 + 8*t. Let f(r) = u(r) - 4*z(r). Solve f(c) = 0.
-1, 1
Suppose g + 6*n - 2*n + 9 = 0, n + 12 = 3*g. Factor 1 + 3*o**3 + 3 - o**g - 6*o.
2*(o - 1)**2*(o + 2)
Let a be 3 - (-8 + 52/6). Find l such that -1 + a*l - 5/3*l**2 + 1/3*l**3 = 0.
1, 3
Let m(s) = s. Let u(b) = 5*b**2 - 14*b + 20. Let r(z) = 6*m(z) - u(z). Factor r(t).
-5*(t - 2)**2
Let k be (-23)/(-15) + (-8)/6. Let -k*g + 0 - 2/5*g**5 - 1/5*g**2 + 1/5*g**4 + 3/5*g**3 = 0. Calculate g.
-1, -1/2, 0, 1
Let f be (0 + 1 + 4)*1. Suppose 4 = 3*r - 5*i + f, 4*i - 44 = -3*r. Factor -2*g**4 + 3*g**3 - 3*g - g**2 + r - 7 + 2*g**2.
-(g - 1)**2*(g + 1)*(2*g - 1)
Let d = -720 - -723. Factor -4/9*x**2 + 0*x**d + 0 + 4/9*x**4 - 2/9*x + 2/9*x**5.
2*x*(x - 1)*(x + 1)**3/9
Let t(x) be the third derivative of 3*x**5/20 - 5*x**4/4 - 4*x**3 - 29*x**2. Solve t(n) = 0 for n.
-2/3, 4
Let c(r) be the third derivative of -r**7/42 - r**6/12 + 2*r**5/3 + 15*r**4/4 + 15*r**3/2 - 21*r**2. Find a such that c(a) = 0.
-3, -1, 3
Let x(f) be the 