3*g**3 - 72*g**5 + 8*g**2. Factor l(x).
x*(x - 2)**2*(9*x - 2)**2
Let f(r) be the first derivative of -5*r**4/4 + 5*r**2/2 + 1. Factor f(h).
-5*h*(h - 1)*(h + 1)
Let o = 289/2 + -144. Determine c, given that 7/4*c**2 + 0 + 5/4*c**3 + o*c = 0.
-1, -2/5, 0
Let x = -1554/5 - -312. Solve -x*l + 27/5*l**3 + 9/5*l**2 + 0 = 0.
-2/3, 0, 1/3
Let s(n) = -7*n**2 + 11*n + 1. Let f(v) = -8*v**2 + 12*v + 2. Let i(c) = 5*f(c) - 6*s(c). Suppose i(r) = 0. Calculate r.
1, 2
Let k(p) be the first derivative of p**5/10 - p**4/8 - p**3/2 + p**2/4 + p + 7. Factor k(z).
(z - 2)*(z - 1)*(z + 1)**2/2
Let d(r) be the second derivative of -r**4/6 - r**3 - 2*r**2 + 11*r - 2. Factor d(c).
-2*(c + 1)*(c + 2)
Suppose -7*j + 10*j = 0. Let z(o) be the third derivative of 1/735*o**7 + 0*o**3 - 1/420*o**6 + 0*o**5 + 0 + 0*o + o**2 + j*o**4. Determine v so that z(v) = 0.
0, 1
Let v be 12 - 11 - (48/(-15))/(-4). What is j in 0*j + 0 - v*j**2 = 0?
0
Let n(w) = -w**4 - w**3 - w**2 + 1. Let p(z) = 12*z**4 + 6*z**3 + 6*z**2 + 3*z - 9. Let v(u) = u**2 - 6*u. Let o be v(3). Let b(a) = o*n(a) - p(a). Factor b(d).
-3*d*(d - 1)**2*(d + 1)
Let d(z) be the second derivative of 0*z**2 + 0*z**3 - 1/110*z**5 + 0 - z - 1/66*z**4. Let d(g) = 0. What is g?
-1, 0
Let h(o) be the third derivative of -o**8/2688 - o**7/1680 + o**6/960 + o**5/480 + 3*o**2. Factor h(z).
-z**2*(z - 1)*(z + 1)**2/8
Suppose 25 = -5*i, 4*f + 0*f + 21 = -5*i. Factor 4*j**3 + f - 5 + 8 - 4*j - 4*j**2.
4*(j - 1)**2*(j + 1)
Factor -2*h - 1/3*h**2 - 5/3.
-(h + 1)*(h + 5)/3
Let u(r) be the third derivative of r**7/840 + r**6/120 + r**5/40 + 5*r**4/24 - r**2. Let s(b) be the second derivative of u(b). Factor s(j).
3*(j + 1)**2
Let p(o) = -5*o**3 - 4*o**2 - 3*o. Let m(f) = -5*f - 4*f**2 + 6*f - f - 4*f**3 - 2*f. Let b(z) = -6*m(z) + 4*p(z). Factor b(r).
4*r**2*(r + 2)
Let f(x) be the first derivative of x**7/140 - x**6/36 + x**5/30 + x**3 + 3. Let b(r) be the third derivative of f(r). Factor b(i).
2*i*(i - 1)*(3*i - 2)
Suppose 0 = 3*w + q + 6, 2*w - q = w - 2. Let o = w + 34. Determine c so that 32*c**4 + 9*c**2 - o*c**3 + 5/2*c - 1 - 21/2*c**5 = 0.
-2/7, 1/3, 1
Let d(j) = -j**2 + 1 - 9*j + 0*j**2 - 3. Let i be d(-8). Factor 1 - l**4 + l + l + 4*l**3 - i*l**3.
-(l - 1)*(l + 1)**3
Let t be 3/(-1) + (-1)/((-12)/39). Solve 1/4*o**2 + t - 1/2*o = 0 for o.
1
Let y = -25 - -41. Factor 0*v**3 + 2*v**3 - 18*v + y*v.
2*v*(v - 1)*(v + 1)
Let j(b) = -b**3 + 8*b**2 - 6*b - 7. Let w be j(7). Factor 0 - 2/5*g + w*g**2 + 2/5*g**3.
2*g*(g - 1)*(g + 1)/5
Let l(z) be the third derivative of -z**8/224 - 11*z**7/420 - z**6/16 - 3*z**5/40 - z**4/24 - 7*z**2. Find n, given that l(n) = 0.
-1, -2/3, 0
Factor -2 + 6*i**2 - 3*i**3 - 4 + 6*i + 5*i**3 + 8.
2*(i + 1)**3
Determine w, given that 13*w + 4 - w**4 + 5*w**3 - 3*w**4 + 15*w**2 - 6*w - 27*w = 0.
-2, 1/4, 1, 2
Let p = -14 + 18. Suppose 0*b = -p*b. Factor -2/3*m**4 + 0*m**2 + b + 0*m + 2/3*m**3.
-2*m**3*(m - 1)/3
Suppose -1/5*r + 1/5 - 2/5*r**2 = 0. Calculate r.
-1, 1/2
Factor -3*w - 5*w**2 - w**2 + 3*w**2 + 12*w.
-3*w*(w - 3)
Let l(b) be the first derivative of b**7/120 + b**6/180 - 7*b**5/120 - b**4/12 + b**3/3 + 3. Let m(i) be the third derivative of l(i). Factor m(g).
(g - 1)*(g + 1)*(7*g + 2)
Let m(b) = 2*b**2 - b + 1. Let a(h) = 9*h**2 - 7*h + 6. Let o(y) = -a(y) + 4*m(y). Find p such that o(p) = 0.
1, 2
Let h(d) be the first derivative of 0*d + 1 + 0*d**2 + 1/4*d**4 + 0*d**3. Determine f so that h(f) = 0.
0
Let v(d) be the first derivative of d**6/360 - d**4/72 + 5*d**2/2 - 1. Let z(f) be the second derivative of v(f). Factor z(g).
g*(g - 1)*(g + 1)/3
Let c(u) be the third derivative of u**7/175 - u**6/200 - u**5/100 + 12*u**2. Determine r, given that c(r) = 0.
-1/2, 0, 1
Let i(p) be the third derivative of 1/9*p**3 + 1/18*p**4 - 2*p**2 + 1/90*p**5 + 0*p + 0. Suppose i(q) = 0. What is q?
-1
Let t(h) = 2*h**3 - 9*h**2. Let d(o) = o**3 - 4*o**2. Let y(s) = 14*d(s) - 6*t(s). Factor y(x).
2*x**2*(x - 1)
Let x = -6 + 10. Suppose 8 + 0 = x*t. What is y in 6*y**t + 0*y - 2*y - 2*y - 2*y**3 = 0?
0, 1, 2
Suppose 28*h**3 - 4*h**2 + 18 + 0*h**5 - 8*h**4 - 30*h + 0*h**5 + 2*h**5 - 6*h**4 = 0. What is h?
-1, 1, 3
Factor 4*r**2 + 5*r + r - r**2.
3*r*(r + 2)
Let v(q) = 4*q - 3. Let s(i) be the first derivative of -i**3/3 + 5*i**2/2 - 4*i - 5. Let t(y) = -3*s(y) + 4*v(y). Determine a so that t(a) = 0.
-1/3, 0
Let v(n) = -5 + 6*n - 1 + 5 + 7*n**2. Let z(d) = 6*d**2 + 6*d. Let g(h) = -4*v(h) + 5*z(h). Let g(p) = 0. Calculate p.
-2, -1
Let n = -13 + 15. Let l(y) = y**4 + y**3 + y**2 - y + 1. Let d(k) = -k**4 - 3*k**3 - 2*k**2 + 2*k - 2. Let q(r) = n*l(r) + d(r). Find v such that q(v) = 0.
0, 1
Let s(r) = -6*r**2 - r - 29. Let p(x) be the first derivative of -x**3/3 - 5*x - 1. Let l(v) = -34*p(v) + 6*s(v). Factor l(n).
-2*(n + 1)*(n + 2)
Let j(d) = d**2 - 1. Let r be 1/8 - (-468)/96. Let m(x) = -x**3 + 4*x**2 - 27*x + 32. Let l(s) = r*j(s) + m(s). Solve l(q) = 0 for q.
3
Let h(y) be the first derivative of 0*y**2 + 1/12*y**6 - 1/8*y**4 + 0*y + 1/10*y**5 - 1/6*y**3 + 1. Determine t so that h(t) = 0.
-1, 0, 1
Let c(u) = 2*u**3 + u**2 + 3*u. Let w(r) = r. Suppose 0 = 2*f - 3*f + 1, a + 2*f = 6. Let m(o) = a*w(o) - c(o). Suppose m(x) = 0. What is x?
-1, 0, 1/2
Let t(k) = k**2 - 9*k - 19. Let y be t(11). Let n(j) be the first derivative of -1 - j**2 + j + 1/3*j**y. Suppose n(o) = 0. What is o?
1
Let w(v) be the first derivative of 39/2*v**2 + 9*v + 4*v**3 - 1. Solve w(d) = 0 for d.
-3, -1/4
Let u(t) be the second derivative of -t**6/420 - t**2 + 3*t. Let x(s) be the first derivative of u(s). Solve x(j) = 0.
0
Find h, given that 9*h**3 + 23*h**4 - 32*h**3 + 4*h**4 - 37*h**3 + 39*h**2 - 6*h = 0.
0, 2/9, 1
Let v(h) be the first derivative of 2*h**2 + 7 - 8*h - h**4 + 8/3*h**3. Factor v(d).
-4*(d - 2)*(d - 1)*(d + 1)
Determine v, given that -5*v - 7*v**2 + 3*v**2 - 3*v = 0.
-2, 0
Suppose m + 3 = 5. What is w in -3*w**4 + 80*w**3 - 43*w**3 + 3*w**m - 37*w**3 = 0?
-1, 0, 1
Let i(r) = -r**4 - r. Let m(a) = 7*a**4 - 4*a**3 + 2*a**2 + 5*a. Let v be (3 - -1)*(-5)/4. Let d = 10 + v. Let n(l) = d*i(l) + m(l). Factor n(h).
2*h**2*(h - 1)**2
Let h(r) be the third derivative of -r**7/3780 - r**6/810 + 2*r**3/3 - r**2. Let o(s) be the first derivative of h(s). Factor o(v).
-2*v**2*(v + 2)/9
Suppose -5*x = -2 - 3, x - 1 = -2*h. Let 4*a**3 + 0*a**4 + h*a**2 + 2*a**2 + 2*a**4 = 0. Calculate a.
-1, 0
Let f(p) be the first derivative of -p**6/18 + 4*p**5/15 - 5*p**4/12 + 2*p**3/9 + 26. What is q in f(q) = 0?
0, 1, 2
Let z(d) = d**2 + 6*d + 4. Let a be z(-5). Let f be 16/(-10) - (-1 + a). Factor f + 2/5*n**2 + 4/5*n.
2*(n + 1)**2/5
Let x(n) = n**3 - 8*n**2 + 7*n + 3. Let l be x(7). Suppose c = -l*c. Factor c*w**2 + 0*w**2 + w**3 - 4*w**4.
-w**3*(4*w - 1)
Let s(w) be the first derivative of 3/14*w**4 + 3 - 2/21*w**3 + 2/7*w - 3/7*w**2. Solve s(z) = 0 for z.
-1, 1/3, 1
Let w = 100/13 - 274/39. Suppose 0*f**4 + 0*f**2 - 2/3*f**5 + 0 + 4/3*f**3 - w*f = 0. Calculate f.
-1, 0, 1
Let w(b) be the second derivative of b**7/280 - b**6/240 - b**4/4 + 4*b. Let t(x) be the third derivative of w(x). Suppose t(s) = 0. What is s?
0, 1/3
Factor -2/3*l**2 + 10/3*l - 8/3.
-2*(l - 4)*(l - 1)/3
Suppose -57 = -5*v + 4*x, -9 = 2*x + x. Let g = v - 4. Determine i so that 0*i**4 + 1 + 2*i + i**g - i - 2*i**2 - 2*i**3 + i**4 = 0.
-1, 1
Let q be 3/4 - (-5)/20. Let v(y) = -2*y - 3. Let s be v(-3). Factor 9*w**5 - 2*w - w - 2*w**2 + 21*w**4 + 10*w**s + q - 4*w**2.
(w + 1)**3*(3*w - 1)**2
Let y(g) be the third derivative of -g**7/1680 - g**6/320 + g**5/96 + g**4/64 - g**3/12 + g**2 + 5. Factor y(h).
-(h - 1)**2*(h + 1)*(h + 4)/8
Let p(t) be the second derivative of t**4/48 - t**3/8 + t**2/4 + t. Factor p(c).
(c - 2)*(c - 1)/4
Factor 1/5*c**2 + 0 + 1/5*c.
c*(c + 1)/5
Suppose 5*i - 11 - 4 = f, 0 = -4*i + 5*f + 12. Factor 0*h**i + 0*h - 2/7*h**4 + 4/7*h**2 - 2/7.
-2*(h - 1)**2*(h + 1)**2/7
Let v(q) = q**2 - 1. Let g(a) = 4*a**3 + 7*a**2 + 11*a + 8. Let f(z) = -5*g(z) - 30*v(z). Factor f(y).
-5*(y + 1)*(y + 2)*(4*y + 1)
Let y(s) = -s**5 - s**2 + s + 1. Let g(p) = -3*p**5 + 2*p**4 + 7*p**3 + 2*p**2 + 2*p + 2. Let v(k) = -2*g(k) + 4*y(k). Suppose v(x) = 0. What is x?
-1, 0, 4
Let i(f) be the second derivative of 0 - 1/2*f**2 + 1/30*f**6 - 1/10*f**5 + 0*f**4 + 5*f + 1/3*f*