*3 + 0*g - g**2 + 4 - 3*g**2.
2*(g - 2)*(g - 1)*(g + 1)
Let b(f) = -f**3 + f - 1. Let z(u) = -80*u**4 + 204*u**3 + 115*u**2 - 304*u - 176. Let d(j) = -4*b(j) - z(j). Determine a so that d(a) = 0.
-3/4, 2
Let a be 160/(-600)*(-6)/4. Factor -a*n**3 - 4/5 - 8/5*n**2 - 2*n.
-2*(n + 1)**2*(n + 2)/5
Let w = 12 + -7. Let q = 9 - w. Find h, given that 3*h**2 + 0*h**2 + 0*h**4 - 2*h**q - h**2 = 0.
-1, 0, 1
Suppose -4*v - 144 = -5*c, 0 = -3*c + 12 - 0. Let q = -123/4 - v. Find m, given that -1/4*m**4 + q*m**2 - 1/4*m + 1/4*m**3 + 0 = 0.
-1, 0, 1
Let r be ((-34)/(-8) - 3)*1. Suppose -9/4*p**2 + 2*p**3 + 1 + r*p**4 - 2*p = 0. What is p?
-2, -1, 2/5, 1
Find k, given that -2*k**5 - 2*k**4 + 4*k**2 - 2*k - 2 + 0 + 339*k**3 - 335*k**3 = 0.
-1, 1
Let g be (4 + -2 + 1 + -3)/(-2). Let h(y) be the third derivative of y**2 + 0*y - 4/9*y**3 - 1/9*y**4 - 1/90*y**5 + g. Let h(o) = 0. What is o?
-2
Let a(p) be the second derivative of -p**5/60 + p**3/18 + 12*p. Suppose a(o) = 0. What is o?
-1, 0, 1
Suppose g = 5*g - 16. Suppose c = 2*z - 7, g*c + 3*z - z - 22 = 0. Factor 2/5*t**2 + 0 - 2/5*t - 2/5*t**4 + 2/5*t**c.
-2*t*(t - 1)**2*(t + 1)/5
Let s(f) be the first derivative of f**3/9 + f**2/2 + 2*f/3 - 9. Factor s(g).
(g + 1)*(g + 2)/3
Let u(n) be the third derivative of -n**8/168 + 2*n**7/735 + n**6/60 - n**5/105 - 31*n**2. Find m, given that u(m) = 0.
-1, 0, 2/7, 1
Let b be (23 + -5)*1/10. Determine y, given that 3/5*y**3 - b*y**2 + 9/5*y - 3/5 = 0.
1
Let s(o) be the third derivative of -o**6/96 + o**5/80 + o**4/48 - 4*o**2. Factor s(k).
-k*(k - 1)*(5*k + 2)/4
Let v(o) = 4*o**5 + 2*o**4 - 12*o**3 + 10*o**2 - 2. Let z(i) = -8*i**5 - 5*i**4 + 24*i**3 - 21*i**2 + 5. Let w(l) = 5*v(l) + 2*z(l). Factor w(j).
4*j**2*(j - 1)**2*(j + 2)
Let i(o) be the first derivative of 5 - 1/14*o**2 + 0*o - 1/21*o**3. Factor i(u).
-u*(u + 1)/7
Suppose 12/7 - 90/7*d**3 + 75/7*d**4 - 33/7*d**2 + 36/7*d = 0. Calculate d.
-2/5, 1
Let r = 3/58 + 23/116. Factor 0 + 0*y**2 - 1/4*y**3 - 1/2*y**4 - r*y**5 + 0*y.
-y**3*(y + 1)**2/4
Let c(u) = u**2 + u - 20. Let f be c(-5). Factor f*n + 1/5*n**3 + 0 - 1/5*n**2.
n**2*(n - 1)/5
Let k(s) be the third derivative of s**8/112 + 2*s**7/35 + 3*s**6/40 - s**5/5 - s**4/2 + 47*s**2. Factor k(h).
3*h*(h - 1)*(h + 1)*(h + 2)**2
Let x(d) = -2*d**4 + d**3 + 3*d**2 + d - 1. Let w(j) = j**3 - j**2 + j + 1. Let b(h) = w(h) - x(h). Factor b(g).
2*(g - 1)**2*(g + 1)**2
Let v(j) = 4*j**3 + 14*j**2 - 14*j - 70. Let m(w) = 8*w**3 + 27*w**2 - 29*w - 139. Let n(g) = -2*m(g) + 5*v(g). Find o, given that n(o) = 0.
-3, 2
Let g(h) be the first derivative of 1/12*h**4 + 3 + 0*h**2 + 2/15*h**5 + 0*h**3 + 0*h + 1/18*h**6. Factor g(z).
z**3*(z + 1)**2/3
Let p(d) be the second derivative of -d**4/54 + d**3/27 + 13*d. Let p(s) = 0. What is s?
0, 1
Let 2/9 - 4/9*o**3 + 2/9*o**5 + 2/9*o**4 - 4/9*o**2 + 2/9*o = 0. What is o?
-1, 1
Let q(t) be the first derivative of -3/7*t**4 + 8/21*t**3 - 1/21*t**6 - 3 + 0*t + 8/35*t**5 - 1/7*t**2. Factor q(u).
-2*u*(u - 1)**4/7
Let i(g) be the third derivative of -g**7/70 - 3*g**6/40 - g**5/10 + 6*g**2. Factor i(r).
-3*r**2*(r + 1)*(r + 2)
Let -9/4*o**3 - 9/4*o**4 - 3/4*o**5 - 3/4*o**2 + 0*o + 0 = 0. What is o?
-1, 0
Let v(w) = -w**4 + 4*w**3 - 5*w**2 - w - 3. Let r(q) = -3*q**4 + 8*q**3 - 11*q**2 - q - 7. Let h(i) = -6*r(i) + 14*v(i). Solve h(z) = 0 for z.
-2, -1, 0, 1
Suppose 0 = -5*p - 4*b + 26, p + b = -4*b + 1. Let k be p/(-15) - 1*-2. Determine n so that -7*n**5 + 4/5*n**2 + 0*n + k*n**3 + 0 - 31/5*n**4 = 0.
-1, -2/7, 0, 2/5
Let u(v) = -v**5 + 6*v**4 + 11*v**3 - v**2 + 5*v + 5. Let d(y) = 3 + 5*y + 2*y**4 - 2*y + 6*y**3 + y**4. Let w(l) = -5*d(l) + 3*u(l). Factor w(r).
-3*r**2*(r - 1)**2*(r + 1)
Let d(y) be the second derivative of 9*y**6/40 - 9*y**5/16 - 2*y**4 - 3*y**3/2 - 12*y. Factor d(o).
3*o*(o - 3)*(3*o + 2)**2/4
Let p = 5 + 1. Suppose -i = -p*i. Factor -4/11*r**3 + 0*r**4 + i*r**2 + 2/11*r**5 + 2/11*r + 0.
2*r*(r - 1)**2*(r + 1)**2/11
Let d(z) be the third derivative of z**7/945 + z**6/540 - 2*z**5/135 - z**4/27 - 4*z**2 + 2. Factor d(i).
2*i*(i - 2)*(i + 1)*(i + 2)/9
Let j = -7028/13803 + 44/321. Let h = j - -338/215. Suppose 2/5*m**2 + h*m + 4/5 = 0. What is m?
-2, -1
Let w(v) be the third derivative of -v**6/40 + 3*v**5/20 - v**4/4 + 27*v**2. Factor w(r).
-3*r*(r - 2)*(r - 1)
Let j be ((-58)/435)/(3/(-5)). Suppose 2/9 - 2/9*u**2 - 2/9*u + j*u**3 = 0. What is u?
-1, 1
Suppose -11 + 1 = -5*d. Factor -4 + 2*j**2 - j**d - 5*j**3 + 12*j - 4*j**2.
-(j - 1)*(j + 2)*(5*j - 2)
Let a(x) be the first derivative of -x**8/560 + x**7/280 + x**6/60 - 4*x**3/3 - 3. Let r(s) be the third derivative of a(s). Suppose r(b) = 0. Calculate b.
-1, 0, 2
Let v(m) be the third derivative of m**7/350 + m**6/120 - m**5/300 - m**4/24 - m**3/15 + 8*m**2. Let v(r) = 0. Calculate r.
-1, -2/3, 1
Determine g so that 6*g**2 + 8*g**3 + 2*g**2 - 5*g**4 - 4*g**2 = 0.
-2/5, 0, 2
Let k(b) be the second derivative of b**4/4 - 3*b**3 + 27*b**2/2 - 4*b. Factor k(j).
3*(j - 3)**2
Let q(j) be the third derivative of j**6/60 + 2*j**5/45 + j**4/36 + 4*j**2. Factor q(i).
2*i*(i + 1)*(3*i + 1)/3
Factor -28/3*z + 10/3 - 2/3*z**4 - 4/3*z**3 + 8*z**2.
-2*(z - 1)**3*(z + 5)/3
Let r(b) = -5*b**4 - 16*b**3 - 15*b**2 + 24*b + 20. Let m(d) = -10*d**4 - 31*d**3 - 30*d**2 + 49*d + 40. Let g(z) = -4*m(z) + 9*r(z). Factor g(t).
-5*(t - 1)*(t + 1)*(t + 2)**2
Let r(y) = 17*y**2 + 29*y + 24. Let s(o) = 100*o**2 + 175*o + 145. Let b(x) = -35*r(x) + 6*s(x). Suppose b(c) = 0. What is c?
-6, -1
Suppose 2*s - 12 = -2*s. Factor 2*v + 1 - 3*v - v**2 + s*v + 2*v**2.
(v + 1)**2
Let a(x) = x**5 - 5*x**4 + x**3 - 3*x**2 + 3*x + 3. Let s(z) = -12*z**5 + 56*z**4 - 10*z**3 + 34*z**2 - 34*z - 34. Let k(n) = -68*a(n) - 6*s(n). Factor k(o).
4*o**3*(o - 1)*(o + 2)
Suppose 21 = -c + 21. Let i(p) be the third derivative of c + 0*p**3 + 0*p + 1/4*p**4 - 3/20*p**5 + 1/40*p**6 + 2*p**2. Factor i(u).
3*u*(u - 2)*(u - 1)
Suppose 4/3*p**2 + 0*p + 0 + 10/3*p**3 + 2/3*p**5 + 8/3*p**4 = 0. Calculate p.
-2, -1, 0
Suppose -13 - 3 = -4*v. Factor -10*g**4 - 6*g**2 - 27*g**5 - 21*g**3 + 3*g**2 - 23*g**v - 12*g**4.
-3*g**2*(g + 1)*(3*g + 1)**2
Let v(k) be the third derivative of -k**6/60 + k**5/30 + 8*k**2. Factor v(a).
-2*a**2*(a - 1)
Let a(k) be the first derivative of k**7/2520 + k**6/180 + k**5/40 + k**4/18 + k**3 + 4. Let q(m) be the third derivative of a(m). Factor q(t).
(t + 1)**2*(t + 4)/3
What is w in -2*w + 1/5*w**2 + 5 = 0?
5
Let s(v) be the first derivative of -2*v**3/3 - 2*v**2 - 2*v + 24. Factor s(t).
-2*(t + 1)**2
Suppose -14 = -3*y - 5*u, 7 = -0*y + 2*y + u. Factor 16*s**4 - 2*s**3 - 3*s + y*s**3 - 4*s**4 - 12*s**2 + 2*s**3.
3*s*(s - 1)*(s + 1)*(4*s + 1)
Let v(m) = -m**2 - 5*m. Suppose 0 = 4*c + k + 19, 1 = -3*c + 2*c - 4*k. Let w be v(c). Factor 2/9*o + 2/9*o**5 + 0 + w*o**4 - 4/9*o**3 + 0*o**2.
2*o*(o - 1)**2*(o + 1)**2/9
Let y(c) be the second derivative of c**7/126 - c**5/30 + c**3/18 + 4*c. Factor y(l).
l*(l - 1)**2*(l + 1)**2/3
Let q(g) be the second derivative of g**4/21 - 8*g**3/7 + 72*g**2/7 - 12*g. Determine k, given that q(k) = 0.
6
Suppose -8 = -3*d - 2. Factor 2/5*f**d + 4/5*f + 2/5.
2*(f + 1)**2/5
What is j in -1/2*j**5 + 0 + 1/2*j**4 + 0*j + 0*j**2 + j**3 = 0?
-1, 0, 2
Suppose 3*v - 5*b + 5 = 2*v, -4*b + 4 = 0. Let h = 76/85 + 12/17. Factor 0*o**2 + h*o**4 + v + 2/5*o**5 + 0*o + 8/5*o**3.
2*o**3*(o + 2)**2/5
Let r(o) be the first derivative of o**6/480 - o**5/240 + o**3 + 2. Let u(y) be the third derivative of r(y). Factor u(p).
p*(3*p - 2)/4
Let s(x) be the first derivative of x**8/1680 - x**7/840 - x**6/360 + x**5/120 - x**3 + 2. Let w(k) be the third derivative of s(k). Solve w(o) = 0 for o.
-1, 0, 1
Let d(m) be the first derivative of -m**7/525 - m**6/100 + m**4/15 - 2*m**2 - 4. Let w(a) be the second derivative of d(a). Find z, given that w(z) = 0.
-2, 0, 1
Let u(g) = 7*g**2 - 7*g + 7. Let v(a) = 5*a**2 - 6*a + 6. Let k(h) = 2*u(h) - 3*v(h). Factor k(r).
-(r - 2)**2
Suppose 0 = -2*y + 2*i - 2, -4*y + 2*i = y - 4. Let m be (-3 - -1) + 24/10. Find p, given that -6/5*p + m - 2/5*p**3 + 6/5*p**y = 0.
1
Let k(y) be the second derivative of -5*y**4/4 - y**3 + 2*y. Factor k(g).
-3*g*(5*g + 2)
Let f(p) be the second derivative of -p**4/6 + p**3/3 - 6*p. Factor f(w).
-2*w*(w - 1)
Suppose 4*z = 23 - 7,