**3 - 3*h**3 + 3*h**2.
-3*h*(h - 1)**2*(h + 1)
Let g(n) = -22*n**3 + 12*n**2 + 10*n. Let f = -6 + 11. Let c(z) = 0*z - 9*z**3 + 2*z + f*z**2 + 2*z. Let v(r) = 12*c(r) - 5*g(r). Solve v(i) = 0 for i.
-1, 0, 1
Let r(m) = m**4 - m**3 - m**2 - m. Let o(i) = 6*i**4 - 11*i**2 - 5*i**3 + i**2 - i + 4*i**2. Let c = -6 - -3. Let f(s) = c*r(s) + o(s). What is v in f(v) = 0?
-1, 0, 2/3, 1
Let o(a) be the first derivative of -a**3/3 + 4. Factor o(x).
-x**2
Factor 0*j - 3/2*j**2 + 2 - 1/2*j**3.
-(j - 1)*(j + 2)**2/2
Let j(g) = -g**4 + g**3. Let o(u) = 5*u**4 + u**3 + 8*u**2 + 4*u. Let n(w) = 12*j(w) + 3*o(w). Suppose n(d) = 0. What is d?
-2, -1, 0
Let g = 44 - 131/3. Factor -1/3*a**2 + 0 + g*a.
-a*(a - 1)/3
Suppose 2*s - 6*s = -8. What is r in -3*r - s*r + 3*r**3 + 2*r = 0?
-1, 0, 1
Let l be ((-2)/3)/((6 - 5)/(-1)). Factor -l + 2/3*g - 1/6*g**2.
-(g - 2)**2/6
Let l be (0 - -1)*(-150 + -8). Let n = l + 478/3. Solve -n*y**3 - 5/3*y**2 - 1/3*y**4 - 2/3*y + 0 = 0.
-2, -1, 0
Let q(s) = s**3 - 4*s**2 + 3*s. Let l be q(3). Let t = 0 + l. Let -1/2*o**5 + 1/2*o**4 + 0*o + t - 1/2*o**2 + 1/2*o**3 = 0. What is o?
-1, 0, 1
Let y(u) = u**5 - u**4 - u**3 + u**2. Let n(c) = -c**5 + 6*c**4 - 9*c**3 + 4*c**2. Let z(a) = n(a) - 4*y(a). Let z(r) = 0. Calculate r.
0, 1
Let r be (-62)/364 - (-20)/70. Let f = r - -17/78. Let 0 - 1/3*k - 2/3*k**2 + f*k**5 + 0*k**3 + 2/3*k**4 = 0. What is k?
-1, 0, 1
Factor -15/7*n + 3*n**2 - 6/7.
3*(n - 1)*(7*n + 2)/7
Let w(a) be the third derivative of -a**5/20 + a**4 - 8*a**3 - 7*a**2. Solve w(t) = 0.
4
Let w be 3 + 52/12 + -6. Solve 0*z + 0 - 4/3*z**3 + 0*z**2 + 0*z**4 + w*z**5 = 0.
-1, 0, 1
Let s = 1 + 3. Let l(d) = d**3 - 5*d**2 + 4*d + 4. Let x be l(s). Factor 4*f**3 + 8*f**2 + 2*f**2 - 10*f**4 - f**2 - x*f + f**2.
-2*f*(f - 1)*(f + 1)*(5*f - 2)
Factor -3*w**5 - w**2 + 0*w**2 + 2*w**5 + w**4 - 2*w + 3*w**3.
-w*(w - 2)*(w - 1)*(w + 1)**2
Let w(s) be the third derivative of s**6/420 - s**5/210 - s**4/42 + 11*s**2. Factor w(a).
2*a*(a - 2)*(a + 1)/7
Let t(z) be the second derivative of -z**6/30 + z**5/20 + z**4/6 - 7*z. Suppose t(h) = 0. Calculate h.
-1, 0, 2
Factor -16*r**2 - 8*r - 12*r**2 - 18*r**3 - 2*r**3.
-4*r*(r + 1)*(5*r + 2)
Suppose -f = -4*o + 17, -f - 13 = -3*o - 0*f. Let s(a) be the second derivative of -1/6*a**o + a + 0 + 0*a**2 - 1/5*a**5 + 0*a**3 - 1/15*a**6. Factor s(n).
-2*n**2*(n + 1)**2
Suppose -3*p - 3*c + 12 = 3, 0 = 4*c - 12. Find x such that p - 4/9*x**2 - 2/9*x**3 - 2/9*x = 0.
-1, 0
Let l be ((-165)/35 + 5)*7. Factor -3/7*j + 0 - 1/7*j**l.
-j*(j + 3)/7
Let i(c) = 74*c**4 - 20*c**3 + 8*c**2. Let m(y) = 49*y**4 - 13*y**3 + 5*y**2. Let v(j) = -5*i(j) + 8*m(j). Factor v(q).
2*q**3*(11*q - 2)
Let q(d) be the second derivative of 5*d**4/12 + 5*d**3/6 - 8*d. Factor q(r).
5*r*(r + 1)
Let j(s) = -4*s**3 - 45*s**2 - 195*s - 253. Let g(p) = 8*p**3 + 91*p**2 + 389*p + 507. Let h(d) = -3*g(d) - 5*j(d). Let h(i) = 0. What is i?
-4
Let s = -8 + 12. Factor 7*a**3 + 2 + s*a + 11*a**2 + 7*a + 5*a**2.
(a + 1)**2*(7*a + 2)
Let -1/3*y**2 - 1/3*y + 0 = 0. What is y?
-1, 0
Let -60*f**3 + 10*f - 20*f**2 + 2*f + 125*f**4 - 12*f - 45*f**5 = 0. Calculate f.
-2/9, 0, 1, 2
Let m(h) be the third derivative of h**5/540 + h**4/216 - 18*h**2. Determine b, given that m(b) = 0.
-1, 0
Let q(t) be the first derivative of -t**3/15 + 4*t**2/5 - 12*t/5 + 8. Factor q(h).
-(h - 6)*(h - 2)/5
Let s(j) = -5*j**4 - 8*j**3 + 4*j**2 + j - 6. Let w(n) = 2*n**4 + 4*n**3 - 2*n**2 - n + 3. Let g(h) = 3*s(h) + 7*w(h). Let g(v) = 0. What is v?
-1, 1, 3
Let h = -155 + 3721/24. Let o(r) be the second derivative of 2*r + 0 - h*r**3 + 1/48*r**4 + 0*r**2. Factor o(j).
j*(j - 1)/4
Suppose 4/15*x**3 + 2/15*x**2 + 0 + 2/15*x**4 + 0*x = 0. What is x?
-1, 0
Let r(j) be the third derivative of j**8/4200 + j**7/2100 - 2*j**3/3 + 8*j**2. Let f(p) be the first derivative of r(p). Factor f(o).
2*o**3*(o + 1)/5
Factor 2 + 2*b + 1/2*b**2.
(b + 2)**2/2
Let x(a) be the first derivative of -a**4/4 - a**2/2 + a + 8. Let u(w) = -3*w**3 - 3*w**2 - 5*w + 1. Let q(y) = -u(y) + 2*x(y). What is b in q(b) = 0?
-1
Solve 3 + 9/4*u**2 - 9/2*u - 3/8*u**3 = 0.
2
Let u be (-50)/(-10) - 3*1. Factor 0*t**3 - 3*t**3 - u*t**3 + 6*t**3 + 27 + 9*t**2 + 27*t.
(t + 3)**3
Suppose -3*t + 2*t = 6*t. Find i, given that t*i + 0 + 8/9*i**3 + 2/9*i**2 - 2/9*i**4 - 8/9*i**5 = 0.
-1, -1/4, 0, 1
Let i = 1171 - 3593/3. Let j = -26 - i. What is c in -j*c - 2/3*c**2 + 0 = 0?
-1, 0
Let p(y) be the first derivative of y**6/2 + 6*y**5/5 + 3*y**4/4 - 9. Solve p(b) = 0.
-1, 0
Let d = -10/87281 + -137030180/8640819. Let t = d - -194/11. Factor 0 + 8/3*c**2 + 2/9*c**4 - t*c - 4/3*c**3.
2*c*(c - 2)**3/9
Let l(z) be the third derivative of 1/21*z**4 + 6*z**2 - 1/105*z**5 - 2/21*z**3 + 0*z + 0. Let l(q) = 0. Calculate q.
1
Let u(z) be the third derivative of 1/240*z**5 + 1/32*z**4 - 1/160*z**6 + 1/840*z**7 + 0*z - 1/12*z**3 + 0 + 2*z**2. What is g in u(g) = 0?
-1, 1, 2
Let j(h) be the second derivative of h**5/100 - h**4/30 - h**3/30 + h**2/5 + 66*h. Factor j(k).
(k - 2)*(k - 1)*(k + 1)/5
Let q = 11 + -9. Suppose -2*z**2 + z + 0*z**2 - z**3 + 4*z**3 - q*z**3 = 0. What is z?
0, 1
Let i(m) = -m**3 + 22*m**2 - 42*m + 44. Let u be i(20). Factor v**3 + 1/2 - 1/2*v**5 - v**2 + 1/2*v**u - 1/2*v.
-(v - 1)**3*(v + 1)**2/2
Let l(j) = -j**3 - 8*j**2 + 9*j + 4. Let d be l(-9). Factor -4*p**2 + 2*p**2 - 4*p**3 + d*p + 2*p**3 + 0*p.
-2*p*(p - 1)*(p + 2)
Determine j, given that 2 + 448*j**4 - 9*j**3 - 87*j**3 - 260*j**2 - 84*j - 10 = 0.
-2/7, -1/4, 1
Let m(j) = 0*j + 3*j + 0 + 2*j**2 - 6*j + 3. Let z be m(1). Factor -1/2*c**z - c + 0.
-c*(c + 2)/2
Let b(x) be the first derivative of -1/5*x**5 + 0*x - x**2 - 4 + 0*x**4 + x**3. Determine d so that b(d) = 0.
-2, 0, 1
Let b(o) be the first derivative of -2*o**5/35 + 4*o**3/21 - 2*o/7 - 4. Factor b(t).
-2*(t - 1)**2*(t + 1)**2/7
Let h(s) = -2*s**3 + 6*s**2 + 5*s. Let c(y) = -4*y**3 + 11*y**2 + 11*y + 1. Let g(q) = 6*c(q) - 10*h(q). Factor g(z).
-2*(z - 3)*(z + 1)*(2*z + 1)
Let p be 1/2*(1 + -4 - -4). Let i(m) be the first derivative of -2 + 0*m + p*m**2 - m**3. What is g in i(g) = 0?
0, 1/3
Let c(p) = -2*p**3 + 2*p - 5. Let v(k) = -3*k**3 + 3*k - 7. Let i(x) = -7*c(x) + 5*v(x). Factor i(s).
-s*(s - 1)*(s + 1)
Let b(f) be the first derivative of 2/3*f**3 + 2 - 2/7*f**2 + 0*f. Factor b(g).
2*g*(7*g - 2)/7
Let r(s) be the third derivative of s**6/200 - 3*s**4/10 + 8*s**3/5 + 2*s**2 - 22*s. Find x such that r(x) = 0.
-4, 2
Let m(b) = -b**2 + 11*b - 5. Let v be m(10). Factor -3*l**v + 4*l**3 - 7*l + 4*l + 2*l**3.
-3*l*(l - 1)**2*(l + 1)**2
Let o be (6/(-9))/((-15)/9). Factor 0*b + 2/5*b**2 + 0 + o*b**3.
2*b**2*(b + 1)/5
Let c = 31 - 29. Let y be 1/(2 - (-10)/(-6)). Factor -2*t**2 + 3 - c - 1 - y*t**3.
-t**2*(3*t + 2)
Suppose 25 = -4*n + 9*n. Let z(g) be the second derivative of 0*g**4 + g**3 - 1/10*g**n - g - 2*g**2 + 0. Solve z(v) = 0.
-2, 1
Let l be ((-1)/3)/((-2)/12). Let q be (l/(-6))/((-5)/30). Solve -2/3*g + 0 - 2/3*g**q = 0.
-1, 0
Let -756/5*b + 648/5*b**2 - 4/5*b**5 + 52/5*b**4 - 264/5*b**3 + 324/5 = 0. What is b?
1, 3
Let d = 343/993 - 4/331. Factor -8/3*i - 16/3 - d*i**2.
-(i + 4)**2/3
Let p = 253/4 - 62. Suppose 21 = 5*m + 6. What is f in 3/4*f**m - 7/4*f**2 + p*f - 1/4 = 0?
1/3, 1
Suppose 6*z - z - 10 = 0. Suppose z*f = f. Find q such that 1/4*q**4 - 1/4*q**2 + f - 1/4*q**3 + 1/4*q = 0.
-1, 0, 1
Let k(m) be the third derivative of -1/10*m**5 - 1/15*m**6 + 4/3*m**3 - 4*m**2 + 0*m + 1/3*m**4 + 0 - 1/105*m**7. Factor k(g).
-2*(g - 1)*(g + 1)*(g + 2)**2
Let n = 5/2392 + -242195/2392. Let o = -197/2 - n. Find w, given that 3*w - 1 - o*w**2 + 3/4*w**3 = 0.
2/3, 1, 2
Let c = -17 - -29. Let -8*o**2 - 5*o**4 - c*o**3 + 6 + 5*o**4 + 3*o**5 + 9*o + 2*o**2 = 0. What is o?
-1, 1, 2
Let j(u) be the third derivative of u**5/15 - u**4 - 14*u**3/3 - 27*u**2. Factor j(p).
4*(p - 7)*(p + 1)
Suppose -2*b = -4*u + 42, -2*u + 2*b + 31 = -b. Suppose m - 4 = -l, 5*l = -4*m + 10 + u. Factor 0*j - 2/3*j**l - 2/3*j**3 + 0.
-2*j**2*(j + 1)/3
Let b(j) be the first derivative of j**6/120 - j**5/20 + j**4/8 + j**3 + 5. Let m(y) be the third derivative of b(y). Find v such that m(v) = 0.
1
Suppose 8*w - 2 + 2 = 0. Suppose 0*x**3 + 0 - 2/3*x**2 + 2/3*x**4 + w*x = 0. Calculate x.
-1, 0, 1
Factor 7*k - 69*k**2 + 57*k**2 - 3*k**3