32. Factor -1/3*f**2 + 1/3*f**3 - x*f + 1/3.
(f - 1)**2*(f + 1)/3
Let a = -2 - -2. Solve a - 2/5*b + 1/5*b**2 = 0.
0, 2
Let o(s) be the third derivative of -s**9/756 + s**7/840 - s**3 + 5*s**2. Let f(q) be the first derivative of o(q). Factor f(d).
-d**3*(2*d - 1)*(2*d + 1)
Let f(o) = 1. Let d(z) be the second derivative of z**5/20 - z**4/6 - z**3/6 - 3*z**2/2 - 9*z. Let y(q) = d(q) + 5*f(q). Let y(s) = 0. Calculate s.
-1, 1, 2
Let t(w) be the first derivative of w**6/1620 + w**5/90 + w**4/12 + 2*w**3 + 4. Let l(h) be the third derivative of t(h). Find v such that l(v) = 0.
-3
Suppose c + 0*c - 5 = 0. Let j(f) be the first derivative of -1/2*f**2 - 1/3*f**3 - 3 + 0*f + 1/3*f**6 + f**c + 3/4*f**4. Factor j(m).
m*(m + 1)**3*(2*m - 1)
Factor 2/5*m**4 - 4/5*m**3 - 2/5*m**2 + 0 + 4/5*m.
2*m*(m - 2)*(m - 1)*(m + 1)/5
Let k(v) be the second derivative of v**5/150 - v**4/60 + v**2 + 3*v. Let a(f) be the first derivative of k(f). Factor a(p).
2*p*(p - 1)/5
Let i(l) be the second derivative of 0*l**2 + 1/21*l**7 + 0 + 16/3*l**3 - 8/15*l**6 + 12/5*l**5 - 16/3*l**4 - 3*l. What is u in i(u) = 0?
0, 2
Let f be (4/6)/(2/9). Let y be f/5 + 6/90. Factor 0 + 0*b - y*b**2.
-2*b**2/3
Let k(l) = l**3 + l**2 - 1. Let f(g) = -g**4 - 4*g**3 - g**2 - 2*g + 4. Let z(n) = f(n) + 4*k(n). Solve z(m) = 0 for m.
-2, 0, 1
Let j(p) be the third derivative of -p**6/1320 - p**5/660 + 15*p**2. Solve j(s) = 0.
-1, 0
Suppose d - 2*d = 0. Suppose 6*i - i = d. Factor -1/2*w**5 + 0 - 1/2*w**4 + 0*w**3 + 0*w + i*w**2.
-w**4*(w + 1)/2
Suppose y + 15 = 48. Factor -10*p**4 - 20*p**2 + 2*p**5 + 10*p - 19 + 8 + y*p**3 - 13*p**3 + 9.
2*(p - 1)**5
Let k(d) = -d + 11. Let h be k(5). Suppose 2*r = -3*v - h, 7 - 1 = -2*v - 2*r. Let 0 + v*w + 0*w**2 + 1/3*w**3 = 0. Calculate w.
0
Let d(u) be the second derivative of -u**6/30 - 4*u**5/15 - 2*u**4/3 - 5*u**2/2 - 7*u. Let k(t) be the first derivative of d(t). Factor k(i).
-4*i*(i + 2)**2
Solve 0 + c + 7/2*c**4 - 7/2*c**2 + 9/2*c**5 - 11/2*c**3 = 0 for c.
-1, 0, 2/9, 1
Suppose 6*r - 5*r = 0. Let i(u) be the first derivative of r*u**3 + 0*u + 4 + 1/8*u**4 - 1/4*u**2. Factor i(c).
c*(c - 1)*(c + 1)/2
Suppose -2 + 4 = -2*r. Let v be 9/6 - (-1)/r. Determine d, given that v*d - 1/4 - 1/4*d**2 = 0.
1
Let y(p) = -15*p**5 + 18*p**4 + 16*p**3 - 18*p**2 - p - 4. Let l(s) = -s**3 + s + 1. Let v(t) = -4*l(t) - y(t). Solve v(d) = 0.
-1, 0, 1/5, 1
Let r(i) = i**2 + 6*i. Let v be r(-6). Let u(q) be the third derivative of -4*q**2 + 0*q**3 + 0*q + 1/210*q**5 + v - 1/84*q**4. Factor u(n).
2*n*(n - 1)/7
Suppose -q = -2*q - 3*z + 54, 2*z = 0. Let p = q + -484/9. Determine c, given that -2/3*c**2 + 2/3*c**3 + 2/9*c - p*c**4 + 0 = 0.
0, 1
Let i(g) be the third derivative of 0*g**4 + 0*g**3 + 0*g**5 + 0 + 1/70*g**7 + 3/112*g**8 + 0*g - 2*g**2 - 1/20*g**6. Solve i(v) = 0.
-1, 0, 2/3
Let k be (40/30 - 4/3)/(-2). Factor 0*m + 0 + 1/3*m**3 + k*m**2.
m**3/3
Suppose -5*d + 5 + 8 = 2*g, -8 = -2*d + 2*g. Suppose 1/4*z**2 + 0 - 1/2*z - 1/4*z**5 + 3/4*z**d - 1/4*z**4 = 0. What is z?
-2, -1, 0, 1
Let l(x) = x**2 - x - 1. Let q(k) be the third derivative of k**5/10 - k**4/4 - 5*k**3/6 - 2*k**2. Let s(j) = 5*l(j) - q(j). Find h, given that s(h) = 0.
0, 1
Let s(a) be the first derivative of 2 - 1/60*a**6 - a**2 - 1/3*a**4 + 0*a - 2/15*a**5 + 0*a**3. Let p(y) be the second derivative of s(y). Factor p(u).
-2*u*(u + 2)**2
Let m = 5 + -2. Let s be (m/3)/(2/4). Find h such that h + 3*h**3 + 5*h**4 - 5*h - s*h**4 - 2*h**4 = 0.
-2, 0, 1
Let g = 13 + -7. Factor -2*m**2 + m - 3*m + g*m - 2 + 0.
-2*(m - 1)**2
Suppose -g = 4*g. Let j be (-6 - -3) + 17 + g. Suppose 41*i + 0 + 26*i**2 + 2*i**4 + 16 + 10*i**2 - i + j*i**3 = 0. What is i?
-2, -1
Let y(r) = -r**3 - r**2 - r. Let v(k) = 3*k**3 - 3*k**2 + 6*k + 12. Let z(n) = -v(n) - 6*y(n). Let z(i) = 0. Calculate i.
-2, 1
Let w = 382 - 3427/9. Let k(p) be the first derivative of -1 - 1/3*p**2 + 0*p - 4/3*p**4 + w*p**3 + 7/15*p**5. Factor k(f).
f*(f - 1)**2*(7*f - 2)/3
Let q be (4/5)/2*5. Factor -7/4*u**3 - 4*u**q - 11/4*u - 1/2.
-(u + 1)**2*(7*u + 2)/4
Suppose -2 = -z - 8. Let o = z + 6. Factor o + 1/4*w**2 + 0*w.
w**2/4
Let c(f) be the second derivative of -f**5/130 + f**4/26 - 27*f. Factor c(w).
-2*w**2*(w - 3)/13
Suppose 0 = 5*v - 5 - 10. Suppose m - 2*c = 8, 0 = v*c - 7*c - 8. Let -3*u**4 + 6*u**4 - u**3 + u**2 - 4*u**m + u**5 = 0. Calculate u.
-1, 0, 1
Let j(w) = -w**3 - w**2 - w + 1. Let u(q) = 4*q**3 + 4*q**2 + 7*q - 5. Let l(s) = -15*j(s) - 3*u(s). Factor l(k).
3*k*(k - 1)*(k + 2)
Find z such that 8/9 - 2/3*z**2 - 2/9*z**3 + 0*z = 0.
-2, 1
Let x be ((-4)/(-20))/(48/20) - 0. Let n(r) be the second derivative of -r + 0 + 1/48*r**4 - x*r**3 + 1/8*r**2. Solve n(l) = 0.
1
Let f(r) be the second derivative of 0 - 1/48*r**4 + 0*r**2 - 1/24*r**3 + r. Factor f(q).
-q*(q + 1)/4
Let a(y) be the first derivative of 4*y**3/3 - 8*y**2 - 6. Solve a(x) = 0 for x.
0, 4
Suppose 3*y - y = 6. Factor -y*q**2 - q**3 - 4 + 0*q**2 + 0 + 3 - 3*q.
-(q + 1)**3
Let c(p) be the third derivative of 2*p**7/525 - p**6/50 + 2*p**5/75 - 8*p**2. Find j, given that c(j) = 0.
0, 1, 2
Let h(m) be the second derivative of m**7/252 - m**6/90 + m**4/36 - m**3/36 + 3*m. Factor h(l).
l*(l - 1)**3*(l + 1)/6
Let t(h) = 2*h**4 + 2*h**3 - 6*h**2 - 10*h - 2. Let d(u) = -8*u**4 - 8*u**3 + 23*u**2 + 41*u + 9. Let k(i) = -4*d(i) - 18*t(i). Suppose k(s) = 0. What is s?
-2, -1, 0, 2
Let r(h) be the second derivative of -h**5/60 + h**4/24 + h**3/3 - 2*h**2 + h. Let y(k) be the first derivative of r(k). Factor y(i).
-(i - 2)*(i + 1)
Solve -2*a**4 - 12*a**5 + 39*a**3 - 6 - 10*a**4 + 2*a**4 + a**4 + 9*a + 51*a**2 = 0 for a.
-1, 1/4, 2
Let h(y) be the third derivative of y**8/672 - y**7/210 + y**6/240 + 7*y**2. Suppose h(k) = 0. What is k?
0, 1
Let w(s) = s**2 - s - 1. Let y be w(0). Let p(g) = 8*g**3 - 8*g**2 + 4*g - 10. Let t(x) = -x**3 + x + 1. Let b(o) = y*p(o) - 6*t(o). Factor b(u).
-2*(u - 2)*(u - 1)**2
Let f be (-3)/15 - (-52)/10. Let v(p) be the second derivative of -2*p + 1/18*p**4 + 0 - 1/90*p**f - 1/9*p**3 + 1/9*p**2. Factor v(y).
-2*(y - 1)**3/9
Let g(z) be the first derivative of -4*z**3/3 - 12*z**2 - 36*z - 57. Determine h so that g(h) = 0.
-3
Let r(w) be the second derivative of w**8/6720 + w**7/2520 + w**4/3 + 5*w. Let u(p) be the third derivative of r(p). What is s in u(s) = 0?
-1, 0
Let z(x) be the third derivative of -1/108*x**4 + 1/270*x**6 + 0*x**7 + 0*x**5 + 4*x**2 + 0 + 0*x - 1/1512*x**8 + 0*x**3. Find i, given that z(i) = 0.
-1, 0, 1
What is u in 1/2*u**2 - u - 3/2 = 0?
-1, 3
Let k(m) be the third derivative of -m**7/210 + m**6/40 - m**5/20 + m**4/24 - 7*m**2. Let k(f) = 0. What is f?
0, 1
Let z = 359 - 357. Factor 2/17*a**z + 0 - 2/17*a.
2*a*(a - 1)/17
Let q(a) = a**2 - 1. Let l be q(2). Determine x so that -l*x**3 - 5*x - 4*x**2 + 0 + 8*x**2 + 1 + 3*x**2 = 0.
1/3, 1
Let g(p) = -p**3 + 3*p**2 + 20*p - 10. Let j be g(6). Factor j*q**2 + 4/3*q**3 + 1/3 + 4/3*q + 1/3*q**4.
(q + 1)**4/3
Let t(w) be the third derivative of 0*w + 0*w**3 + 0*w**4 - 1/240*w**6 + w**2 + 1/120*w**5 + 0. Solve t(s) = 0.
0, 1
Let z(s) = 8*s**4 + 4*s**3 - 7*s**2 - 4*s - 1. Let d(b) be the first derivative of b**5/5 - b**3/3 + 6. Let g(j) = 5*d(j) - z(j). Factor g(k).
-(k - 1)*(k + 1)**2*(3*k + 1)
Let p(o) be the third derivative of 0*o - 1/10*o**5 - 1/60*o**6 - 4*o**2 - 1/4*o**4 + 0 - 1/3*o**3. Factor p(b).
-2*(b + 1)**3
Let i(p) be the second derivative of -3*p - 1/5*p**5 + 0*p**2 + 0 - 1/3*p**3 + 1/2*p**4. Let i(j) = 0. Calculate j.
0, 1/2, 1
Let w(t) be the second derivative of t**7/21 - 7*t**6/5 + 147*t**5/10 - 343*t**4/6 + 27*t. Find l, given that w(l) = 0.
0, 7
Let p(d) be the third derivative of 1/30*d**4 + 1/15*d**3 + 0*d + 0 + 1/150*d**5 - 8*d**2. Factor p(f).
2*(f + 1)**2/5
Let r(i) be the third derivative of 3*i**2 - 1/1050*i**7 + 0*i - 1/120*i**6 - 1/40*i**4 + 0*i**3 + 0 - 7/300*i**5. Factor r(z).
-z*(z + 1)**2*(z + 3)/5
Factor o**4 + 2*o**3 + o**4 - o**4 - o**3 - o**2 - o**5.
-o**2*(o - 1)**2*(o + 1)
Let g(i) = i**3 + 16*i**2 - 27*i - 170. Let p be g(-17). Determine b so that 0 + p*b + 3/4*b**2 = 0.
0
Let x = 320 + -959/3. Factor -x*c**3 + 0*c + 0 - 1/3*c**4 + 2/3*c**2.
-c**2*(c - 1)*(c + 2)/3
Solve -11*c**3 - 23*c**5 + 26*c**3 + 6*c**2 + 0*c**4 - 6*c**4 + 8*c**5 = 0 for c.
-1, -2/5, 0