 1)**2
Factor 20 - 5 + 16*y + 0*y**4 + 4*y**4 - 12*y**2 + 1 - 8*y**3.
4*(y - 2)**2*(y + 1)**2
Let d be 4/((-220)/(-155)) + (-4)/(-22). Let g(p) be the second derivative of 3*p + 1/60*p**5 + 0 - 1/6*p**2 - 1/12*p**4 + 1/6*p**d. Let g(v) = 0. What is v?
1
Let r be (-228)/(-133) + 5/(35/2). Suppose -3 = -p - 0*p. Factor 1/4*b + 0*b**r - 1/4*b**p + 0.
-b*(b - 1)*(b + 1)/4
Suppose -18/5 - 9/5*i**2 - 33/5*i = 0. What is i?
-3, -2/3
Let r(w) be the second derivative of w**9/1512 + w**8/840 - w**7/420 - w**6/180 - w**3/6 + 2*w. Let d(k) be the second derivative of r(k). Factor d(s).
2*s**2*(s - 1)*(s + 1)**2
Let s(p) = -64*p**4 + 94*p**3 + 4*p**2 - 34*p - 14. Let b(z) = 13*z**4 - 19*z**3 - z**2 + 7*z + 3. Let i(l) = -28*b(l) - 6*s(l). Factor i(o).
4*o*(o - 1)**2*(5*o + 2)
Let y(o) = -o**2 + 3*o + 3. Suppose -2*u + 0*u + 6 = 0. Let v be y(u). Suppose 5*j + 2 - 2*j + 3*j**2 + j**v - 1 = 0. What is j?
-1
Solve -2/5*c**4 - 2*c**2 + 12/5 + 2*c - 2*c**3 = 0.
-3, -2, -1, 1
Let f(u) be the first derivative of -u**3/9 + 7*u**2/6 - 32. Factor f(n).
-n*(n - 7)/3
Let t(l) be the second derivative of -5/7*l**3 - 4*l + 1/6*l**4 + 0 + 9/7*l**2 - 1/70*l**5. Factor t(z).
-2*(z - 3)**2*(z - 1)/7
Let f(s) = -1. Let w(b) = -4*b**2 - 8*b + 20. Let a(c) = -20*f(c) - w(c). Determine u so that a(u) = 0.
-2, 0
Let u = 241/2 + -119. Suppose u + j - 1/2*j**2 = 0. Calculate j.
-1, 3
Let s(h) be the first derivative of h**4/4 + 2*h**3/3 + h**2/2 + 8. Let s(l) = 0. Calculate l.
-1, 0
Let i(m) = m. Let g be (-27)/(-6)*(-2)/(-3). Let j be i(g). Factor -2*c**4 + 0*c**4 - 4*c**j - 2*c**2 + 0*c**4.
-2*c**2*(c + 1)**2
Find j such that 20 + 13*j - 49*j - 12*j**4 - 138*j**2 - 9*j**4 - 99*j**3 + 4 = 0.
-2, -1, 2/7
Suppose 1 + 12*x - 11*x - 3*x + x**2 = 0. Calculate x.
1
Let g = 1/208 - 457/8528. Let w = g - -45/82. Find f such that w*f**4 + 0*f + 0*f**2 + 0 + 1/2*f**3 = 0.
-1, 0
Let k(r) = -r**5 - r**4 + r**2 - r + 1. Let y(g) = 10*g**5 + 6*g**4 - 6*g**3 - 6*g**2 + 12*g - 8. Let z(f) = 8*k(f) + y(f). Solve z(j) = 0.
-1, 0, 1, 2
Factor 2*u**3 + 3*u**2 + 0*u - 2 - 4*u + u**4 - 2 - 2*u**4.
-(u - 2)**2*(u + 1)**2
Let z(v) be the first derivative of 3*v**4/32 + 3*v**3/4 + 3*v**2/2 + 36. Factor z(l).
3*l*(l + 2)*(l + 4)/8
Let o = 1/36 - -2/9. Determine u, given that o + u + u**2 = 0.
-1/2
Let s(f) = f**3 + 19*f**2 + 3. Let v be s(-19). Let -3/2*d**v - 3/2*d**2 + 7/2*d**4 + d - 3/2*d**5 + 0 = 0. Calculate d.
-2/3, 0, 1
Factor -4/9 + 2*h + 10/9*h**2.
2*(h + 2)*(5*h - 1)/9
Let x(a) = -a**2. Let g(s) be the first derivative of -4*s**3/3 - s**2 - s - 3. Let p(d) = g(d) - 3*x(d). What is r in p(r) = 0?
-1
Let l be 72/20*5/2. Let g be (4*(-1)/l)/(-2). Determine v so that -2/9*v**2 + g*v + 0 = 0.
0, 1
Let a = -48 - -36. Let d be 30/(-10)*2/a. Find j, given that -1/4*j**2 + d*j - 1/4 = 0.
1
Let r(h) = -h + 14. Let o be r(11). Suppose f + 0*f - 8 = 0. Let 0 + 0*w**3 + 8*w - f*w**2 + 0 + 2*w**o = 0. What is w?
0, 2
Let g(z) be the second derivative of z**8/84 - z**6/10 + 2*z**5/15 + z**2 + 5*z. Let j(r) be the first derivative of g(r). Suppose j(a) = 0. What is a?
-2, 0, 1
Determine w, given that 3*w**3 + 35*w**4 + w - 36*w**4 - 2*w**2 - w**2 = 0.
0, 1
Let o(z) be the third derivative of z**8/10080 - z**7/3780 - z**6/1080 + z**5/180 + z**4/24 + 2*z**2. Let n(f) be the second derivative of o(f). Factor n(c).
2*(c - 1)**2*(c + 1)/3
Suppose 2/13 + 6/13*q**4 + 4/13*q**3 - 8/13*q**2 - 4/13*q**5 + 0*q = 0. What is q?
-1, -1/2, 1
Let i(d) be the third derivative of d**6/180 - d**5/60 - d**4/6 + d**3 + 6*d**2. Let n(p) be the first derivative of i(p). Factor n(s).
2*(s - 2)*(s + 1)
Find m such that 12/7*m - 3/7*m**4 - 9/7*m**3 + 0 + 0*m**2 = 0.
-2, 0, 1
Let 25/4 + 1/4*w**2 - 5/2*w = 0. Calculate w.
5
Let f(u) be the second derivative of -u**4/2 - u**3/3 + u. Factor f(l).
-2*l*(3*l + 1)
Suppose 6*b - 10*b = 0. Let p be (b/(-2) - 4)/(-2). Factor 2*t**p + 0*t**2 + 6*t**3 + 0*t**3 - 8*t**4.
-2*t**2*(t - 1)*(4*t + 1)
Let d = 36 - 139/4. Factor -7/4*s**3 - d*s**2 + 1/2*s + 0.
-s*(s + 1)*(7*s - 2)/4
Suppose -k - 17 - 17 + 22 + k**2 = 0. Calculate k.
-3, 4
Let s(x) be the third derivative of -5*x**8/504 - 2*x**7/315 + 4*x**2. Factor s(y).
-2*y**4*(5*y + 2)/3
Let l(h) = -5*h**3 + 10*h - 5. Let w(g) = -5*g**3 + g**2 + 10*g - 4. Let r(u) = 4*l(u) - 5*w(u). Factor r(o).
5*o*(o - 2)*(o + 1)
Let t(n) be the second derivative of -n**9/45360 - n**8/20160 + 5*n**4/12 - 2*n. Let v(d) be the third derivative of t(d). Factor v(f).
-f**3*(f + 1)/3
Let k(w) = 2*w - 12. Let q be k(11). Determine j so that -4*j - q*j**2 + 0*j - 6 - 12*j = 0.
-1, -3/5
Let z(l) be the second derivative of l**9/1008 + l**8/560 - l**7/280 - l**6/120 + l**3/2 - 7*l. Let j(o) be the second derivative of z(o). Factor j(v).
3*v**2*(v - 1)*(v + 1)**2
Factor -6*t**3 + 9*t**4 - 9*t**2 + 9*t**3 - 6*t + 3*t**3.
3*t*(t - 1)*(t + 1)*(3*t + 2)
Suppose 4*o**2 + 3*o**2 + 27 + 24*o - o**2 - 9*o**2 = 0. What is o?
-1, 9
Let t(y) be the second derivative of y**8/1260 + y**7/420 + y**6/540 - y**3/6 + 6*y. Let u(z) be the second derivative of t(z). Factor u(b).
2*b**2*(b + 1)*(2*b + 1)/3
Let s be -1 + 4 - (-6)/(-3). Let t(q) be the first derivative of 0*q**4 - 1/5*q**5 + 0*q**3 + 0*q**2 - s + 1/6*q**6 + 0*q. Factor t(o).
o**4*(o - 1)
Let d(x) be the third derivative of x**7/12600 - x**6/1800 - x**5/200 + x**4/12 - x**2. Let o(p) be the second derivative of d(p). Solve o(y) = 0 for y.
-1, 3
Let c be (1/4 - 584/160) + 4. Factor -c*v**2 - 1/5*v**3 + 0 - 2/5*v.
-v*(v + 1)*(v + 2)/5
Let j = 2/37555 - 8825449/450660. Let m = 89/4 + j. Factor -8*u - m - 6*u**2.
-2*(3*u + 2)**2/3
Let d(r) = -7*r**2 - 9*r + 1. Suppose -3 = -3*b - 0. Let h = b - 4. Let n(k) = -7*k**2 - 8*k. Let i(x) = h*n(x) + 4*d(x). Factor i(y).
-(y + 2)*(7*y - 2)
Find c such that 0 - 8/3*c**4 - 2*c**3 + 2*c + 8/3*c**2 = 0.
-1, -3/4, 0, 1
Let g(c) be the first derivative of 3*c**4/16 - c**3 - 5. Factor g(u).
3*u**2*(u - 4)/4
Let g be (17/3)/(12/76). Let f = g - 107/3. Let f*r + 0 + 2/9*r**2 = 0. What is r?
-1, 0
Let d(w) be the second derivative of 3*w**5/20 - 5*w**4/4 + 7*w**3/2 - 9*w**2/2 + 3*w. Factor d(k).
3*(k - 3)*(k - 1)**2
Let o(k) be the second derivative of 0*k**4 + 0*k**2 + 0 - 1/540*k**6 + 1/90*k**5 + 1/3*k**3 - 2*k. Let r(y) be the second derivative of o(y). Factor r(z).
-2*z*(z - 2)/3
Let y(l) = -l**2 - 8*l - 2. Let z be y(-7). Factor c**3 - c**4 + z*c**2 - 3*c**2 + 0*c**2.
-c**2*(c - 2)*(c + 1)
Let s(k) be the second derivative of -k**5/10 - 5*k**4/6 - 4*k. Factor s(f).
-2*f**2*(f + 5)
Let h(n) be the second derivative of -n**5/180 + n**4/18 - 2*n**3/9 - 3*n**2 - 6*n. Let u(s) be the first derivative of h(s). Let u(x) = 0. Calculate x.
2
Let y = -181/348 + 5/12. Let s = 38/87 + y. Suppose s*z**4 + 0*z - 1/3*z**2 + 0 + 1/3*z**5 - 1/3*z**3 = 0. What is z?
-1, 0, 1
Let h be -1*(-2)/(-4)*-4. Let s be h/(-9) - (-114)/27. Factor 8*q - s + q**3 + 2*q**2 - 3*q**2 - 4*q**2.
(q - 2)**2*(q - 1)
Let s be 28/(-16) + -3 + 5. Solve s*n**3 + 0 + 1/2*n**4 - 1/4*n**2 + 0*n = 0 for n.
-1, 0, 1/2
Let z = -9 - -11. Factor -a**2 + a**3 - 3*a**3 + a**2 - z*a**4.
-2*a**3*(a + 1)
Let c(v) = -v**3 - v**2 - v + 1. Let r = -5 + 7. Let h(w) = 12*w**3 + 11*w**2 + 10*w - 11. Let m(q) = r*h(q) + 22*c(q). Factor m(g).
2*g*(g - 1)*(g + 1)
Let v be 4*-1 - (-2019)/504. Let a(s) be the second derivative of 0 + v*s**7 - 1/120*s**6 + s + 0*s**3 + 1/48*s**4 + 0*s**2 - 1/80*s**5. Factor a(x).
x**2*(x - 1)**2*(x + 1)/4
Let y(n) be the third derivative of n**5/30 + n**4/6 + 14*n**2. Factor y(h).
2*h*(h + 2)
Suppose 0 = 2*u - 2*i, 0 = -2*u + 2*i + 3*i - 6. Suppose n + 2*n**u - 3 + n - 1 = 0. Calculate n.
-2, 1
Let b be (12/(-189))/((-6)/7). Let u(j) be the first derivative of -b*j**3 - 2 - 1/3*j**2 - 4/9*j. Factor u(f).
-2*(f + 1)*(f + 2)/9
Let q(a) be the first derivative of -5*a**4/6 + 14*a**3/9 + a**2/3 - 2*a + 5. Factor q(f).
-2*(f - 1)**2*(5*f + 3)/3
Let -424*y**5 - 3*y**3 + 2*y**3 + 425*y**5 = 0. What is y?
-1, 0, 1
Factor 4*s - 4*s**2 + 5*s**2 - 2*s.
s*(s + 2)
Let a = -3 + 10. What is t in -t**2 - 3*t**3 + a*t**2 + t**3 - 4*t = 0?
0, 1, 2
Suppose -4*z + 2*t = -2*t, 6 = 2*z + t. Let k = 4 - z. Solve -2*c - 2*c**4 + 2*c**k + 2*c + c - c**5 = 0 for c.
-1, 0, 1
Let j(r) be the second derivative of -1/48*r**4 + 0*r**3 - 5*r + 0*r**2 + 0. S