
Let x(v) = v**2 - v - 3. Let z(c) = -4. Let r(t) = -4*x(t) + 3*z(t). Factor r(q).
-4*q*(q - 1)
Let c(y) = -32*y**4 - 9*y**3 + 73*y**2 + 79*y + 24. Let b(q) = 33*q**4 + 9*q**3 - 72*q**2 - 78*q - 24. Let g(l) = 5*b(l) + 6*c(l). Determine f so that g(f) = 0.
-1, -2/3, 2
Let l be 1 + 2/(2 + 0). Suppose 4 - l = i. Factor -4/3*v**i + 4/3 - 2/3*v**3 + 2/3*v.
-2*(v - 1)*(v + 1)*(v + 2)/3
Let f = -7/65 + 4/13. Factor -f*w - 1/5*w**2 + 2/5.
-(w - 1)*(w + 2)/5
Let g(p) = p**4 - 2*p**4 + p**5 + p**2 - 1 - p**3 + p - p**2. Let f(a) = -a**5 - 15*a**4 + 13*a**3 + 41*a**2 + 30*a - 2. Let j(o) = -f(o) + 6*g(o). Factor j(t).
(t - 2)*(t + 1)**3*(7*t + 2)
Let f = 13 - 9. Let v = f - 4. Solve v + 2/7*a**5 + 6/7*a**4 + 0*a + 2/7*a**2 + 6/7*a**3 = 0.
-1, 0
Let s(y) = 15*y**3 + 27*y**2 - 27*y - 15. Let g(z) = 6*z**3 + 11*z**2 - 11*z - 6. Let x(i) = 12*g(i) - 5*s(i). Factor x(l).
-3*(l - 1)*(l + 1)**2
Suppose -8 = 5*m - 2*c, 8 + 8 = m + 4*c. Suppose y - 2*o = 4*y - 12, m = -y + 4*o - 10. What is l in 1/3*l**y + 0 + 2/3*l = 0?
-2, 0
Let z(d) = -2*d - 2. Let n = -3 + 1. Let g be z(n). Factor -g*v**3 - 4*v**4 - 4 + 2*v + 2*v**4 + 10*v**2 - 4*v**2.
-2*(v - 1)**2*(v + 1)*(v + 2)
Let b(r) = 15*r**3 + 60*r**2 - 240*r + 320. Let q(o) = o**3. Let w(u) = b(u) - 20*q(u). Factor w(l).
-5*(l - 4)**3
Factor -6*m**3 + 6/7*m**4 + 90/7*m**2 - 54/7*m + 0.
6*m*(m - 3)**2*(m - 1)/7
Suppose -1 = -3*l + 5. Factor -d**l - 2*d - 7*d - 2*d**2 - 6.
-3*(d + 1)*(d + 2)
Let y(x) be the first derivative of 2*x**3/3 + 11*x**2 + 20*x - 2. Let y(a) = 0. Calculate a.
-10, -1
Let s(i) be the second derivative of -1/10*i**5 + 1/9*i**3 + 2/63*i**7 + 1/18*i**4 - 4*i + 0*i**2 - 1/45*i**6 + 0. Determine m so that s(m) = 0.
-1, -1/2, 0, 1
Let w(h) = -2*h**4 + 4*h - 6. Let m(s) = -2*s**4 + s**2 + 3*s - 5. Let a(k) = -4*m(k) + 3*w(k). Solve a(t) = 0 for t.
-1, 1
Let l(s) be the third derivative of 0*s**3 + 0*s**4 - 3*s**2 + 0*s + 0 - 1/120*s**5. Solve l(q) = 0 for q.
0
Let m = 1289/78 - 204/13. Let u = 189 + -1133/6. Find i, given that 2/3*i**2 - m*i + u = 0.
1/4, 1
Let s(b) be the first derivative of -b**5/20 + b**4/8 + b**3/4 - b**2/2 - b + 19. Factor s(f).
-(f - 2)**2*(f + 1)**2/4
Let v(q) = -7*q**3 + 6*q**2 + 7*q. Let m(u) = 24*u - 4*u + 14*u**2 + 3*u**2 - 20*u**3. Let t be 4/(-6) - (-98)/(-6). Let z(i) = t*v(i) + 6*m(i). Factor z(h).
-h*(h - 1)*(h + 1)
Let w(c) be the third derivative of 0 + 1/210*c**7 - 1/60*c**5 + 0*c**3 + c**2 + 1/120*c**6 - 1/24*c**4 + 0*c. Factor w(d).
d*(d - 1)*(d + 1)**2
Let g(m) = 0*m**3 - 11*m**3 - 5*m + 8*m**3 - 4*m**2 + 4*m**3. Suppose 5*d - 6 = 14. Let k(f) = -f**2 - f. Let h(c) = d*k(c) - g(c). Factor h(b).
-b*(b - 1)*(b + 1)
Let u(p) be the first derivative of -p**5/10 - p**4/8 + p**3/2 + p**2/4 - p - 37. Suppose u(r) = 0. What is r?
-2, -1, 1
Factor 3/8*f**3 + 0 + 0*f - 1/8*f**2 - 3/8*f**4 + 1/8*f**5.
f**2*(f - 1)**3/8
Suppose 74 = k - 3*k. Let c = k - -149/4. Suppose -1/4*l**2 + c*l**4 + 0*l + 0*l**3 + 0 = 0. What is l?
-1, 0, 1
Let j be (-3652)/1155*(-2 + -1). Let x = 72/7 - j. Factor -x - 2/5*b**3 - 8/5*b**2 - 2*b.
-2*(b + 1)**2*(b + 2)/5
Let f be (18/4)/(-3) + 7/2. Factor -1/3*d + 1/3*d**f + 0.
d*(d - 1)/3
Let n(h) = 2*h**2 + 2*h - 4. Let b be n(-3). Factor 4 + 17*l**3 + 8*l**3 + 20*l + 22*l**2 + b*l**4 + 3*l**3 + 14*l**2.
4*(l + 1)**3*(2*l + 1)
Let p = 23 + 5. Let a be 0*(-3 + p/8). Factor 0*y**2 + 2/5*y - 2/5*y**3 + a.
-2*y*(y - 1)*(y + 1)/5
Let x = -14 + 16. Let r(b) be the third derivative of 0 + 1/40*b**6 - 1/15*b**5 + 1/24*b**4 - x*b**2 + 0*b + 0*b**3. Factor r(i).
i*(i - 1)*(3*i - 1)
Suppose -11*v + 7*v = 0. Factor 1/3*u**5 - 1/3*u**2 + 1/3*u**4 + 0*u - 1/3*u**3 + v.
u**2*(u - 1)*(u + 1)**2/3
Let f be 14/24*2 - (-7)/14. What is t in 0 - 8/3*t**3 + f*t**4 + 2/3*t + 1/3*t**2 = 0?
-2/5, 0, 1
Suppose -11 = -4*u + 5. Solve a + 3*a**3 + 5*a**4 - 3*a**4 - a**u + 3*a**2 = 0 for a.
-1, 0
Let x be 4/2 - (9 - 13). Let b(u) be the second derivative of 0*u**4 - 1/120*u**5 - 4*u + 0*u**3 + 0 + 0*u**2 - 1/180*u**x. Determine z, given that b(z) = 0.
-1, 0
Let t(p) = p**3 + 12*p**2 - 12*p + 13. Let j be t(-13). Factor 2/7*h**2 + 2/7*h + j.
2*h*(h + 1)/7
Let q(t) be the second derivative of t**7/7560 + t**6/1080 + t**5/360 - t**4/12 - 4*t. Let l(r) be the third derivative of q(r). Find z, given that l(z) = 0.
-1
Let k be (1 + -1)/2 - 0. Suppose -4*n + 11 + 1 = k. Factor -v**5 + 3*v**3 - v**5 - v**n.
-2*v**3*(v - 1)*(v + 1)
Let a(q) be the third derivative of -q**7/420 + q**6/120 - 2*q**2 + 8*q. What is r in a(r) = 0?
0, 2
Let a(c) be the third derivative of 1/20*c**5 + 0*c + 0 + 0*c**4 + 0*c**3 + 4*c**2. Factor a(p).
3*p**2
Suppose 4*p = -5*d + 73, 0*p = -5*p + 10. Suppose 0 = -d*g + 17*g. Factor -2/3*w**2 + g*w + 0.
-2*w**2/3
Let r(h) be the first derivative of 2*h**5/15 + 7*h**4/18 + 10*h**3/27 + h**2/9 + 7. Factor r(d).
2*d*(d + 1)**2*(3*d + 1)/9
Let r = 22 - 21. Solve -14*m**2 + 15*m + 9*m**4 + 9 - r - m**2 - 15*m**3 - 2 = 0 for m.
-1, -1/3, 1, 2
Let g(w) be the second derivative of -w**4/30 - 4*w**3/15 - 4*w**2/5 + 2*w. Factor g(j).
-2*(j + 2)**2/5
Let o(w) be the third derivative of -w**5/150 + 8*w**4/15 - 256*w**3/15 - 30*w**2. Find b, given that o(b) = 0.
16
Let o(m) be the first derivative of 1/10*m**4 + 2/25*m**5 - 2/15*m**3 + 7 + 0*m**2 + 0*m - 1/15*m**6. Factor o(k).
-2*k**2*(k - 1)**2*(k + 1)/5
Let d(n) = 2 - 3 + 0 + 3*n**2 - n**3 - 4*n**2. Let y be d(-2). Suppose 0*j - 1/2*j**2 - j**y - 1/2*j**4 + 0 = 0. Calculate j.
-1, 0
Let n = -11 + 14. Let b(m) be the first derivative of -1/9*m**n + 1 - 4/3*m - 2/3*m**2. Let b(c) = 0. What is c?
-2
Solve 4/3*o**2 + 8*o - 22/3*o**3 + 4*o**4 - 16/3 - 2/3*o**5 = 0 for o.
-1, 1, 2
Let p be (-32)/24 - 1/(1/(-2)). Let 0*s - p*s**2 + 0 - 1/3*s**3 = 0. Calculate s.
-2, 0
Let o = 359/4596 - -2/383. Let v(h) be the second derivative of 0 + 0*h**2 + 1/6*h**3 - 2*h + o*h**4. Suppose v(d) = 0. Calculate d.
-1, 0
Let k(r) be the third derivative of -r**6/1320 - r**5/330 - r**4/264 + 10*r**2. Factor k(l).
-l*(l + 1)**2/11
Factor -26*f**2 + 10*f**4 - 5*f**3 + 7*f**5 - 2*f**5 + 16*f**2.
5*f**2*(f - 1)*(f + 1)*(f + 2)
Let d(s) = -s + 2. Let z be d(-1). Let g(c) = 4*c**2 + 1. Let f(w) = 2*w**2 + 1. Let r(b) = z*g(b) - 5*f(b). Let r(p) = 0. What is p?
-1, 1
Suppose 0*n = -2*n + 32. Suppose 3*u = -u + n. Find b, given that -2/3*b**3 + 2/3*b + 0 - 2/3*b**2 + 2/3*b**u = 0.
-1, 0, 1
Let o = -510 - -2564/5. Suppose -4/5*l + o*l**3 - 2*l**2 + 0 = 0. Calculate l.
-2/7, 0, 1
Let y = -43 - -130/3. Find k such that y*k**2 - 2/3*k + 1/3 = 0.
1
Let a(u) be the first derivative of u**4/30 + u**3/15 - u - 3. Let c(t) be the first derivative of a(t). Factor c(y).
2*y*(y + 1)/5
Let s(q) be the third derivative of 0*q**4 + 1/70*q**7 - 1/336*q**8 - 1/40*q**6 + 3*q**2 + 1/60*q**5 + 0*q + 0*q**3 + 0. Factor s(u).
-u**2*(u - 1)**3
Factor 4/3*a**2 + 4/9*a**3 - 4/9*a - 4/3.
4*(a - 1)*(a + 1)*(a + 3)/9
Let t(j) be the second derivative of -j**8/1050 - j**7/420 - j**6/900 + j**3/3 - j. Let r(n) be the second derivative of t(n). Suppose r(m) = 0. Calculate m.
-1, -1/4, 0
Let y(r) = r. Let l(t) = -t**2 + 2*t. Let f = -5 - -3. Let m(b) = f*y(b) + l(b). Factor m(d).
-d**2
Let o(d) be the first derivative of -d**3/15 - d**2/5 - 2. Factor o(b).
-b*(b + 2)/5
Let i(d) be the third derivative of -d**6/40 - d**5/10 + d**4/8 + d**3 - 2*d**2. Factor i(l).
-3*(l - 1)*(l + 1)*(l + 2)
Factor -10 + 0 - 5 - 5*d**2 - 5*d**3 + 25*d.
-5*(d - 1)**2*(d + 3)
Let u(i) be the second derivative of -i**4/6 - i**3 + 6*i. Suppose u(v) = 0. What is v?
-3, 0
Suppose 4/3*p - 2/3 - 2/3*p**2 = 0. Calculate p.
1
Let z(s) be the third derivative of s**5/15 + s**4/3 + 2*s**3/3 + 14*s**2. Factor z(u).
4*(u + 1)**2
Factor -28*v**2 - 3*v**4 - 21*v**3 + v**2 - 27*v + 5*v**2 - 23*v**2.
-3*v*(v + 1)*(v + 3)**2
Let z(y) be the third derivative of y**7/84 - y**6/240 - y**5/24 + y**4/48 + 7*y**2. Let z(l) = 0. Calculate l.
-1, 0, 1/5, 1
Suppose 0 = 6*h - h - 5. Suppose 4*g = -5*i + h + 34, 3*g = -i + 18. What is x in -8*x + 5*x**i + 0*x**2 + 24*x**2 - 14*x**4 + 13*x**3 = 0?
-1, 0, 2/7, 2
Let t(p) = p**3 - 6*p**2 + 5*p - 4. Let j be t(5). Let a = 7 + j. Let 3/5*c**2 - 3/5*c**a + 0 + 0*c = 0. Calculate c.
0, 1
Let c(s) be the first derivative of -2*s**5/5 + s**4/2 + 22. Factor c(u).
-2*u**3*(u - 1)
Let z(h) = h**3