3/2 - 3*f**2 + 5*f. Factor g(p).
3*(p - 2)*(p + 1)**2
Let p(d) = 90*d**2 - 820*d + 505. Let b(n) = 13*n**2 - 117*n + 72. Let w(m) = -15*b(m) + 2*p(m). Factor w(z).
-5*(z - 7)*(3*z - 2)
Suppose 3 = 3*l - 3. Determine y so that -y**2 + 5*y**2 - 4*y**l - 2*y**2 + 2 = 0.
-1, 1
Let w(z) be the second derivative of 1/8*z**2 + 0 + 0*z**3 - 4*z - 1/48*z**4. Factor w(t).
-(t - 1)*(t + 1)/4
Suppose 3*z - 4*z = 0. Suppose -8 = -2*f - z*f. Factor 5/2*w**f - w + 0 + 1/2*w**2 + 4*w**3.
w*(w + 1)**2*(5*w - 2)/2
Let u be 1/3 - (-596)/12. Let d = 152/3 - u. Factor 1/3*i**5 + 1/3*i + 1/3 - 2/3*i**3 + 1/3*i**4 - d*i**2.
(i - 1)**2*(i + 1)**3/3
Let u(z) be the second derivative of z**6/120 - z**5/40 + 5*z**3/6 - 4*z. Let j(d) be the second derivative of u(d). Factor j(q).
3*q*(q - 1)
Suppose 3*h - k + 24 = 2, 32 = -3*h - k. Let w be (4/3)/((-42)/h). Factor 0*v + 6/7*v**3 + 0 + 2/7*v**2 + 6/7*v**4 + w*v**5.
2*v**2*(v + 1)**3/7
Let s be 1*-3 + (-9)/(-12)*4. Suppose s + 1/4*h**2 + 0*h = 0. What is h?
0
Let p = 26 - 22. Suppose -p*m + 3 = -j, -3*m + j = -0 - 1. Find f such that m*f**4 - 8/3*f**2 - 4/3*f + 4/3*f**3 + 2/3 = 0.
-1, 1/3, 1
Suppose -12*k + 36 = -0*k. Let c(i) be the first derivative of -1 - 1/6*i**4 + 2/9*i**k + 0*i + 0*i**2. Factor c(a).
-2*a**2*(a - 1)/3
Suppose -y - 2*y = 6. Let r = 0 - y. Let -1/3*j + 0 - j**r - 1/3*j**4 - j**3 = 0. What is j?
-1, 0
Let f be 141/189 + (-11)/(-99). Find v such that -f*v - 3/7*v**2 - 3/7 = 0.
-1
Suppose -l + 5*l + 12 = 0. Let r(o) = -o**2 - 9*o - 9. Let k(z) = z**2 + 10*z + 9. Let b(t) = l*k(t) - 4*r(t). What is h in b(h) = 0?
-3
Let p(d) be the first derivative of d**3/5 + 6*d**2/5 + 12*d/5 - 10. Factor p(y).
3*(y + 2)**2/5
Solve -2/9*m**2 - 2/3*m - 4/9 = 0 for m.
-2, -1
Suppose -s - 2*l - 5 = 5, s + 16 = -5*l. Let f = -4 - s. Suppose -w + 0*w + 2*w**4 + 4*w**3 + 2*w**f + w = 0. Calculate w.
-1, 0
Let t(k) = k**2 - 3*k - 2. Let u be t(2). Let w(b) = -b**4 - 1. Let p(l) = -3*l**4 + 2*l**3 - 2*l - 5. Let n = -5 - -6. Let f(r) = n*p(r) + u*w(r). Factor f(h).
(h - 1)*(h + 1)**3
Let l(q) be the third derivative of q**7/63 - q**6/45 - q**5/90 + q**2. Factor l(j).
2*j**2*(j - 1)*(5*j + 1)/3
Let f(w) be the first derivative of -2*w**3/3 - 5*w**2 - 8*w + 11. Factor f(m).
-2*(m + 1)*(m + 4)
Suppose 8 - 4 = 2*l. Suppose 5*c - r - 8 = -0*r, -c = -l*r + 2. Factor -1/4*q + 0 + 1/4*q**c.
q*(q - 1)/4
Let i(k) be the third derivative of -k**6/660 - k**5/110 - k**4/44 - k**3/33 + 5*k**2. Factor i(g).
-2*(g + 1)**3/11
Let g(k) be the third derivative of -k**6/120 + k**5/60 + 5*k**4/12 + 4*k**3/3 + 32*k**2. Suppose g(c) = 0. Calculate c.
-2, -1, 4
Let g = -2 + 7. Solve -2*o**3 + 0 + 2 + 4*o**2 + g*o + 0 + 3*o**3 = 0 for o.
-2, -1
Factor r**4 + 8*r + 9 + 7*r**2 + 6*r + 15*r**2 + 10*r + 8*r**3.
(r + 1)**2*(r + 3)**2
Suppose -2*d - b = 86, -2*b - 12 + 65 = -d. Let s be ((-4)/5)/(42/d). Factor -2/7 - 6/7*k + s*k**4 + 2/7*k**5 + 4/7*k**3 - 4/7*k**2.
2*(k - 1)*(k + 1)**4/7
Factor 6*n**3 + 6*n**5 - 24*n**4 + 20*n**2 - 6*n + 2*n**3 - 12*n + 4 + 4*n**5.
2*(n - 1)**3*(n + 1)*(5*n - 2)
Find v such that 122*v**3 - 48*v**2 - 10 + 35*v**5 - 152*v**2 + 128*v**3 - 150*v**4 + 75*v = 0.
2/7, 1
Let w(y) = -2*y**3 - 25*y**2 + 75*y - 5. Let j(m) = m**3 - m**2 + 1. Let c(b) = -5*j(b) - w(b). Factor c(t).
-3*t*(t - 5)**2
Let z be ((-24)/80)/(3/(-4)). Let x(h) be the first derivative of 0*h**2 + z*h - 2/5*h**3 - 1/5*h**4 - 2. Suppose x(d) = 0. What is d?
-1, 1/2
Let v = 50/9 + -173/36. Suppose 2*y - 5*r = 5*y + 20, -3*r = 3*y + 12. Solve y + 1/4*l + 1/4*l**4 + v*l**3 + 3/4*l**2 = 0 for l.
-1, 0
Let p(f) be the first derivative of 5*f**6/6 + 8*f**5/5 + f**4/4 - 2*f**3/3 + 1. Factor p(c).
c**2*(c + 1)**2*(5*c - 2)
Suppose -2 - 4 = 3*i. Let y be ((-24)/(-18))/(i/(-3)). Factor 2/3*l**3 + 0 + 0*l + 0*l**y + 2/3*l**4.
2*l**3*(l + 1)/3
Determine i so that -1/4*i + 3/8 - 1/8*i**2 = 0.
-3, 1
Let p = -38 - -42. Let k(l) = l**3 - l**2 + 2. Let a be k(0). Let 1/2*u**p + 1/2 - u**3 + 1/2*u**5 - u**a + 1/2*u = 0. What is u?
-1, 1
Let r(y) be the first derivative of 1/12*y**4 + 0*y**3 - 1/6*y**2 + 0*y - 1. Suppose r(j) = 0. Calculate j.
-1, 0, 1
Factor 14*c + 0*c - 6*c**2 + c**2 + 11*c.
-5*c*(c - 5)
Let i be (-48 + 66)/(5/1). Factor -6/5*y - 10*y**3 + i*y**4 - 4/5 + 42/5*y**2.
2*(y - 1)**3*(9*y + 2)/5
Factor -2*v**4 + 14*v**3 - 2*v + 2*v - 4*v**3 + 6*v - 14*v**2.
-2*v*(v - 3)*(v - 1)**2
Factor 0*n**2 + 0 - 1/2*n**3 - n**5 + 0*n + 3/2*n**4.
-n**3*(n - 1)*(2*n - 1)/2
Let x(y) be the second derivative of y**5/4 - 5*y**4/4 + 5*y**3/2 - 5*y**2/2 + 17*y. Solve x(p) = 0 for p.
1
Let p = -68 + 70. Suppose 4/7*s - 2/7*s**p - 2/7 = 0. What is s?
1
Factor -4*z**2 + 547 - 546 + 3*z**2.
-(z - 1)*(z + 1)
Let l be (-27)/(-54)*(2 + -1). Factor l*h + 1 - 1/2*h**2.
-(h - 2)*(h + 1)/2
Let j(u) be the second derivative of u**9/3024 - u**8/840 + u**6/180 - u**5/120 + u**3 + 3*u. Let a(r) be the second derivative of j(r). Solve a(q) = 0.
-1, 0, 1
Let t(k) be the second derivative of -k**6/30 + 3*k**5/20 - k**4/4 + k**3/6 + 3*k. Suppose t(o) = 0. Calculate o.
0, 1
Let i(s) be the second derivative of -s**7/14 + s**6/5 - s**4/2 + s**3/2 - 34*s. Factor i(m).
-3*m*(m - 1)**3*(m + 1)
Suppose 2*m - 16 = -2*m. Factor t**2 + 0*t**3 + 2*t**3 + 4*t**m - 3*t**4.
t**2*(t + 1)**2
Let 2/3*u**2 + 0*u - 2/3 = 0. Calculate u.
-1, 1
Let o(n) be the third derivative of -n**7/840 - n**6/160 - n**5/120 + 5*n**2. Determine p, given that o(p) = 0.
-2, -1, 0
Let v(b) = 437*b**3 - 557*b**2 + 128*b - 8. Let l(n) = 219*n**3 - 279*n**2 + 64*n - 4. Let x(z) = 13*l(z) - 6*v(z). Determine k so that x(k) = 0.
2/15, 1
Let a(m) = -13*m**2 + 13*m. Let u(p) = -7*p**2 + 7*p. Let d be 6/(-3) + (4 - 1). Let c be ((-55)/(-15))/(d/3). Let o(b) = c*u(b) - 6*a(b). Factor o(z).
z*(z - 1)
Let h be 31/155 + (-1)/5. Factor -3*s + h - 3/2*s**5 - 27/2*s**3 - 21/2*s**2 - 15/2*s**4.
-3*s*(s + 1)**3*(s + 2)/2
Let j(q) be the second derivative of -q**4/54 - 4*q**3/27 - 6*q. Let j(r) = 0. What is r?
-4, 0
Let l(v) = v. Let w(i) = i**2 + 6*i + 2. Let g(z) = -3*l(z) + w(z). Determine m, given that g(m) = 0.
-2, -1
Let j be (-10)/5 + -1 + -1 + 4. Solve j*h - 1/2*h**3 + 0*h**2 + 0 = 0.
0
Let u(d) = -d**4 - 3*d**3 - 8*d**2 - 3. Let h(b) = b**4 + b**3 + 1. Let p(a) = 3*h(a) + u(a). Find s such that p(s) = 0.
-2, 0, 2
Let m be 16/6 - (18 - 16). Factor -m*x**2 + 2/3*x**4 - 2/3*x + 0 + 2/3*x**3.
2*x*(x - 1)*(x + 1)**2/3
Let n(u) be the second derivative of -1/147*u**7 + 0*u**4 + 0*u**3 - 2*u - 2/105*u**6 + 0*u**2 + 0 - 1/70*u**5. Factor n(x).
-2*x**3*(x + 1)**2/7
Let p(x) be the second derivative of x**4 - 5*x**3/2 + 3*x**2/2 + 9*x. Suppose p(m) = 0. Calculate m.
1/4, 1
Let f(d) be the first derivative of d**3/15 + d**2/10 - 2. Suppose f(v) = 0. Calculate v.
-1, 0
Factor -1/4*x**2 - 9/4 - 3/2*x.
-(x + 3)**2/4
Let t(y) be the second derivative of y**6/50 - 3*y**5/20 + 3*y**4/20 + y**3/2 - 6*y**2/5 - 11*y. Determine m so that t(m) = 0.
-1, 1, 4
Let o be 1/((-2)/(-4)) - 0. Factor 2*l**2 + 40*l**3 - 6*l**o - 39*l**3.
l**2*(l - 4)
Let h be 0/(1*6/2 - 5). Factor 0 + h*a - 10/9*a**4 - 14/9*a**3 - 4/9*a**2.
-2*a**2*(a + 1)*(5*a + 2)/9
Let i(l) = -l**2 - 9*l - 9. Let h be i(-7). Suppose 0 = -h*t - 0*t + 35. Find o such that 1 + 8*o**2 + t*o**2 + 9*o - 9 + 2 = 0.
-1, 2/5
Let q(l) be the third derivative of -l**6/480 - l**5/240 + 5*l**4/96 - l**3/8 + 28*l**2. Factor q(v).
-(v - 1)**2*(v + 3)/4
Let g(a) be the first derivative of -a**4/14 - 4*a**3/21 + a**2/7 + 4*a/7 - 3. Suppose g(p) = 0. What is p?
-2, -1, 1
Factor 23*c**2 - 3*c**4 + 5*c**2 - 25*c**4 + 8*c**3 - 8*c.
-4*c*(c - 1)*(c + 1)*(7*c - 2)
Let k(s) = 8*s**2 - 11*s - 3. Let x(m) = m**2 - m - 1. Let n(y) = -3*k(y) + 21*x(y). What is p in n(p) = 0?
2
Suppose 12/5 + 3/5*m**2 - 12/5*m = 0. What is m?
2
Factor 0 + k**2 + 0*k + 5/2*k**3.
k**2*(5*k + 2)/2
Let a be 10/4*12/15. Suppose 4*i - 2*p - 6 = 0, -5*i + a*p + 13 = 4. Solve -2 + d + 1/4*d**4 - 5/4*d**i + 3/2*d**2 = 0 for d.
-1, 2
Let x(i) be the second derivative of 1/18*i**4 + 0 + i + 1/90*i**5 + 1/9*i**3 + 1/2*i**2. Let p(j) be the first derivative of x(j). Find b, given that p(b) = 0.
-1
Let q(t) be the third derivative of -2/3*t**3 + 7/12*t**4 + 0 + 0*t - 1/10*t**5 - 6*t**2. Factor q(k).
-2*(k - 2)*(3*k - 1)
Suppose -2*n - 2 = 2*p, -4*n + p - 3*p = -4. Let 