5. Let a(o) be the third derivative of 0*o + 2*o**2 + 1/105*o**7 + 1/4*o**4 + 2/9*o**3 + 1/6*o**5 + 11/180*o**6 + r. Factor a(l).
2*(l + 1)**3*(3*l + 2)/3
Let d(m) = 5*m**2 - 10*m + 9. Suppose 0 = 2*a - a - 2. Let h(j) = -66*j**2 + 129*j - 117. Let t(w) = a*h(w) + 27*d(w). Factor t(i).
3*(i - 3)*(i - 1)
Let j(l) be the third derivative of -l**5/30 + l**4/6 - l**3/3 + 3*l**2. Factor j(p).
-2*(p - 1)**2
Let r(s) be the first derivative of s**6/15 - s**5/5 + s**4/6 - 2*s - 1. Let h(c) be the first derivative of r(c). Determine a so that h(a) = 0.
0, 1
Let g be 2*(-6)/(-4) + 2. Suppose -g*n = 4*h - 37, 3*h - 2*h - 3 = 0. Let 8*d**5 - 9*d**5 + 11*d**n - 8*d**2 + 32*d**3 - 34*d**4 = 0. What is d?
0, 2/5, 1, 2
Factor -2/5*i**4 + 4/5*i**3 - 2/5*i**5 - 2/5 + 4/5*i**2 - 2/5*i.
-2*(i - 1)**2*(i + 1)**3/5
Let p be 2*2 - (-12)/(-6). Determine l so that l**2 + 13*l**4 + 0*l**2 - 12*l**4 - p*l**2 = 0.
-1, 0, 1
Let i = -31/2 - -16. Let h be 5 - 2 - 1 - -2. Solve 0*m**3 + 0 + i*m**2 - 1/4*m**5 - 1/2*m**h + 1/4*m = 0 for m.
-1, 0, 1
Suppose -18 + 2 = -4*d. Let z be 7/4 - 2/(-8). Determine w, given that 0*w**z + 0*w + 1/4*w**5 - 1/4*w**3 + 0 + 0*w**d = 0.
-1, 0, 1
Let l(z) = 5*z**3 - z**2 + z. Let d be l(1). Let p(g) be the first derivative of -1/12*g**4 + 0*g**3 + 0*g**d + 1 + 0*g + 1/18*g**6 + 0*g**2. Factor p(w).
w**3*(w - 1)*(w + 1)/3
Suppose -5*x = 2*b - 3, 0*b = -2*b - 3*x + 5. Let j(p) be the third derivative of 0*p**3 + 0*p - 1/150*p**5 - p**2 + 0 - 1/60*p**b. Factor j(n).
-2*n*(n + 1)/5
Let l(a) be the first derivative of -5*a**6/6 + a**5 + 5*a**4/4 - 5*a**3/3 - 5. Factor l(s).
-5*s**2*(s - 1)**2*(s + 1)
Let s = -1 - -3. Suppose 5*y = -3*l - 12, 2*y = -l - 4*l - 20. Factor -2*g + g**s - 4*g**2 + y*g.
-g*(3*g + 2)
Let g(u) be the first derivative of -2*u**3/21 - u**2/7 - 2. Factor g(v).
-2*v*(v + 1)/7
Let f(p) be the first derivative of -3*p**4/28 + 5*p**3/7 - 3*p**2/2 + 9*p/7 + 7. Find j such that f(j) = 0.
1, 3
Let d = -13 + 16. Find v, given that d - 5 + 7*v - 1 - 4*v + 6*v**2 = 0.
-1, 1/2
Let 16/11*l - 14/11*l**2 - 2/11 = 0. What is l?
1/7, 1
Let o(p) be the third derivative of p**6/1080 + p**5/108 + p**4/54 - 8*p**2. Factor o(r).
r*(r + 1)*(r + 4)/9
Let h = 45 - 41. Solve -s**h + s**2 - 1/2*s**5 + 0*s**3 + 0 + 1/2*s = 0 for s.
-1, 0, 1
Let x(f) be the third derivative of f**6/720 - f**5/80 + f**4/24 + f**3/6 + 3*f**2. Let v(s) be the first derivative of x(s). Factor v(c).
(c - 2)*(c - 1)/2
Let h(c) be the second derivative of c**5/80 - c**4/48 - c**3/12 - 6*c. Factor h(f).
f*(f - 2)*(f + 1)/4
Let n(y) = y**2 - 3*y - 2. Let r be n(4). Suppose q + 3 = 2*q. Suppose 0*p**r + 0 - 1/4*p**q + 1/4*p = 0. What is p?
-1, 0, 1
Let y(c) be the first derivative of 1/15*c**3 + 7 + 0*c**2 + 0*c + 1/20*c**4. Factor y(f).
f**2*(f + 1)/5
Solve 4/11*r**3 - 8/11 - 6/11*r**2 + 2/11*r**4 - 16/11*r = 0.
-2, -1, 2
Let g(m) = 2*m**2 + 35*m + 50. Let s be g(-16). Determine h so that -2/9 - 2/9*h**4 + 0*h + 4/9*h**s + 0*h**3 = 0.
-1, 1
Find u such that 8*u - 29/3*u**2 - 4/3 + 3*u**3 = 0.
2/9, 1, 2
Suppose -2*p + 5*z = -3, -2*p + 4*p + 3*z - 27 = 0. Suppose 5*a = p + 6. Factor -t**4 - 2*t**2 - t**a + 2*t**2.
-t**3*(t + 1)
Suppose 3*x + 2*z = 7*z + 34, 5*z = 2*x - 31. Factor -69*y**2 - 2*y + 69*y**2 + 2*y**x.
2*y*(y - 1)*(y + 1)
Let r be (-8)/(-60)*(11 + -2)/3. Solve 0*w**2 + 3/5*w**5 - 1/5*w**3 + 0*w + 0 + r*w**4 = 0 for w.
-1, 0, 1/3
Let i = 2 - 7. Let x = 9 + i. Let f(n) = -n**4 - n**3 - n - 1. Let k(t) = 5*t**4 + 6*t**3 + 4*t + 4. Let o(g) = x*f(g) + k(g). Factor o(w).
w**3*(w + 2)
Let s(x) be the second derivative of x**7/189 + x**6/135 - x**5/90 - x**4/54 + 31*x. Find j such that s(j) = 0.
-1, 0, 1
Factor -2/15 + 2/15*p**2 - 2/15*p + 2/15*p**3.
2*(p - 1)*(p + 1)**2/15
Suppose -m + 2*r = 2*m - 1, 13 = -m - 2*r. Let k be (-102)/27 - m - -1. Suppose -4/9 + 10/9*n**2 - 2/3*n**4 - 2/9*n**3 + k*n = 0. Calculate n.
-1, 2/3, 1
Let m(g) be the third derivative of -g**7/105 - g**6/30 - 16*g**2. Determine f, given that m(f) = 0.
-2, 0
Let j(f) = -f**4 + f**3 + f**2 - f - 2. Let k(p) = -10*p**3 + 10*p**2 + 10*p - 6. Let u(t) = 4*j(t) + 2*k(t). Factor u(w).
-4*(w - 1)**2*(w + 1)*(w + 5)
Let w(q) be the second derivative of -3*q - 1/10*q**5 - 1/42*q**7 + 1/6*q**4 + 1/2*q**3 + 1/2*q**2 + 0 - 1/10*q**6. Factor w(r).
-(r - 1)*(r + 1)**4
Let q(h) be the third derivative of -h**8/1344 - h**7/840 + h**6/480 + h**5/240 + h**2. Find s such that q(s) = 0.
-1, 0, 1
Let g(x) = 2*x**2 - 7*x + 5. Let k be g(3). Suppose -2*j + 3 + 1/3*j**k = 0. Calculate j.
3
Suppose 2/3 - 2/3*b**2 + 0*b = 0. Calculate b.
-1, 1
Let p(y) be the first derivative of 49/5*y**3 + 12/5*y + 42/5*y**2 - 2. Factor p(x).
3*(7*x + 2)**2/5
Let h(f) be the first derivative of -7/10*f**5 - 1 + 0*f + 1/3*f**3 + 0*f**2 - 5/8*f**4. Let h(g) = 0. What is g?
-1, 0, 2/7
Let l(a) be the second derivative of 12*a**6/5 + 9*a**5/5 + a**4/2 + a**3/18 - a. Factor l(z).
z*(6*z + 1)**3/3
Let z(p) = -p - 2. Let o be z(-6). Let y(c) be the second derivative of 0*c**3 - 1/12*c**o + 1/2*c**2 + 0 - 3*c. Suppose y(u) = 0. What is u?
-1, 1
Let y = -34 + 6. Let t = y + 57/2. Factor -9/2 - 3*z - t*z**2.
-(z + 3)**2/2
Suppose -k - 10 = 5*v, 0 = 3*k + 4*v - 4 + 1. Suppose -4 = k*d - 14. Find s, given that -2*s - 14 - 3*s**d - 13*s + 3*s + 5 = 0.
-3, -1
Let o be 39/35 - (12/5 + -2). Let u(c) be the first derivative of -2/7*c**5 + 5/7*c**4 - 1 + o*c**2 - 20/21*c**3 + 1/21*c**6 - 2/7*c. Let u(g) = 0. Calculate g.
1
Solve 3*p**2 + 1 - 6 - 7 = 0 for p.
-2, 2
Suppose 0 = -4*l + 11 + 5. Let b(a) = -6*a**3 - 2*a**2 - 2*a + 2. Let p(h) = 7*h**3 + 3*h**2 + 3*h - 3. Let m(w) = l*p(w) + 5*b(w). Factor m(t).
-2*(t - 1)**2*(t + 1)
Solve 0*y + 0 - 6/5*y**4 - 2/5*y**5 - 6/5*y**3 - 2/5*y**2 = 0 for y.
-1, 0
Let h = 1 - -1. Suppose 2*u = -4*q + 2 + h, -5*u = -10. Solve 1/2*j**3 + q*j + 0 - 1/2*j**2 = 0 for j.
0, 1
Let q = 8 + -5. Suppose 2 = -5*c + 12. Factor -q*w**4 - 2*w**3 - c*w + w**4 - 7*w**2 - 5*w**3.
-w*(w + 1)*(w + 2)*(2*w + 1)
Let n = -49/27 + 1234/675. Let s(g) be the second derivative of -1/50*g**5 + g + 0 + 1/15*g**3 - n*g**6 + 1/30*g**4 + 0*g**2. Solve s(t) = 0.
-1, 0, 1
Let k(b) = 4*b**2 - b. Let d be k(1). Solve 299 - 8*o**2 - 299 + 6*o**d + 2*o = 0 for o.
0, 1/3, 1
Let y(n) be the second derivative of 0*n**4 + 0*n**2 - 3*n + 1/360*n**5 - 1/1080*n**6 - 1/6*n**3 + 0. Let z(c) be the second derivative of y(c). Factor z(p).
-p*(p - 1)/3
Let i(b) = -2*b**2 - 1. Let s(u) = -u**2. Let c(x) = -i(x) + 3*s(x). Factor c(o).
-(o - 1)*(o + 1)
Let p(h) be the second derivative of -h**7/210 + h**6/150 + h**5/50 - h**4/30 - h**3/30 + h**2/10 - 8*h. Factor p(l).
-(l - 1)**3*(l + 1)**2/5
Let i(y) = 4*y**3 - y**2 - 3*y - 3. Let j(d) be the first derivative of -3*d**4/4 + d**3/3 + d**2 + 2*d - 1. Let l(w) = -4*i(w) - 6*j(w). Factor l(h).
2*h**2*(h - 1)
Factor -3/8*s**2 + 9/4 - 15/8*s.
-3*(s - 1)*(s + 6)/8
Let x(l) be the third derivative of l**8/28 - 2*l**7/21 - 2*l**6/15 + 4*l**5/15 - 2*l**2. Determine n, given that x(n) = 0.
-1, 0, 2/3, 2
Let s be (25/2)/(1/2). Let y be (4/(-10))/((-5)/s). Find k such that 0*k + 2/7*k**3 + 2/7*k**5 + 0 + 4/7*k**4 + 0*k**y = 0.
-1, 0
Factor 4/7*m + 2/7*m**2 + 0.
2*m*(m + 2)/7
Let o(q) = q**2 + 2*q. Let u(j) = j**2 + 4*j. Suppose 4*i - 3*i + 11 = 0. Let d(w) = i*o(w) + 6*u(w). Factor d(g).
-g*(5*g - 2)
Let o(g) be the first derivative of -1/120*g**5 + 1/48*g**4 + 1 + 0*g**3 + 0*g + 3/2*g**2. Let p(m) be the second derivative of o(m). Let p(z) = 0. Calculate z.
0, 1
Let h(z) be the second derivative of 5/63*z**7 - 7/30*z**5 + 0 + z - 1/6*z**4 + 1/15*z**6 + 0*z**2 + 2/9*z**3. Determine g, given that h(g) = 0.
-1, 0, 2/5, 1
Let g = 63 - 59. What is x in 2/3*x**2 + 6 - g*x = 0?
3
Let m(q) = q**3 - 6*q**2 - 9*q + 10. Let d be m(7). Let u = 6 + d. Factor 5 - 2*r**u + 0 - 3.
-2*(r - 1)*(r + 1)
Let b = -9 - -9. Suppose b = 4*o - 3*o. Factor 0*s**2 + 0*s + 0 - 1/2*s**4 + 1/2*s**5 + o*s**3.
s**4*(s - 1)/2
Let q be (6/666)/((-5)/6). Let h = q + 191/555. Solve 0 + h*g**2 + 0*g = 0.
0
Let n(i) be the second derivative of i**4/18 - i**2/3 - 2*i. Factor n(l).
2*(l - 1)*(l + 1)/3
Let -3/2*t**3 - 3/4*t**4 + 9/8*t**5 + 0 + 3/4*t**2 + 3/8*t = 0. Calculate t.
-1, -1/3, 0, 1
Let t(n) be the first derivative of -2*n**3/3 + 2*n**2 - 12. Suppose t(b) = 0. Calcu