 q. Let n(o) = o**3 - o**2. Let p(l) = w*n(l) + s(l). Factor p(c).
c*(c - 1)*(c + 1)
Let r be (8/(-12))/(2/6). Let z be 3*(8/(-6))/r. Factor 2*o**2 - 4*o + z + 4*o + 4*o.
2*(o + 1)**2
Let y = -27 + 31. Factor -2/11*h - 8/11*h**2 - 12/11*h**3 - 8/11*h**y - 2/11*h**5 + 0.
-2*h*(h + 1)**4/11
Suppose 4*f - 18 = -2*l, 2*f - 3*l = 6*f - 21. Find d, given that -6*d**2 - f*d - d**5 + 4*d**5 + 2*d**4 + 4*d**4 = 0.
-1, 0, 1
Let l(f) be the second derivative of -f**7/2520 + f**6/720 + f**5/60 - f**4/12 - 3*f. Let v(r) be the third derivative of l(r). Let v(n) = 0. What is n?
-1, 2
Factor 0 - 1/4*r**2 + 1/4*r.
-r*(r - 1)/4
Let s(g) = -9*g**2 + 19*g - 15. Let b(v) = -v**2 - v - 1. Let q(y) = 3*b(y) - s(y). Factor q(z).
2*(z - 3)*(3*z - 2)
Let w = 230/329 + -6/47. Factor 2/7*r**2 + 2/7 - w*r.
2*(r - 1)**2/7
Find k such that 63*k**4 - 3 + 54*k**5 - 37*k**3 + 0 - 57*k**2 + 12*k - 11*k**3 + 15 = 0.
-1, -1/2, 2/3
Let l(r) = 4*r**2 - 44*r + 32. Let h(q) = 3*q**2 - 29*q + 21. Let g(a) = 8*h(a) - 5*l(a). Solve g(j) = 0.
1, 2
Let o(p) be the third derivative of -p**5/20 - p**4/8 + p**3 + 3*p**2. Factor o(s).
-3*(s - 1)*(s + 2)
Let u(s) be the second derivative of -s**6/15 + 3*s**5/10 - s**4/6 - s**3 + 2*s**2 - 62*s. Find m, given that u(m) = 0.
-1, 1, 2
Let h(x) = 5*x + 13. Let o(k) = -k - 1. Let j(l) = h(l) + 4*o(l). Let s be j(-7). Solve 0 - 3*p**2 + 2*p - 3*p**2 + 5*p**s - 1 = 0.
1
Let y(x) be the first derivative of x**4/8 + x**3/2 + 3*x**2/4 + x/2 - 7. What is b in y(b) = 0?
-1
Let i be -2 + 1 + (-4)/(-4). Find d such that -2/5*d**4 + 0*d + i + 2/5*d**3 + 0*d**2 = 0.
0, 1
What is c in 0 - 4/11*c - 6/11*c**2 = 0?
-2/3, 0
Let m(n) be the third derivative of -2*n**6/3 + 5*n**4/24 - 6*n**2. Suppose m(d) = 0. Calculate d.
-1/4, 0, 1/4
What is i in -2*i**2 - i - 2*i**2 - 4*i - i**2 = 0?
-1, 0
Let x(j) be the first derivative of -5*j**6/18 - 2*j**5/3 + 5*j**4/6 + 20*j**3/9 - 5*j**2/6 - 10*j/3 + 10. Suppose x(v) = 0. What is v?
-2, -1, 1
Let m(o) be the first derivative of -7/3*o**4 + 4 + 1/2*o**2 + 0*o - 49/30*o**5 - 4/3*o**3. Let v(z) be the second derivative of m(z). What is b in v(b) = 0?
-2/7
Let n(b) = 9*b**2 + 3*b + 6. Let m(g) = -8*g**2 - 4*g - 6. Let z(q) = -6*m(q) - 5*n(q). Factor z(v).
3*(v + 1)*(v + 2)
Let y be 8 + (6 - 0)/(-3). Let 2*j**2 + 0 + 7*j**3 - 2 - j**3 - y*j = 0. What is j?
-1, -1/3, 1
Let i(f) = 5*f + 8. Let o(k) = k + 1. Let z(l) = -i(l) + 4*o(l). Let s be z(-4). Let -2/7*m**2 + 0*m + 2/7*m**3 + s = 0. What is m?
0, 1
Let b = 44 + -41. Solve 3/4*l - 1/4 - 3/4*l**2 + 1/4*l**b = 0.
1
Let k(g) be the first derivative of -g**7/630 + g**6/360 - 7*g**2/2 - 3. Let s(y) be the second derivative of k(y). Determine t so that s(t) = 0.
0, 1
Let a(b) = -9*b + 5. Let i(f) = 4*f - 2. Let q(n) = 2*a(n) + 5*i(n). Let u(g) = g**5 + g**4 - g**3 - g**2 + 3*g. Let h(s) = -3*q(s) + 2*u(s). Factor h(c).
2*c**2*(c - 1)*(c + 1)**2
Let x be 5/2 + -6 + 4. Solve o + 0*o**2 - 1/2*o**4 + x - o**3 = 0 for o.
-1, 1
Let g(a) = 3*a**2 + 6*a - 9. Let n be (2 + -4)*(-5)/2. Let h(r) = 2*r**2 + 6*r - 8. Let c(l) = n*h(l) - 4*g(l). What is s in c(s) = 0?
1, 2
Let y(p) be the third derivative of -p**8/15120 + p**7/630 - p**6/60 + p**5/60 + 6*p**2. Let d(n) be the third derivative of y(n). Factor d(o).
-4*(o - 3)**2/3
Suppose -2/5*n**4 + 1/5*n + 0*n**3 + 2/5*n**2 - 1/5*n**5 + 0 = 0. What is n?
-1, 0, 1
Let j(o) be the first derivative of -o**6/165 + o**4/33 - o**2/11 + 3*o + 4. Let r(d) be the first derivative of j(d). Let r(n) = 0. What is n?
-1, 1
Let o be ((-4)/(-6))/(32/144). Let g(t) be the first derivative of -2/25*t**5 - 1/10*t**4 - 1 + 2/15*t**o + 0*t + 1/5*t**2. Let g(d) = 0. What is d?
-1, 0, 1
Determine l, given that 3/5*l**2 - 9/5*l + 6/5 = 0.
1, 2
Suppose -u - 3 = -2*u. Factor 2/5*z**u + 2/5*z**2 - 2/5*z - 2/5.
2*(z - 1)*(z + 1)**2/5
Let a(u) be the second derivative of 0*u**2 + 0 + 1/10*u**5 - 3*u + 0*u**6 + 0*u**4 + 0*u**3 - 1/21*u**7. Find o such that a(o) = 0.
-1, 0, 1
Let h(n) = 2*n**2 - 10*n**4 + n**3 - n - n**2 + 9*n**4. Let w(y) = -y**4 + 15*y**3 - 29*y**2 + 17*y - 2. Let m(f) = 5*h(f) + w(f). Factor m(t).
-2*(t - 1)**3*(3*t - 1)
Let f(w) be the second derivative of w**4/12 - w**3/6 + 3*w**2/2 - w. Let y be f(0). Factor -1/3*g**y - 1/3*g + 0 + 2/3*g**2.
-g*(g - 1)**2/3
Let a(t) = t**5 - t**3 - t**2 - t + 1. Let k(f) = -7*f**5 + 6*f**3 + 6*f**2 + 6*f - 6. Let z(w) = -6*a(w) - k(w). What is h in z(h) = 0?
0
Suppose -5*d = -4*p + 17, -2*p - 4*d - 1 = -3. Let a(i) be the third derivative of -7/150*i**5 + 0*i + 3*i**2 - 1/30*i**4 + 0*i**p + 0. Factor a(z).
-2*z*(7*z + 2)/5
Let q(k) be the second derivative of -2*k**7 - 8*k**6/3 + 17*k**5/5 + 20*k**4/3 + 8*k**3/3 - 8*k. Solve q(r) = 0 for r.
-1, -2/3, -2/7, 0, 1
Let x = 4 + 0. Factor -2*n**3 + 3 + 8*n**2 - 3 + 2*n + 2*n**4 - 10*n**x.
-2*n*(n - 1)*(n + 1)*(4*n + 1)
Suppose 2*o - 7*o - 515 = 0. Let d = -925/9 - o. Let 0 + 0*q**3 - d*q**4 + 0*q + 2/9*q**2 = 0. Calculate q.
-1, 0, 1
Suppose 2*w + 4 = 0, -2*w + 6 = 2*h - w. Let x(k) be the first derivative of 0*k**3 + 1/6*k**2 - 1 + 0*k - 1/12*k**h. Find p such that x(p) = 0.
-1, 0, 1
Factor -94/7*k**3 - 17/7*k**4 - 7 - 1/7*k**5 - 190/7*k**2 - 23*k.
-(k + 1)**3*(k + 7)**2/7
Let y = 467/3 - 155. Factor y*m**2 - 1/3*m**3 + 0 - 1/3*m.
-m*(m - 1)**2/3
Suppose 5*a - 10 + 0 = 0. Factor -1 - a*s**2 + 5 - 4 + 4*s - 2.
-2*(s - 1)**2
Let a be 1/(-9)*((-69)/30 + 2). Let h(s) be the second derivative of s + 0*s**3 + 0 + 1/40*s**5 + 0*s**4 - a*s**6 + 1/84*s**7 + 0*s**2. Factor h(t).
t**3*(t - 1)**2/2
Let v(c) be the third derivative of c**5/140 + c**4/56 + c**2. Factor v(p).
3*p*(p + 1)/7
What is j in 10*j**4 - 10*j**2 - 8*j**3 + 13*j**3 + 2*j**5 - 4*j**5 - 3*j**5 = 0?
-1, 0, 1, 2
Suppose 5*b - 3*b = 8. Suppose -g + g**b - 2*g**2 + g**4 + g**5 + 0*g**3 + 0*g**3 = 0. Calculate g.
-1, 0, 1
Let t = -2 - -1. Let w be (t - 0)*-2 - 1. Suppose s**2 - w - 1 + 1 = 0. Calculate s.
-1, 1
Factor 2/11*n**5 - 4/11*n**2 + 4/11*n**4 + 0*n**3 - 2/11*n + 0.
2*n*(n - 1)*(n + 1)**3/11
Determine k so that 4*k**3 + 3 - 20*k**2 + 1 + 32*k - 3 - 17 = 0.
1, 2
Let h be -3 - (-4 - -3 - 4). Suppose k**2 + 3*k**2 - 3*k**2 - 4*k**h - 6*k - 3 = 0. Calculate k.
-1
Determine n so that 5*n**5 + 21*n**3 + 7*n**2 + n**2 + 17*n**4 + 2*n + 3*n**2 = 0.
-1, -2/5, 0
Let s be 461/(-129) - 12/(-4). Let x = 4/43 - s. Suppose 1/3*b**4 + 1/3*b**5 - 2/3*b**2 + 1/3*b + 1/3 - x*b**3 = 0. What is b?
-1, 1
Let a(n) be the first derivative of 2*n**3/27 - 4*n**2/9 + 8*n/9 + 5. What is x in a(x) = 0?
2
Factor 35*u - 34*u - 68*u**3 - 171*u**2 - 161*u - 16 - 41*u**2.
-4*(u + 1)*(u + 2)*(17*u + 2)
Let w(s) = s**3 - s**2 + s + 1. Let n(z) = 39*z**3 + 66*z**2 + 51*z + 12. Let i(x) = n(x) - 6*w(x). Factor i(y).
3*(y + 1)**2*(11*y + 2)
Factor 7/6*a**5 - 1/6*a**2 - 1/3*a + 0 - 19/6*a**4 + 5/2*a**3.
a*(a - 1)**3*(7*a + 2)/6
Let b(h) be the second derivative of -h**4/24 + h**3/4 + h**2 - 14*h. Suppose b(r) = 0. What is r?
-1, 4
Let w(l) be the third derivative of 3*l**8/112 + 11*l**7/70 + 3*l**6/10 + l**5/5 - 28*l**2 - 2*l. What is g in w(g) = 0?
-2, -1, -2/3, 0
Let o(c) be the second derivative of 0*c**4 - c + 0 + 0*c**2 - 1/120*c**6 + 0*c**3 + 1/80*c**5. Find t such that o(t) = 0.
0, 1
Factor 4/5*k**2 - 4/5 + 0*k.
4*(k - 1)*(k + 1)/5
Suppose -2*p = -3*u + 28, -5*p - 1 = 2*u - 26. Suppose -3*b + y - 5*y + u = 0, 4*y = 4. Solve -m**2 + 13 + b*m + 0*m**2 - 14 = 0 for m.
1
Suppose -9 = -3*w - 3*v, -2*w - 3*w + 4*v = 12. Factor n - 19 - n**2 + w*n + 19.
-n*(n - 1)
Let w(v) = -2*v**2 - 3*v + 5. Let j(c) = -3*c**2 - 3*c + 6. Let n(q) = 6*j(q) - 7*w(q). Factor n(m).
-(m - 1)*(4*m + 1)
Let w(q) be the first derivative of -5*q**6/6 - q**5 + 5*q**4/4 + 5*q**3/3 + 8. Determine l, given that w(l) = 0.
-1, 0, 1
Let s(x) be the third derivative of x**6/60 + x**5/3 + 17*x**4/12 + 8*x**3/3 - 33*x**2. Determine y, given that s(y) = 0.
-8, -1
Let h(g) be the third derivative of -g**9/30240 + g**8/10080 - g**5/12 + 6*g**2. Let w(t) be the third derivative of h(t). Solve w(f) = 0 for f.
0, 1
Let x = 848/13 - 16580/247. Let a = x + 404/133. Suppose 2/7 + 6/7*h**2 + a*h = 0. Calculate h.
-1, -1/3
Solve 20*u - 36 + 13*u - 5*u**2 + 8*u**2 = 0 for u.
-12, 1
Let b be 5 + -2 + (3 + -3 - -1). Let j = 2 - 2. Let 0*f - 2/7*f**b + j + 2/7*f**2 - 2/7*f**3 + 2/7*f**5 = 0. Wh