. Let p(k) = 5*h(k) + 18*y(k). Factor p(i).
3*i*(i - 2)*(i - 1)**2
Let k be (-9 - (-4 + 3 + -2))/(-2). Factor 0 - 1/5*d + 1/5*d**k - 1/5*d**4 + 1/5*d**2.
-d*(d - 1)**2*(d + 1)/5
Let u(m) be the first derivative of -m**8/5040 + m**7/2520 + m**6/1080 - m**5/360 + m**3/3 - 3. Let v(s) be the third derivative of u(s). What is r in v(r) = 0?
-1, 0, 1
Let u(l) = -l**3 - 5*l**2 - l - 3. Let t be u(-5). Let m = 2 + 2. Let t + m - 5 - a**2 = 0. Calculate a.
-1, 1
Let c(a) be the second derivative of 1/56*a**7 - 1/48*a**4 + 0*a**2 + 1/80*a**5 + a + 0*a**3 + 0 + 1/24*a**6. Solve c(b) = 0 for b.
-1, 0, 1/3
Suppose 4*w - 4 = 5*o, 2*w - 2*o - 4 = -0*o. Let a(u) be the first derivative of 0*u + 0*u**3 + 1 - 1/4*u**4 + 0*u**2 + 1/6*u**w + 0*u**5. Factor a(y).
y**3*(y - 1)*(y + 1)
Let n(j) be the first derivative of -j**7/105 + j**5/15 - j**3/3 - j**2/2 - 1. Let f(q) be the second derivative of n(q). Factor f(p).
-2*(p - 1)**2*(p + 1)**2
Let u = -1 - -3. What is z in -z**3 - u*z + z**2 - z**4 + 0*z**4 + 3*z = 0?
-1, 0, 1
Let c(b) be the third derivative of b**5/120 - b**4/24 - 7*b**2. Factor c(w).
w*(w - 2)/2
Let m(c) = c**3 - 5*c**2 - 5*c + 5. Let a be m(5). Let l be (-48)/a + 6/10. Let 4/5*r + 14/5*r**2 - 4/5*r**l - 14/5*r**4 + 0 = 0. What is r?
-1, -2/7, 0, 1
Let d(c) be the second derivative of c**6/195 - c**4/78 - 12*c. Suppose d(t) = 0. Calculate t.
-1, 0, 1
Let o(m) be the third derivative of m**8/26880 - m**7/5040 + m**6/2880 - m**4/12 + 4*m**2. Let z(q) be the second derivative of o(q). Factor z(t).
t*(t - 1)**2/4
Let c be (0 + 3)/6*12. Let s = -4 + c. Determine p, given that 3*p**3 - 2*p**5 + 6*p - 2 + 6*p**4 - 7*p**3 - 5*p**2 + p**s = 0.
-1, 1
Let m = 379/132 + -9/44. Determine v so that m*v**2 + 10/3*v + 2/3 = 0.
-1, -1/4
Factor -4/3*u**5 + 0 + 64/3*u**2 + 0*u + 12*u**4 - 32*u**3.
-4*u**2*(u - 4)**2*(u - 1)/3
Solve 0 + 1/5*i**3 + 2/5*i - 3/5*i**2 = 0 for i.
0, 1, 2
Let f(d) = -d**5 - d**3 - d**2 - d - 1. Let z(h) = -12*h**5 - 10*h**4 - 28*h**3 - 24*h**2 - 14*h - 10. Let p(w) = 20*f(w) - 2*z(w). Factor p(t).
4*t*(t + 1)**3*(t + 2)
Let o(w) be the first derivative of -w**4/6 - 2*w**3/9 + w**2/3 + 2*w/3 - 9. Determine g so that o(g) = 0.
-1, 1
Suppose 0 = 5*u + 4 - 29. Factor 8/7*m**4 - 2/7*m**u - 2/7*m + 8/7*m**2 + 0 - 12/7*m**3.
-2*m*(m - 1)**4/7
Let x = 14 + -6. Suppose x = 4*m + 3*i, -3*i + 3 = m + 1. Factor c**2 + 7*c**3 + 11*c + 8*c**2 + 11*c**2 + m - 4*c**2.
(c + 1)**2*(7*c + 2)
Let p be 12 - 11 - (-7)/(-9). Let q(t) be the first derivative of -2/27*t**3 + 0*t - p*t**2 - 2. Factor q(a).
-2*a*(a + 2)/9
Let x = 20 + -18. Determine w, given that -3*w + 4*w**x + w - 5*w**2 = 0.
-2, 0
Solve 3/4*r**3 - 3/4 - 3/4*r + 3/4*r**2 = 0 for r.
-1, 1
Let o(s) be the first derivative of -5*s**4/4 - 5*s**3 - 15*s**2/2 - 5*s + 1. Factor o(d).
-5*(d + 1)**3
Let w be (2 - (-170)/(-75))/(4/(-12)). Factor -14/5*m**3 + 18/5*m**2 + 0 - w*m.
-2*m*(m - 1)*(7*m - 2)/5
Let u(i) = -i**3 + 8*i**2 - i + 10. Let y be u(8). Suppose 3*r - 16 = -2*w, 3*w - r - y = -0*r. Factor 0*l**w + l - l**3 - 1/2 + 1/2*l**4.
(l - 1)**3*(l + 1)/2
Let w(u) be the second derivative of -u**4/24 + u**3 - 9*u**2 - 4*u. Factor w(m).
-(m - 6)**2/2
Let w(i) be the second derivative of i**4/30 - 4*i**2/5 - 8*i. Factor w(x).
2*(x - 2)*(x + 2)/5
Let i(c) = -c**2 + 31*c + 36. Let y(m) = 5*m**2 - 125*m - 145. Let x(g) = -15*i(g) - 4*y(g). Let x(v) = 0. Calculate v.
-1, 8
Let i(l) be the third derivative of l**8/4200 - l**7/2100 - l**6/900 + l**5/300 + l**3/3 - l**2. Let b(o) be the first derivative of i(o). Factor b(h).
2*h*(h - 1)**2*(h + 1)/5
Let f = -214/3 - -72. Let y(c) be the second derivative of f*c**2 + 1/30*c**5 + 0 - c + 2/9*c**4 + 5/9*c**3. Determine h so that y(h) = 0.
-2, -1
Let a(u) be the first derivative of 3/2*u**4 - 3*u**5 - 3/2*u**6 + 0*u**3 - 1 + 0*u + 0*u**2. Factor a(t).
-3*t**3*(t + 2)*(3*t - 1)
Let v be (-3 - 0)/(-3) - 0. Factor -2*r**2 + v - 2*r**4 + 4*r**3 + 4 - 5.
-2*r**2*(r - 1)**2
Suppose -2/5 + 1/5*b**2 - 1/5*b = 0. What is b?
-1, 2
Factor 5*b**4 - 3*b**3 + 0*b**3 + b**2 - b**5 + 0*b**4 - 2*b**4.
-b**2*(b - 1)**3
Let d(i) be the first derivative of i**7/280 - i**6/180 - i**5/40 + i**4/12 - i**3/3 - 1. Let r(j) be the third derivative of d(j). Factor r(p).
(p - 1)*(p + 1)*(3*p - 2)
Let t be ((-36)/(-27))/(-4*15/(-18)). Factor 0 - 4/5*v**2 + t*v + 2/5*v**3.
2*v*(v - 1)**2/5
Let n(q) be the third derivative of q**10/15120 + q**9/2520 + q**8/1120 + q**7/1260 - q**4/8 + 2*q**2. Let i(x) be the second derivative of n(x). Factor i(s).
2*s**2*(s + 1)**3
Suppose 0 - 2/5*j**2 + 8/5*j = 0. Calculate j.
0, 4
Suppose 25 + 47 = 4*z. Let g be 58/18 + (-4)/z. Determine j so that -2/7*j**g + 0 + 2/7*j + 0*j**2 = 0.
-1, 0, 1
Suppose -5*g + 2*n - 13 = 0, -1 = 2*g - 4*n + 1. Let z be 2/6 + (-5)/g. Factor -d - d**2 - d**z - d.
-2*d*(d + 1)
Let 2/7*v**2 + 4/7 + 6/7*v = 0. Calculate v.
-2, -1
Let q(k) = -k**3 - 3*k**2 + 3*k - 1. Let a be q(-4). Let z be (4/(-10))/(3/(-30)). Factor 0*d**2 + 1/2*d**a - 1/2*d**z + 0 + 0*d.
-d**3*(d - 1)/2
Let k = 0 - 1. Let y(c) = -25*c**3 - 5*c**2 + 20*c - 8. Let h(v) = 1 + v**2 + 0*v**2 + 0*v**2 - v + v**3. Let x(a) = k*y(a) - 4*h(a). What is w in x(w) = 0?
-1, 2/7, 2/3
Let s(y) be the first derivative of -2*y**5/55 + y**4/22 - 37. Factor s(k).
-2*k**3*(k - 1)/11
Suppose 0 = 3*w - 6 - 0. Let w + 1 + 4*y**2 - 3 - 4 = 0. Calculate y.
-1, 1
Let m(u) = -4*u**3 - 8*u**2 + 10*u + 8. Let n(g) = 4*g**3 + 8*g**2 - 9*g - 8. Let x(r) = -5*m(r) - 6*n(r). Factor x(s).
-4*(s - 1)*(s + 1)*(s + 2)
Let y = -16 - -17. Let n(s) be the first derivative of y + s + 1/3*s**3 + s**2. Factor n(f).
(f + 1)**2
Let f = -100 - -401/4. Let h(o) be the first derivative of -1/6*o**3 - f*o**2 + 1 + o. Factor h(k).
-(k - 1)*(k + 2)/2
Let f be (12 + -2)*(-2)/(-5). Suppose o + 20 = -4*k, -14 = 3*o + 2*k - f. Let o*s**3 + 0*s**2 + 0 - 1/4*s**4 + 0*s = 0. What is s?
0
Let a(j) be the first derivative of j**5 - 15*j**4/4 + 10*j**2 - 1. Find u such that a(u) = 0.
-1, 0, 2
Let f be 212/16 - 6 - 5. Factor f + 1/4*t**2 + 3/2*t.
(t + 3)**2/4
Let u(t) be the third derivative of -t**6/12 + t**5/4 - 5*t**4/24 - 22*t**2. Solve u(a) = 0.
0, 1/2, 1
Suppose 0 = 93*y - 95*y + 16. Factor 0 + 55/2*n**3 + 121/6*n**4 + 2/3*n + y*n**2.
n*(n + 1)*(11*n + 2)**2/6
Let a(o) = -10*o**2 + 3*o - 2. Let v be a(1). Let b be ((-8)/v)/(12/18). Factor 0 - b*x**3 - 2/3*x**2 - 2/3*x**4 + 0*x.
-2*x**2*(x + 1)**2/3
Let v(r) be the third derivative of -r**6/30 + r**5/15 + r**4/6 - 2*r**3/3 + 30*r**2. Suppose v(s) = 0. Calculate s.
-1, 1
Let b be (-190)/(-30) - (-2)/(-6). Let n(l) = l - 3. Let v be n(b). Solve -u**v + 1 - u - 13*u**2 + 11*u**2 + 1 + 2*u**3 = 0.
-1, 1, 2
Suppose -5*f + 75 = 3*s, -23 = -2*f + s - 4. Factor 4 + 3*q**2 + 0*q**2 + 0 + f*q + 5.
3*(q + 1)*(q + 3)
Let d(k) = -k - 8. Let j be d(-11). Let g(t) be the third derivative of 1/27*t**j + 2/135*t**5 + 0 + 3*t**2 - 5/108*t**4 + 0*t. Solve g(c) = 0.
1/4, 1
Factor 2*c**5 + 2*c - 14*c**3 + 7*c**3 + 3*c**3.
2*c*(c - 1)**2*(c + 1)**2
Let x = -5 - 10. Let q be 6/15 + (-24)/x. Factor 3 + 2*a**q - 3 + 2*a**4 - 4*a**3.
2*a**2*(a - 1)**2
Let r(h) be the first derivative of h**4/6 + h**3/3 + 4*h + 1. Let j(d) be the first derivative of r(d). Solve j(c) = 0 for c.
-1, 0
Let 0*k + 53*k**2 - 3*k**4 - 44*k**2 + 6*k = 0. Calculate k.
-1, 0, 2
Let f = -2759/11 - -251. Factor -f*w**4 + 0*w + 0 - 2/11*w**3 + 2/11*w**2 + 2/11*w**5.
2*w**2*(w - 1)**2*(w + 1)/11
Let z**2 - 1/4*z**5 + 0 - 2*z**3 + 5/4*z**4 + 0*z = 0. Calculate z.
0, 1, 2
Let i(s) = -2*s**2 - 3*s + 6. Let r(y) = y**2 + y - 3. Let p(u) = 3*i(u) + 7*r(u). Determine a, given that p(a) = 0.
-1, 3
Find k, given that 4/11*k + 26/11*k**2 + 46/11*k**3 + 6/11*k**4 + 0 - 18/11*k**5 = 0.
-1, -1/3, 0, 2
Suppose 13 = 5*h - 52. Suppose 0 = 16*x - h*x. Factor -1/4*b + 1/4*b**2 + x.
b*(b - 1)/4
Let g(m) be the third derivative of m**7/70 + m**6/20 - 3*m**5/20 - m**4/2 + 2*m**3 - 4*m**2. Factor g(p).
3*(p - 1)**2*(p + 2)**2
Factor -6 + 19 - 21*r**3 - 33*r - 48*r**2 - 11 - 8.
-3*(r + 1)**2*(7*r + 2)
Factor -5/2*f**4 + 5*f**3 - 1/2 + 5/2*f + 1/2*f**5 - 5*f**2.
(f - 1)**5/2
Let h be 2 + -1 - (2 - 3). Suppose -k = k - h. Let p(g) = g - 1. Let y(l) = -2*l**2 - 4*l + 2. Let c(m) = k*y(m) + 2*p(m). Determine s, given that c(s) = 0.
-1, 0
Factor 14*u