Factor 2 + 35*p**3 + 25/2*p**4 + 69/2*p**2 + 14*p.
(p + 1)**2*(5*p + 2)**2/2
Suppose 0 = -4*o + 11*o. Suppose o*m - 1/4*m**3 + 1/2*m**4 + 0*m**2 - 1/4*m**5 + 0 = 0. Calculate m.
0, 1
Let u = -2818 - -8582/3. Let o = -42 + u. Factor p**5 - o*p**4 + 0*p + 0*p**2 + 0 - 1/3*p**3.
p**3*(p - 1)*(3*p + 1)/3
Let k(h) = 2*h**2 - 2*h - 6. Let r(w) = -w**2 - 1. Let y(t) = 2*k(t) - 6*r(t). Factor y(s).
2*(s - 1)*(5*s + 3)
Let b(n) be the first derivative of 0*n + 2/3*n**3 + 7/10*n**4 + 1/5*n**2 + 6/25*n**5 + 1. Let b(r) = 0. Calculate r.
-1, -1/3, 0
Let p = 21 + -14. Let j(x) = -x + 9. Let f be j(p). Factor 2/3*z**4 + 0*z - 2/3*z**3 + 0*z**f + 0.
2*z**3*(z - 1)/3
Factor -9/4*j**3 - 3/4*j**4 + 0 - 3/4*j - 9/4*j**2.
-3*j*(j + 1)**3/4
Let g(z) = 2*z**5 - 8*z**4 + 2*z**3 - 6*z**2 + 6*z - 6. Let u(h) = h**5 - 8*h**4 + h**3 - 5*h**2 + 5*h - 5. Let b(q) = 5*g(q) - 6*u(q). Factor b(y).
4*y**3*(y + 1)**2
Let r(q) be the first derivative of -q**6/33 - 4*q**5/55 + 4*q**3/33 + q**2/11 - 15. Factor r(h).
-2*h*(h - 1)*(h + 1)**3/11
Let o be (6/4 - 1)*0. Let s(i) be the third derivative of 0 + 0*i**5 - 1/1344*i**8 + 0*i**3 + 0*i - 3*i**2 + 1/240*i**6 + 1/840*i**7 + o*i**4. Factor s(l).
-l**3*(l - 2)*(l + 1)/4
Let u = 4 - 2. Suppose -y + 1 + 3 = 0. Solve -6*x**4 - 10*x**5 - 5*x**2 + y*x**3 + 5*x**u = 0.
-1, 0, 2/5
Let u = 11 - 6. Suppose u*z + 1 = -q + 11, -5*q = 3*z - 6. Let -2*b**3 + b**2 - b**z = 0. What is b?
0
Let f be (0/1)/((-12 + -12)/12). Factor f - 4/7*h - 4/7*h**2.
-4*h*(h + 1)/7
Find r, given that -6/7 - 12/7*r**3 - 20/7*r - 24/7*r**2 - 2/7*r**4 = 0.
-3, -1
Let h be (-4)/8*(-3 + 3 - 4). Let g(n) be the first derivative of h - 3/5*n**5 - 1/2*n**6 + n**3 + 0*n + 3/4*n**4 + 0*n**2. Factor g(v).
-3*v**2*(v - 1)*(v + 1)**2
Determine m, given that m**2 + 9*m**4 - 9*m**4 - 3*m**3 + m**5 - 3*m**2 = 0.
-1, 0, 2
Let k(m) be the third derivative of -m**5/60 - m**4/8 - m**3/3 + 12*m**2. Suppose k(g) = 0. Calculate g.
-2, -1
Let s(h) be the third derivative of 0*h + 1/6*h**5 + 0 - 1/6*h**3 - h**2 - 1/24*h**4 - 1/15*h**6. What is a in s(a) = 0?
-1/4, 1/2, 1
Let o(t) be the first derivative of t**6/360 - t**5/60 + t**4/24 - 2*t**3/3 + 1. Let y(b) be the third derivative of o(b). Factor y(w).
(w - 1)**2
Let n(z) be the second derivative of 0 + 1/6*z**3 + 1/60*z**5 + 0*z**2 + 3*z + 5/36*z**4 - 1/90*z**6. Let n(x) = 0. Calculate x.
-1, 0, 3
Factor 22*h**3 - 14*h**3 + 20*h - 13*h**3 - 15*h**2.
-5*h*(h - 1)*(h + 4)
Suppose 291*b + 5*b**3 - 1080 - 107*b**2 + 17*b**2 + 68*b + 181*b = 0. Calculate b.
6
Let i(z) be the second derivative of -75*z**5/4 + 75*z**4/4 - 15*z**3/2 + 3*z**2/2 + 11*z. Find w such that i(w) = 0.
1/5
Let j = -1 - 2. Let l = 5 + j. Factor 0 - 4/9*t - 2/9*t**l.
-2*t*(t + 2)/9
Let k(i) = -6*i**4 - 6*i**3 + 20*i**2 - 8*i. Let v(b) = 2*b**4 + 2*b**3 - 7*b**2 + 3*b. Let h(r) = -5*k(r) - 14*v(r). What is u in h(u) = 0?
-1, 0, 1
Find g, given that -40*g**3 + 104*g**4 - 74*g**2 - 40*g**3 + 84*g - 8*g**4 - 18 = 0.
-1, 1/3, 3/4
Let t(b) be the first derivative of 1/3*b**3 + 0*b - 7 + 1/2*b**2. Factor t(s).
s*(s + 1)
Let n = -9 + 0. Let l be n/(-3) - (-3)/(-1). Factor 1/3*v**5 + 2/3*v**4 + 0*v**2 + 0*v + 1/3*v**3 + l.
v**3*(v + 1)**2/3
Let r(u) be the first derivative of -u**3 + 5/4*u**4 + 0*u - u**2 - 3. Determine a, given that r(a) = 0.
-2/5, 0, 1
Let b(u) = -u**2 + u - 1. Suppose 4*w - 69 = -1. Let h(o) = 8 + o + 7*o**2 - 19*o + w*o**2. Let s(j) = -6*b(j) - h(j). Suppose s(z) = 0. What is z?
1/3
Let q(k) be the third derivative of -5*k**8/336 - 2*k**7/21 - k**6/4 - k**5/3 - 5*k**4/24 + 11*k**2. What is b in q(b) = 0?
-1, 0
Let d be (-2)/3*(-13 + 25). Let g be 0/d - 2*-2. Factor 1/2 - 1/2*w - w**2 - 1/2*w**5 + 1/2*w**g + w**3.
-(w - 1)**3*(w + 1)**2/2
Suppose 35/3*p + 11/3*p**2 + 25/3 + 1/3*p**3 = 0. Calculate p.
-5, -1
Let x(r) = r**3 - 8*r**2 - 4*r + 22. Let d(i) = i**3 - 7*i**2 - 4*i + 20. Let k(o) = 5*d(o) - 4*x(o). Factor k(p).
(p - 3)*(p - 2)*(p + 2)
Let r(b) be the third derivative of -b**5/420 + 5*b**4/168 + 12*b**2. Let r(g) = 0. Calculate g.
0, 5
Solve 6*p**4 + p**4 - 6*p**5 + 2*p**5 - 3*p**4 + 8*p**3 = 0.
-1, 0, 2
Suppose 0 = 5*f + 10 - 0. Let q be (f + -3 + 5)/(-1). Factor -2/3*g**3 + q*g - 2/3*g**2 + 0.
-2*g**2*(g + 1)/3
Determine f, given that -90 - 15*f - 18*f**2 + 38*f**2 - 9*f**3 + 14*f**3 = 0.
-3, 2
Let j(x) be the first derivative of x**6/60 + x**5/40 - x**4/24 - x**3/12 + 3*x - 2. Let k(p) be the first derivative of j(p). Factor k(m).
m*(m - 1)*(m + 1)**2/2
Let v(i) be the second derivative of -i**7/21 + 7*i**6/30 - 3*i**5/10 - i**4/12 + i**3/3 + 2*i. Find k such that v(k) = 0.
-1/2, 0, 1, 2
Let i(r) be the first derivative of 0*r + 0*r**5 - 1/240*r**6 + 0*r**3 + 1/48*r**4 - 1 - 2*r**2. Let a(q) be the second derivative of i(q). Factor a(l).
-l*(l - 1)*(l + 1)/2
Let u(h) be the third derivative of 19/240*h**6 + 1/672*h**8 + 0*h + 0 - h**2 + 5/24*h**5 + 1/60*h**7 + 1/3*h**4 + 1/3*h**3. Factor u(n).
(n + 1)**3*(n + 2)**2/2
Let f be 12/(-7) - (-6)/(-21). Let q be 0 + f + 140/12. Solve -q*r**2 + 9*r**4 - r - 28/3*r**5 + 2/3 + 31/3*r**3 = 0 for r.
-1, -2/7, 1/4, 1
Let p(m) be the second derivative of -m**7/280 + m**6/60 - m**5/40 + m**3/2 + 2*m. Let g(a) be the second derivative of p(a). Solve g(j) = 0.
0, 1
Let h = 24 - 20. Factor -g**3 + 528*g**5 - 4*g**h - 530*g**5 - g**3.
-2*g**3*(g + 1)**2
Determine r, given that -9*r**5 - 8*r**4 + 1041*r**2 - 3*r**3 - 7*r**4 - 1038*r**2 = 0.
-1, 0, 1/3
Let u(l) be the second derivative of 1/48*l**4 + 0*l**2 + 1/40*l**5 + 2*l + 0*l**3 + 0 + 1/120*l**6. Determine y so that u(y) = 0.
-1, 0
Let a(g) be the third derivative of 0*g**3 + 1/60*g**5 + 1/48*g**6 + 0*g + 1/672*g**8 + 0*g**4 + 0 + 1/105*g**7 - 5*g**2. Factor a(s).
s**2*(s + 1)**2*(s + 2)/2
Determine k, given that 24/5*k**3 + 16/5 + 4/5*k**4 + 48/5*k + 52/5*k**2 = 0.
-2, -1
Suppose 24 = 4*j + 2*j. Suppose -6*x - j*z + 24 = -4*x, -4*x - 2 = -2*z. Suppose 0*g**3 + 0*g**x + 4/7*g**4 - 2/7*g**5 + 0 + 0*g = 0. Calculate g.
0, 2
Let s(t) = t**4 - t**3 - t**2 + t. Let m(u) = 21*u**5 + 23*u**4 + 10*u**3 + 4*u**2 - 4*u. Let a(j) = m(j) + 4*s(j). Factor a(z).
3*z**3*(z + 1)*(7*z + 2)
Let i be 448/(-21) + (-4)/6. Let a = -20 - i. Factor 0*f + 0 - 2/3*f**a + 2/3*f**3.
2*f**2*(f - 1)/3
Let d = 418 - 415. Factor -4/5*c**2 + 0 - 2/5*c - 2/5*c**d.
-2*c*(c + 1)**2/5
Suppose l + 5*x = -13, -1 - 8 = -3*l + x. Suppose 0 = 3*o + l*o - 10. Let 0*q**5 + 0*q**3 - o*q**4 + q**3 + q**5 = 0. What is q?
0, 1
Let p(s) be the first derivative of -2 - 1/6*s**4 + 0*s - 1/9*s**3 + 1/15*s**5 + 1/3*s**2. Factor p(f).
f*(f - 2)*(f - 1)*(f + 1)/3
Let n = -165 - -345/2. Let h(p) be the first derivative of 6*p + 4*p**3 + 1 - 3/4*p**4 - n*p**2. Factor h(c).
-3*(c - 2)*(c - 1)**2
Factor 0 - w**2 + 0*w - 7/6*w**3 - 1/6*w**4.
-w**2*(w + 1)*(w + 6)/6
Let b(i) = -i**3 - 4*i**2 - 3*i. Let l be b(-3). Let z**4 + l*z**2 + 1/2*z**3 + 0 + 0*z + 1/2*z**5 = 0. What is z?
-1, 0
Let w(s) = -s**4 + s**3 + s + 1. Let g(j) = j**5 - 3*j**4 - j**3 + 8*j**2 - 6*j + 3. Let x = 3 + -6. Let t(l) = x*w(l) + 3*g(l). Factor t(q).
3*(q - 1)**4*(q + 2)
Let c(p) be the third derivative of -6*p**7/175 - 29*p**6/200 - p**5/25 + 11*p**4/40 - p**3/5 - 15*p**2. Solve c(y) = 0.
-2, -1, 1/4, 1/3
Suppose 1/3*u**3 + 3 + 7/3*u**2 + 5*u = 0. What is u?
-3, -1
Factor 22/3*v + 14/3*v**3 - 32/3*v**2 - 4/3.
2*(v - 1)**2*(7*v - 2)/3
Let v = -24 - -31. Let g = v + -7. Solve g + 0*y + 1/4*y**3 - 1/4*y**2 = 0.
0, 1
Let u(f) be the first derivative of 2*f**5/75 + f**4/30 - 2*f**3/45 - f**2/15 + 1. Find h, given that u(h) = 0.
-1, 0, 1
Let a(s) be the second derivative of s**5/20 - s**4/6 - s**3/6 + s**2 - 21*s. Find g such that a(g) = 0.
-1, 1, 2
Let o(z) be the third derivative of -z**6/540 + z**5/270 + z**4/108 - z**3/27 + 2*z**2. Factor o(x).
-2*(x - 1)**2*(x + 1)/9
Let w = -1 + 6. Factor -2*t**3 - t**5 - 3*t + 3*t**w + 4*t - t**5.
t*(t - 1)**2*(t + 1)**2
Let z = 306 + -1524/5. What is a in z*a**3 + 6/5*a**2 + 2/5*a**4 + 2/5*a + 0 = 0?
-1, 0
Suppose 0 = 4*t - 10 + 2. Let c(m) be the first derivative of -3/2*m**4 - 9/5*m**5 + 1 + 0*m - 1/3*m**3 + 0*m**t. Determine l so that c(l) = 0.
-1/3, 0
Let p(x) be the second derivative of -x**8/1120 - x**7/840 - x**6/2160 - x**3/3 - 3*x. Let j(w) be the second derivative of p(w). Factor j(d).
-d**2*(3*d