p**2 - 12*p.
-4*(p - 1)*(3*p - 2)*(4*p + 1)
Suppose r + 12 = 3*r. Let t(a) = a**3 - 8*a**2 + 11*a + 6. Let b be t(r). Determine y, given that -3*y**2 + b - 3/4*y = 0.
-1/4, 0
Find y, given that 0*y**4 - 16*y**5 + 3*y**3 + 3*y**4 - 3*y**2 + 13*y**5 = 0.
-1, 0, 1
Determine m so that -22/5*m - 2/5*m**2 + 0 = 0.
-11, 0
Let m(u) be the first derivative of -u**5/40 - u**4/16 + u**3/2 - 2*u**2 + 13. Let x(l) be the second derivative of m(l). What is z in x(z) = 0?
-2, 1
Factor 1/2*s**4 + 3 + 21/2*s**2 - 9/2*s**3 - 19/2*s.
(s - 6)*(s - 1)**3/2
Let l(s) be the first derivative of s**5/25 - 27*s**4/20 + 81*s**3/5 - 729*s**2/10 + 102. Find c such that l(c) = 0.
0, 9
Let x(t) be the third derivative of t**6/60 - 103*t**5/120 + 325*t**4/24 + 169*t**3/12 + 2*t**2 - 83*t. Factor x(f).
(f - 13)**2*(4*f + 1)/2
Let g(t) = -t**3 + t**2 - 5*t + 1. Let c(x) = 15*x**3 + 66*x**2 + 93*x - 27. Let m(r) = -c(r) - 3*g(r). Determine s so that m(s) = 0.
-4, -2, 1/4
Let s(h) be the second derivative of h**5/30 + h**4/9 - h**3/3 + h + 34. Suppose s(w) = 0. Calculate w.
-3, 0, 1
Suppose -3*c = -4*n - 16 + 41, 2*c = -2*n + 2. Let z be ((-5)/(-2) + -2)*n. Factor 0 - 3/2*r**z + 0*r.
-3*r**2/2
Factor 174 - 4*b**3 + 192 - 366 + 8*b**2 - 4*b.
-4*b*(b - 1)**2
Let u(b) = b**4 + b**3 + b**2 + b - 1. Let a(q) = 11*q**4 + 5*q**3 + 3*q**2 + 9*q - 9. Let w(p) = -2*a(p) + 18*u(p). Factor w(k).
-4*k**2*(k - 3)*(k + 1)
Let m(i) = -i**2 + 1. Let z(y) = 2*y**2 + 14. Let l(h) = 4*m(h) + z(h). Determine a, given that l(a) = 0.
-3, 3
Let z(i) = -i**2 - i - 12. Let b be z(-11). Let t = -117 - b. Factor -5/2*y**5 + 5*y**2 + 5/2*y + 0 + 0*y**3 - t*y**4.
-5*y*(y - 1)*(y + 1)**3/2
Let f be 2 + (-4)/(-5) + 2/10. Factor -6*i + 53*i**f - 14*i**2 - 10*i - 115*i**3 - 6 + 58*i**3.
-2*(i + 1)**2*(2*i + 3)
Let p(h) be the first derivative of -4*h**5/5 - 12*h**4 - 184*h**3/3 - 120*h**2 - 100*h - 59. Solve p(v) = 0 for v.
-5, -1
Let h(r) be the first derivative of 1/2*r**4 + 0*r**2 - 1/3*r**6 + 0*r - 2/5*r**5 + 8 + 2/3*r**3. Factor h(t).
-2*t**2*(t - 1)*(t + 1)**2
Let x(z) = -z**2 + 10*z + 1. Let n be x(9). Factor 0*r + r**2 + n*r - 9*r.
r*(r + 1)
Let s(i) be the third derivative of i**5/100 + 7*i**4/40 + i**3 + 76*i**2. Factor s(x).
3*(x + 2)*(x + 5)/5
Let j(h) = 2*h**5 - 18*h**4 + 10*h**3 - 6*h**2 + 12*h + 8. Let x(i) = i**4 + i**3 - i**2 - i - 1. Let g(l) = j(l) + 8*x(l). Factor g(m).
2*m*(m - 2)*(m - 1)**3
Factor 40 - 10*s**2 - 20*s + 23*s**2 - 11*s**2 - 12*s**2 + 5*s**3.
5*(s - 2)**2*(s + 2)
Let q(b) be the first derivative of b**6/105 + b**5/70 - b**4/42 - b**3/21 + b - 4. Let h(a) be the first derivative of q(a). Factor h(o).
2*o*(o - 1)*(o + 1)**2/7
Find a such that 2/7*a**2 + 76/7*a + 722/7 = 0.
-19
Suppose -26 = -13*f - 0*f. Let m(d) be the first derivative of d**f - 2/3*d**3 + 2*d - 1/2*d**4 + 5. Solve m(n) = 0 for n.
-1, 1
Suppose 5*a = -0*a + 10. Let j = 5/3 - 4/3. Determine v so that 0 + 5/3*v**a + j*v = 0.
-1/5, 0
Determine t so that 338/3 - 2/3*t**3 - 130*t + 18*t**2 = 0.
1, 13
Let j = 2 + -2. Suppose j = -4*r - p + 7, r + 2*p + 0*p = -7. Factor 10 - 11 - 8*w**2 + r + 6*w.
-2*(w - 1)*(4*w + 1)
Let v(k) be the third derivative of -k**6/24 - k**5/6 + 25*k**4/8 + 30*k**3 + 5*k**2 - 2*k. What is q in v(q) = 0?
-3, 4
Let 32/11 + 2/11*u**2 + 16/11*u = 0. Calculate u.
-4
Let c(u) = u**2 - 600*u + 4154. Let z be c(7). Factor 0*r + 0 + 3/7*r**2 - 3/7*r**z.
-3*r**2*(r - 1)/7
Let b be -1 - (1*(-10)/2)/(-1 + 2). Factor 2/9*a**3 - 2/9*a**b - 2/9*a + 2/9*a**2 + 0.
-2*a*(a - 1)**2*(a + 1)/9
Let d(b) be the first derivative of 0*b**2 - b**3 + 15/4*b**4 - 4 + 0*b. Find r such that d(r) = 0.
0, 1/5
Let i = -14 + 21. Factor 5*b**2 - 3*b**3 + 14*b**4 - 9*b**4 - i*b**3.
5*b**2*(b - 1)**2
Let a(c) be the first derivative of -5*c - 4 - 2/9*c**3 - 1/6*c**4 - 1/9*c**2. Let z(d) be the first derivative of a(d). Factor z(g).
-2*(3*g + 1)**2/9
Let u = 6311/7371 - -1/1053. Let l(g) be the first derivative of 3/4*g**4 - 3/2*g**2 + u*g + 11 - 2/7*g**3. Factor l(s).
3*(s - 1)*(s + 1)*(7*s - 2)/7
Let h be (16/4 - -2) + ((-1892)/165)/2. Factor 0 + 2/15*z**2 - 2/15*z + 2/5*z**3 + h*z**5 - 2/3*z**4.
2*z*(z - 1)**3*(2*z + 1)/15
Let x(o) be the third derivative of 0*o**5 - 1/48*o**4 - 20*o**2 + 1/720*o**6 + 0 + 0*o - 1/18*o**3. Factor x(d).
(d - 2)*(d + 1)**2/6
Factor -17/2*w**2 + 5/2 + 2*w**3 - 8*w.
(w - 5)*(w + 1)*(4*w - 1)/2
Factor -37*m**2 - 40*m - 20*m - 4658*m**3 - 36 + 4648*m**3 - m**4.
-(m + 2)**2*(m + 3)**2
Let b = -8604 - -34427/4. Factor -1/2*r**3 - 13/4*r - 1 - b*r**2.
-(r + 1)*(r + 4)*(2*r + 1)/4
Let o be (-2)/(-11) + 20/11. Let h(w) = 3*w - 6. Let q be h(o). Factor 0*b**2 + q - 2/5*b**3 + 0*b.
-2*b**3/5
Let t = 48686 - 340772/7. Suppose t*p + 6/7*p**2 + 0 = 0. What is p?
-5, 0
Let h(b) = b**3 - 3*b**2 + 3*b - 2. Let g be h(2). Let d be 1 + g - (-5 + 4). Let -8*n + 4*n**2 + n**2 + 10*n + 1 - 4*n**d = 0. Calculate n.
-1
Let y(h) be the first derivative of 3*h**4/4 + 45*h**3 + 66*h**2 + 298. Factor y(x).
3*x*(x + 1)*(x + 44)
Let y(d) = d**2 + 64*d + 729. Let h(g) = -5*g**2 - 325*g - 3645. Let i(p) = -4*h(p) - 22*y(p). Factor i(m).
-2*(m + 27)**2
Suppose 5*k - 24 = -2*v, -3*v - k + 12 = v. Determine s so that 6*s**3 - v*s**4 - 6*s**3 + 0*s**3 = 0.
0
Let i(h) = -h**3 - 2*h**2 + h + 3. Let p be i(-2). Let q = p + -1. Find d, given that 0*d**4 + 1/6*d + 1/6*d**5 - 1/3*d**3 + 0*d**2 + q = 0.
-1, 0, 1
Suppose -5*h = -4*g + 8, 0 = 7*g - 3*g + 5*h - 8. Let w(j) be the first derivative of -4 - 1/2*j**g + 0*j + 1/3*j**3. Find y, given that w(y) = 0.
0, 1
Let a(j) be the first derivative of -2*j**3/33 - 15*j**2/11 - 52*j/11 + 306. Solve a(q) = 0 for q.
-13, -2
Let m(f) be the third derivative of f**10/40320 + f**9/20160 - f**8/8960 - f**7/3360 - f**4/4 + 45*f**2. Let l(r) be the second derivative of m(r). Factor l(p).
3*p**2*(p - 1)*(p + 1)**2/4
Suppose -2*f = 5*q + 23 - 438, -4*f - 190 = -2*q. Suppose -10*l = 5 - q. Factor l + 1/2*a**2 - 4*a.
(a - 4)**2/2
Factor -3 - 8 - 13*k - 26 + 7 + k**2.
(k - 15)*(k + 2)
Suppose -t + 23 = t - 3*a, t + a - 9 = 0. Factor 63*v - 17*v**5 - 52*v**3 + v**2 + 16 + 15*v**2 + t*v**5 - 37*v**4 + v.
-(v - 1)*(v + 2)**3*(7*v + 2)
Let s(b) be the third derivative of -b**8/5040 + 7*b**4/24 - 6*b**2. Let j(f) be the second derivative of s(f). Suppose j(z) = 0. Calculate z.
0
Let l(h) = -24*h**3 + 34*h**2 + 12*h - 12. Let r(y) = 2*y**3 - y + 2. Let x(q) = -2*l(q) - 12*r(q). Factor x(b).
4*b*(b - 3)*(6*b + 1)
Let n(w) be the third derivative of w**4/24 + 2*w**3/3 - 4*w**2. Let z be n(-2). Determine h, given that 3*h**4 - 2*h**4 - z*h**4 = 0.
0
Let l(d) be the first derivative of d**6/120 - d**5/20 + 15*d**2/2 - 15. Let i(m) be the second derivative of l(m). Factor i(h).
h**2*(h - 3)
Find u, given that 9*u**2 - 65*u - 1/3*u**3 + 169/3 = 0.
1, 13
Let d(i) be the third derivative of -i**5/30 - i**4/2 - 8*i**3/3 + 8*i**2 + 5. Solve d(r) = 0 for r.
-4, -2
Find n such that 34/5*n + 0 + 2/5*n**2 = 0.
-17, 0
Let v = 39 + -39. Let a(z) be the third derivative of v*z + 27/8*z**4 - 27/2*z**3 + 0 - 9/20*z**5 + 2*z**2 + 1/40*z**6. Determine w, given that a(w) = 0.
3
Factor 0 + 32/3*r - 16/3*r**2 + 2/3*r**3.
2*r*(r - 4)**2/3
Let l be ((-104)/(-20) - 5)/((-4)/(-80)*6). Suppose 0*g + 2/3*g**3 - 2/3*g**4 + 0 - l*g**5 + 2/3*g**2 = 0. Calculate g.
-1, 0, 1
Let s(t) be the third derivative of t**8/8400 + t**7/4200 - t**6/900 + 11*t**3/2 - 11*t**2. Let k(m) be the first derivative of s(m). Factor k(w).
w**2*(w - 1)*(w + 2)/5
Let z(k) be the third derivative of 1/105*k**7 - 1/30*k**6 - 1/10*k**5 + 0*k + 0 + 12*k**2 + 2/3*k**4 - 4/3*k**3. Factor z(c).
2*(c - 2)*(c - 1)**2*(c + 2)
Let t(i) be the second derivative of -2*i**7/21 + 8*i**6/15 + 12*i**5/5 + 2*i**4/3 - 22*i**3/3 - 12*i**2 - 177*i. What is y in t(y) = 0?
-1, 1, 6
Let h(b) = b**3 - 7*b**2 + 10*b - 9. Let x be h(6). Factor -12*i**2 - 14*i + 10*i**3 - 5 + 2*i**2 + x*i**4 + 5*i**5 - i.
5*(i - 1)*(i + 1)**4
Suppose 29*r = 4*r. Let h = 100 + -696/7. Find u such that 16/7*u + h*u**2 + r = 0.
-4, 0
Let a be ((-78)/24)/(-13)*0. Factor 3*f**3 + a*f + 0 + 3*f**2 + 3/4*f**4.
3*f**2*(f + 2)**2/4
Let i(c) = 11*c**2 + 8*c - 16. Let j(w) = 14*w**2 + 8*w - 16. Let n(h) = 5*i(h) - 4*j(h). Solve n(x) = 0 for x.
4
Let f(o) be the third derivative of 0 + 3/55*o**5 + 0*o - 1/660*o**6 + 72