et w(x) = -x. Let b(l) = -l**3 + 3*l**2 - l - 4. Let u(o) = -b(o) + 3*w(o). Let y be u(4). Factor -a**2 + y*a**3 - 10*a**3 + 2*a + a**5 + a**4 - 5*a**3.
a*(a - 1)**2*(a + 1)*(a + 2)
Let n(c) be the second derivative of -441*c**5/130 - 161*c**4/26 - 43*c**3/39 - c**2/13 + 9*c - 35. Suppose n(a) = 0. Calculate a.
-1, -1/21
Let i(r) be the third derivative of r**6/280 + r**5/140 - 5*r**4/28 + 4*r**3/7 - 160*r**2. What is x in i(x) = 0?
-4, 1, 2
Factor 5/3*r - 5/3*r**2 + 0.
-5*r*(r - 1)/3
Suppose 216/11 - 36/11*k**3 - 72/11*k**4 + 6/11*k**5 + 558/11*k + 384/11*k**2 = 0. What is k?
-1, 3, 12
Let v(t) be the first derivative of t**8/840 - t**7/840 - 8*t**3/3 + 14. Let b(r) be the third derivative of v(r). Factor b(j).
j**3*(2*j - 1)
Solve 2/13*p**3 + 32/13*p**2 + 96/13 + 8*p = 0.
-12, -2
Let f(t) be the third derivative of t**7/10080 + t**6/2880 - t**5/240 + 7*t**4/8 - 13*t**2. Let a(d) be the second derivative of f(d). Factor a(v).
(v - 1)*(v + 2)/4
Let w be ((-1)/20)/(78/(-130)). Let b(n) be the third derivative of 0*n - w*n**4 - 4*n**2 + 0 + 0*n**3 - 1/60*n**5. Factor b(q).
-q*(q + 2)
Let v(f) = -15*f**4 + 19*f**3 + 19*f**2 - 27*f + 1. Let r(b) = -7*b**4 + 9*b**3 + 9*b**2 - 13*b. Let q(t) = 13*r(t) - 6*v(t). Factor q(u).
-(u - 3)*(u - 2)*(u + 1)**2
Let v be 14 + 174/(-8) + 8. Factor 1/4*h + 1/4*h**4 + 0 - 1/4*h**2 - v*h**3.
h*(h - 1)**2*(h + 1)/4
Determine h so that -11/2*h**4 - 1/2*h**5 - 45*h**2 - 81/2*h - 27/2 - 23*h**3 = 0.
-3, -1
Factor 116/3 - 2/3*q**2 + 38*q.
-2*(q - 58)*(q + 1)/3
Let 12/7*u**3 + 0 + 4/7*u**4 - 4/7*u**5 - 8/7*u - 4/7*u**2 = 0. What is u?
-1, 0, 1, 2
Let s(x) be the second derivative of -5*x**7/42 + x**6 - 2*x**5 + 5*x + 2. Find u such that s(u) = 0.
0, 2, 4
Let d(g) be the first derivative of 10*g - 40/3*g**2 - 5/36*g**4 + 3 - 20/9*g**3. Let j(u) be the first derivative of d(u). Factor j(y).
-5*(y + 4)**2/3
Let j(x) be the first derivative of x**4/2 + 2*x**3/3 - 5*x**2 + 6*x - 14. Determine l so that j(l) = 0.
-3, 1
Let n(t) be the first derivative of -1/4*t**4 + 2/3*t**3 + 0*t + 3/2*t**2 + 12. Let n(i) = 0. Calculate i.
-1, 0, 3
Let t be (3 - (-2829)/15) + (-2)/(-5). Factor 30*d**2 - 36*d**3 + 1593*d - 33*d**4 - t*d**2 - 1512*d + 243 - 90*d**3 - 3*d**5.
-3*(d - 1)*(d + 3)**4
Let s(x) be the second derivative of -x**7/2520 + x**6/720 + 2*x**4/3 - 10*x + 1. Let p(v) be the third derivative of s(v). Factor p(h).
-h*(h - 1)
Let v(p) = 4*p**4 - 4*p**3 - p**2 + 5*p - 3. Let u(l) = l**4 + l**3 - 1. Suppose 4*k = k + 9. Let i be (-1)/(k/2)*3. Let b(w) = i*u(w) + 2*v(w). Factor b(c).
2*(c - 1)**2*(c + 1)*(3*c - 2)
Let k(m) be the second derivative of m**9/12096 + m**8/6720 - m**7/1680 + 5*m**3 + 6*m. Let o(y) be the second derivative of k(y). Factor o(b).
b**3*(b - 1)*(b + 2)/4
Let m = 38 - 35. Factor 9*t + 47*t**3 - 2 - 31*t**m + 2*t**2 - 25*t**3.
-(t - 1)*(t + 1)*(9*t - 2)
Let c**5 - 3246*c**2 - 2*c**4 + 3246*c**2 + c**3 = 0. What is c?
0, 1
Factor -4*x**2 - 17722*x + 152 + 2 + 17706*x + 86.
-4*(x - 6)*(x + 10)
Let g = 1/261 + 73/3654. Let m(p) be the second derivative of -2/21*p**3 + 0 + 3/7*p**2 - g*p**4 - 9*p. Solve m(c) = 0 for c.
-3, 1
Let d = 425/1716 - -1/429. Let p(z) be the first derivative of 0*z**3 - 1/12*z**6 + d*z**4 + 4 - 1/4*z**2 + 0*z + 0*z**5. Factor p(f).
-f*(f - 1)**2*(f + 1)**2/2
Let t(q) be the third derivative of 1/132*q**4 + 1/66*q**3 + 0 - 11*q**2 + 0*q + 1/660*q**5. Determine x so that t(x) = 0.
-1
Suppose -12*o - 2*b + 18 = -6*o, b - 11 = -4*o. Factor -2/11*h**4 + 2/11*h**3 - 10/11*h + 4/11 + 6/11*h**o.
-2*(h - 1)**3*(h + 2)/11
Let v(l) be the first derivative of l**4/7 - 4*l**3/3 + 22*l**2/7 - 20*l/7 - 100. Solve v(a) = 0.
1, 5
Let j be 4/2*12/8. Let w be (-3 - 0) + (-4)/((-4)/j). Factor w*x + 2/13 - 2/13*x**2.
-2*(x - 1)*(x + 1)/13
Let z(n) = -8*n**4 + 5769*n**3 - 558749*n**2 - 7. Let m(d) = 3*d**4 - 1924*d**3 + 186249*d**2 + 2. Let v(u) = -7*m(u) - 2*z(u). Suppose v(o) = 0. What is o?
0, 193
Let s(q) be the second derivative of -q**5/30 + 7*q**4/18 + 17*q**3/9 + 3*q**2 - 515*q. Factor s(m).
-2*(m - 9)*(m + 1)**2/3
Let i = 4/25 + 38/75. Let g(d) = d**2 - 5*d + 6. Let l be g(1). Determine x so that 4/3 + l*x + i*x**2 = 0.
-2, -1
Let f(x) be the third derivative of x**8/840 + 4*x**7/175 + 7*x**6/60 - 2*x**5/25 - 3*x**4/5 - 21*x**2 - 3*x. Determine y so that f(y) = 0.
-6, -1, 0, 1
Let f = 1/447 + 742/1341. Let d(p) be the first derivative of f*p**2 + 1/18*p**4 + 4 + 4/9*p + 8/27*p**3. Factor d(i).
2*(i + 1)**2*(i + 2)/9
Let l be ((-6)/21)/(39/(-273)). Suppose 3/2 - 1/2*p**l + p = 0. What is p?
-1, 3
Factor -85*f**2 - 9*f**4 - 9*f**4 - 50*f - 40*f**3 - 10*f**4 + 23*f**4.
-5*f*(f + 1)*(f + 2)*(f + 5)
Suppose 4*m + 2*b + 124 = 0, -3*m - 2*b - 103 = -9. Let c be 12/5 + 2*m/100. Determine h so that c*h - 3/5 + 3/5*h**3 - 9/5*h**2 = 0.
1
Let p(u) be the second derivative of -5*u + 11/6*u**4 + 1/30*u**6 - 4*u**3 - 2/5*u**5 + 9/2*u**2 + 0. Factor p(k).
(k - 3)**2*(k - 1)**2
Let w(m) = -m**2 - 2. Suppose 2*g - 3*g = 3*v - 29, 0 = 4*v - 4. Let x be (-17)/(-3) - (-31)/93. Let y(b) = 4*b**2 + 9. Let u(d) = g*w(d) + x*y(d). Factor u(q).
-2*(q - 1)*(q + 1)
Suppose 2*r + 12 = -2*f + f, -f = -5*r - 16. Let v(l) = -51*l**2 + 33*l - 27. Let x(z) = -13*z**2 + 8*z - 7. Let u(b) = r*v(b) + 15*x(b). Factor u(n).
3*(n - 1)*(3*n - 1)
Factor -23544/5*a - 218/5*a**3 + 1/5*a**4 + 11664/5 + 12097/5*a**2.
(a - 108)**2*(a - 1)**2/5
Let g(u) be the first derivative of 4*u**3/3 - 194*u**2 + 384*u + 200. Solve g(o) = 0.
1, 96
Let b(a) be the second derivative of a**7/1470 + a**6/210 + a**5/70 + a**4/42 + 2*a**3 - 31*a. Let g(d) be the second derivative of b(d). Factor g(o).
4*(o + 1)**3/7
Let g(s) = -s**3 - 3*s**2 + 3*s - 1. Let f be g(-4). Suppose -5*m = -6*m + f. Determine r so that -34*r + 34*r + r**m + r**4 = 0.
-1, 0
Let s(g) = 12*g**2 - g. Let j(d) = 31*d**2 + 292*d + 610. Let x(q) = -j(q) + 3*s(q). Factor x(c).
5*(c - 61)*(c + 2)
Let j(p) be the first derivative of 4*p**3/21 - 10*p**2/7 + 60. Factor j(m).
4*m*(m - 5)/7
Let v(k) = -k**3 - 8*k**2 + 7*k + 4. Let i(n) = -3*n**2 + 3*n - 3. Let c be i(2). Let h be v(c). Solve 2*m**3 + 48*m + 42 + 12*m**2 + h - m**3 = 0 for m.
-4
Let z(d) = -d**2 - 6*d - 4. Let o be z(-4). Suppose -j = o*t - 13, -5*j + j = -20. Find p such that 6*p**2 + 4*p**2 - 10*p**t - p**2 = 0.
0
Let v(y) be the third derivative of y**6/240 + y**5/40 + y**3 - 9*y**2. Let k(z) be the first derivative of v(z). Determine b so that k(b) = 0.
-2, 0
Suppose -k + 6*k = b + 212, 5*b + 1100 = 5*k. Let v = b + 2000/9. Suppose 8/9*h**3 - 10/9*h + 4/9*h**2 + v*h**5 + 4/9 - 8/9*h**4 = 0. What is h?
-1, 1, 2
Let i(s) be the third derivative of -7/8*s**4 - 3/20*s**5 + 3*s**3 + 3/40*s**6 + 1/70*s**7 + 0*s + 0 + 2*s**2. Solve i(b) = 0 for b.
-3, -2, 1
Factor -7/4*c + 9/2 - 1/4*c**2.
-(c - 2)*(c + 9)/4
Let u = -356 + 358. Let i(f) be the second derivative of -1/2*f**u + 6*f + 0 + 1/5*f**5 + f**3 - 3/4*f**4. Solve i(m) = 0.
1/4, 1
Let a(l) be the second derivative of 2*l**7/21 - l**5 + 8*l**3/3 - 135*l. Let a(k) = 0. Calculate k.
-2, -1, 0, 1, 2
Let r(w) be the second derivative of -w**6/120 + 3*w**5/80 + 3*w**4/16 + 5*w**3/24 + 97*w. Find i, given that r(i) = 0.
-1, 0, 5
Let y = -11033 - -11033. Factor l**2 + 2*l**4 + 0 + 1/2*l**5 + 5/2*l**3 + y*l.
l**2*(l + 1)**2*(l + 2)/2
Suppose 74 = 2*g + 70. Let u(t) be the first derivative of 1/3*t**2 + g - 1/18*t**3 - 2/3*t. Factor u(o).
-(o - 2)**2/6
Suppose -4*h - 2*a - 96 = 0, 5*h = a + 36 - 156. Let s be ((-8)/12)/(h/9). Factor 0 + s*v**3 + 1/4*v - 1/2*v**2.
v*(v - 1)**2/4
Let a(h) be the second derivative of -h**7/168 - h**6/30 + 3*h**5/80 + 7*h**4/24 + h**3/3 - 280*h. Let a(n) = 0. What is n?
-4, -1, 0, 2
Factor 4 - 68/5*r**3 + 112/5*r**2 - 78/5*r + 2/5*r**5 + 12/5*r**4.
2*(r - 1)**4*(r + 10)/5
Factor 17 + 4*x**2 - 64 - 12*x - 7 - 21*x - 7*x**2.
-3*(x + 2)*(x + 9)
Let j be (-22)/99*-1 + (-5)/(-18). Factor 3/2*i + 1/2*i**3 - j - 3/2*i**2.
(i - 1)**3/2
Let q be 9/((-12)/4) - (-24)/4. Solve 0 + 5/3*u**4 + 7/3*u**2 - 1/3*u**5 - 2/3*u - 3*u**q = 0 for u.
0, 1, 2
Let t be ((-4)/(-10))/(3/15). Let h = 1 + 1. Let 0*m**3 - 10*m**2 - h*m**4 - 8*m + 12*m**3 - t*m**3 + 16 - 2*m**2 = 0. Calculate m.
-1, 2
Suppose -2*w - 6 = 0, 0*u - 2*w - 6 = 5*u. Suppose -3*g - 2*g + 25 = u. Factor 4*t**g + 6*t