 that p(o) = 0.
15
Let a(v) be the second derivative of v**6/75 + 17*v**5/100 + 5*v**4/6 + 19*v**3/10 + 9*v**2/5 + 30*v + 2. Factor a(g).
(g + 2)*(g + 3)**2*(2*g + 1)/5
Solve -18*q**2 - 49*q**2 + 19*q**2 - q**3 + 49*q = 0 for q.
-49, 0, 1
Factor 1/3*s**2 + 181/3*s + 0.
s*(s + 181)/3
Let m = -27249/14 - -13628/7. Factor -m*p**2 + 1/2*p**3 - 1/2*p + 1/2.
(p - 1)**2*(p + 1)/2
Let j = 23 - 23. Suppose j + 12 = 4*l. Factor 0*n - 1/6*n**5 + 1/2*n**4 + 0 - 1/3*n**l + 0*n**2.
-n**3*(n - 2)*(n - 1)/6
Let t(k) = -20*k + 183. Let j be t(9). Let y(x) be the third derivative of 1/120*x**5 + 0 + 0*x + 1/24*x**4 + 1/12*x**j + 3*x**2. What is g in y(g) = 0?
-1
Factor 42/13*o + 0*o**2 - 40/13 - 2/13*o**3.
-2*(o - 4)*(o - 1)*(o + 5)/13
Let x(v) be the first derivative of 52/3*v**3 - 3 + 4/5*v**5 + 16*v + 24*v**2 + 6*v**4. Factor x(y).
4*(y + 1)**2*(y + 2)**2
Factor -60/7*r**3 + 0*r - 4*r**4 + 0 - 4/7*r**5 - 36/7*r**2.
-4*r**2*(r + 1)*(r + 3)**2/7
Let u(w) be the third derivative of -w**5/240 + w**4/12 - 2*w**3/3 + 4*w**2 + 3. Determine n, given that u(n) = 0.
4
Let o(n) be the second derivative of -n**4/3 + 6*n**3 + 20*n**2 + 76*n. Solve o(a) = 0 for a.
-1, 10
Factor -2*s**2 - 17 + 87 + 12*s + 53*s - 3*s**2.
-5*(s - 14)*(s + 1)
Let a(h) be the second derivative of -5/2*h**2 + 5/12*h**4 + 10*h + 0 + 0*h**3. Suppose a(p) = 0. Calculate p.
-1, 1
Let h(y) = 5*y + 33. Let z be -1 + (-6)/3 + (-4 - -1). Let q be h(z). Factor -288/5*x**2 + 6/5*x**5 - 64/5 + 176/5*x**q - 52/5*x**4 + 224/5*x.
2*(x - 2)**4*(3*x - 2)/5
Let r(k) be the second derivative of k**8/1680 + k**7/630 - k**6/45 - 2*k**5/15 - 31*k**4/12 + 8*k. Let f(c) be the third derivative of r(c). Factor f(x).
4*(x - 2)*(x + 1)*(x + 2)
Let d be (-7)/(14/(-12))*-7. Let i be (2*(-6)/d)/((-3)/(-3)). Find p such that 6/7*p - i*p**3 - 4/7 + 0*p**2 = 0.
-2, 1
Let m(k) be the first derivative of -k**4/46 + 8*k**3/69 - 5*k**2/23 + 4*k/23 + 32. What is u in m(u) = 0?
1, 2
Let r(g) = 2*g**2 + 229*g - 2221. Let m be r(9). Factor 2/13*s**3 + 0 - 2/13*s**m - 12/13*s.
2*s*(s - 3)*(s + 2)/13
Let t(a) be the third derivative of a**8/1680 + 11*a**7/525 + a**6/10 + 29*a**5/150 + 19*a**4/120 + 181*a**2. Determine n so that t(n) = 0.
-19, -1, 0
Let f be (-26)/(-3) - (-1 - (-40)/24). Let -16*z**2 + 3*z**2 - f*z**2 + 21*z - 6 + 6*z**3 = 0. Calculate z.
1/2, 1, 2
Let z(u) be the second derivative of 1/20*u**5 + 1/20*u**2 + 1/12*u**4 + 1/12*u**3 + 1/60*u**6 + 1/420*u**7 + 0 - 14*u. Factor z(l).
(l + 1)**5/10
Suppose -19*r + 8 = -17*r - 4*s, -27 = -4*r - 3*s. Let a(o) be the first derivative of -6*o + 3/2*o**2 + o**3 - r. Let a(p) = 0. Calculate p.
-2, 1
Determine t so that -1/2*t**3 + 1/2*t**2 - 1/2 + 1/2*t = 0.
-1, 1
Solve -20 - 25*u**3 + 77*u - 5*u**4 - 7*u**5 + 12*u**5 - 57*u + 25*u**2 = 0 for u.
-2, -1, 1, 2
Let c = 34399 - 34397. Factor 90 + 2/5*o**c + 12*o.
2*(o + 15)**2/5
Find a, given that -20 - 95*a**2 - 55/2*a**5 - 205/2*a**3 + 130*a + 115*a**4 = 0.
-1, 2/11, 1, 2
Let i(j) = -59*j**2 + 22*j + 39. Let g(b) = -29*b**2 + 10*b + 18. Let s(h) = 13*g(h) - 6*i(h). Let s(y) = 0. What is y?
-2/23, 0
Let g(u) be the first derivative of u**6/216 + u**5/36 - u**3 - 18. Let m(z) be the third derivative of g(z). What is n in m(n) = 0?
-2, 0
Let h(m) = -m**4 - 2*m**2 + m - 1. Let n(c) = 10*c**4 - 30*c**3 + 70*c**2 - 55*c + 20. Let j(z) = 5*h(z) + n(z). Find a such that j(a) = 0.
1, 3
Find t such that -85*t - 635*t - 244*t**2 + 96*t**3 - 71 - 4*t**4 - 329 - 24*t**3 = 0.
-1, 10
Factor 0 + 60*s - 13*s**2 + 38*s**2 - 100 - 15*s**3.
-5*(s - 2)*(s + 2)*(3*s - 5)
Let z be 5/(-10)*-1 - 35/126. Factor 4/9*p**2 - 2/9*p**3 + 0 - z*p**4 + 0*p.
-2*p**2*(p - 1)*(p + 2)/9
Let t be (-5)/(1 - (2 + 0)). Suppose j + 8 = t*j. Factor j*h + 3*h**4 + h + h**2 - 4*h**2 - 3*h**3.
3*h*(h - 1)**2*(h + 1)
Find a such that 125 - 25*a + 75*a + 5*a**2 + 0*a**2 = 0.
-5
Let m(n) be the second derivative of -n**7/147 - n**6/15 - n**5/7 - 124*n + 2. Factor m(t).
-2*t**3*(t + 2)*(t + 5)/7
Let z(t) be the third derivative of 0 + 1/60*t**6 + 0*t**4 + 0*t**3 - 4*t**2 - 1/30*t**5 + 0*t. Let z(b) = 0. Calculate b.
0, 1
Let a = -3260 + 387971/119. Let k = a + -2/17. Factor -2/7*p + k*p**2 + 0.
p*(p - 2)/7
Let p(t) be the second derivative of t**4/3 + 26*t**3/3 - 60*t**2 + 5*t - 11. Factor p(j).
4*(j - 2)*(j + 15)
Let a(v) be the first derivative of -v**3/6 - 35*v**2/4 + 144. Factor a(g).
-g*(g + 35)/2
Let b(k) be the second derivative of k + 0 - 1/60*k**6 - 1/24*k**4 + 1/4*k**3 - 3/40*k**5 + 1/2*k**2. What is q in b(q) = 0?
-2, -1, 1
Let i be (-36)/24*4/(-3). Factor -4*p**i + 34 - 15*p + 4*p**3 - 10 - 6.
(p + 2)*(2*p - 3)**2
Factor -186 + 8*u**3 + 4*u**3 - 168*u + 81*u**2 - 54 - u**3 - 5*u**3 - 3*u**4.
-3*(u - 4)**2*(u + 1)*(u + 5)
Suppose -2*j + 3*v = -2, -v = -3*j + 4*j - 6. Suppose -14*z**2 + 6*z**2 + 4*z**2 + j*z = 0. Calculate z.
0, 1
Let b(r) be the second derivative of -2*r**7/21 + 8*r**6/15 - 10*r**4/3 + 2*r**3/3 + 12*r**2 - 4*r - 13. Solve b(d) = 0 for d.
-1, 1, 2, 3
Let n(m) be the third derivative of m**6/200 + m**5/30 - 23*m**4/120 + m**3/3 - 221*m**2 + 2*m. Find x, given that n(x) = 0.
-5, 2/3, 1
Let r = 4304/3 - 1779. Let a = 345 + r. Factor 0*h - 2/3*h**3 + 0*h**2 + 0 + a*h**4.
2*h**3*(h - 1)/3
Let k(t) be the first derivative of -12/25*t**5 - 42 - 9/5*t**2 + 4/5*t**4 + 8/5*t + 4/15*t**3 + 1/15*t**6. Let k(f) = 0. What is f?
-1, 1, 4
Suppose 0 = g + 48*l - 43*l + 43, -l - 11 = -g. Factor -8/19*b + 2/19*b**g + 8/19.
2*(b - 2)**2/19
Suppose -28/9*n**3 - 18*n**2 + 8/3 + 40/9*n = 0. What is n?
-6, -2/7, 1/2
Suppose 8*b - 11*b = 4*d - 9, 2*d + 2*b - 4 = 0. Find x, given that -12/17*x**2 + 12/17 + 2/17*x**d - 2/17*x = 0.
-1, 1, 6
Suppose 0 = -3*k + 14 - 5. Solve 4*u**2 - k*u**2 - 2*u**3 + 4*u**2 + 2*u - 2*u**2 = 0.
-1/2, 0, 2
Let h(q) = 4*q**4 + 2*q**2 + q - 1. Let v(u) = 21*u**4 + 30*u**3 + 24*u**2 - 114*u - 6. Let k(g) = -6*h(g) + v(g). Solve k(b) = 0 for b.
-2, 0, 2, 10
Let z = -50 - -56. Suppose 2*x - 2*d + 4 = z*x, -5*x - 3*d + 4 = 0. Suppose -2/5*m + 0*m**x + 2/5*m**3 + 0 = 0. Calculate m.
-1, 0, 1
Let n(v) = 17*v - 4. Let a be n(1). What is f in 5*f + 23 + 7*f + a + f**3 - 20*f**2 + 3*f**3 = 0?
-1, 3
Let l be (2/26)/(((-18)/390)/(9/(-30))). Factor l*w**2 - 3*w + 9/2.
(w - 3)**2/2
Let s(u) = -5*u**4 + 30*u**3 - 61*u**2 + 18*u + 6. Let r(t) = -t**2 - 2*t + 1. Let j(w) = -6*r(w) + s(w). Factor j(x).
-5*x*(x - 3)*(x - 2)*(x - 1)
Factor -1/2*q**2 + 0 - 11/2*q.
-q*(q + 11)/2
Factor 48/7*k - 44/7 - 4/7*k**2.
-4*(k - 11)*(k - 1)/7
Let a(o) be the first derivative of -8/5*o**6 - 4/5*o**2 - 28/15*o**3 + 18 + 52/25*o**5 + 0*o + 8/5*o**4. Find m, given that a(m) = 0.
-2/3, -1/4, 0, 1
Factor 7*l**2 + 0*l - l**3 - 3*l + 2*l**3 - 12*l**2 + 10*l - 3.
(l - 3)*(l - 1)**2
Let j(d) = -8*d**2 + 48*d + 225. Let m(i) = 4*i**2 - 24*i - 112. Let s(f) = -4*j(f) - 9*m(f). Solve s(a) = 0.
-3, 9
Let t(h) be the second derivative of -h**7/105 - 8*h**6/75 - 12*h**5/25 - 17*h**4/15 - 23*h**3/15 - 6*h**2/5 - 183*h + 2. What is j in t(j) = 0?
-3, -2, -1
Suppose -5*i + 13 = -k - 10, -4*i + 14 = -3*k. Factor -7/2*g**3 + 0 + i*g**2 - 3/2*g.
-g*(g - 1)*(7*g - 3)/2
Let m(y) = y**2 - 4*y + 3. Let k be m(4). Factor -11*t**3 + 0*t**4 - 4*t**k + 5*t**3 + 4*t**2 + 6*t**4.
2*t**2*(t - 1)*(3*t - 2)
Let y(r) be the second derivative of 0 - 1/6*r**4 - 2*r - 1/9*r**3 + 2/3*r**2. Factor y(p).
-2*(p + 1)*(3*p - 2)/3
Let l**3 - 4*l**3 - 12*l**2 + l**4 + 3*l**4 + 11*l**3 = 0. What is l?
-3, 0, 1
Let k(v) be the third derivative of -v**7/5460 + 7*v**6/2340 - v**5/130 - 2*v**3/3 - 21*v**2. Let r(b) be the first derivative of k(b). Factor r(y).
-2*y*(y - 6)*(y - 1)/13
Suppose 3*p = -p + 20. Suppose -5*y - p = -15. Determine v so that -6*v + 13*v - 6*v + v**3 + 2*v**y = 0.
-1, 0
Let -22/7*i + 0 + 2/7*i**3 - 20/7*i**2 = 0. What is i?
-1, 0, 11
Factor 4/9*y**3 - 2/9 - 2/9*y + 4/9*y**2 - 2/9*y**5 - 2/9*y**4.
-2*(y - 1)**2*(y + 1)**3/9
Let s(m) be the third derivative of m**5/100 + m**4 + 39*m**3/10 + 2*m**2 - 2. Factor s(v).
3*(v + 1)*(v + 39)/5
Let r be 0 + 2 - (4 + 1 + -5). Let -10*i**2 + 1 + 39 + 6*i**r + 12*i = 0. Calculate i.
-2, 5
Suppose -5*t - 5*a = -10, 4*a - 21 = -13. Factor 2/3*r - 1/3*r**2 + t.
-r*(r - 2)/3
Let g(s) = 4*s**2 - 368*s - 16. Let c(a) = 2*a**2 - 245*a - 10. Let y(r) = 8*c(r) - 5*g(r). What is k 