**2. Determine p so that k(p) = 0.
-1, 1
Factor 863*x**3 + 63*x - 63*x - 84*x**2 - 859*x**3.
4*x**2*(x - 21)
Let c(k) be the first derivative of k**4/4 - 7*k**3/3 - 4*k**2 - 700. Let c(u) = 0. Calculate u.
-1, 0, 8
Suppose 4/9 - 40/9*s**3 - 74/9*s - 118/9*s**2 = 0. Calculate s.
-2, -1, 1/20
Let p = -1148/423 - -138/47. Factor -48 - 4*r**2 - p*r**3 - 24*r.
-2*(r + 6)**3/9
Let t be (-45)/25 + 4 + -2. Let n(f) be the first derivative of -2/25*f**5 + t*f**2 + 2 + 0*f + 2/15*f**3 - 1/10*f**4. Factor n(w).
-2*w*(w - 1)*(w + 1)**2/5
Let r(q) be the first derivative of -2*q**5/45 + 2*q**4/9 - 2*q**3/27 - 2*q**2/3 - 53. Factor r(g).
-2*g*(g - 3)*(g - 2)*(g + 1)/9
Let v be -2 - (10/20 + -3). Factor -v + 1/2*i**2 + 0*i.
(i - 1)*(i + 1)/2
Let m(u) be the first derivative of 28 + 1/22*u**4 - 50/11*u - 2/3*u**3 + 35/11*u**2. Factor m(k).
2*(k - 5)**2*(k - 1)/11
Let q(c) be the second derivative of -3*c**5/20 + c**4 + 5*c**3/2 - 46*c. Let q(w) = 0. What is w?
-1, 0, 5
Let v(r) be the second derivative of r**5/10 + 2*r**4/3 - 5*r**3/3 - 6*r + 2. Find d, given that v(d) = 0.
-5, 0, 1
Suppose -160 = -0*w - 5*w. Factor 1 - 1 + d**2 + 33*d - w*d.
d*(d + 1)
Let u(z) be the first derivative of z**6/2 + 3*z**5 - 3*z**4/4 - 5*z**3 + 123. Factor u(c).
3*c**2*(c - 1)*(c + 1)*(c + 5)
Let t(l) be the second derivative of 0 - 10/3*l**3 + 9*l - 1/3*l**4 + 0*l**2. Factor t(z).
-4*z*(z + 5)
Let m be (127 + -4 + 0)*(-3)/(-9). Let l = 41 - m. Factor 0*x**2 + 2/3*x**4 + 0 + l*x - x**5 + 1/3*x**3.
-x**3*(x - 1)*(3*x + 1)/3
Suppose -8 = k - 5*q + 19, 16 = -4*k - 3*q. Let f be ((-3)/6)/(k - (-18)/3). Factor 0 + 1/4*u**2 + f*u - 1/4*u**3.
-u*(u - 2)*(u + 1)/4
Let v(m) be the third derivative of m**9/5040 - m**8/2240 - m**7/1680 - 29*m**5/60 - 20*m**2. Let f(n) be the third derivative of v(n). Factor f(i).
3*i*(i - 1)*(4*i + 1)
Let d(t) be the second derivative of -t**3/3 - 6*t**2 - t. Let n be d(-7). Let -p - n*p**2 + p**2 + p = 0. Calculate p.
0
Let n = 6539/3 - 2179. Find d, given that n + 0*d - 2/3*d**2 = 0.
-1, 1
Let b be (-55)/(-19) - (2 - (-600)/(-285)). Suppose -1 + 1/3*j - 1/3*j**b + j**2 = 0. Calculate j.
-1, 1, 3
Let n(o) = -2*o**5 + o**4 + o**2 + 4*o + 6. Let f(u) = -u**3 + u + 1. Let v(x) = 6*f(x) - n(x). Determine c, given that v(c) = 0.
-1, 0, 1/2, 2
Let r(a) be the second derivative of 27*a + 0*a**2 + 0*a**6 - 3/5*a**5 + 2/21*a**7 + 0 - 2/3*a**4 + 0*a**3. Let r(i) = 0. What is i?
-1, 0, 2
Let f = 5 - -3. Let g be ((-10)/(-4))/(4/f). Let 2 - 31*u**5 + 18*u**2 + 6 - 62*u**3 + 7*u**g - 80*u**4 + 32*u = 0. What is u?
-2, -1, -1/2, 2/3
Suppose 3 = 5*z - 12. What is d in -5*d + 2*d**5 - 10*d**4 + 10*d**2 - 3 + 3*d**5 + z = 0?
-1, 0, 1
Solve 3*n**2 + 3*n**5 - 215*n**3 + 3*n**2 + 206*n**3 = 0 for n.
-2, 0, 1
Let o(a) be the first derivative of -16*a**3/3 + 62*a**2 - 84*a + 110. Solve o(n) = 0 for n.
3/4, 7
Let j(r) be the third derivative of -r**5/360 + 25*r**4/24 - 625*r**3/4 + 39*r**2 + 3*r. Factor j(c).
-(c - 75)**2/6
Suppose 0 = 5*n - 20, -y + 4*y - 431 = -2*n. Let o = y - 141. Let o + 0*g**2 + 2/5*g - 2/5*g**3 = 0. Calculate g.
-1, 0, 1
Let s(m) = -m + 12. Let f be s(0). Let g = 17 - f. Factor -3*z - 6 - 2*z**2 + g*z**2 + z**2 - z**2.
3*(z - 2)*(z + 1)
Let q(u) be the second derivative of -u**4/30 + u**3/5 - 2*u**2/5 + 16*u. Determine p, given that q(p) = 0.
1, 2
Let g(r) be the third derivative of -2/3*r**3 + 13/270*r**5 + 0*r - 7/540*r**6 + 1/945*r**7 + 0 + 1/36*r**4 + 9*r**2. Factor g(v).
2*(v - 3)**2*(v - 2)*(v + 1)/9
Suppose -31*p = -8*p - 46. Let l be ((-24)/(-45))/((-3)/(-27)). Determine m so that -p*m**3 + l*m**2 + 4/5 - 18/5*m = 0.
2/5, 1
Let u(r) = -10*r**3 + 300*r**2 - 3005*r + 9990. Let c(x) = 15*x**3 - 450*x**2 + 4508*x - 14984. Let d(v) = -5*c(v) - 8*u(v). Factor d(g).
5*(g - 10)**3
Let q(i) be the first derivative of -10*i**6/3 + 7*i**5 + 55*i**4/2 - 95*i**3/3 - 15*i**2 - 218. Let q(j) = 0. Calculate j.
-2, -1/4, 0, 1, 3
Let d(o) be the first derivative of -o**6/165 + 3*o**5/110 - 4*o**3/33 + 46*o - 23. Let r(q) be the first derivative of d(q). Let r(i) = 0. Calculate i.
-1, 0, 2
Let p(o) be the third derivative of -o**8/420 - 8*o**7/525 + 11*o**6/150 + 26*o**5/75 - 14*o**4/15 - 16*o**3/3 + 85*o**2 + 1. Find v such that p(v) = 0.
-5, -2, -1, 2
Let s = 2/335 + 7/1072. Let i(p) be the third derivative of -3*p**2 + 0*p + 0 + 0*p**3 - 1/60*p**5 + 0*p**4 - s*p**6. Determine q so that i(q) = 0.
-2/3, 0
Let -4/3 + 5/3*l - 1/3*l**2 = 0. What is l?
1, 4
Factor 4327*c**4 + 82*c + 423*c**2 - 1337*c**4 - 1058*c**5 + 107*c**2 - 2630*c**3 + 8 + 78*c.
-2*(c - 1)**3*(23*c + 2)**2
Let k(x) be the first derivative of -3/2*x**3 - 3/8*x**4 - 22 - 9/4*x**2 - 3/2*x. Solve k(y) = 0.
-1
Factor 792025 - b**3 + 7*b - 5*b**2 + 5*b - 791989.
-(b - 3)*(b + 2)*(b + 6)
Suppose -20 = 2*z - 6*z. Let a(f) = -f**2 + f - 1. Let u(x) = 6*x**2 - 12*x + 13. Let j(p) = z*u(p) + 35*a(p). Factor j(r).
-5*(r - 1)*(r + 6)
Let h(o) be the second derivative of 2/3*o**3 + 0 - 1/12*o**4 - 2*o**2 - 11*o. Let h(f) = 0. What is f?
2
Solve -32/3*i**4 + 88/3*i**2 + 304/3*i - 92/3*i**3 + 4/3*i**5 + 160/3 = 0 for i.
-2, -1, 2, 10
What is r in 192 - 94*r**3 + 320*r - 2/3*r**5 - 16*r**4 + 148/3*r**2 = 0?
-12, -1, 2
Let q = 58 + -172/3. Let g(m) be the second derivative of -q*m**2 + 1/9*m**4 - 7/30*m**5 + 10*m + 7/9*m**3 + 0. Factor g(d).
-2*(d - 1)*(d + 1)*(7*d - 2)/3
Let k(y) = -y**3 - 5*y**2 + 5*y - 6. Let a be k(-6). Factor 13*n**3 + 2*n - 9*n**3 + 4*n**2 + a*n - 6*n - 4*n**4.
-4*n*(n - 1)**2*(n + 1)
Let 16/19 + 50/19*d**3 - 100/19*d**2 - 14/19*d**5 + 24/19*d**4 + 24/19*d = 0. Calculate d.
-2, -2/7, 1, 2
Let w(t) be the third derivative of t**7/210 - 19*t**6/120 + 9*t**5/4 - 425*t**4/24 + 250*t**3/3 + 68*t**2. Let w(x) = 0. What is x?
4, 5
Let s be 6 + 502*3/(-252). Let g(d) be the second derivative of -s*d**7 + 6*d + 0*d**2 + 0 + 3/20*d**5 + 0*d**3 - 1/6*d**4 + 0*d**6. Solve g(p) = 0 for p.
-2, 0, 1
Let z = 2308 + -2306. Let n(q) be the first derivative of -1/10*q**4 + 1/5*q**z - 4/5*q + 4/15*q**3 + 11. Factor n(g).
-2*(g - 2)*(g - 1)*(g + 1)/5
Suppose -17 - 103 = -12*z. Suppose -30*t = -50 - z. Factor 2/9*a**t - 2/9*a**3 + 2/9*a - 2/9.
-2*(a - 1)**2*(a + 1)/9
Let b(m) be the first derivative of -2/15*m**3 - 1/10*m**4 + 1/5*m**2 + 0*m - 12 + 2/25*m**5. Factor b(a).
2*a*(a - 1)**2*(a + 1)/5
Let r(b) be the first derivative of -5*b**7/42 + b**6/2 - 3*b**5/4 + 5*b**4/12 + 12*b - 11. Let q(w) be the first derivative of r(w). Let q(u) = 0. What is u?
0, 1
Let r(n) = n**2 + 64*n - 128. Let j be r(-66). Let f(m) be the second derivative of -1/39*m**3 + 0 + 1/130*m**5 - 3/13*m**2 + 1/26*m**j - m. Factor f(o).
2*(o - 1)*(o + 1)*(o + 3)/13
Let s(x) be the third derivative of 5*x**8/336 + x**7/21 - x**5/6 - 5*x**4/24 + 76*x**2. Suppose s(k) = 0. Calculate k.
-1, 0, 1
Suppose -2*k = 2*u + 2, -7*u - 4*k = -20*u + 55. Suppose 0*f**2 + 0*f**4 - 2/3*f**5 + 0*f**u + 0 + 0*f = 0. What is f?
0
Let n(v) = 4*v**4 + 140*v**3 + 2594*v**2 + 4758*v + 2314. Let l(t) = -9*t**4 - 280*t**3 - 5192*t**2 - 9515*t - 4629. Let k(g) = 2*l(g) + 5*n(g). Factor k(u).
2*(u + 1)**2*(u + 34)**2
Let j = -1661/2 - -844. Let s(c) be the first derivative of 3 - j*c - 1/8*c**4 - 27/4*c**2 - 3/2*c**3. Factor s(b).
-(b + 3)**3/2
Suppose v - 17 = -l, 2*v - 14 = -6. Suppose -3*m**2 + 5*m**2 + 21*m**4 - 14*m**4 - 4*m - l*m**4 + 8*m**3 = 0. Calculate m.
-2/3, 0, 1
Factor -8/5 - 2/15*a**2 - 14/15*a.
-2*(a + 3)*(a + 4)/15
Let a = -98 - -104. Let l(i) be the third derivative of 0 + 2*i**2 + 1/12*i**a - 5/12*i**4 - 1/15*i**5 + 2/3*i**3 + 0*i. Factor l(m).
2*(m - 1)*(m + 1)*(5*m - 2)
Let t(f) be the first derivative of 2*f**5/15 - 2*f**4/3 - 10*f**3/3 + 6*f**2 - 392. Determine n, given that t(n) = 0.
-3, 0, 1, 6
Factor -81/2*n**3 - 15/2*n + 0 + 91/2*n**2 + 5/2*n**4.
n*(n - 15)*(n - 1)*(5*n - 1)/2
Let k(u) be the first derivative of -u**4/4 - 7*u**3/3 - 3*u**2 + 16. Suppose k(c) = 0. What is c?
-6, -1, 0
Let x be (1 - 4/3) + 308/528. Let l(z) be the second derivative of 3/40*z**5 + 0*z**2 - 3*z + 0 + x*z**4 + 1/3*z**3 + 1/120*z**6. Suppose l(y) = 0. What is y?
-2, 0
Suppose s - 21 = -19. Let f be 1/s - (-3)/(5*-6). Solve -1/5*n**2 + 3/5*n - f = 0 for n.
1, 2
Let r = 24 - 23. Suppose -2*g - 5*g**2 + r - 1 + 14*g**4 + 2*g**3 - 9*g**4 = 0. Calculate g.
-1, -2/5,