 Find k, given that v(k) = 0.
-1, 4/29
Let l(r) be the second derivative of 5*r**7/42 - 8*r**6/3 + 15*r**5/4 + 2*r - 51. Factor l(z).
5*z**3*(z - 15)*(z - 1)
Factor -32/7 - 72/7*q + 0*q**3 + 4/7*q**4 - 44/7*q**2.
4*(q - 4)*(q + 1)**2*(q + 2)/7
Let v(q) be the first derivative of -729*q**4/20 - 27*q**3 - 63*q**2/10 - 3*q/5 + 60. Factor v(d).
-3*(3*d + 1)*(9*d + 1)**2/5
Factor 3/4*q**2 + 0*q + 0 + 9/8*q**3 - 3/8*q**5 + 0*q**4.
-3*q**2*(q - 2)*(q + 1)**2/8
Let v be 3 - (-9*(-8)/(-12) + 3). Let d(f) be the first derivative of v + 0*f**4 + 2/35*f**5 - 2/7*f**3 + 0*f + 2/7*f**2. Let d(q) = 0. Calculate q.
-2, 0, 1
Let n(h) be the third derivative of h**6/270 - 2*h**5/135 - 4*h**4/27 + 214*h**2. Solve n(a) = 0 for a.
-2, 0, 4
Suppose -9*w**4 + 5*w**4 + 2139*w**3 + 40*w**2 - 2175*w**3 = 0. What is w?
-10, 0, 1
Let a be (-9831)/(-1017) - (1 - -8). Let y = 58 - 40. Factor -a*c**3 - 6*c**2 - 18 - y*c.
-2*(c + 3)**3/3
Suppose -5/2*k**2 + 310*k - 9610 = 0. Calculate k.
62
Suppose 0 = -3*x + 4*x + 5*x. Let y(m) be the first derivative of 5/2*m**4 + m**6 + 14/5*m**5 + 0*m**2 - 5 + 2/3*m**3 + x*m. Find o, given that y(o) = 0.
-1, -1/3, 0
Let g(d) be the first derivative of -d**5/5 - 5*d**4/2 - 4*d**3 + 36*d**2 + 384. Let g(k) = 0. Calculate k.
-6, 0, 2
Determine l, given that -24*l**3 + 0 - 5776/7*l + 2052/7*l**2 + 4/7*l**4 = 0.
0, 4, 19
Find s such that -12/5 - 3/5*s**4 + 12/5*s - 6/5*s**3 + 9/5*s**2 = 0.
-2, 1
Suppose -9*p + 84 + 60 = 0. Let u be 8/4 + 2/(p/(-4)). Factor 0*h**4 - u*h**3 + 3/4*h + 3/4*h**5 + 0 + 0*h**2.
3*h*(h - 1)**2*(h + 1)**2/4
Suppose 2*c + 2 = 5*p, 167 = 4*p + 5*c + 172. Let d(k) be the first derivative of 3/7*k - 1/7*k**3 + 4 + p*k**2. Factor d(l).
-3*(l - 1)*(l + 1)/7
Let n(u) be the third derivative of u**6/27 - u**5/45 - 5*u**4/27 + 2*u**3/9 + 306*u**2. Determine b so that n(b) = 0.
-1, 3/10, 1
Let x(f) = 7*f**3 + 10*f**2 - 12*f - 32. Let y(m) = -27*m**3 - 39*m**2 + 48*m + 126. Let d(b) = 15*x(b) + 4*y(b). Factor d(v).
-3*(v - 2)*(v + 2)**2
Let j(o) be the third derivative of -o**6/200 + 7*o**4/40 - 3*o**3/5 - 90*o**2. What is d in j(d) = 0?
-3, 1, 2
Let o(m) be the second derivative of 130321*m**6/270 + 13718*m**5/45 + 722*m**4/9 + 304*m**3/27 + 8*m**2/9 - 48*m. Factor o(j).
(19*j + 2)**4/9
Find z such that -11*z + 78/7 - 1/7*z**2 = 0.
-78, 1
Factor -2/5*s**2 + 44/5 + 42/5*s.
-2*(s - 22)*(s + 1)/5
Let x(h) be the third derivative of 1/24*h**6 - h**2 + 0 + 5/8*h**4 + 0*h**3 + 1/3*h**5 + 0*h. Factor x(u).
5*u*(u + 1)*(u + 3)
Factor 432/5*z**2 - 4/5*z**5 - 324/5*z + 0 + 48/5*z**4 - 216/5*z**3.
-4*z*(z - 3)**4/5
Let z(k) be the third derivative of k**7/420 + 19*k**6/720 + 13*k**5/360 - 19*k**4/144 - 4*k**3/9 - 623*k**2. Determine g, given that z(g) = 0.
-16/3, -1, 1
Let v(x) = 429*x + 2149. Let b be v(-5). Factor -8/3*s**2 - 8/3*s + 0 + 2/3*s**b + 2/3*s**3.
2*s*(s - 2)*(s + 1)*(s + 2)/3
Let a be (-17)/(-18) - (-232)/(-522). Factor -1/2*l**4 + 0 + a*l**2 + 0*l + 0*l**3.
-l**2*(l - 1)*(l + 1)/2
Suppose 0 = -4*i + 40 + 12. Let a = i - 11. What is z in -2*z**3 + 2 - 10*z - a*z**3 - 10*z**3 + 20*z**2 - 2*z**5 - 6*z**3 + 10*z**4 = 0?
1
Let x = 276 + -191. Let q = x - 167/2. Factor 0 - q*g**2 - 3/2*g**4 + 0*g + 3*g**3.
-3*g**2*(g - 1)**2/2
Let o(g) = -g**3 - 9*g**2 - 4*g - 8. Let k be o(-13). Find v, given that -k*v + 720*v - 4 + 4*v**2 = 0.
-1, 1
Let f be 1887/(-378) + 23 + -18. Let v(o) be the second derivative of 0 + 0*o**2 + 0*o**3 - 1/90*o**6 + f*o**7 - 1/60*o**5 + 1/36*o**4 - 5*o. Factor v(p).
p**2*(p - 1)**2*(p + 1)/3
Factor 1554*y**2 - 24 + 340*y**3 - 759*y - 866*y**2 - 245*y.
4*(y - 1)*(y + 3)*(85*y + 2)
Let f(r) be the first derivative of -r**4/4 + 13*r**3/3 - 5*r**2 - 24*r + 86. Factor f(w).
-(w - 12)*(w - 2)*(w + 1)
Suppose -26/3*y**2 - 10*y**3 + 4/3*y + 0 = 0. Calculate y.
-1, 0, 2/15
Let x(k) be the third derivative of 0*k - 19*k**2 - 1/76*k**4 + 0*k**3 - 1/1140*k**6 + 0 - 2/285*k**5. Factor x(p).
-2*p*(p + 1)*(p + 3)/19
Let f be (-1)/2 - (5 - 74/12). Find m such that -16/9*m**4 + 2/3*m**5 + f*m**3 + 0 + 0*m + 4/9*m**2 = 0.
-1/3, 0, 1, 2
Let b(w) be the third derivative of 7*w**6/480 + 37*w**5/240 + 5*w**4/48 + 2*w**2 - 58*w. Factor b(x).
x*(x + 5)*(7*x + 2)/4
Let n(i) be the second derivative of 1/6*i**3 - i - 1/4*i**5 + 0 - 1/3*i**4 + 0*i**2. Factor n(s).
-s*(s + 1)*(5*s - 1)
Let j(k) be the second derivative of -k**8/336 + k**6/120 + 3*k**2/2 + k. Let b(d) be the first derivative of j(d). Factor b(a).
-a**3*(a - 1)*(a + 1)
Let j(b) = -b**3 - 4*b**2 - 6*b + 4. Let g be j(-4). Factor 0 - g*o**2 + 1 + 59*o**2 - 32*o**2.
-(o - 1)*(o + 1)
Let h(p) be the second derivative of -1/24*p**4 + 2*p**2 + 1/6*p**3 + 0 + 22*p. Let h(x) = 0. What is x?
-2, 4
Suppose 3*l - 7 = 4*a, 5*a + 5*l + 2 - 37 = 0. Factor -3/2 - 1/4*d + 1/4*d**a.
(d - 3)*(d + 2)/4
Let r = 2 + 1. Factor -1 + 3*f**2 - 5*f**2 + 8*f + r*f**2 + 17.
(f + 4)**2
Determine j so that 37*j + 2*j - 33*j**2 - 7*j + j**3 = 0.
0, 1, 32
Let d(y) be the first derivative of -y**6/3 + 112*y**5/45 - 31*y**4/6 + 4*y**3/3 - 137. Factor d(x).
-2*x**2*(x - 3)**2*(9*x - 2)/9
Let i = 1093/3009 + -30/1003. Determine j so that -1/3*j + i*j**3 + 4/3*j**2 - 4/3 = 0.
-4, -1, 1
Let p(l) be the first derivative of l**4/5 - 8*l**3/15 - 26*l**2/5 - 8*l + 66. Factor p(g).
4*(g - 5)*(g + 1)*(g + 2)/5
Let i = 29/956 - -274021/106116. Let o = i - -2/37. Factor 0*f + 0 + 2/3*f**5 + 4/3*f**2 + o*f**4 + 10/3*f**3.
2*f**2*(f + 1)**2*(f + 2)/3
Let b(r) be the third derivative of r**6/280 + 2*r**5/35 + 3*r**4/14 - 93*r**2. Suppose b(o) = 0. What is o?
-6, -2, 0
Let u(k) be the third derivative of 0*k**5 + 0*k**3 + 1/720*k**6 - 25*k**2 + 1/1260*k**7 + 0 + 0*k**4 + 0*k. Factor u(w).
w**3*(w + 1)/6
Suppose 0*f + 5*f - 40 = 0. Find r such that f*r**2 - r + 2*r**3 - r**3 - 2 - 6*r**2 = 0.
-2, -1, 1
Let f(t) be the second derivative of -t**4/60 + 34*t**3/15 - 578*t**2/5 - 25*t. Suppose f(k) = 0. What is k?
34
Let y(s) be the third derivative of 0*s**3 + 27*s**2 - 1/1155*s**7 + 0 + 1/132*s**4 - 1/110*s**5 + 1/220*s**6 + 0*s. Suppose y(t) = 0. What is t?
0, 1
What is w in 8*w - 6 - 3/2*w**2 - 1/2*w**3 = 0?
-6, 1, 2
Let m(z) = -z**2. Let s(y) = -3*y**2 + 40*y. Let x(a) = 2*m(a) + s(a). Find f, given that x(f) = 0.
0, 8
Factor -2/5*r**3 + 6/5*r**2 + 0 + 8/5*r.
-2*r*(r - 4)*(r + 1)/5
Let h(f) = 2*f**4 - 8*f**3 - 52*f**2 + 270*f - 326. Let a(x) = -4*x**4 + 17*x**3 + 103*x**2 - 540*x + 653. Let d(b) = 2*a(b) + 5*h(b). Factor d(j).
2*(j - 3)**3*(j + 6)
Let d(i) be the third derivative of -1/18*i**4 + 13*i**2 + 0*i**3 + 0*i + 0 - 1/180*i**5. Let d(g) = 0. Calculate g.
-4, 0
Let c(p) be the second derivative of p**6/30 + 6*p**5/5 + 52*p**4/3 + 128*p**3 + 512*p**2 - 107*p - 1. Factor c(x).
(x + 4)**2*(x + 8)**2
Find p such that -6*p - 22/5*p**2 + 28/5 = 0.
-2, 7/11
Suppose 4*l + 5*q + 1070 = 0, -9*q + 5*q = -5*l - 1317. Let n = l + 268. Factor 2/7*r + 0*r**2 - 1/7*r**4 - 2/7*r**n + 1/7.
-(r - 1)*(r + 1)**3/7
Let p(h) = h**2 + 4*h - 1. Let k be p(-5). Let o(b) = 10*b**2 - 7*b + 4. Let u be o(k). Factor -u*w - 2*w**2 + 2*w**3 + 136*w.
2*w**2*(w - 1)
Let o = -42739/20 - -2137. Let q(c) be the first derivative of -o*c**5 + 3/16*c**4 + 0*c + 9 - 1/4*c**3 + 1/8*c**2. Find v such that q(v) = 0.
0, 1
Let o(t) be the first derivative of -81*t**4/16 + 123*t**3/4 - 93*t**2/4 + 6*t + 52. Find h such that o(h) = 0.
2/9, 1/3, 4
Factor -1837*m**4 + 30 - 1837*m**4 + 3670*m**4 - 6 + 28*m**3 - 20*m**2 - 28*m.
-4*(m - 6)*(m - 1)**2*(m + 1)
Suppose 0 = 3*t - 4 + 19. Let b be 1/(t/2)*-25. Factor -5*w - b*w**2 + 11*w**2 + 3*w + 3*w.
w*(w + 1)
Let o = -15/34 + 353/646. Find v such that -18/19*v**3 + 2/19*v - 22/19*v**4 - 8/19*v**5 - o*v**2 + 0 = 0.
-1, 0, 1/4
Suppose 0 = -j + 8 + 11. Let d = j - 7. Factor -u - u + 7*u**4 + d*u**3 + 3*u**2 + 5*u**4 - 5*u**4.
u*(u + 1)**2*(7*u - 2)
Let w(x) = -3*x**4 - 9*x**3 - 18*x**2 - 12*x. Let f = -36 + 37. Let p(t) = t**3 + t**2. Let o(h) = f*w(h) + 18*p(h). Factor o(z).
-3*z*(z - 2)**2*(z + 1)
Let q(p) = 8*p**2 - 9*p - 3. Let u(s) = 7*s**2 - 8*s - 3. Suppose -3*x + 4 = 3*b + 16, 22 = -x + 5*b. Let g(a) = x*u(a) + 6*q(a). Factor g(r).
-(r - 3)*(r + 1)
Suppose 4/5*x**3 - 36/5*x + 18/5 - 2/5*x**2 = 0. What is x?
-3, 1/2, 3
Let u be (-3 + 4)/(0 - -1). Suppose s + u = 2, -2*s = -3*r + 4. Factor 0 - t**r - 2*t**2 - 