5*w**2. Factor m(h).
-h*(h + 4)/5
Let k(d) = 7*d**2 - 723*d + 15782. Let w(l) = -20*l**2 + 2025*l - 44190. Let h(p) = 45*k(p) + 16*w(p). What is x in h(x) = 0?
-42, 15
Let f = -6/1087 - -6757/1027215. Let i(m) be the third derivative of 0*m + f*m**7 + 1/45*m**5 + 0 + 1/27*m**3 + 16*m**2 + 1/135*m**6 + 1/27*m**4. Factor i(j).
2*(j + 1)**4/9
Suppose 2*q = 31 - 53. Let u(p) = -p**3 - 11*p**2 - p - 9. Let s be u(q). Let -2522 + 2522 + 3*z - z**s = 0. Calculate z.
0, 3
Let w(y) be the third derivative of -y**5/420 - 19*y**4/84 - 31*y**3/6 + 1153*y**2. Let w(r) = 0. Calculate r.
-31, -7
Let v = -6 + 9. Suppose -2*m = -4*l - 2 + 12, 5*l = 3*m + 13. Let 44*w**3 - 24*w - v*w**2 - 45*w**3 - 8*w**l + 36 = 0. What is w?
-6, 1
Let r(j) = -j**2 + 8*j + 1. Let s be r(4). Let -2*f + 4*f**3 + 2*f**3 - 8*f**3 - 8*f**2 + s - 5 = 0. What is f?
-3, -2, 1
Let n be 102/4*(-16)/(-6). Suppose n = -8*g + 12*g. Factor -81 + 18*w - 33*w**2 + g*w**2 + 15*w**2.
-(w - 9)**2
Suppose -31*z - 18*z - 5439 = 0. Let v = 113 + z. Factor -2/15*j**v - 4/15*j + 2/5.
-2*(j - 1)*(j + 3)/15
Let s(j) = 3*j**2 - 11*j - 2. Let p(i) = -i + 5. Let b be p(1). Let w be s(b). Factor 4*u**w - 2*u - 2*u**4 - 5*u**2 - 6*u**3 + u**2 - 6*u**2.
-2*u*(u + 1)**3
Suppose 0*c - g = 5*c, 0 = -g. Let z = -2770 + 2772. Suppose 21/5*t**z - 9/5*t**4 - 9/5*t**3 + 18/5*t + 3/5*t**5 + c = 0. Calculate t.
-1, 0, 2, 3
Let r be -2 + -46*(-18)/(-54) + 18. Factor 34/3*v + r*v**2 - 12.
2*(v - 1)*(v + 18)/3
Let w(n) be the second derivative of n**7/147 - 38*n**6/105 + 17*n**5/35 + 8*n**4/3 - 5*n**3/3 - 74*n**2/7 + 87*n + 13. Solve w(m) = 0 for m.
-1, 1, 2, 37
What is x in 1440*x - 1237*x**2 + 1235*x**2 - 156455 - 102745 = 0?
360
Factor 8/3 + 1/3*i**3 + 10/3*i**2 + 17/3*i.
(i + 1)**2*(i + 8)/3
Let l(i) be the third derivative of i**5/30 - 125*i**4 + 187500*i**3 - 2*i**2 + 2*i - 3345. Determine b so that l(b) = 0.
750
Let s = -199/12 - -863/52. Let b(f) be the second derivative of -13*f + 1/130*f**5 - 2/13*f**3 + 0*f**2 + 0 + s*f**4. Let b(a) = 0. Calculate a.
-3, 0, 2
Factor 181*r**2 + 1172*r + 288*r + 500 + 414*r**2 - 80 - 15*r**3.
-5*(r - 42)*(r + 2)*(3*r + 1)
Let i = -9 + 12. Suppose -i*h - 2*b + 18 = 0, 0 = 5*b - 11 - 4. Factor -2750*w**2 - h*w**5 + 4*w**3 + 2750*w**2.
-4*w**3*(w - 1)*(w + 1)
Let v(a) be the first derivative of -4/3*a**3 + 0*a - 103 + 30*a**2. Suppose v(x) = 0. Calculate x.
0, 15
Let x(a) be the second derivative of -a**8/13440 + a**7/840 - a**6/180 - a**4/2 + a**3 + 8*a + 16. Let s(z) be the third derivative of x(z). Solve s(w) = 0.
0, 2, 4
Let w(j) = -62*j**3 + 36*j**2 - 124*j - 4. Let r(p) = -109*p**3 + 71*p**2 - 247*p - 7. Let q(a) = -4*r(a) + 7*w(a). Factor q(m).
2*m*(m - 10)*(m - 6)
Let a(z) be the second derivative of z**7/945 + z**6/1080 - z**5/270 - z**4/216 + 63*z**2 - 26*z. Let t(o) be the first derivative of a(o). Factor t(s).
s*(s - 1)*(s + 1)*(2*s + 1)/9
Suppose 20*t - 1108 = -848. Let j(m) be the first derivative of -3/14*m**4 + 1/21*m**6 + 2/7*m**2 + 0*m - 2/35*m**5 - t + 2/21*m**3. Let j(w) = 0. Calculate w.
-1, 0, 1, 2
Let g(z) be the second derivative of -58*z + 1/6*z**3 + 3/4*z**2 + 1/72*z**4 + 0. Let g(h) = 0. Calculate h.
-3
Let b(g) be the third derivative of -g**11/665280 + g**9/120960 - 19*g**5/60 + 63*g**2. Let y(u) be the third derivative of b(u). Suppose y(l) = 0. What is l?
-1, 0, 1
Let v(f) be the second derivative of 3*f**7/1400 + 7*f**6/600 - f**5/120 - 5*f**4/24 + f**3/2 - f + 5. Let u(m) be the second derivative of v(m). Factor u(p).
(p - 1)*(3*p + 5)**2/5
Let q = 26/4457 + 17750/13371. Factor q*b**2 + 10/3*b**3 + 0*b + 0.
2*b**2*(5*b + 2)/3
Let d = -10935 + 10939. What is x in -x**3 + 32/5*x + 32/5 + 1/5*x**d - 6/5*x**2 = 0?
-2, -1, 4
Let q = -501 + 501. Suppose -5*w = -4*j + 16, 0 = 4*w - j + 3 + 1. Factor q - 3/5*x**4 + w*x + 0*x**3 - 3/5*x**5 + 0*x**2.
-3*x**4*(x + 1)/5
Let w be ((-3)/(15/(-10)))/((-5)/10). Let l be 10 - 3 - (-26)/w. Factor j**2 + l*j - 1/2*j**3 - 1.
-(j - 2)*(j - 1)*(j + 1)/2
Let w(s) be the third derivative of -s**7/420 - s**6/60 + s**5/24 + 3*s**4/4 + 3*s**3 - 9*s**2 - 48*s. Determine l, given that w(l) = 0.
-3, -2, 3
Factor -4*l**4 + 10*l**3 - 8*l**2 + 0 + 0*l + 1/2*l**5.
l**2*(l - 4)*(l - 2)**2/2
Let m(b) = 2*b**2 + 42*b + 127. Let g be m(-3). Suppose -5*i = -2*c - g, 172*c - 169*c - 29 = -4*i. Factor -f**2 - 1/2*f**4 + 3/2*f**c + 0*f + 0.
-f**2*(f - 2)*(f - 1)/2
Let a(q) = 84*q**2 + 399*q - 887. Let f(t) = -26*t**2 - 134*t + 296. Let c(o) = -4*a(o) - 13*f(o). Factor c(y).
2*(y - 2)*(y + 75)
Let h(d) be the second derivative of d**6/105 + 41*d**5/70 + 73*d**4/7 + 320*d**3/21 - 800*d**2/7 - 556*d. Suppose h(n) = 0. Calculate n.
-20, -2, 1
Let b = -773 - -798. Factor -b*x**3 - 215*x**2 + 5462*x - 2635*x - 2737*x.
-5*x*(x + 9)*(5*x - 2)
Let o = -37 + 14. Let r = o - -27. Factor -c**4 - 7*c**4 - 36*c**3 - 9*c**2 - 13*c**r - c + 7*c.
-3*c*(c + 1)**2*(7*c - 2)
Let w(v) = -v**3 - 42*v**2 - 80*v - 3. Let o be w(-40). Let j(p) = -23*p**3 + 35*p**2 + 7*p - 3. Let t(i) = i**3 + i + 1. Let q(y) = o*t(y) - j(y). Factor q(n).
5*n*(n - 2)*(4*n + 1)
Suppose -369 = 19*h - 27. Let k be (6 + -3 - 0)*(-8)/h. Factor -44*n**2 + k*n**3 - 5324/3 + 484*n.
4*(n - 11)**3/3
Suppose -111*p + 2104 = -782. Let v(u) be the first derivative of -3/8*u**4 - 1/2*u - 5/4*u**2 + p - 7/6*u**3. Determine i, given that v(i) = 0.
-1, -1/3
Let c = 66152 - 200618/3. Let q = c - -721. Factor -1/3*i**3 + 0 - q*i + 2/3*i**2.
-i*(i - 1)**2/3
Let a = -187 - -190. Factor -417605 + a*p**4 - 340*p**3 - 34633*p - 8670*p**2 - 63627*p - 8*p**4.
-5*(p + 17)**4
Factor 34 + 13*f + 52869*f**2 + f**3 + 2*f - 52887*f**2.
(f - 17)*(f - 2)*(f + 1)
Suppose 0 + 0*s - 12/5*s**3 + 36/5*s**2 - 3/5*s**4 = 0. What is s?
-6, 0, 2
Let -268/15*a**2 - 22/5*a**3 - 98/5*a - 4/15*a**4 - 88/15 = 0. What is a?
-11, -4, -1, -1/2
Let s(r) be the first derivative of -r**5 - 128 + 5/3*r**3 + 25/2*r**2 - 25/4*r**4 + 0*r. Find b, given that s(b) = 0.
-5, -1, 0, 1
Suppose 9*n - 44 = 55. Let z(o) = -9*o**2 - 9*o + 32. Let m(q) = 5*q**2 + 4*q - 16. Let b(p) = n*m(p) + 6*z(p). Let b(l) = 0. What is l?
2, 8
Let l(w) be the second derivative of w**6/24 - w**5/4 - 5*w**4/24 + 5*w**3/2 + 41*w**2 + 2*w + 23. Let y(n) be the first derivative of l(n). Factor y(u).
5*(u - 3)*(u - 1)*(u + 1)
Let w = -88 + 72. Let z = w + 18. Factor 6*d + 15*d - 19*d + 6*d + 4*d**z.
4*d*(d + 2)
Let a(b) = -9*b**4 + 108*b**3 + 237*b**2 + 138*b. Let k(r) = 19*r**4 - 215*r**3 - 474*r**2 - 279*r. Let c(m) = 13*a(m) + 6*k(m). Find x such that c(x) = 0.
-1, 0, 40
Let s(d) = 14*d**3 - d**2 + 2*d - 3. Let c be s(2). Let u = -105 + c. Suppose -35*v**u - 8*v**5 - v**5 - v**5 + 5*v**5 = 0. What is v?
-7, 0
Let m(a) be the third derivative of 1/490*a**7 - 47*a**2 + 0*a - 1/280*a**6 + 0 + 0*a**3 + 0*a**4 + 0*a**5. Factor m(v).
3*v**3*(v - 1)/7
Let u(z) be the second derivative of -z**5/40 - 11*z**4/24 + z**3/12 + 11*z**2/4 - 136*z. Factor u(c).
-(c - 1)*(c + 1)*(c + 11)/2
Factor -835*x**5 + 2*x**4 - x**3 - 14*x**2 - 4*x**2 + 834*x**5 + 3*x**4 + 18*x - 3*x**2.
-x*(x - 3)**2*(x - 1)*(x + 2)
Let f(b) = b**2 - 8*b + 1. Let o(w) = -2*w**3 - 19*w**2 + 326*w + 1937. Let y(t) = 14*f(t) + 2*o(t). Factor y(j).
-4*(j - 12)*(j + 9)**2
Let j(k) = -5*k**3 + 4*k**2 + 14*k + 7. Let c be j(5). Let r = 1346/3 + c. Factor -2/3*o**4 + 0 + 2/3*o**2 - 2/3*o + r*o**3.
-2*o*(o - 1)**2*(o + 1)/3
Let k(j) be the second derivative of 2*j**7/525 - j**6/75 - j**5/15 + j**4/5 - j**2/2 + 16*j + 2. Let d(c) be the first derivative of k(c). Factor d(t).
4*t*(t - 3)*(t - 1)*(t + 2)/5
Let 77/4*c**4 + 975*c**3 + 1/8*c**5 + 0 - 35152*c + 15548*c**2 = 0. What is c?
-52, 0, 2
Let q(l) be the third derivative of l**7/840 - 7*l**6/480 - l**5/240 + 7*l**4/96 - 844*l**2. Factor q(y).
y*(y - 7)*(y - 1)*(y + 1)/4
Suppose -494*o + 82 = -62*o + 37 + 45. Solve -16/5*c**2 + 2/5*c**5 - 4*c**3 + 0 + o*c - 2/5*c**4 = 0.
-2, -1, 0, 4
Let k(w) be the first derivative of -9*w**2 + 148*w - 104. Let n be k(8). Factor -39/4*p**3 + 12*p**2 + 9/4*p**n + 0 - 3*p.
3*p*(p - 2)**2*(3*p - 1)/4
Factor -3000*b + 2685*b - 260*b**2 + 270*b**2.
5*b*(2*b - 63)
Suppose -h + 5*m = 88 - 17, 2*h - 2*m + 150 = 0. Let l = -67 - h. Factor 2*g - l*g**2 + 3*g**3 + g - 10*g - 5*g.
3*g*(g - 4)*(g + 1)
Suppose -94*g + 92*g + 4 = 0. Find d such