p). Determine c so that t(c) = 0.
-9, -1
Let s(i) be the second derivative of -i**6/15 + i**5 - 29*i**4/6 + 32*i**3/3 - 12*i**2 - 337*i. What is r in s(r) = 0?
1, 2, 6
Factor 204/7 - 106/7*a + 2/7*a**2.
2*(a - 51)*(a - 2)/7
Let a(j) = j**2 + 11*j + 16. Let x be a(-10). Let s be 6/(1 - x/(-12)). Determine k, given that -1/4*k**s + 1/4*k**3 - 1/4*k**5 + 0*k + 1/4*k**2 + 0 = 0.
-1, 0, 1
Suppose 0 = -3*r - 1 + 16. Let b be (((-12)/18)/(15/9))/((-8)/40). Factor 4/3*t**4 - 1/3*t - 1/3*t**r + 4/3*t**2 - b*t**3 + 0.
-t*(t - 1)**4/3
Factor 3/4*q**4 - 48*q + 36*q**2 - 9*q**3 + 0.
3*q*(q - 4)**3/4
Find c, given that -15/2*c + 9/4*c**4 + 0 - 15*c**3 + 81/4*c**2 = 0.
0, 2/3, 1, 5
Suppose -3*l = -5*q + 18 - 17, 6 = 3*q. Let m(x) be the first derivative of 2/25*x**5 - 2/5*x**2 + 1/5*x**4 + 0*x - 2/15*x**l - 5. Factor m(r).
2*r*(r - 1)*(r + 1)*(r + 2)/5
Suppose -4*p + 2*n = -2*p - 8, -p - 2*n = 2. Factor -227*z**2 + 227*z**p - 2*z**4 + 2*z**5.
2*z**4*(z - 1)
Let w be (8/4)/((-126)/(-3) - 2). Let y(z) be the second derivative of -5/12*z**4 + 5*z + 0 - 2*z**2 + w*z**5 + 4/3*z**3. Suppose y(h) = 0. What is h?
1, 2
Let d(y) be the first derivative of y**6/6 - 113*y**5/5 + 2165*y**4/2 - 58978*y**3/3 + 105413*y**2/2 - 50653*y - 105. Let d(w) = 0. Calculate w.
1, 37
Let v(x) = x**2 + 7*x - 4. Let u be v(-8). Let h be 70/(-6)*u*-3. Factor 140*g - h*g + 20 + 5*g**3 - 15*g**2.
5*(g - 2)**2*(g + 1)
Let p(n) = 3*n**2 - 30*n + 65. Let m be p(3). Factor 1/3*j**3 + 0 + 0*j + 2/3*j**m.
j**2*(j + 2)/3
Find v, given that 14/5*v - 3/5*v**2 - 8/5 = 0.
2/3, 4
Let w = 107/43 - -1/86. Let g = 2066 - 2062. Factor -5*v**2 - 10*v**g - w*v**5 + 0*v - 25/2*v**3 + 0.
-5*v**2*(v + 1)**2*(v + 2)/2
Let s(w) = 5*w**3 - 18*w**2 - 102*w + 10. Let l(y) = y**3 + y + 1. Let d(j) = -6*l(j) + s(j). Let x(c) be the first derivative of d(c). Factor x(i).
-3*(i + 6)**2
Let i = -67 + 102. Let g be 5 - i/3*21/91. Let g*h**2 - 16/13*h + 14/13*h**3 - 6/13*h**5 - 8/13 - 14/13*h**4 = 0. Calculate h.
-2, -1/3, 1
Let t = 107 - 103. Let u(p) be the first derivative of 4 + 2*p - 1/8*p**t + 0*p**2 - 1/2*p**3. Factor u(w).
-(w - 1)*(w + 2)**2/2
Let v(i) = i**3 - 38*i**2 - 36*i - 115. Let z be v(39). Factor 9/4 - 1/4*n**4 - 3/2*n**3 + 3/2*n - z*n**2.
-(n - 1)*(n + 1)*(n + 3)**2/4
Suppose 10 = 3*w - 29. Find l such that 19*l**2 - w*l**4 - 6*l**4 - 7*l**2 + 16 + 80*l + 36*l**5 - 116*l**3 - 9*l**4 = 0.
-1, -2/9, 1, 2
Let w(n) be the first derivative of -2*n**5/45 - n**4/3 - 225. Let w(b) = 0. What is b?
-6, 0
Suppose -54*y - 12 - 5 + 17 = 0. Factor y + 2/21*f**4 + 8/21*f**3 + 0*f + 2/7*f**2.
2*f**2*(f + 1)*(f + 3)/21
Let c(b) = b**3 - b**2 - 2*b + 7. Let x be c(0). Suppose 5*j - 3*j = -f + 7, -3*f = -j - x. Factor -12*a**2 - 2*a**3 - 8*a**j - 20*a + 17*a**3.
5*a*(a - 2)*(3*a + 2)
Let r(p) be the second derivative of -p**6/90 - 3*p**5/10 - 19*p**4/12 + 130*p**3/9 + 50*p**2 + 125*p. Determine d, given that r(d) = 0.
-10, -1, 3
Solve n**4 + 301*n**2 + 16*n - 17*n**3 - 221*n**2 - 80*n = 0 for n.
0, 1, 8
Suppose 2*w = -4*l - 14, -5*w + l - 5*l = 29. Let n be w/(-1) - (4/1)/2. Factor -2/13*u**n + 0 + 6/13*u**2 + 0*u.
-2*u**2*(u - 3)/13
Let p be (850/15)/17*(-12)/(-10). Let w(a) be the second derivative of 1/90*a**p + 4/15*a**2 + 8*a + 4/45*a**3 + 0. Factor w(z).
2*(z + 2)**2/15
Suppose -3*s + 4*w + 24 = 0, -3*w + 39 = 2*s + 2*w. Factor 8*h**2 - h**5 + s*h**3 + 13*h**3 - 21*h**3 - 2*h**4.
-h**2*(h - 2)*(h + 2)**2
Let m(b) = -b**2 - 5*b - 1. Let x be m(-2). Suppose x*a - 3*a = 4. Find c, given that -12*c**5 + c**2 + 15*c**3 + 0*c**2 - 3*c + 8*c**a - 9*c**4 = 0.
-1, 0, 1/4, 1
Determine b so that 3/2*b**4 + 0 - b - 1/4*b**5 + 3*b**2 - 13/4*b**3 = 0.
0, 1, 2
Let z(a) be the third derivative of -a**9/211680 - a**8/70560 + 4*a**5/15 - 19*a**2. Let i(m) be the third derivative of z(m). Factor i(p).
-2*p**2*(p + 1)/7
Suppose 2*n + 2*n + 2*g - 6 = 0, -2 = -2*g. Let b(l) = l - 3. Let h be b(7). Solve n - h*f - 6*f - 4 + 5*f - f**2 + f**3 = 0.
-1, 3
Let u be (-336)/(-66) + 5/(-55). Let o(j) be the first derivative of 5/18*j**4 + 0*j - 1/9*j**2 + 2/27*j**3 - 4 + 2/15*j**u. Factor o(p).
2*p*(p + 1)**2*(3*p - 1)/9
Let a(p) be the second derivative of p**5/10 + 7*p**4/5 - 28*p**3/5 - 8*p**2 - 25*p + 6. Factor a(n).
2*(n - 2)*(n + 10)*(5*n + 2)/5
Suppose 90*p = 115*p. Factor 6/7*a**3 + 9/7*a**2 + 3/7*a + p.
3*a*(a + 1)*(2*a + 1)/7
Let k(j) = j**2 + 6*j + 8. Let u be k(-6). Let g be 3/(u/(-12) + 1). Factor -x + 9*x - 10*x**2 - 4*x**4 + 16*x**3 - x**2 - g*x**2.
-4*x*(x - 2)*(x - 1)**2
Suppose -6 = -s - 2*q, -3 + 0 = -2*s + 5*q. Factor -s*i**2 - 3*i**3 + 6*i**3 + i**3 + 0*i**3.
4*i**2*(i - 1)
Let t(x) = x**2 + 13*x - 7. Let w be t(-7). Let a = w + 443/9. Suppose -2/9 - a*h + 2/9*h**2 + 2/9*h**3 = 0. What is h?
-1, 1
Let t(n) be the second derivative of -n**7/252 + n**5/20 - n**4/9 + n**3/12 - 128*n. Factor t(q).
-q*(q - 1)**3*(q + 3)/6
Factor 35*y - 24*y - 16*y**2 + 21*y + 40*y + 20 + 4*y.
-4*(y - 5)*(4*y + 1)
Suppose -45*n + 2*i + 10 = -44*n, -8*n = 4*i. Suppose -7*x**n - 69/4*x**3 - 25/4*x**5 + 0 - 35/2*x**4 - x = 0. What is x?
-1, -2/5, 0
Let x be -1*423/(-378) + 3/18. Factor -9/7*k**4 - 33/7*k - 46/7*k**2 - 30/7*k**3 - x - 1/7*k**5.
-(k + 1)**3*(k + 3)**2/7
Let g be 7/(-2)*(-3 - 39/(-21)). Factor -18*a - 6*a**3 + 2*a**3 + g + 6*a + 12*a**2.
-4*(a - 1)**3
Let d(y) be the second derivative of y**4/48 - 17*y**3/12 + 289*y**2/8 + 66*y + 4. Factor d(g).
(g - 17)**2/4
Determine k so that 17/2*k - 1/2*k**3 - 7/2*k**2 - 9/2 = 0.
-9, 1
Let q(i) be the third derivative of i**5/510 - 113*i**4/102 + 75*i**3/17 - 153*i**2 - 3. Factor q(n).
2*(n - 225)*(n - 1)/17
Let q(g) be the first derivative of -g**4/28 - 2*g**3/21 + g**2/2 - 4*g/7 + 229. What is y in q(y) = 0?
-4, 1
Let x be ((-28)/(-8))/(5/10). Factor -12*a - 2*a + 4 + 2*a**2 + 9*a**2 + 2*a**4 - 10*a**3 + x*a**2.
2*(a - 2)*(a - 1)**3
Let k(g) be the third derivative of -g**5/30 - 5*g**4/12 + 14*g**3/3 - 22*g**2 + 3. Factor k(i).
-2*(i - 2)*(i + 7)
Let i(v) = -9*v**3 - 195*v**2 - 300*v + 92. Let m(g) = -g**2 + 2. Let u(j) = -5*i(j) + 40*m(j). Factor u(z).
5*(z + 2)*(z + 19)*(9*z - 2)
Let u be (1 - -1)/1*7. Suppose -3*s - 5 = -u. Factor -1/5*i**4 + 2/5*i + 0 + 3/5*i**2 + 0*i**s.
-i*(i - 2)*(i + 1)**2/5
Let v = 2237/3351 - 1/1117. Suppose -1/3*s**4 + s**3 - s + v - 1/3*s**2 = 0. What is s?
-1, 1, 2
Let z(i) = -175*i**2 + 1225*i + 2. Let l be z(7). Suppose 9*r + 3/2*r**l + 15/2 = 0. What is r?
-5, -1
Let n(t) be the second derivative of -t**4/84 - 19*t**3/21 + 40*t**2/7 + 28*t + 5. Factor n(j).
-(j - 2)*(j + 40)/7
Let z(c) be the third derivative of -2*c**7/105 + 2*c**6/15 + 28*c**5/15 + 16*c**4/3 - 1088*c**2. Factor z(l).
-4*l*(l - 8)*(l + 2)**2
Suppose 3*g - 12 = 0, 4*g = n + 3*n. Let v(s) be the first derivative of -2 - 3/5*s**5 + 0*s + 0*s**2 + s**3 + 0*s**n. Factor v(k).
-3*k**2*(k - 1)*(k + 1)
Let b = -539 - -3235/6. Factor -b*k + 1/6*k**3 + 0 + 0*k**2.
k*(k - 1)*(k + 1)/6
Suppose 3 = 2*a + a. Let t be 24/30 - 0/a. What is z in t + 44/5*z + 121/5*z**2 = 0?
-2/11
Let h(q) be the second derivative of q**5/110 - 13*q**4/33 + 25*q**3/33 - 54*q. Find p such that h(p) = 0.
0, 1, 25
Suppose -54/7*p - 2/7*p**3 + 18/7*p**2 + 54/7 = 0. What is p?
3
Suppose 2/13*d**3 - 2/13 - 6/13*d**2 + 6/13*d = 0. Calculate d.
1
Let l = 255 - 247. Let k(p) be the third derivative of -1/6*p**3 + 1/8*p**4 - 1/10*p**7 - 3/112*p**l + 0 - 5*p**2 + 1/10*p**5 - 1/12*p**6 + 0*p. Factor k(c).
-(c + 1)**3*(3*c - 1)**2
Let l(u) be the third derivative of u**9/756 - u**7/210 - 3*u**3 - 27*u**2. Let j(y) be the first derivative of l(y). Find x such that j(x) = 0.
-1, 0, 1
Suppose -3*q + 5 + 1 = 0. Suppose -2*u = 4*b + 2 - 6, q*b + 2*u = 0. Factor 0 - 2/11*j + 2/11*j**b.
2*j*(j - 1)/11
Suppose -48*w = -51*w + 12. Let g(y) be the second derivative of -4/3*y**2 + 13*y + 1/18*y**w + 2/9*y**3 + 0 - 1/60*y**5. Factor g(q).
-(q - 2)**2*(q + 2)/3
Let j = 8 - 5. Suppose -x**2 - 4*x**j - 7*x**2 - 2*x**4 + 14*x**3 = 0. Calculate x.
0, 1, 4
Solve 1004*c**2 - 2000*c**2 + 998*c**2 - c**3 + 3*c = 0 for c.
-1, 0, 3
Let m(v) be the first derivative of -25*v**6/2 + 46*v**5 - 255*v**4/4 + 40*v**3 - 10*v**2 - 200. Let m(s) = 0. Calculate s.
0, 2/5, 2/3, 1
Suppose 21*o + 166 = 23*o. Factor o*j - 3 + 6 + 3*j**2 - 77*j.
3*(j + 1)**2
Let k be (-16)/12