u). Factor j(c).
4*(c - 1)*(c + 1)*(c + 3)
Let t = -824/9 + 278/3. Factor 38/9*l + 4/3 - t*l**3 + 16/9*l**2.
-2*(l - 3)*(l + 1)*(5*l + 2)/9
Let i(g) be the first derivative of 26*g**3/75 + 24*g**2/25 - 8*g/25 - 48. Find n such that i(n) = 0.
-2, 2/13
Let j(m) be the second derivative of -3*m**5/20 - 2*m**4 - 6*m**3 + 12*m + 7. Solve j(o) = 0 for o.
-6, -2, 0
Let b(u) be the third derivative of u**7/630 - u**6/72 + u**5/36 + 5*u**4/72 - u**3/3 + 195*u**2. Suppose b(p) = 0. Calculate p.
-1, 1, 2, 3
Let j(g) = -4*g**3 + 32*g**2 - 154*g + 194. Let x(d) = -13*d**3 + 96*d**2 - 462*d + 581. Let v(m) = -7*j(m) + 2*x(m). Let v(p) = 0. What is p?
2, 7
Let q(r) be the second derivative of r**5/10 - 11*r**4/3 - 23*r**3/3 - 106*r. Factor q(p).
2*p*(p - 23)*(p + 1)
Let x be (-40)/(-22) - 10/(-55). Suppose x*y - 3 - 5 = 0. What is j in 4*j**5 - j**2 + 5*j**y - 3*j + j**4 - 5*j**2 - j**5 = 0?
-1, 0, 1
Let z(s) = s + 11. Let o be z(-7). Suppose 0 = 4*n + 5*v + 4, o + 12 = 3*n - v. Find g, given that 46*g**2 - 11 + 16 + 34*g**n - 66*g**3 - 13 - 6*g**5 = 0.
-1/3, 1, 2
Factor 8/19*p**4 + 8/19*p**2 - 2/19*p**5 - 2/19*p + 0 - 12/19*p**3.
-2*p*(p - 1)**4/19
Let a(k) be the second derivative of k**5/180 + 13*k**4/54 + 49*k**3/54 + 4*k**2/3 + 327*k. What is n in a(n) = 0?
-24, -1
Let d(y) be the second derivative of -2*y**5/135 - y**4/9 - y**3/3 - 5*y**2 + 12*y. Let n(a) be the first derivative of d(a). Factor n(g).
-2*(2*g + 3)**2/9
Let i(l) be the first derivative of l**5 - 25*l**3/3 + 20*l + 53. Determine t, given that i(t) = 0.
-2, -1, 1, 2
Let q(f) be the second derivative of -f**6/15 - 2*f**5/5 - 2*f**4/3 - 43*f + 3. Find p, given that q(p) = 0.
-2, 0
Let m be 2/12*(-14)/28*0. Let v(t) be the third derivative of 1/70*t**7 - t**2 + m*t + 5/4*t**4 + 3/2*t**3 + 0 + 3/20*t**6 + 3/5*t**5. Solve v(o) = 0 for o.
-3, -1
Let j(s) be the third derivative of 2/15*s**6 + 1/3*s**4 + 0*s + 0 - 3/5*s**5 + 0*s**3 + 37*s**2. Factor j(f).
4*f*(f - 2)*(4*f - 1)
Let v = -1669 + 1669. Let j(d) be the first derivative of 1/2*d**5 + 4 - d**6 + v*d**2 + 1/6*d**3 + 3/4*d**4 + 0*d. Determine w, given that j(w) = 0.
-1/3, -1/4, 0, 1
Solve 836*c - 73*c**3 + 76*c**3 - 168 - 368*c**2 + 33*c**3 = 0 for c.
2/9, 3, 7
Determine n, given that 4/3*n**2 + 8/3*n - 1/3*n**5 - 2*n**3 - 5/3*n**4 + 0 = 0.
-2, 0, 1
Let f be (2/(-6))/((-1)/9). Factor -g**f + g + 0 + 0*g + 0.
-g*(g - 1)*(g + 1)
Let t(c) be the third derivative of -c**5/270 + 53*c**4/54 - 2809*c**3/27 - 192*c**2 + c. Let t(q) = 0. What is q?
53
Suppose -2*m - 2 = -3*k + 3, 0 = -5*m + 10. Factor c**2 - 20*c + 24*c - 9*c**2 + 4*c**k.
4*c*(c - 1)**2
Let f(k) = 4*k**5 - 3*k**4 + 3*k**3 - 5*k**2. Let i(d) = -2*d**5 + 2*d**4 - 2*d**3 + 3*d**2. Let c(b) = 3*f(b) + 5*i(b). Find h, given that c(h) = 0.
-1, 0, 1/2
Let h = -312 - -312. Let o(b) be the third derivative of -1/60*b**5 + 0*b + h + 1/12*b**4 + 0*b**3 - 10*b**2. Let o(y) = 0. What is y?
0, 2
Factor -8*v - 9*v - 2 + 13*v + v - v**2.
-(v + 1)*(v + 2)
Solve -24/11 - 1002*g**2 - 13254/11*g**4 + 1080/11*g - 25380/11*g**3 = 0.
-1, 2/47
Let j(n) be the second derivative of n**5/70 + 5*n**4/21 + 16*n**3/21 - 5*n - 6. Factor j(f).
2*f*(f + 2)*(f + 8)/7
Let p = 644 + -1916/3. Suppose -2/3*b**2 - 2*b**3 - 8/3 + p*b = 0. What is b?
-2, 2/3, 1
Factor 3/8*z**3 + 39/8*z**2 + 27/2*z + 0.
3*z*(z + 4)*(z + 9)/8
Let y be (150/45)/(2/3). Let m(v) be the second derivative of 3/20*v**y + 0 + 2*v + 0*v**2 + v**4 + 3/2*v**3. Determine n so that m(n) = 0.
-3, -1, 0
Let q(a) be the first derivative of -5/3*a**3 - 1 + 10*a**2 + 0*a. Factor q(j).
-5*j*(j - 4)
Let x(g) be the third derivative of -13/45*g**5 - 2/9*g**6 - 1/9*g**4 + 0*g + 20*g**2 + 0*g**3 - 2/35*g**7 + 0. Factor x(k).
-4*k*(k + 1)**2*(9*k + 2)/3
Let v = -5680/171 + 648/19. Factor -2/9*o**4 + 0*o**3 + 0 + 0*o + v*o**2.
-2*o**2*(o - 2)*(o + 2)/9
Let p = 32 - 120. Let m be (-4)/4 - p/48. Factor m*c**2 - 4/3 - 3*c.
(c - 4)*(5*c + 2)/6
Let c(d) be the second derivative of d**7/2 - 23*d**6/5 + 1839*d**5/140 - 118*d**4/7 + 74*d**3/7 - 24*d**2/7 + 29*d + 3. Find k, given that c(k) = 0.
2/7, 1, 4
Let g(t) be the first derivative of t**3/33 - t**2 + 11*t + 24. Factor g(c).
(c - 11)**2/11
Factor -60/7 + 92/7*v - 36/7*v**2 + 4/7*v**3.
4*(v - 5)*(v - 3)*(v - 1)/7
Let m(h) be the third derivative of h**9/10584 - h**7/980 - h**6/630 - 13*h**3/3 + 19*h**2. Let b(r) be the first derivative of m(r). Solve b(v) = 0 for v.
-1, 0, 2
Let c be ((-12)/(-15))/(8/(-5) + 2). Factor 2*o**5 - 6*o**4 - 2 + 3*o**5 - o**5 + 3*o**c + 5*o**2 - 4*o**3.
2*(o - 1)**3*(o + 1)*(2*o + 1)
Solve 1/6*a**2 + 31/6*a - 16/3 = 0 for a.
-32, 1
Let m(c) be the second derivative of -c**6/45 + c**5/15 + c**4/6 - 8*c**3/9 + 4*c**2/3 - 70*c. Let m(y) = 0. Calculate y.
-2, 1, 2
Let a(c) be the first derivative of c**5/90 - c**4/18 + c**3/9 + 6*c**2 - 2. Let u(d) be the second derivative of a(d). Factor u(f).
2*(f - 1)**2/3
Let v(a) be the third derivative of -a**7/245 - 3*a**6/280 + a**5/28 + 3*a**4/28 - 9*a**2 + 3. Solve v(w) = 0.
-2, -1, 0, 3/2
Find s such that 13*s**4 - 10*s - 19*s**4 + 6*s + 6*s**2 + 2*s**5 + 2*s**3 = 0.
-1, 0, 1, 2
Let a(b) be the second derivative of b**6/280 + b**5/140 - 13*b**2/2 - 15*b. Let k(z) be the first derivative of a(z). Determine h, given that k(h) = 0.
-1, 0
Let i(u) = -3*u**3 + u**2 + u. Let h be i(-1). Factor 6*r - 60*r**2 + 1 - 28*r**2 + h.
-2*(4*r - 1)*(11*r + 2)
Let z(o) be the first derivative of o**8/336 - o**7/70 - o**6/120 + o**5/20 + 19*o**2/2 - o - 23. Let a(w) be the second derivative of z(w). Factor a(r).
r**2*(r - 3)*(r - 1)*(r + 1)
Factor 32*h - 139 + 69 + 70*h**2 - h**3 + 6*h**3 - 37*h.
5*(h - 1)*(h + 1)*(h + 14)
Factor 0*b - 6/17*b**3 - 2/17*b**2 + 0.
-2*b**2*(3*b + 1)/17
What is v in 0*v - 18*v**3 + 15/2*v**4 + 0 + 0*v**2 - 3/4*v**5 = 0?
0, 4, 6
Let m(q) = 25*q**3 + 53*q**2 - 2*q - 4. Let c(s) = 50*s**3 + 107*s**2 - 4*s - 9. Let a(j) = -4*c(j) + 9*m(j). Solve a(w) = 0 for w.
-2, 0, 1/25
Let q(u) be the second derivative of u**7/6930 - u**6/3960 - u**5/660 + 41*u**4/12 - u - 2. Let c(a) be the third derivative of q(a). Let c(p) = 0. What is p?
-1/2, 1
Let r(o) = 11*o**3 - 20*o**2 + 15*o - 14. Suppose -7*h = -46 - 10. Let v(z) = -4*z**3 + 7*z**2 - 5*z + 5. Let y(x) = h*v(x) + 3*r(x). Let y(f) = 0. Calculate f.
1, 2
Let k(u) = 3*u**4 - 43*u**3 + 160*u**2 - 283*u + 173. Let o(i) = i**4 - 14*i**3 + 53*i**2 - 94*i + 58. Let m(y) = -2*k(y) + 7*o(y). Factor m(r).
(r - 5)*(r - 3)*(r - 2)**2
Let b = 184 - 180. Let v(z) be the second derivative of 0 + 1/42*z**b - 4*z + 0*z**3 + 0*z**2. Factor v(r).
2*r**2/7
Let l(o) be the first derivative of -o**6/18 - 11*o**5/15 - 5*o**4/6 + 106*o**3/9 - 133*o**2/6 + 49*o/3 - 25. Solve l(k) = 0 for k.
-7, 1
Let a(h) be the second derivative of 0 + 6*h + 1/25*h**5 - 8/15*h**3 - 2/15*h**4 + 16/5*h**2. Factor a(k).
4*(k - 2)**2*(k + 2)/5
Find t such that -47976*t**5 - 363*t - 498*t**3 - 919*t**2 + 127*t**2 + 47973*t**5 - 72*t**4 = 0.
-11, -1, 0
Let p(r) be the second derivative of r**7/231 - r**6/165 - 3*r**5/110 + 5*r**4/66 - 2*r**3/33 + 8*r - 2. Solve p(n) = 0 for n.
-2, 0, 1
Let i(m) be the first derivative of -m**6/360 + m**5/40 + 2*m**3/3 - 3*m - 27. Let v(t) be the third derivative of i(t). Factor v(x).
-x*(x - 3)
Factor 0 - 34/15*u - 2/15*u**2.
-2*u*(u + 17)/15
Let x(b) be the second derivative of -b - 1/420*b**5 + 1/84*b**4 - 1/420*b**6 + 1/42*b**3 - 3/2*b**2 + 0. Let o(m) be the first derivative of x(m). Factor o(v).
-(v - 1)*(v + 1)*(2*v + 1)/7
Suppose -2 = u + 1. Let x(k) = 7*k**5 - k**4 - 20*k**3 - 15*k**2. Let f(d) = -20*d**5 + 4*d**4 + 60*d**3 + 44*d**2. Let b(m) = u*f(m) - 8*x(m). Factor b(n).
4*n**2*(n - 3)*(n + 1)**2
Let u = -528 - -533. Let t(n) be the third derivative of 4/3*n**3 + 8*n**2 + 1/30*n**6 + 0*n - 1/6*n**4 - 2/15*n**u + 0. Determine c, given that t(c) = 0.
-1, 1, 2
Let z(l) be the second derivative of -14*l**6/75 + 12*l**5/25 + 32*l**4/15 - 32*l**3/5 - 32*l**2/5 + 21*l + 12. Let z(t) = 0. Calculate t.
-2, -2/7, 2
Let x be (((-6136)/80)/(-13) - 6)/((-4)/48). Solve 2/5*l + 0 + 6/5*l**3 + x*l**2 + 2/5*l**4 = 0.
-1, 0
Let h(n) be the third derivative of n**5/30 + n**4/6 - n**3 - 22*n**2 - 2*n. Determine j, given that h(j) = 0.
-3, 1
Let j(a) be the second derivative of a**9/5040 + 3*a**8/2240 - a**7/210