67. Solve -14/5*w**2 + 24/5*w + h = 0.
-2/7, 2
Factor 78/5 + 4*r - 2/5*r**2.
-2*(r - 13)*(r + 3)/5
Determine s, given that 90*s**2 - 205*s - 626 + 3*s**3 + 1024*s + 2978 = 0.
-16, -7
Let g(t) be the second derivative of -t**4/6 - 14*t**3/3 + 32*t**2 + 4*t - 28. Factor g(d).
-2*(d - 2)*(d + 16)
Let r(l) be the first derivative of -1/4*l**4 + 0*l + 2*l**2 + 36 - l**3. Suppose r(o) = 0. What is o?
-4, 0, 1
Suppose -10/3*z - 28/3 + 2/3*z**2 = 0. What is z?
-2, 7
Factor 4 + 16*l**2 + 0*l + 4*l**3 - 4*l**2 - l + 13*l.
4*(l + 1)**3
Let v(x) be the second derivative of -27*x**4/28 - 19*x**3/2 + 15*x**2/7 - 209*x. Factor v(l).
-3*(l + 5)*(27*l - 2)/7
Factor 4 - 1 - 16*x**4 - 15*x**2 - 9*x + 15*x**4 + 4*x**3 + 5*x**3 + 13*x**4.
3*(x - 1)*(x + 1)**2*(4*x - 1)
Let n(x) be the second derivative of -x**5/100 + x**4/15 - 2*x**3/15 + 3*x - 15. Suppose n(u) = 0. What is u?
0, 2
Suppose -896 + 1799 - 26*i - 891 + 10*i**2 = 0. Calculate i.
3/5, 2
Let c(y) = -2*y**2 + 6*y - 1. Let d(h) = -5*h**2 + 19*h + 58. Let b(l) = 6*c(l) - 3*d(l). Factor b(g).
3*(g - 12)*(g + 5)
Let d(s) be the second derivative of s**4/3 - 4*s**3/3 + 143*s. Let d(g) = 0. Calculate g.
0, 2
Let v be (-5)/(-50)*(-5)/(-1)*1. Let i(l) be the first derivative of v*l**2 - 2*l + 5 - 1/4*l**4 + 2/3*l**3. Suppose i(o) = 0. Calculate o.
-1, 1, 2
Let h(o) be the third derivative of 0*o**3 + 10*o**2 - 1/12*o**4 + 1/300*o**6 + 0*o + 2/75*o**5 + 0. Factor h(d).
2*d*(d - 1)*(d + 5)/5
Factor 3/4*l**3 - 3/4*l**2 - 12*l + 12.
3*(l - 4)*(l - 1)*(l + 4)/4
Let c(z) = 20*z**2 + 29*z - 231. Let l(f) = 15*f**2 + 22*f - 173. Let m(h) = 7*c(h) - 9*l(h). Factor m(d).
5*(d - 3)*(d + 4)
Let v(j) be the first derivative of -j**4/26 - 140*j**3/39 + j**2/13 + 140*j/13 - 233. Factor v(x).
-2*(x - 1)*(x + 1)*(x + 70)/13
Let b(y) = -2*y**2 - y - 1. Let f(z) = -1. Suppose 3*s + 6 + 3 = 0. Let j be -2 - 2 - (50 + -57). Let a(i) = j*b(i) + s*f(i). Find n such that a(n) = 0.
-1/2, 0
Factor -2/11*s**2 - 32/11*s + 34/11.
-2*(s - 1)*(s + 17)/11
Let g be (-8)/2 + (-314)/8. Let n = g - -44. Factor 0 - 3/4*a**2 + 3/4*a**4 + 3/4*a**5 + 0*a - n*a**3.
3*a**2*(a - 1)*(a + 1)**2/4
Let b be (-14)/63*-18*(42/40 - 1). Factor 0*r - 4/5 - b*r**3 + 3/5*r**2.
-(r - 2)**2*(r + 1)/5
Let g(z) be the third derivative of z**8/504 - 2*z**7/315 - z**6/60 + 2*z**5/45 + z**4/9 + 11*z**2 + 10*z. Suppose g(q) = 0. Calculate q.
-1, 0, 2
Let n(d) be the second derivative of -9*d**6/260 + 18*d**5/65 - 12*d**4/13 + 64*d**3/39 + 16*d**2 + 18*d. Let y(i) be the first derivative of n(i). Factor y(r).
-2*(3*r - 4)**3/13
Suppose -3*o - 4*g - 6 = -o, -o = g + 6. Let k be -7 - o - (-8)/4. Factor -260*q**3 - 554/3*q**2 - 40*q - 8/3 - 338/3*q**k.
-2*(q + 1)**2*(13*q + 2)**2/3
Let -4/3*s**4 + 1/2*s**5 + 0 + s**3 + 0*s**2 - 1/6*s = 0. What is s?
-1/3, 0, 1
Let g be ((-2)/(-3))/(-2*(-1)/15). Factor 5*d + d**2 - d + 2*d - g - 2*d.
(d - 1)*(d + 5)
Let v be 1207/51 - (16 + 7). Factor v*s**2 + 0 - 2/3*s**3 + 4/3*s.
-2*s*(s - 2)*(s + 1)/3
Let n(a) = 170*a**2 - 1265*a - 4180. Let r(j) = 15*j**2 - 115*j - 380. Let m(l) = -4*n(l) + 45*r(l). Suppose m(z) = 0. Calculate z.
-19, -4
Let u(w) be the third derivative of -w**5/600 + 263*w**4/120 - 69169*w**3/60 - 79*w**2. Suppose u(q) = 0. What is q?
263
Let d(v) be the second derivative of -7*v**4/78 - 37*v**3/39 - 30*v**2/13 - 665*v. Find j, given that d(j) = 0.
-30/7, -1
Let i(c) = -3*c**4 + 5*c**3 - 17*c**2 + 21*c - 6. Let l(a) = -13*a**4 + 19*a**3 - 68*a**2 + 86*a - 24. Let m(x) = -9*i(x) + 2*l(x). Factor m(b).
(b - 3)*(b - 2)*(b - 1)**2
Let m = 8121 - 8119. Find c, given that 9/4*c**m + 1/2*c + 0 = 0.
-2/9, 0
Let n(t) be the second derivative of 7*t**6/15 + 3*t**5 + 43*t**4/6 + 8*t**3 + 4*t**2 - t + 27. Determine h, given that n(h) = 0.
-2, -1, -2/7
Let u be (-39)/(-15) + 4/10. Determine o, given that -75*o + 59*o**u - o**2 - 38*o**3 - 35*o**2 - 18 = 0.
-1, -2/7, 3
Let p(f) = f**3 + 4*f**2 - 7*f - 1. Let y be p(-5). Solve -y*b + 15*b**3 + 0*b + 9*b + 10*b**2 + 5*b**4 = 0 for b.
-2, -1, 0
Suppose 6 = 29*h - 27*h. Solve 12*q**2 - 16*q**4 - 28*q + 62 - 54 + 32*q**3 + 0*q**h = 0 for q.
-1, 1/2, 2
Let g(l) be the first derivative of 3*l**5/10 - 45*l**4/8 + 375*l**2 + 200. Determine p so that g(p) = 0.
-5, 0, 10
Suppose p + 12*d = 17*d + 2, 0 = -5*p + d + 10. Factor 8*g**2 + 3 - 13*g**p + 27 + 25*g.
-5*(g - 6)*(g + 1)
Let o(p) = -p + 6. Let x be o(4). Factor -7*d - 12*d + 2*d**2 + d**x + 4*d.
3*d*(d - 5)
Let w(b) be the third derivative of b**6/15 - b**5 + 19*b**4/6 - 4*b**3 + 326*b**2. What is h in w(h) = 0?
1/2, 1, 6
Let 0 - 20*s**2 + 5*s**4 - 1/2*s**5 - 21/2*s**3 + 50*s = 0. Calculate s.
-2, 0, 2, 5
Let x = -2295 + 20657/9. Find w, given that 2*w**2 + x - 4/3*w = 0.
1/3
Suppose -2/9*v**2 + 2/3*v + 20/9 = 0. What is v?
-2, 5
Let t(u) be the second derivative of u**4/72 + 13*u**3/18 + 169*u**2/12 + 86*u. Factor t(z).
(z + 13)**2/6
Factor -1/2*o**4 - 5/2*o**3 + 3*o**2 + 0*o + 0.
-o**2*(o - 1)*(o + 6)/2
Let g(s) be the first derivative of -s**5 + 5*s**4/4 + 10*s**3 - 127. Suppose g(m) = 0. What is m?
-2, 0, 3
Let b be (224/(-120))/((-84)/72). Let -4/5*y**2 - 4/5*y + b = 0. What is y?
-2, 1
Let a(b) be the second derivative of -5*b**4/12 + 305*b**3/6 + b - 190. Factor a(t).
-5*t*(t - 61)
Let k(p) = -p. Let t(q) be the first derivative of -10*q**3/3 - 31*q**2/2 + 12*q + 9. Let h(o) = 5*k(o) - t(o). Solve h(l) = 0 for l.
-3, 2/5
Let o = -6934 - -41605/6. Find x such that 1/2*x**2 + 0 - 1/3*x - o*x**4 + 0*x**3 = 0.
-2, 0, 1
Let v(n) = 10*n**2. Let i(w) = 12*w**2 - 3*w - 4. Let c(l) = -23*l**2 + 5*l + 7. Let j(z) = 3*c(z) + 5*i(z). Let g(a) = -5*j(a) - 4*v(a). Solve g(m) = 0 for m.
-1, 1
Let f(r) be the first derivative of 10*r**5 - 85*r**4/2 + 22*r**3/3 + 121*r**2 + 128. Factor f(u).
2*u*(u + 1)*(5*u - 11)**2
Let k be 34/(-6) - 336/(-48). What is l in -2/3*l**5 + 0 - 10/3*l**3 - k*l**2 - 8/3*l**4 + 0*l = 0?
-2, -1, 0
Let q(j) be the first derivative of -4 + 4*j + 2/3*j**3 + 3*j**2. Factor q(l).
2*(l + 1)*(l + 2)
Determine t so that -1/3*t**2 - 1024/3 - 64/3*t = 0.
-32
Let v(d) be the second derivative of d**6/2700 + d**5/45 + 5*d**4/9 + 4*d**3 - 7*d. Let s(u) be the second derivative of v(u). Let s(g) = 0. What is g?
-10
Let o = 6893 + -6893. Factor 0*z + o + 2/11*z**2 + 4/11*z**3 + 2/11*z**4.
2*z**2*(z + 1)**2/11
Find v such that 12/11*v - 2/11*v**2 + 14/11 = 0.
-1, 7
Factor -28 + 32*n**2 - 24*n - 11*n**2 - 17*n**2.
4*(n - 7)*(n + 1)
Suppose -5*l = -25, y = 5*l - 4 - 5. Solve -13*d**2 + 41*d**2 - 14*d**2 - y*d**2 - d**3 = 0.
-2, 0
Let k(r) = -39210*r**2 + 798*r + 44. Let y(j) = 117629*j**2 - 2393*j - 124. Let o(u) = -17*k(u) - 6*y(u). Factor o(w).
-4*(99*w - 1)**2
Let v(b) = -b**3 - 11*b**2 - 9*b + 22. Let p be v(-10). Find t such that 0 + p - 12*t**2 + 12*t + 33*t = 0.
-1/4, 4
Let w(n) be the third derivative of 3*n**8/28 - 52*n**7/7 + 4477*n**6/30 - 364*n**5 + 294*n**4 - 2*n**2 - 29*n. Determine g so that w(g) = 0.
0, 2/3, 21
Suppose -2/9*q**2 + 40/9*q + 0 = 0. Calculate q.
0, 20
Let c(s) be the first derivative of 2*s**3/3 + 7*s**2 + 24*s - 72. Factor c(p).
2*(p + 3)*(p + 4)
Let t = -7 - -9. Factor 19*u - 45 + 4*u**t + 73 - 51*u.
4*(u - 7)*(u - 1)
Let t(h) be the first derivative of -49*h**4 - 2660*h**3/3 - 736*h**2 - 208*h - 122. Let t(k) = 0. Calculate k.
-13, -2/7
What is r in -28*r - r**2 - 10 + 27*r + r**3 + 10*r**2 + r**2 = 0?
-10, -1, 1
Find s, given that -393 + 393 - 71*s + 4*s**2 - 221*s = 0.
0, 73
Let f = 3889415/425404 + -1/60772. Factor -f - 1/7*m**2 + 16/7*m.
-(m - 8)**2/7
Let y(a) be the third derivative of 11*a**2 - 3/8*a**4 - 1/40*a**6 + 0 - 1/4*a**5 + 0*a**3 + 0*a + 1/70*a**7. Find w, given that y(w) = 0.
-1, 0, 3
Let f(r) be the third derivative of -1/1080*r**6 + 0*r + 9*r**2 + 0 - 1/2*r**3 + 0*r**4 - 1/180*r**5. Let y(m) be the first derivative of f(m). Factor y(u).
-u*(u + 2)/3
Suppose 4*m + 0*m - 22 = 3*n, -4*n = -3*m + 20. Let -7*w**m - 14*w**5 - 5*w**4 + 12*w**3 - 4*w**2 + 18*w**5 = 0. What is w?
0, 1
Suppose -3*b - 1841 = 418. Let a = b - -5283/7. Factor 4/7*u**2 - a*u + 8/7.
4*(u - 2)*(u - 1)/7
Let z(c) be the first derivative of 2/3*c**6 + 0*c**2 + 10 + 0*c + 0*c**4 + 8/5*c**5 + 0*c**3. Factor z(s).
4*s**4*(s + 2)
Let s = 3 + 0. Solve -2*x**3 + 4*x + 2*x**s - 3*x**3 - 3*x**2 + 2*x = 0 for x.
-2, 0, 1
Factor 4