r). Find a such that l(a) = 0.
-3
Let w = -2427/8 + 2431/8. Solve -3/2*g**2 - w - 1/2*g**3 - 3/2*g = 0.
-1
Let s(i) be the third derivative of i**7/42 + i**6/4 + 2*i**5/3 - 5*i**4/4 - 15*i**3/2 + 6*i**2 + 3*i. Suppose s(h) = 0. Calculate h.
-3, -1, 1
Let q be 26/637*7 + (-723250)/(-847). Factor q*a**2 + 16/11 + 664/11*a + 4374*a**3 + 39366/11*a**4.
2*(a + 1)*(27*a + 2)**3/11
Let h(r) be the third derivative of -r**5/20 + 3*r**4 + 26*r**3 - 15*r**2 + 3*r. Suppose h(i) = 0. Calculate i.
-2, 26
Factor 4802/3 + 196/3*d + 2/3*d**2.
2*(d + 49)**2/3
Let j(p) be the second derivative of -1/5*p**5 + 14*p + 0*p**2 - 1/3*p**4 + 4/3*p**3 + 0. Factor j(v).
-4*v*(v - 1)*(v + 2)
Let c(x) = 1. Let i(n) = 2*n + 1. Let h be i(4). Let g(m) = 1 + 3*m - 6 - h*m - 9*m**3 - 15*m**2. Let y(f) = -5*c(f) - g(f). Factor y(q).
3*q*(q + 1)*(3*q + 2)
Let u be 0/(4 - 6) + (-1 - 0). Let d(y) = y**2 - y + 1. Let l(n) = -4*n**3 + 24*n**2 - 36*n + 20. Let o(a) = u*l(a) + 4*d(a). Factor o(c).
4*(c - 2)**2*(c - 1)
Let m = -1/224 - -1349/1120. Let x(u) be the first derivative of 2/5*u**3 - 3/10*u**2 - m*u + 3/20*u**4 + 6. Solve x(q) = 0.
-2, -1, 1
Let g = 477 - 9527/20. Let z(b) be the first derivative of g*b**5 + 33/8*b**4 + 189/8*b**2 + 81/4*b - 7 + 1/24*b**6 + 27/2*b**3. Solve z(u) = 0.
-3, -1
Let o = 113 - 65. Factor -o*h**5 + 108*h**5 + 345*h**5 + 200*h**3 - 20*h**2 - 585*h**4.
5*h**2*(h - 1)*(9*h - 2)**2
Let h(w) = -25*w**3 - 35*w**2 + 25*w - 25. Let j be ((0 - 2) + 32)*-1. Let m(g) = g**3 + g**2 - g + 1. Let i(n) = j*m(n) - h(n). Let i(p) = 0. Calculate p.
-1, 1
Factor 0 - 3/5*w**2 + 12/5*w.
-3*w*(w - 4)/5
Let j(u) be the second derivative of -u**10/68040 + u**9/34020 - 5*u**4/4 + 18*u. Let q(c) be the third derivative of j(c). Factor q(n).
-4*n**4*(n - 1)/9
Let x = -1277/14 - -649/7. Factor x*o**2 + 0 + 9/2*o**3 - 6*o**4 + 0*o.
-3*o**2*(o - 1)*(4*o + 1)/2
Let l(u) be the third derivative of u**7/105 + u**6/20 - u**5/30 - u**4/4 - u**2 + 1. Solve l(y) = 0 for y.
-3, -1, 0, 1
Let d = 0 + 3. Suppose 7*b = d*b + 4, 4*x + 2*b = 10. Factor -1 + 1 - 1 - 2*l**x + 3*l**2.
(l - 1)*(l + 1)
Let b(m) be the third derivative of m**7/7560 + m**6/810 + m**5/216 + m**4/108 + 13*m**3/2 - 21*m**2. Let n(o) be the first derivative of b(o). Factor n(l).
(l + 1)**2*(l + 2)/9
Factor 14428*i - 14470*i + 3*i**4 + 17*i**2 + 24*i**3 - 2*i**2.
3*i*(i - 1)*(i + 2)*(i + 7)
Factor -15*t - 105*t - 154*t + 34*t - 64*t**3 + 72 - 34*t**3 + 266*t**2.
-2*(t - 1)*(7*t - 6)**2
Factor 281*i - 578*i**3 + 582*i**3 - 97*i - 100*i**2.
4*i*(i - 23)*(i - 2)
Let -47 + 35*a - 43 + 55 - 115 + 5*a**2 = 0. Calculate a.
-10, 3
Let z = 3043 + -3041. Solve 2*n - 3 - 1/3*n**z = 0.
3
Let d(w) be the first derivative of 14/3*w + 2/9*w**3 - 13 - 8/3*w**2. Factor d(n).
2*(n - 7)*(n - 1)/3
Let r(f) be the second derivative of f**4/24 + 17*f**3/12 + 21*f**2/2 + 12*f - 11. Solve r(i) = 0 for i.
-14, -3
Let s(d) be the first derivative of -7*d**6/15 + 88*d**5/25 - 15*d**4/2 + 12*d**3/5 - 82. Let s(x) = 0. What is x?
0, 2/7, 3
Let t = 111 - 111. Let i(s) be the first derivative of -4 - 1/10*s**4 + 0*s + t*s**2 + 0*s**3. Solve i(m) = 0 for m.
0
Let x = 69019/70 - 986. Let m = x - -11/70. Factor 10/7*o**3 + 5/7*o - 10/7*o**2 + m*o**5 - 5/7*o**4 - 1/7.
(o - 1)**5/7
Let u(s) = -6*s + 31. Let w be u(4). Find t, given that -3*t**5 + w*t**5 + t**5 = 0.
0
Let c(x) be the third derivative of -9/16*x**4 - 2*x**3 + 0 + 0*x + 17*x**2 - 1/40*x**5. Determine k, given that c(k) = 0.
-8, -1
Let f(g) be the second derivative of -98*g**6/15 - 126*g**5/5 - 109*g**4/3 - 24*g**3 - 8*g**2 + 28*g. Factor f(z).
-4*(z + 1)**2*(7*z + 2)**2
Let b(p) = -p**4 - 12*p**3 - 78*p**2 - 116*p - 45. Let d(i) = i**4 + 11*i**3 + 78*i**2 + 117*i + 44. Let g(u) = 5*b(u) + 4*d(u). Factor g(s).
-(s + 1)**2*(s + 7)**2
Let r(m) be the third derivative of 0*m - 12*m**2 - 1/24*m**4 + 1/60*m**5 + 0*m**3 + 0. What is h in r(h) = 0?
0, 1
Let u(p) be the first derivative of 1/9*p**6 + 7/3*p**4 - 4/5*p**5 - 32/9*p**3 - 4/3*p + 22 + 3*p**2. Determine z so that u(z) = 0.
1, 2
Suppose -11 + 5 = -3*w. Find m, given that -10*m + 80*m**3 + 20*m**2 + 0*m - 6*m**2 + 45*m**4 + 11*m**w = 0.
-1, 0, 2/9
Let n(f) = 5*f + 1. Let x be n(0). Let r(m) = -1. Let c(w) be the first derivative of -w**3 + 9*w**2 - 36*w + 1. Let d(s) = x*c(s) - 9*r(s). Factor d(i).
-3*(i - 3)**2
Factor -14*f**2 + 63 + 32*f**2 - 17*f**2 + 2*f - 18*f.
(f - 9)*(f - 7)
Let g = 7 - -9. Find h such that -16*h + h**2 + 3*h**2 + 0*h**2 + g = 0.
2
Let a(t) = 10*t - 13. Let n be a(0). Let b = n - -13. Factor b*i + 2*i**5 + 16/3*i**4 + 14/3*i**3 + 4/3*i**2 + 0.
2*i**2*(i + 1)**2*(3*i + 2)/3
Let r(h) = -6*h**5 - h**4 - 34*h**3 - 56*h**2 - 44*h - 17. Let p(y) = 7*y**5 - y**4 + 33*y**3 + 55*y**2 + 44*y + 18. Let t(d) = 5*p(d) + 6*r(d). Factor t(l).
-(l + 1)**3*(l + 2)*(l + 6)
Let y(f) = -6*f**2 - 72*f - 209. Let v(j) = 3*j**2 + 36*j + 105. Let r be -3*1 + (0 - 4). Let g(o) = r*v(o) - 3*y(o). Determine h so that g(h) = 0.
-6
Let z = 17214 - 17212. Suppose 1/6*d - 1/3*d**3 + 1/6*d**5 + 0*d**z + 0*d**4 + 0 = 0. What is d?
-1, 0, 1
Let a(r) = -r**2 + 38*r - 103. Let y be a(35). Let k(u) be the third derivative of 0*u**4 - 1/180*u**5 + 0*u**3 + 0*u - 5*u**y + 0. Solve k(h) = 0.
0
Let j(c) be the third derivative of c**7/630 - 13*c**6/720 - 13*c**5/180 + c**4/9 + 358*c**2 - 2*c. Let j(s) = 0. What is s?
-2, 0, 1/2, 8
Let a(v) be the first derivative of 5*v**4/4 - 5*v**3/3 - 33. Factor a(q).
5*q**2*(q - 1)
Let l = -246 - -248. Let n(z) be the second derivative of 1/27*z**3 - 1/54*z**4 - 4*z + 0 + 0*z**l. Suppose n(h) = 0. What is h?
0, 1
Let p(o) be the second derivative of -2*o**7/21 + o**6/15 + 7*o**5/5 + 5*o**4/6 - 2*o**3 + 53*o. Determine a, given that p(a) = 0.
-2, -1, 0, 1/2, 3
Let a be 0 + ((-4)/(-3) - 1). Suppose -2*k + m + 10 = 0, -2*k - 21*m - 8 = -19*m. Suppose -w + 0*w**k + a*w**3 - 2/3 = 0. What is w?
-1, 2
Let z be (-2 + 1)/((-2)/15 + 238/(-2040)). Suppose -5/7*n**z + 1/7*n**5 - n**2 + 9/7*n**3 + 2/7*n + 0 = 0. What is n?
0, 1, 2
Let f(z) = -31*z**4 + 85*z**3 - 83*z**2 + 15*z - 2. Let n(m) = -30*m**4 + 84*m**3 - 84*m**2 + 21*m - 3. Let k(o) = -3*f(o) + 4*n(o). Let k(q) = 0. What is q?
1/3, 2/3, 1
Let a(f) be the first derivative of 1/15*f**3 - 18 - 2/5*f**2 + 3/5*f. Factor a(g).
(g - 3)*(g - 1)/5
Suppose -116*g = 159*g - 1375. Factor 0*b - 4/3*b**3 + 0*b**2 + 0 - 4*b**4 - 5/3*b**g.
-b**3*(b + 2)*(5*b + 2)/3
Factor 82*p - 6 - 2*p**2 - 16 - 58.
-2*(p - 40)*(p - 1)
Solve 319*t**3 + 34 - t**4 + 104*t + 108*t**2 + 3*t**4 - 279*t**3 = 0.
-17, -1
Let i = -2/61 - -69/244. Let o(c) be the first derivative of -i*c**2 - 1/12*c**3 + 1 + 3/4*c. Factor o(q).
-(q - 1)*(q + 3)/4
Let k be (4/(-50))/(47/16450*-14). Determine o so that 24/5*o - 2/5*o**4 + 12/5*o**3 - 26/5*o**k - 8/5 = 0.
1, 2
Let r(s) be the third derivative of s**8/336 + s**7/210 - s**6/40 - s**5/60 + s**4/12 - 84*s**2. Factor r(j).
j*(j - 1)**2*(j + 1)*(j + 2)
Let z be (96/18)/(-4) + (-4)/6. Let x be (z/6)/(7/(-42)). Determine b so that 0 + 0*b - b**x + 1/2*b**5 - 2*b**4 + 5/2*b**3 = 0.
0, 1, 2
Suppose 4*f = -32 + 20. Let k(l) = -3*l**3 - 19*l + 1. Let b(t) = t**3 + 9*t - 1. Let g(p) = f*k(p) - 7*b(p). Let g(h) = 0. What is h?
-2, 1
Let m = -575 - -579. Let v(g) be the second derivative of 5*g - 1/225*g**6 + 0*g**2 + 0*g**m + 0*g**3 + 0 + 1/75*g**5. Let v(c) = 0. Calculate c.
0, 2
Let i(j) be the second derivative of 5*j**4/4 + 50*j**3/3 - 35*j**2/2 - j + 17. Suppose i(k) = 0. What is k?
-7, 1/3
Let s = 2437/974 - 1/487. Let q(i) be the second derivative of 3*i**2 + 0 - s*i**3 + i**4 + 7*i - 3/20*i**5. Factor q(l).
-3*(l - 2)*(l - 1)**2
Let q be 6/(-48)*6*202/(-3). Let v = q + -50. Let -a + a**3 + 0*a**2 - 1/2*a**4 + v = 0. What is a?
-1, 1
Let r(u) be the second derivative of 0*u**3 + u + 1/84*u**7 + 0*u**4 + 0*u**2 - 1/60*u**6 + 0*u**5 + 0. Factor r(d).
d**4*(d - 1)/2
Let x(i) = -i**3 - i**2 - i + 1. Let k(m) = m**3 - 21*m**2 - 39*m - 23. Let y(h) = k(h) + 3*x(h). Factor y(c).
-2*(c + 1)**2*(c + 10)
Suppose 6 - 34 = -7*p. Let l(j) be the second derivative of 0 - 1/10*j**3 + 0*j**2 + 3/20*j**4 + p*j. Find f, given that l(f) = 0.
0, 1/3
Solve 0 + 14/5*w**2 + 2/5*w**3 + 0*w = 0 for w.
-7, 0
Let p(x) = 7*x**3 - 12*x**2 + 11*x. Let q(y) = 2*y**3 - 3*y**2 + 3*y. Let w be (-2)/5 - 