(k) be the third derivative of u(k). Factor v(d).
-(d - 3)*(9*d - 2)
Let j be 5/((-45)/(-18))*(-1 + 2). Suppose 2*z + z = 12. Suppose -10 + 4*t**j + 10 + z*t = 0. Calculate t.
-1, 0
Let m = 72 - 55. Let p(d) = -44*d**2 + 51*d - 16. Let j(s) = -133*s**2 + 152*s - 47. Let f(t) = m*p(t) - 6*j(t). Factor f(k).
5*(2*k - 1)*(5*k - 2)
Let g be 3/(-2)*4/(-3). Let f = -3829 - -3829. Determine q so that -8/3*q**3 + 10/3*q**g + 2/3*q**4 + f - 4/3*q = 0.
0, 1, 2
Factor -708 + 708 + 4*l**3 - 16*l.
4*l*(l - 2)*(l + 2)
Let r(z) be the second derivative of -3*z**5/80 + 5*z**4/8 - 7*z**3/8 - 27*z**2/4 - 100*z. Factor r(x).
-3*(x - 9)*(x - 2)*(x + 1)/4
Let 10 - 35/3*z**3 + 40*z**2 - 115/3*z = 0. Calculate z.
3/7, 1, 2
Let z(l) be the first derivative of 5*l**8/336 + l**7/7 + 3*l**6/8 + 9*l**2/2 - 12. Let o(v) be the second derivative of z(v). Determine q, given that o(q) = 0.
-3, 0
Let q(z) be the third derivative of 0 - 5/12*z**4 + 1/30*z**5 + 6*z**2 + 0*z**3 + 0*z. Suppose q(k) = 0. Calculate k.
0, 5
Suppose -97*t + 304 = 13*t - 26. Factor -3*s + 3*s**t + 6/5*s**2 - 6/5.
3*(s - 1)*(s + 1)*(5*s + 2)/5
Let k(l) = -4*l**3 - l**2 + 21. Let a(b) = -4*b**3 - 2*b**2 + 21. Let u(w) = -3*a(w) + 4*k(w). Let o(c) be the first derivative of u(c). Factor o(h).
-4*h*(3*h - 1)
Let m = 45 - 43. Solve -5 - 8 - 12*a**m - 2 - 27*a + 9 = 0 for a.
-2, -1/4
Factor -30/11*p**2 - 18/11 - 6/11*p**3 - 42/11*p.
-6*(p + 1)**2*(p + 3)/11
Let g(n) be the second derivative of 1/40*n**5 + 1/8*n**4 + 0 + 1/6*n**3 - 2*n + 0*n**2. Let g(i) = 0. What is i?
-2, -1, 0
Let 2/13*p**4 - 14/13*p**2 + 0 - 4/13*p**3 - 8/13*p = 0. Calculate p.
-1, 0, 4
Let m be 855/(-513) - 4/(120/(-74)). Factor 2/5*p**4 + 2/5 - m*p**2 + 0*p**3 + 0*p.
2*(p - 1)**2*(p + 1)**2/5
Let f = 48325 - 144973/3. Factor -f*h + 1/3*h**2 + 1/3.
(h - 1)**2/3
Let p(d) be the second derivative of -d**6/60 - 11*d**5/40 - 3*d**4/8 + 11*d**3/12 + 5*d**2/2 - 24*d - 8. Determine m so that p(m) = 0.
-10, -1, 1
Let c be ((-16)/72)/(2/(-12)). Let g = -80 + 82. Factor -c + 2*f - 2/3*f**g.
-2*(f - 2)*(f - 1)/3
Let i = -513 + 516. Let t(f) be the second derivative of 0*f**2 + 1/51*f**4 + 0*f**i + 0 - 1/357*f**7 - 1/34*f**5 + 8*f + 4/255*f**6. Let t(p) = 0. What is p?
0, 1, 2
Let i(j) be the second derivative of j**8/6720 + j**7/2520 - 7*j**4/6 - 3*j. Let m(n) be the third derivative of i(n). Solve m(p) = 0.
-1, 0
Factor 3/2*o**2 + 3*o - 12.
3*(o - 2)*(o + 4)/2
Factor 6784*i**3 + 103 + 202 + 382*i - 6804*i**3 - 2*i - 608*i**2 - 57.
-4*(i - 1)*(i + 31)*(5*i + 2)
Let h(l) = 16*l**3 + 34*l**2 - 32*l. Let g(i) = -47*i**3 - 100*i**2 + 95*i + 1. Let o(r) = -6*g(r) - 17*h(r). Factor o(b).
2*(b - 1)*(b + 3)*(5*b + 1)
Let h = -904 - -908. Let j(s) be the second derivative of -s**2 + 0*s**h - 1/20*s**5 + 3*s + 0 + 1/2*s**3. Factor j(x).
-(x - 1)**2*(x + 2)
Let l(x) = 2*x. Let z be l(3). Suppose -u = -3*c + 2*c - z, 0 = -2*u - 3*c + 12. Solve -6*f**5 - 4 + 4*f**2 + 0*f**2 - u*f - 3*f**3 + 4*f**5 + 11*f**3 = 0.
-1, 1, 2
Let q(i) be the third derivative of i**8/840 - 2*i**7/175 - 7*i**6/300 - 7*i**2 - 7. Solve q(f) = 0.
-1, 0, 7
Factor 3*r - 71*r - 139*r**2 + 0*r**3 - r**3 + 103*r**2.
-r*(r + 2)*(r + 34)
Let w(t) be the third derivative of -t**8/30240 - t**7/2520 - 3*t**5/20 - 12*t**2. Let k(f) be the third derivative of w(f). Let k(p) = 0. What is p?
-3, 0
Let n = -3 - -8. Let a = -9 + 13. Suppose 1/2*y**2 - 1/4*y**a + 1/4*y - 1/2*y**3 - 1/4 + 1/4*y**n = 0. What is y?
-1, 1
Factor 49*v + 4*v**2 + 58*v - 3*v**4 - 3*v**3 + v**5 - 103*v + v**4.
v*(v - 2)**2*(v + 1)**2
Let x(j) be the second derivative of j**5/5 - 7*j**4/3 - 80*j**3/3 - 88*j**2 - 95*j - 1. Find b such that x(b) = 0.
-2, 11
Let l(c) be the second derivative of c**6/540 - 13*c**5/180 + c**4/3 + 28*c**3/3 - c - 55. Let y(b) be the second derivative of l(b). Let y(v) = 0. Calculate v.
1, 12
Solve -102/7*y**2 - 194/7*y**3 - 20/7 + 6*y**4 + 114/7*y = 0 for y.
-1, 2/7, 1/3, 5
Let p = -11 - -2. Let z = -7 - p. Suppose -8/3*b - 5/3*b**z - 1/3*b**3 - 4/3 = 0. What is b?
-2, -1
Let n(v) = 26*v**3 - 109*v**2 + 94*v - 11. Let h(r) = 22*r**2 - 19*r + 8 + 12 - 18 - 5*r**3. Let x(q) = 11*h(q) + 2*n(q). Factor x(s).
-3*s*(s - 7)*(s - 1)
Suppose 12 = -3*s - 3*k, -761*s + 3*k + 4 = -766*s. Let 6 + 2/3*u**2 - s*u = 0. Calculate u.
3
Let d(u) be the second derivative of 0*u**2 + 5/6*u**4 + 2/3*u**6 + 0 + 5/42*u**7 + 5/4*u**5 + 0*u**3 - 11*u. Factor d(s).
5*s**2*(s + 1)**2*(s + 2)
Factor 136*c**2 - 84*c - 417*c - c**3 - 3*c**3 - 600*c - 55*c.
-4*c*(c - 17)**2
Let f be 3*2/3 + -2. Let s be (f - -1)/(1*(4 + 0)). Factor 0 - s*i**3 + 0*i**4 + 0*i**2 + 0*i + 1/4*i**5.
i**3*(i - 1)*(i + 1)/4
Suppose -19*n + 30 = -14*n. Suppose 12 = 5*g - y - 0, n = -3*y. Factor 2/11*f**g - 2/11 + 0*f.
2*(f - 1)*(f + 1)/11
Suppose 4*b - 22 = -2*d, -2*b - 9 = -0*b - 3*d. Let x(h) be the third derivative of 0*h - b*h**2 + 0 + 1/90*h**5 + 0*h**3 + 0*h**4. Factor x(k).
2*k**2/3
Let p(j) be the first derivative of 98*j**5/75 - 476*j**4/15 + 2416*j**3/45 + 928*j**2/15 + 96*j/5 - 189. Suppose p(t) = 0. What is t?
-2/7, 2, 18
Let x(k) = k + 1. Let r be x(5). Factor -48*l**2 - 6*l**3 + 3*l**3 + r*l**3 + 86*l + 106*l.
3*l*(l - 8)**2
Let l(f) = -24*f**3 + 24*f**2 - 45*f + 11*f**2 + 39*f - 9 + 0. Let x(m) = -m**3 + m - 1. Let y(s) = -l(s) + 4*x(s). Factor y(c).
5*(c - 1)**2*(4*c + 1)
Let d = 14/57 - 4/171. Factor 0*k + 0 + d*k**2 + 2/9*k**3.
2*k**2*(k + 1)/9
Let y(r) be the third derivative of 15*r**2 - 18/5*r**5 + 0*r - 7/40*r**6 - 25*r**3 - 195/8*r**4 + 0. Determine s so that y(s) = 0.
-5, -2/7
Suppose -2*x + 32 = -0. Suppose -x = -o - 4*g, 0 - 4 = 3*o - g. What is a in 0 + o*a + 5/4*a**4 - 1/4*a**5 - 2*a**3 + a**2 = 0?
0, 1, 2
Let r = -354 + 683. Let o = r - 2293/7. Find d such that 2/7*d + 6/7*d**4 - 6/7*d**2 + 8/7*d**5 + 0 - o*d**3 = 0.
-1, 0, 1/4, 1
Let p be (-6)/(-10) - 36/(-15). Let m(s) be the second derivative of 1/5*s**3 + 1/5*s**2 + 1/50*s**5 + 0 + 1/10*s**4 + p*s. Suppose m(o) = 0. Calculate o.
-1
Suppose 5*v - 9 = -w, -2*v = -4*w - 5 - 3. Let m = w - -6. Factor m*b - 5*b + 2*b**2.
2*b**2
Let b(u) be the second derivative of -14*u + 0 - 1/165*u**6 + 1/66*u**4 - 1/110*u**5 + 1/33*u**3 + 0*u**2. Find v such that b(v) = 0.
-1, 0, 1
Factor -8 - z - 2*z**2 + 6*z**2 + 2 - z**3.
-(z - 3)*(z - 2)*(z + 1)
Let d(s) be the first derivative of 4*s**3/3 - 68*s**2 + 1156*s - 265. Let d(m) = 0. Calculate m.
17
Let k(a) be the second derivative of -a**5/12 - 5*a**4/18 + 5*a**3/6 - 138*a. Factor k(n).
-5*n*(n - 1)*(n + 3)/3
Let s(r) be the third derivative of r**6/960 + 7*r**5/480 - 17*r**4/192 + 3*r**3/16 + 22*r**2 + 2*r. Factor s(u).
(u - 1)**2*(u + 9)/8
Determine x, given that -16/11*x - 24/11 - 2/11*x**2 = 0.
-6, -2
Factor 754*c - 778*c + 2*c**2 + 4*c**3 - 6*c**2.
4*c*(c - 3)*(c + 2)
Suppose 284 = -12*f + 308. Let s = 2/5 - 0. Factor -2/5*o**f - 4/5*o - s.
-2*(o + 1)**2/5
Let r(k) = -k**4 + k**3 - k**2. Let o(h) be the second derivative of 4*h**6/15 - 11*h**5/20 + 5*h**4/6 - 8*h. Let m(g) = 3*o(g) + 21*r(g). Factor m(i).
3*i**2*(i - 3)*(i - 1)
Let d be 7 - (-8)/120*-99. Let i(b) be the first derivative of 3 + 0*b**2 + 0*b**3 + 0*b + 1/5*b**4 - d*b**5 - 7/15*b**6. Factor i(s).
-2*s**3*(s + 1)*(7*s - 2)/5
Let a(s) be the third derivative of -s**6/120 + 2*s**5/15 + 3*s**4/8 - 2*s**2 + 4*s. Let a(c) = 0. Calculate c.
-1, 0, 9
Factor 1270*k**4 + 21*k**3 + 16*k - 1274*k**4 - 32*k**2 - k**3.
-4*k*(k - 2)**2*(k - 1)
Let z = 8/1921 + 17233/13447. Factor 6/7*j - z + 3/7*j**2.
3*(j - 1)*(j + 3)/7
Let v(p) be the second derivative of -33*p - 1/30*p**6 - 1/20*p**5 + 0 + 1/6*p**3 + 1/12*p**4 + 0*p**2. Factor v(u).
-u*(u - 1)*(u + 1)**2
Let c(u) be the third derivative of -u**10/25200 + u**9/5670 + u**8/7560 - u**5/20 - 9*u**2. Let p(l) be the third derivative of c(l). Factor p(b).
-2*b**2*(b - 2)*(9*b + 2)/3
Let j(a) be the third derivative of -a**8/336 - 4*a**7/105 - 11*a**6/60 - 2*a**5/5 - 3*a**4/8 - 3*a**2 - 10*a. Solve j(x) = 0 for x.
-3, -1, 0
Let z(w) be the third derivative of -w**5/240 + 11*w**4/32 + 17*w**3/12 + 533*w**2. Factor z(m).
-(m - 34)*(m + 1)/4
Suppose -x + 4*f - 13 = 0, -12 = -5*x - 2*f + 33. Factor -7*g**3 - 3*g**4 + 18 - g**2 - x*g**3 - 2*g - 15 - 15*g**2.
-(g + 1)**2*(g + 3)*(3*g - 1)
Let u(j) be the first derivative of j**4/8 - 4*j**3/3 +