(x). Determine a, given that t(a) = 0.
438
Let n(z) = 5*z**2 + 38*z + 69. Let m(k) = -k**2 - 10*k - 17. Let q be ((-32)/(-20) - 6/10)*-2. Let i(f) = q*n(f) - 9*m(f). Suppose i(y) = 0. What is y?
-1, 15
Let c be 1/(-5) + (1116/(-5))/(-6). Let -3*g**2 - c*g - 20*g + 0*g**2 = 0. What is g?
-19, 0
Let i = 370 - 367. Factor -43 + 39*o**3 + 43 + 24*o**2 + 21*o**4 + 3*o**5 + i*o**3.
3*o**2*(o + 1)*(o + 2)*(o + 4)
Suppose 0 = c, 116*i - c - 1456 = 120*i. Let l be 2 + ((-26)/i)/((-1)/24). Factor -10/7 - l*d**2 - 12/7*d.
-2*(d + 1)*(d + 5)/7
Let n(v) = -31*v**3 - 60*v**2 - 61*v. Let p(k) = -38*k**3 - 60*k**2 - 62*k. Let z(o) = 5*n(o) - 4*p(o). Factor z(i).
-3*i*(i + 1)*(i + 19)
Let c(x) be the third derivative of x**6/72 - x**5/12 - 5*x**4/8 + 53*x**3/6 + 2*x**2 + 8. Let h(l) be the first derivative of c(l). Factor h(k).
5*(k - 3)*(k + 1)
Let x(a) = -3*a + 2*a + 7 - 11 - 8. Let r be x(-15). Factor -80*d**3 + 54*d**3 - 12*d + 10*d**2 - 15*d**4 - 3*d + 36*d**r + 5 + 5*d**5.
5*(d - 1)**4*(d + 1)
Suppose 0 = 18*u - 21*u - 2*t - 54, 4*u + 3*t = -73. Let b be u/18*9/(-12). Factor -8/3*h + 10/3 - b*h**2.
-2*(h - 1)*(h + 5)/3
Suppose -3*z - 6*f + f + 53 = 0, -4*z + 59 = -5*f. Find t, given that 9*t**3 + 9*t**3 + 6*t**3 + 8*t + 4*t**4 + 44*t**2 + z*t = 0.
-3, -2, -1, 0
Let k = 37 + -29. Let v(a) = -a**2 + 11*a - 11. Let r be v(k). Suppose 2*p - 42*p - 80 + 6*p**2 - 24*p**2 + r*p**2 = 0. Calculate p.
-4
Suppose -x = -4*o - 4*x + x, 5*o + x = 0. Determine g so that 0*g + 2/11*g**5 - 38/11*g**3 - 20/11*g**2 - 16/11*g**4 + o = 0.
-1, 0, 10
Factor -274 + 123*u + 274 - u**3 - 154*u**2 + 32*u**2.
-u*(u - 1)*(u + 123)
Factor 62644*c**2 + 44567*c - 646*c**4 + 121104 - 702*c**3 + 320*c**4 + 328*c**4 - 227615*c.
2*(c - 174)**2*(c - 2)*(c - 1)
Let u = -9554 + 9559. Let l(c) be the first derivative of 392*c**3 + 9604*c + 28*c**4 + 2744*c**2 + 4/5*c**u + 26. What is g in l(g) = 0?
-7
Let y(v) = 5*v**3 + 155*v**2 + 764*v + 1198. Let d(l) = -35*l**3 - 1095*l**2 - 5350*l - 8385. Let j(f) = -2*d(f) - 15*y(f). Factor j(m).
-5*(m + 3)*(m + 4)*(m + 20)
Let w(n) be the first derivative of -4/17*n + 0*n**3 + 1/34*n**4 - 3/17*n**2 - 60. What is m in w(m) = 0?
-1, 2
Find y such that -1953/2 + 3/4*y**2 + 123/4*y = 0.
-62, 21
Let i be -2 + 16/12 + 1 - 12/((-288)/40). Factor -2/5*d**3 - 4/5*d**i + 0 - 2/5*d.
-2*d*(d + 1)**2/5
Suppose 0 = -124*a + 102*a + 44. Solve 24049*q - 34*q**2 - 67649 - 388884 - 218*q**a - 6262*q + q**3 + 21*q**2 = 0.
77
Factor 164/3*z**2 + 40 - 262/3*z - 22/3*z**3.
-2*(z - 1)**2*(11*z - 60)/3
Let j(q) = -q**3 - 15*q**2 + 55*q + 18. Let k = 1677 + -1695. Let w be j(k). Let -14/3*n**3 - 6*n - 10*n**2 - 2/3*n**4 + w = 0. Calculate n.
-3, -1, 0
Let w(k) = 6*k**4 + 90*k**3 + 376*k**2 - 1822*k + 1354. Let t(g) = g**4 - g**3 + 2*g**2 - g + 1. Let a(f) = -2*t(f) + w(f). Factor a(v).
4*(v - 2)*(v - 1)*(v + 13)**2
Let -1/3*l**3 - 4*l - 4*l**2 + 80/3 = 0. What is l?
-10, -4, 2
Let g(h) be the third derivative of 0*h + 33*h**2 + 1/30*h**5 - 2*h**3 + 0 + 5/12*h**4. Determine v, given that g(v) = 0.
-6, 1
Let z(b) = -2*b - 3. Let k be z(2). Let m(n) = n**3 + 8*n**2 + 6*n - 5. Let j be m(k). Factor 5*q**j - 2*q - 5*q**2 - 2*q**2 + q**2.
-q*(q + 2)
Let i(c) = -c - 1. Let y(v) = 2*v**3 - 2*v**2 - 20*v - 16. Let l be 55/33*(8 + 1). Let r be (-28)/(-20)*1 - (-9)/l. Let o(u) = r*y(u) - 36*i(u). Factor o(m).
4*(m - 1)**2*(m + 1)
Suppose -9*p - 316 - 224 = 0. Let r be 0*5*12/p. Let r*c + 0 + c**3 - 2/3*c**2 = 0. What is c?
0, 2/3
Let w(p) be the first derivative of p**5/5 + 8*p**4 + 85*p**3 - 16*p**2 - 256*p - 225. Factor w(t).
(t - 1)*(t + 1)*(t + 16)**2
Let g(m) be the first derivative of m**5/20 - 13*m**4/32 + 2*m**3/3 - 5*m**2/16 - 1152. Solve g(t) = 0.
0, 1/2, 1, 5
Let x(b) be the first derivative of b**8/1680 - b**7/840 - b**6/60 + 7*b**3/3 - 3*b**2/2 - 32. Let n(g) be the third derivative of x(g). Factor n(s).
s**2*(s - 3)*(s + 2)
Let l(x) be the first derivative of x**4/20 - 469*x**3/5 + 659883*x**2/10 - 103161709*x/5 - 1061. Factor l(h).
(h - 469)**3/5
Factor 65 - 71 + 123 + 5*g**3 - 18 + 100*g**2 + 265*g + 71.
5*(g + 1)*(g + 2)*(g + 17)
Let i = 435 - 430. Factor 30*f**2 + 7*f - 8*f**2 + 2*f**i - 6*f**3 - 6*f**4 - 27*f + 8*f.
2*f*(f - 3)*(f - 1)**2*(f + 2)
Let x(m) be the third derivative of m**6/24 - 95*m**5/12 + 600*m**2 + m. Solve x(o) = 0 for o.
0, 95
Let j(h) = 3*h**2 + 14 + 21*h - 4*h**2 - 32*h. Let q be j(-12). What is w in -w**q + 4*w**3 - 70*w**4 + 68*w**4 - w**2 = 0?
0, 1
Let z(g) be the second derivative of 1 + 9*g + 3/25*g**5 - 9/20*g**4 + 0*g**2 + 1/5*g**3. Determine s so that z(s) = 0.
0, 1/4, 2
Let h(w) be the third derivative of 3*w**6/40 - 349*w**5/20 - 701*w**4/24 - 39*w**3/2 + 250*w**2. Suppose h(k) = 0. Calculate k.
-1/3, 117
Let s = -217978 + 217981. Factor 23/2*j**2 + 1/2*j**4 + 14*j + 4*j**s + 6.
(j + 1)*(j + 2)**2*(j + 3)/2
Factor 0*n + 1/2*n**4 - 118*n**2 + 0 + 55/2*n**3.
n**2*(n - 4)*(n + 59)/2
Let u(x) be the third derivative of -x**8/840 - 4*x**7/525 - x**6/60 - x**5/75 + 1008*x**2. Factor u(a).
-2*a**2*(a + 1)**2*(a + 2)/5
Let i(j) be the third derivative of j**5/270 + 14*j**4/27 + 55*j**3/27 + 7141*j**2. Determine p, given that i(p) = 0.
-55, -1
Let z(w) be the first derivative of 2*w**2 - 71 + 2/39*w**3 - 54/13*w. Suppose z(i) = 0. Calculate i.
-27, 1
Factor -2400/7 + 2/7*y**2 + 470/7*y.
2*(y - 5)*(y + 240)/7
Let z = -2/40599 - -2097617/40599. Factor 160/3 - 5/3*g**2 + z*g.
-5*(g - 32)*(g + 1)/3
Let p(b) be the third derivative of 1/24*b**6 + 0*b**3 + 6 - 5/12*b**4 + 0*b + 2*b**2 + 1/12*b**5. Factor p(v).
5*v*(v - 1)*(v + 2)
Let u(k) be the first derivative of 10*k**5/7 + 3295*k**4/14 - 1352*k**3/21 - 2116*k**2/7 - 1056*k/7 + 2383. Suppose u(g) = 0. What is g?
-132, -2/5, 1
Let h(q) be the first derivative of 504/25*q**5 + 8/5*q**6 - 99/2*q**2 + 200 + 131/5*q**3 + 1419/20*q**4 + 15*q. Suppose h(v) = 0. Calculate v.
-5, -1, 1/4
Let h = 21977/452 + -5240/113. What is g in 0 - h*g + 21/4*g**2 = 0?
0, 3/7
Let o be (-5)/3 - (-73656)/40176. Let -5/2*l**4 - o*l**5 - 10/3 - 59/6*l**3 - 12*l - 97/6*l**2 = 0. What is l?
-10, -2, -1
Let h(b) = -3*b**3 - 66*b**2 + 121*b + 976. Let s(v) = -24*v**3 - 525*v**2 + 969*v + 7809. Let y(a) = -33*h(a) + 4*s(a). What is u in y(u) = 0?
-27, -3, 4
Suppose -45*v - 1119 - 231 = 0. Let r be (-7 + v/(-4))*6/8. Factor -3/8*c + r*c**2 + 0.
3*c*(c - 1)/8
Factor 2/15*k**2 - 212/5 - 314/15*k.
2*(k - 159)*(k + 2)/15
Let u(k) = -13*k**2 + 27*k + 2. Let v(m) be the third derivative of m**5/15 - 3*m**4/8 - m**3/6 - 133*m**2. Let d(i) = 3*u(i) + 8*v(i). Factor d(n).
-(n - 1)*(7*n - 2)
Suppose 40 + 14 = 19*m + 16. Let l(j) be the third derivative of -25/24*j**4 + 0 + 0*j + 1/12*j**5 + 14*j**m + 0*j**3. Factor l(q).
5*q*(q - 5)
Suppose -30 = -g + 8. Suppose 14*h + g = 94. Factor -f**h - 4 + 12*f**2 + 24 + 36*f + 5*f**2.
-(f - 5)*(f + 1)*(f + 2)**2
Let a(d) be the second derivative of -1/55*d**6 - 2 + 0*d**2 - 8/55*d**5 - 23/66*d**4 - 2/11*d**3 + 73*d. Suppose a(u) = 0. Calculate u.
-3, -2, -1/3, 0
Let j = -395746 + 395749. Factor -3/2*n**j + 3/2*n + 27/2*n**2 - 27/2.
-3*(n - 9)*(n - 1)*(n + 1)/2
Let r = 1546 + -943. Solve -20 - 19*i + 32*i**2 - 10*i**2 - r*i**3 - 2*i**4 + 621*i**3 + i = 0.
-1, 1, 10
Let h be -32 + (-8496)/(-252) + (-48)/28. Let -2/11*u**2 - 28/11*u + h = 0. Calculate u.
-14, 0
Let m(a) = 377*a - 2262. Let k be m(6). What is n in -27/5*n - 9/5*n**3 - 27/5*n**2 - 1/5*n**4 + k = 0?
-3, 0
Solve 23/5*m**3 + 1/5*m**5 + 47/5*m**2 - 36/5 - 24/5*m - 11/5*m**4 = 0 for m.
-1, 1, 6
Let x = 7833 + -15665/2. Suppose 3*n - 9 = 4*m, 0 = -5*n + 4*m + 20 - 5. Let -9/4*v**3 - n*v**2 - x + 11/4*v = 0. Calculate v.
-2, 1/3
Find a, given that 500000/9 - 998000/9*a + 2/9*a**4 + 165334/3*a**2 + 1996/9*a**3 = 0.
-500, 1
Let o(s) be the first derivative of -s**6/3 + 2*s**5/5 + s**4 - 414. Find g such that o(g) = 0.
-1, 0, 2
Let o(q) be the second derivative of q**7/294 + 61*q**6/70 + 4407*q**5/70 + 20065*q**4/42 + 7387*q**3/14 - 71289*q**2/14 - 7373*q. Determine d so that o(d) = 0.
-89, -3, 1
Let l(c) = c + 1. Let r = -50 - -44. Let p = -99 + 100. Let z(u) = -u**2 + 8*u + 9. Let s(x) = p*z(x) + r*l(x). Solve s(m) = 0 for m.
-1, 3
Let k(j) be the first derivative of 36 + 28*j - 9/20*j**5 + 3/2*j**3 + 1/4*j**4 + 1/10*j**6 - 3*j**2. Let o(i) be 