et a be w/(-98)*-1*28/(-8). Factor -1/3*k**4 - 4/3*k**2 + 0 + 5/3*k**a + 0*k.
-k**2*(k - 4)*(k - 1)/3
Let m = 1493/4 - 189591/508. Let a = m - -209/1143. Factor 0 + 2/9*u**3 + 4/9*u**2 + a*u.
2*u*(u + 1)**2/9
Let j(b) be the second derivative of -b**6/10 + 13*b**4/4 - 6*b**3 - 10847*b. Factor j(k).
-3*k*(k - 3)*(k - 1)*(k + 4)
Solve -270*q + 555*q**2 - 6*q**3 - 552 + 202*q**3 + 99*q**3 - 3*q**4 - 25*q**3 = 0 for q.
-2, -1, 1, 92
Let v = 402 - 389. Let y(u) = 2*u**4 + 17*u**3 + 7*u**2 + 5*u - 5. Let d(p) = p**4 + 8*p**3 + 3*p**2 + 2*p - 2. Let c(k) = v*d(k) - 6*y(k). Factor c(g).
(g - 1)**2*(g + 2)**2
Let g(z) = 25*z**3 - 506*z**2 - 633*z - 146. Let y(b) = -8*b**3 + 169*b**2 + 210*b + 49. Let o(s) = -4*g(s) - 11*y(s). Factor o(r).
-3*(r - 15)*(r + 1)*(4*r + 1)
Let p(z) = z + 75. Let v be p(7). Let r = -80 + v. Factor -1 - 6*i**r + 8*i**2 + 10 + 14*i + 3.
2*(i + 1)*(i + 6)
Let q = 462 - 314. Suppose 2*u - 6*u - 4*p + q = 0, u - p - 27 = 0. Find s such that s - 33*s**2 + u*s**2 + 0 - s**3 + 1 = 0.
-1, 1
Let j be 23560/110670 + 0 + 8/(-84). What is f in 4/17*f**2 + j*f**5 - 2/17*f**3 - 4/17*f**4 + 0*f + 0 = 0?
-1, 0, 1, 2
Let y(z) be the first derivative of 25*z**5 - 50*z**4 - 370*z**3/3 + 180*z**2 + 405*z + 529. Factor y(w).
5*(w + 1)**2*(5*w - 9)**2
Let c(q) be the third derivative of q**7/1540 - q**6/396 + q**5/330 - 52*q**3/3 + 102*q**2. Let t(n) be the first derivative of c(n). Factor t(w).
2*w*(w - 1)*(3*w - 2)/11
Let g(a) be the second derivative of -a**7/15 - 9*a**6/5 + 51*a**5/25 + 4*a**4/3 + 1892*a. Solve g(w) = 0.
-20, -2/7, 0, 1
Let d(y) be the second derivative of -6*y**5/5 + 7*y**4/6 - 5*y**3/6 - 40*y + 2. Let t(o) = -o. Let n(v) = -d(v) + 3*t(v). Determine b so that n(b) = 0.
0, 1/4, 1/3
What is f in 193210 + 2/5*f**2 + 556*f = 0?
-695
Let f(m) be the first derivative of -2*m**5/25 - 23*m**4/10 - 98*m**3/5 - 229*m**2/5 - 208*m/5 - 12322. Let f(u) = 0. What is u?
-13, -8, -1
Let -46818 - 816*i - 32/9*i**2 = 0. Calculate i.
-459/4
Let t(r) be the third derivative of -3/16*r**4 + 0 - 1/280*r**7 + 0*r**3 + 1/80*r**6 + 0*r + 1/16*r**5 + 6*r**2. Determine b, given that t(b) = 0.
-2, 0, 1, 3
Factor -1826/7*t**2 + 0 - 116/7*t**3 - 2/7*t**4 - 8712/7*t.
-2*t*(t + 11)**2*(t + 36)/7
Let n(f) = -5*f**2 + 8 - 50*f + 3*f**2 + 40*f. Let d be n(-5). Let 2*r**5 + 40 + d*r**4 + 8*r**3 - 40 = 0. Calculate r.
-2, 0
Let s(c) be the third derivative of -c**8/336 - 4*c**7/21 + 29*c**6/20 - 23*c**5/15 - 173*c**4/24 + 22*c**3 - c**2 + 1454. Solve s(v) = 0.
-44, -1, 1, 3
Suppose -5*m - 5*z = -10, -5*z - 32 = m - 3*m. Let h be 4 + ((-40)/12 + 3)*m. Solve -10*c + 4*c**3 + 4*c**5 - 20*c**2 + 8*c**2 + 12*c**4 + h*c = 0.
-2, -1, 0, 1
Let x(o) = 16*o + 80. Let p be x(-4). Factor -16*n**3 + 24*n**2 - 72*n**2 + 23*n**2 + 21*n**2 + 4*n**4 + p*n.
4*n*(n - 4)*(n - 1)*(n + 1)
Let y(a) = -4*a**4 + 805*a**3 - 16901*a**2 - 29830*a - 12145. Let c(w) = w**4 + 2*w**3 - 4*w**2 + w + 1. Let u(v) = -5*c(v) + y(v). Suppose u(t) = 0. What is t?
-1, -2/3, 45
Let c be (120/(-210))/(54/(-21)). Let q be (1/(-6))/(5/(-20)). Find m, given that c*m**2 - 8/9*m + q = 0.
1, 3
Let q(h) be the first derivative of -h**6/24 + 17*h**4/16 - 3*h**3 + 5*h**2/2 + 621. Suppose q(s) = 0. Calculate s.
-5, 0, 1, 2
Suppose -169*g + 6534 = 206*g + 493*g - 142*g. Solve -39/2*i - 29/2*i**2 - 1/2*i**4 - g - 9/2*i**3 = 0.
-3, -2, -1
Factor 2*b**2 - 13*b**2 + 17*b**2 + 16*b - 9*b**2 - 49*b.
-3*b*(b + 11)
Suppose 3*u - 2*u + 1 = 0. Let s(t) = 3*t**4 - 15*t**2 - 12*t + 1. Let i(v) = v**4 - v**2 + 1. Let g(r) = u*s(r) + i(r). Factor g(b).
-2*b*(b - 3)*(b + 1)*(b + 2)
Suppose 0 = -27*k + 29*k - 6. Suppose 12*v**k + 6*v**3 - 11*v**2 + 6*v - v**4 - 12*v**3 = 0. Calculate v.
0, 1, 2, 3
Let -5*c - 7*c**4 + 441 - 31*c**4 + 450*c**2 + 11*c**4 - 3*c**5 - 898*c + 42*c**3 = 0. What is c?
-7, 1, 3
Factor -95*h**2 + 3*h**3 + 2*h**3 + 1246401*h - 1246051*h.
5*h*(h - 14)*(h - 5)
Let v = 116 - 77. Let k be (-41)/9 + (-65)/v*-3. Factor k*a**3 + 2/9*a**4 - 2/9*a - 4/9*a**2 + 2/9 - 2/9*a**5.
-2*(a - 1)**3*(a + 1)**2/9
Let h = 19821 - 19821. Let n(f) be the third derivative of 1/12*f**5 - 55/12*f**4 - 14*f**2 + h*f + 605/6*f**3 + 0. Solve n(i) = 0 for i.
11
Let k be (((-700)/15)/(-5))/((-8)/(-84)). Let z be (-48)/(-14) - 42/k. Determine r, given that -2/3*r**z - 10*r + 14/3 + 6*r**2 = 0.
1, 7
Let y be (1537/(-15370))/(3/(-6)). Determine d so that 0 + 0*d + y*d**5 - 1/5*d**2 + 1/5*d**4 - 1/5*d**3 = 0.
-1, 0, 1
Let z be -19*(-55)/(-7315) + 17*4/84. Suppose 26/21*h - 2/7 + 2/21*h**5 - z*h**4 + 12/7*h**3 - 44/21*h**2 = 0. Calculate h.
1, 3
Let j(r) = r**3 - 24*r**2 - 5*r + 61. Let g be j(22). Let q be (-18 + g/(-54))/(5/4). Factor -4/3*o**2 - q - 2*o.
-2*(o + 1)*(2*o + 1)/3
Let m = 230235/16 + -14388. Let s(n) be the third derivative of 0*n**3 + 0*n + 3/20*n**5 - 1/240*n**6 - m*n**4 + 12*n**2 + 0. Let s(p) = 0. Calculate p.
0, 9
Let x(a) be the first derivative of -8 + 21*a**2 + 9*a**3 - 5*a**4 - 18*a**2 + 4*a**4 + 4*a**4. Let x(h) = 0. Calculate h.
-2, -1/4, 0
Let u(h) be the first derivative of -5/9*h**2 + 0*h - 4/9*h**3 - 48 - 1/18*h**4. What is a in u(a) = 0?
-5, -1, 0
Solve -2 - 2/3*h + 2*h**2 + 2/3*h**3 = 0.
-3, -1, 1
Let o(d) = 3*d - 23. Let f be o(9). Suppose f*c + 12 = 10*c. Determine k, given that 9 - 2*k**c + 11 + 101*k - 107*k = 0.
-5, 2
Let p = 40111 + -40107. Factor -7*a**3 - p - 43/3*a**2 + 56/3*a.
-(a + 3)*(3*a - 2)*(7*a - 2)/3
Let r(l) be the second derivative of -l**7/231 - 68*l**6/165 - 131*l**5/110 + 34*l**4/33 + 4*l**3 - 1391*l. Find k, given that r(k) = 0.
-66, -2, -1, 0, 1
Let z(s) be the second derivative of 104*s**6/15 - 69*s**5/5 + 6*s**4 - 2*s**3/3 + 1054*s. Suppose z(g) = 0. Calculate g.
0, 1/13, 1/4, 1
Let b be 94/60 + (-16)/18*(-222)/(-1184). Suppose -1/5*v**5 + 2/5*v**3 - 46/5*v**2 - 5 - 13*v + b*v**4 = 0. What is v?
-1, 5
Let r = 24 - 22. Factor -73*u**5 - 74*u**5 - 16 - 16*u**4 + 145*u**5 - 56*u - 50*u**3 - 76*u**r.
-2*(u + 1)**2*(u + 2)**3
Let i(a) be the third derivative of -a**5/80 + 13*a**4/32 - 9*a**3/2 - 1574*a**2. Factor i(m).
-3*(m - 9)*(m - 4)/4
Let a(h) be the first derivative of 3*h**4/4 - 116*h**3 - 3*h**2/2 + 348*h - 730. Factor a(g).
3*(g - 116)*(g - 1)*(g + 1)
Let d(l) be the third derivative of l**7/525 + l**6/150 - 9*l**5/50 + 36*l**3/5 - 4039*l**2. Determine s so that d(s) = 0.
-6, -2, 3
Suppose -78 = 2*h + h. Let k be (1 - h/(-6))*(-15)/10. Factor 87*j**3 - 91*j**3 - j**2 - 3*j**2 + 3*j**5 + k*j**4.
j**2*(j - 1)*(j + 2)*(3*j + 2)
Let t(f) be the third derivative of -f**5/40 + 101*f**4/8 - 1226*f**2. Factor t(d).
-3*d*(d - 202)/2
Let l(q) be the second derivative of 0*q**2 + 64/3*q**3 + 0 - 31/3*q**4 + 6*q - 1/5*q**5. Determine h so that l(h) = 0.
-32, 0, 1
Let z(h) = 10*h**2 + 1087*h - 325. Let j be z(-109). Let -22/3*u - 2/3*u**j - 12 = 0. What is u?
-9, -2
Let u(y) = -y**3 - 2*y**2 - 3. Let s(t) = -7*t**3 + 21*t**2 + 10*t - 126. Let q(m) = -s(m) + 2*u(m). Factor q(a).
5*(a - 4)*(a - 3)*(a + 2)
Suppose -28*s = -69 - 15. Let f = 3 + 0. Factor -3*g**2 - 2*g**s - 4*g**4 + g**5 - f + 9*g**2 + g + g**4.
(g - 3)*(g - 1)**2*(g + 1)**2
Suppose -343 + 5*m**2 + 77*m - 4*m**2 + 376 + 189 = 0. What is m?
-74, -3
Let g(z) be the third derivative of 5*z**8/42 + 578*z**7/105 + 209*z**6/5 + 1916*z**5/15 + 532*z**4/3 + 128*z**3 - 1480*z**2 + z. Determine n so that g(n) = 0.
-24, -2, -1/2, -2/5
Let y be (3 - -22)/(-5) - (-3 + 0). Let w be (0/(y - -5))/(-1). Factor -3*u**3 + 2*u**2 + 6*u**3 - u**5 + w*u**2.
-u**2*(u - 2)*(u + 1)**2
Let w(d) be the first derivative of -d**3/12 + 25*d**2/2 - 99*d/4 + 1269. Let w(q) = 0. Calculate q.
1, 99
Let t(x) = 4*x**2 + x - x**3 - 6*x - 9*x**2. Let a(b) = b. Let w be 12/8*(-40)/(-3). Let g(j) = w*a(j) + 4*t(j). Factor g(k).
-4*k**2*(k + 5)
Let j = 80762/3909 + 8/1303. Let 1/3*x**2 + j*x + 961/3 = 0. Calculate x.
-31
Solve -7137*o**2 - 2091431793 - 10051744087 - 16978923*o - o**3 - 1321110059 = 0 for o.
-2379
Let v(q) be the second derivative of q**7/420 + 7*q**6/90 + 49*q**5/60 - 5*q**3/6 - 3*q**2/2 - q - 111. Let a(p) be the second derivative of v(p). Factor a(i).
2*i*(i + 7)**2
Let g = 104 + -108. Let i(f) = -4*f**3 - 14*f**2 + 14*f. Let b(l) = -l**3 - 2*l**2 + l. Let u(k) = g*b(k) + 2*i(k). What is o in u(o) = 0?
-6, 0, 1
Let t(f) = f**2 - 2*f - 30. Let d be 