t r = 514 + -415. Suppose 27*x - 36 = r. Let 3/2*s**x - 39/8*s**2 - 15/8*s + 33/8*s**4 + 3/4 + 3/8*s**3 = 0. Calculate s.
-2, -1, 1/4, 1
Let y(p) = -6*p**2 + 7*p + 6. Let w = -117 + 110. Let b(j) = 3*j**2 - 3*j - 3. Let f(l) = w*b(l) - 3*y(l). Factor f(m).
-3*(m - 1)*(m + 1)
Solve 2/5*q**2 + 1944/5 + 336/5*q = 0 for q.
-162, -6
Let z be 17 - 14 - 1/(1 + 0). Factor r**5 + 16*r**3 + 3*r**5 + 12*r + 8 - 8*r**z - 32*r**3.
4*(r - 2)*(r - 1)*(r + 1)**3
Suppose 4*f + 235 + 22 = x, 2*x = -f + 550. Let d be 130/x*(-9)/(-15). Factor 0 + d*c**2 + 26/7*c.
2*c*(c + 13)/7
Let q(u) be the first derivative of 4*u**6/45 - 32*u**5/75 - 7*u**4/30 + 86*u**3/45 + 13*u**2/5 + 6*u/5 - 456. Determine t so that q(t) = 0.
-1, -1/2, 3
Let b(q) be the first derivative of -2*q**3/39 + 2348*q**2/13 - 2756552*q/13 - 197. Factor b(v).
-2*(v - 1174)**2/13
Let f(r) = -r + 16. Let p be f(20). Let y be ((-308)/(-144))/11 - 1/p. Factor y + 2/9*u**2 - 2/3*u.
2*(u - 2)*(u - 1)/9
Suppose 2*f + 61 = -3*l, 124*f - 119*f + 140 = -5*l. Let x be 8*(24 + f + (-54)/56). Solve 4/7*j**3 + 4/7*j**2 - 2/7*j - 2/7 - x*j**5 - 2/7*j**4 = 0 for j.
-1, 1
Let a = -2598 + 4845. Factor 4499*f**2 + 2*f**3 - a*f**2 - 2316*f**2.
2*f**2*(f - 32)
Factor -63*y**3 + 300*y**2 + 154*y**3 + 63*y**3 + 139*y**4 + 184*y - 113*y**4 - 16.
2*(y + 2)**3*(13*y - 1)
What is p in -169/3*p**3 + 3601/3*p**2 - 1096/3*p + 28 = 0?
2/13, 21
Let m(z) = -10*z**3 + 238*z**2 + 47*z + 26. Let n be m(24). Factor 0*y + 5/3*y**5 - 10*y**4 + 15*y**3 + 0 + 0*y**n.
5*y**3*(y - 3)**2/3
Suppose 10 + 2 = r - g, 0 = 2*r + 4*g. Determine v, given that -91 - v**2 - 56*v + 22 + 19 + 38 - r*v**2 = 0.
-6, -2/9
Let h(b) be the second derivative of 0 + 1/24*b**4 - 14*b**2 - 107*b - 55/12*b**3. Suppose h(c) = 0. Calculate c.
-1, 56
Let j be -2 + (-6)/(-6) + 13/1. Suppose -23*d + 21*d = -j. Suppose 6*i**2 - 10*i**2 + 10*i + d*i = 0. Calculate i.
0, 4
Determine a so that -8484*a**4 + 8470*a**4 + 18*a**3 + 2*a**5 + 6*a**3 = 0.
0, 3, 4
Let g be (-46)/(-16) - (-756)/(-567)*3/(-32). Determine s, given that 0*s + 3/4*s**g - s**2 + 0 = 0.
0, 4/3
Let r(t) be the second derivative of -t**5/10 + 91*t**4/3 - 7708*t**3/3 - 53016*t**2 + 2054*t. Factor r(p).
-2*(p - 94)**2*(p + 6)
Let j(h) be the third derivative of -h**7/210 - h**6/4 + 181*h**5/60 + 35*h**4/4 + 288*h**2. Let j(i) = 0. What is i?
-35, -1, 0, 6
Let x(p) = -2*p**2 + p + 1. Let g = -6 + 4. Let n(u) = -u**2 - 46*u + 47. Let i(m) = g*x(m) + n(m). Factor i(o).
3*(o - 15)*(o - 1)
Let w = 65/43 + 31968/215. Find r such that 441/5*r**4 + w*r**3 + 136/5*r + 81/5*r**5 + 12/5 + 103*r**2 = 0.
-3, -1, -2/9
Let a = -195 - -201. Find s, given that 70*s + 40*s - s**4 - 24 - 48 - 66*s**2 + a*s + 15*s**3 = 0.
2, 9
Let k(g) = g**5 - g**4 + g**3. Let v(t) = 3*t**5 + 3*t**3. Let p = -41 - -39. Let l(i) = p*v(i) + 4*k(i). Let l(u) = 0. What is u?
-1, 0
Let b(f) = 3*f**3 + 5*f**2 + 2*f - 4. Let y(l) = -2*l**3 - 5*l**2 - l + 5. Let h = -227 + 223. Let m(d) = h*y(d) - 3*b(d). Determine i so that m(i) = 0.
-1, 2, 4
Let x(z) = -2*z**2 + 61 + z + z**2 + 2*z**2 - 2*z**2. Let m be x(0). Determine t, given that 57*t - 7*t**4 - 16*t**2 - m*t - 4*t**5 - 9*t**4 - 24*t**3 = 0.
-1, 0
Let j = -1883 + 1889. Let i be j/(-5)*(13 - 2074/153). Factor -4 - 16/3*k**2 - i*k**3 - 26/3*k.
-2*(k + 1)**2*(k + 6)/3
Let j(p) be the second derivative of -1/16*p**4 + 0*p**2 + 2 - 1/4*p**3 + 3/80*p**5 - 282*p. Find k such that j(k) = 0.
-1, 0, 2
Suppose 34*k - 24*k = 30. Determine p, given that -6*p**3 + 11*p**4 + 4*p**5 - 3*p**5 + 2*p**5 - 96*p**2 + 37*p**4 + k*p + 48 = 0.
-16, -1, 1
Suppose 0 = -4*z + 5*r + 417, 3 = 3*r - 6*r. Factor -25*m**2 + 65*m**3 + m**2 + 28*m + 31*m + 3*m**4 - z*m.
m*(m - 1)*(m + 22)*(3*m + 2)
Let w(d) = -13*d**2 + 34*d - 33. Let u(a) = -262*a**2 + 680*a - 654. Let l(x) = 6*u(x) - 118*w(x). Factor l(r).
-2*(r - 1)*(19*r - 15)
Let w be (-2)/4 + 1606/44. Determine q, given that -9*q**2 - q**2 + q + 9*q**5 - 12*q**2 + 2*q + w*q**3 + 4*q**2 - 30*q**4 = 0.
0, 1/3, 1
Let g(y) be the first derivative of -y**5 + 55*y**4/4 + 440*y**3/3 - 290*y**2 - 960*y - 1726. Find v such that g(v) = 0.
-6, -1, 2, 16
Let m(f) = -f**3 - f. Let y(i) = -2*i**3 - i**2 + 1. Let z = -253 + 249. Let r(p) = z*m(p) + 4*y(p). Factor r(d).
-4*(d - 1)*(d + 1)**2
Let t = 2354363/3 - 784787. Factor -4/3 + t*i**2 + 2/3*i.
2*(i - 1)*(i + 2)/3
Let l(d) = -34*d**4 + 2624*d**3 + 6357*d**2 + 4814*d + 1070. Let w(o) = o**4 - o**3 + 2*o**2 - o. Let n(r) = -l(r) - 9*w(r). Find f, given that n(f) = 0.
-1, -2/5, 107
Let 260*s + 139*s + 2*s**2 - 51*s + 1132 + 30*s + 192*s = 0. What is s?
-283, -2
Let m be (-9 + 21)*2/3. Factor 5*h**2 - 169 + 169 - 3*h**2 - m*h.
2*h*(h - 4)
Let d(y) be the second derivative of -y**5/50 + 6*y**4/5 - 19*y**3 - 722*y**2/5 + 242*y. Factor d(z).
-2*(z - 19)**2*(z + 2)/5
Let x be (-16 - -12) + -3 + 9. Let y = -3120 - -9370/3. Let y*s + 0 - 5/2*s**3 + 5/6*s**4 + 0*s**x = 0. What is s?
-1, 0, 2
Suppose -157216 = -n - 5*p, 2*p + 295739 = 2*n - 18693. Solve n + 218*a**2 - 2*a**3 + 346*a**2 - 13872*a + 0*a**3 - 156*a**2 - 2*a**3 = 0 for a.
34
Let q(h) = -3*h**3 - 10*h**2 - 22*h + 8. Let v(t) = 13*t**3 + 39*t**2 + 89*t - 36. Let k(d) = 18*q(d) + 4*v(d). Factor k(s).
-2*s*(s + 2)*(s + 10)
Factor 0*g**3 + 0*g + 0 - 312/7*g**4 + 0*g**2 - 1/7*g**5.
-g**4*(g + 312)/7
Let b(h) be the first derivative of -3*h**4/10 - 68*h**3/15 - 15*h**2 + 1333. Determine m, given that b(m) = 0.
-25/3, -3, 0
Let x(l) = 15*l**2 - 392*l - 221. Let z(a) = 2*a**2 - 2*a + 2. Let r(q) = -x(q) + 5*z(q). Find b, given that r(b) = 0.
-3/5, 77
Find m, given that 38*m - 2/9*m**3 + 20/3*m**2 + 280/9 = 0.
-4, -1, 35
Let c be (-1 - -4 - 13/3)*(-153)/68. Let n(p) be the first derivative of 2/21*p**c + 2/35*p**5 - 25 + 3/14*p**4 - 4/7*p - 3/7*p**2. Factor n(u).
2*(u - 1)*(u + 1)**2*(u + 2)/7
Let n = 76613/574710 + 1/38314. Determine m so that n*m**5 + 8/5 - 26/15*m**2 - 16/15*m + 2/3*m**4 + 2/5*m**3 = 0.
-3, -2, 1
Suppose -3*w + 4*k + 142 = 0, -5*w + 137 + 98 = -5*k. Factor -u**5 + 3*u**2 - 41*u + 45*u**2 + 16*u**2 + 14*u**4 - 8 + 18 - w*u**3.
-(u - 10)*(u - 1)**4
Let b = 22 + -15. Suppose c + 1 = -2*t, 10 + b = -4*t - 5*c. Let 4*q**2 - q**2 + 8 - t*q**2 + 9*q - 3*q = 0. What is q?
-4, -2
Suppose r + 7*d - 25 + 8 = 0, -9 = -5*r + 3*d. Let b(q) be the second derivative of -5/6*q**r + 0 + 2*q**2 + 1/12*q**4 + 23*q. Solve b(c) = 0.
1, 4
Suppose -151/4*j + 1/4*j**3 + 13/2*j**2 + 31 = 0. What is j?
-31, 1, 4
Let n(g) = -g**2 + 15*g + 1. Let c be n(14). Suppose -5*s = -c, -x + 2*s = -3*x + 16. What is p in 4*p**x - 6*p**5 - 2*p**3 - 12*p**4 + 16*p**4 = 0?
0, 1
Let d(n) be the first derivative of -2*n**5/19 - 17*n**4/38 + 26*n**3/19 + 153*n**2/19 + 108*n/19 + 1691. Solve d(p) = 0.
-3, -2/5, 3
Let d(l) = -5*l + 40. Let k be d(10). Let t be (3/6*k)/(-1). Factor z**5 + 0*z**t + 3*z**2 - 3*z**4 - 12*z**3 + 11*z**3.
z**2*(z - 3)*(z - 1)*(z + 1)
Solve 169/2*l**3 - 85*l - 56 + 59/2*l**4 + 53/2*l**2 + 1/2*l**5 = 0.
-56, -2, -1, 1
Let w = -523815 + 523817. Let h = 613/9 + -68. Factor -14/9*u + 49/9 + h*u**w.
(u - 7)**2/9
Factor -32/5*c**4 - 139392/5 - 16912/5*c**3 - 2238722/5*c**2 - 1116192/5*c.
-2*(c + 264)**2*(4*c + 1)**2/5
Let o(h) be the first derivative of h**7/1050 - h**5/75 + 2*h**2 + h - 14. Let w(u) be the second derivative of o(u). What is m in w(m) = 0?
-2, 0, 2
Let h(c) be the first derivative of -33/5*c**5 + 87/2*c**2 + 51/2*c**4 - 21*c - 48 - 46*c**3 + 1/2*c**6. Factor h(a).
3*(a - 7)*(a - 1)**4
Let s be -17 - 18564/(-980) - (3 - 54/14). Solve s*i**2 + 2/5*i - 14/5 - 2/5*i**3 = 0 for i.
-1, 1, 7
Let m(s) be the first derivative of s**4/6 - 16*s**3/9 - 3*s**2 - 611. Solve m(a) = 0.
-1, 0, 9
Factor -705/8 + 177/2*m - 3/8*m**2.
-3*(m - 235)*(m - 1)/8
Let o(t) be the first derivative of -t**4/26 + 12*t**3/13 - 81*t**2/13 + 216*t/13 + 4956. Factor o(a).
-2*(a - 12)*(a - 3)**2/13
Let h be 1 + 20/(-14) - (-127)/(-133)*-1. Find p such that 0 + 2/19*p**4 - h*p**3 - 6/19*p + 14/19*p**2 = 0.
0, 1, 3
Factor -18/11*j**2 + 24*j - 88.
-2*(3*j - 22)**2/11
Factor 28*y**3 + 16*y**4 + 8*y**4 + 0*y**5 + 2*y**5 - 3*y**3 - 3*y**3.
2*y**3*(y + 1)*(y + 11)
Let l = -728/127 + 205409/762. Let v = l + -778/3. Find q such that 0*q + 0 + 3*q**3 + 3/2*q**2 - v*q**4 = 0.
-1/3, 0, 1
Suppose -5*n - g + 24 = 0, -n = 2*n + g