4/21 - 32*x**3/21 - 214*x**2. Determine f so that r(f) = 0.
-4, 1/2, 2, 4
Let q(a) = -5*a**2 - 210*a - 11345. Let c(n) = 9*n**2 + 421*n + 22716. Let v(p) = 4*c(p) + 7*q(p). Factor v(m).
(m + 107)**2
Let m = -36029 - -14215. Let g = 66170/3 + m. Factor 32/3 - 272/3*y + g*y**2 - 196*y**3.
-4*(3*y - 2)*(7*y - 2)**2/3
Let s be 10/(-45) + 7/(-63)*-6. Factor -2/9*m**2 - 2/9 - s*m.
-2*(m + 1)**2/9
Let x = 960793/2241883 + 2/320269. Find f such that x*f**2 - 18/7 + 3/7*f = 0.
-3, 2
Let v(b) be the third derivative of b**5/45 + 4*b**4/3 + 286*b**3/9 - 13*b**2 - 8*b - 1. Factor v(m).
4*(m + 11)*(m + 13)/3
Let i be 10810/5170 - 4/2. Find o such that 2/11*o**3 - i*o**2 + 0 + 1/11*o**4 - 2/11*o = 0.
-2, -1, 0, 1
Let u(d) = -2*d**4 - 144*d**3 + 41*d**2 - 5*d + 5. Let t(j) = -j**4 - 123*j**3 + 40*j**2 - 4*j + 4. Let c(k) = 5*t(k) - 4*u(k). Factor c(g).
3*g**2*(g - 12)*(g - 1)
Suppose 10 = 2*v + 2*r, -71 + 74 = -3*v + 3*r. Find n, given that 0*n**4 + 0 - 2/3*n**v - n**3 + 1/3*n**5 + 0*n = 0.
-1, 0, 2
Suppose 11*q + 3*y - 19 = 0, -3144*q + 3149*q + 3*y - 7 = 0. Suppose 8*u**4 + 0*u**q + 0*u + 0 + 26/3*u**3 - 2/3*u**5 = 0. What is u?
-1, 0, 13
Let a = 431673/2 + -215836. Solve 1/2*o**3 - a*o + 1 - o**2 = 0.
-1, 1, 2
Let f = 179 - 177. Let 2*y**f + 5*y**2 - 24 - y**2 - 70*y = 0. What is y?
-1/3, 12
Let j(s) be the first derivative of -s**6/36 - 5*s**5/6 + 9*s**4/4 - s**3/9 - 53*s**2/12 + 9*s/2 + 2393. Factor j(n).
-(n - 1)**3*(n + 1)*(n + 27)/6
Let z(l) be the second derivative of -1/3*l**3 + 0 - 1/110*l**5 + 1/11*l**4 + 6/11*l**2 + 49*l. Let z(t) = 0. Calculate t.
1, 2, 3
Determine t, given that 744 + 4/5*t**2 + 644/5*t = 0.
-155, -6
Suppose 5*i - 2*y = 6, -y = -4*i - 3*y + 12. Let q(p) = p**i + 6*p**2 + 36*p - 45*p. Let t(l) = -2*l**2 + 2*l. Let b(o) = -6*q(o) - 22*t(o). Factor b(f).
2*f*(f + 5)
Let u(r) be the first derivative of 2*r**5/45 - 227*r**4/18 + 2236*r**3/27 - 1780*r**2/9 + 592*r/3 - 10511. Find w such that u(w) = 0.
1, 2, 222
Let f be 2970/(-1980)*((-7)/3 + 1). Find d such that -1/3*d**f + 0 + 0*d + 1/3*d**3 = 0.
0, 1
Suppose -385 = 20*r - 9*r. Let q be (24/r)/((-936)/(-63) - 15). Determine a so that 108/5*a**2 - 15*a**4 - 18*a**3 + 0 - q*a = 0.
-2, 0, 2/5
Let y(o) = -o**3 + 18*o**2 + 104*o - 2176. Let r be y(16). Factor 32/3*g + 2/3*g**5 + 16*g**3 - 16/3*g**4 - 64/3*g**2 + r.
2*g*(g - 2)**4/3
Suppose -7*k + 3*k = 2*g - 142, 3*g - 145 = -4*k. Let -k + 680*f**3 - 214*f + 659*f + 2 - 18 - 1155*f**2 + 80*f**4 = 0. What is f?
-10, 1/4, 1
Let n(v) be the third derivative of -142*v**2 + 9/80*v**5 + 0 + 0*v - 1/160*v**6 + 21/32*v**4 + 11/8*v**3. Let n(g) = 0. What is g?
-1, 11
Factor 110/3*i**2 + 1/3*i**4 + 0*i + 0 + 19*i**3.
i**2*(i + 2)*(i + 55)/3
Let r(a) be the third derivative of 2/3*a**3 - 1/390*a**5 + 0 + 25/156*a**4 - 9*a + 5*a**2. Determine z so that r(z) = 0.
-1, 26
Suppose 12*b - 26 = 22. Find n, given that 2*n**3 + b*n - 4*n**2 + 0*n - 2*n = 0.
0, 1
Suppose 5*o - f - 2 = 4*o, f = -2*o + 7. Let -5*u**2 - 4*u**2 - 16*u**5 - 6*u**4 - 41*u**4 - 33*u**o + 7*u**4 = 0. Calculate u.
-1, -3/4, 0
Let m(z) = 4*z**2 - 13*z + 11. Let p be m(1). Suppose -355*r + 48 - 241*r**2 + 1612*r**2 - 454*r**p - 437*r + 2350*r**2 = 0. What is r?
4/33
Suppose 0 = h - 43 - 17. Let c(r) = 6*r**2 - 63*r - 8. Let b be c(11). Factor -64*x - b*x**2 + 140*x**2 - 92*x + h + 5*x**4 - 40*x**3 + 16*x.
5*(x - 3)*(x - 2)**2*(x - 1)
Factor -24*m + 0 - 1/2*m**4 - 23*m**3 + 95/2*m**2.
-m*(m - 1)**2*(m + 48)/2
Let w(c) be the second derivative of c**7/6300 - c**6/600 - c**5/75 + 5*c**4/12 + c**2 - 166*c. Let q(m) be the third derivative of w(m). Solve q(j) = 0 for j.
-1, 4
Let o(h) be the second derivative of -3*h**6/20 - 17*h**5/16 + 45*h**4/16 - 5*h**3/6 - 3*h**2/2 - 2*h - 333. What is u in o(u) = 0?
-6, -2/9, 1/2, 1
Suppose b - 6*b = -45. Let w be -2 - 7/((-49)/28). Let b*v - 22*v - w*v**2 + 12*v = 0. What is v?
-1/2, 0
Let d = -3340 + 2098. Let y be d/(-92) - -3*3. Determine n so that 10*n**5 + 5/2*n**2 + 5 - 65/2*n**3 + y*n - 15/2*n**4 = 0.
-1, -1/4, 1, 2
Let q be (-1)/(-18)*(142 + (-32450)/236). Determine p so that 0 + q*p**5 + p**2 - 3/4*p**3 - 1/2*p**4 + p = 0.
-1, 0, 2
Let q(h) be the first derivative of 0*h + 1/9*h**3 - 78 - 1/2*h**2. Factor q(i).
i*(i - 3)/3
Let g(f) = 17*f + 53. Let t be g(-3). Determine m so that 0*m**4 - 2*m**5 - 4*m**4 + 27*m**2 - 50*m**2 + t*m + 27*m**2 = 0.
-1, 0, 1
Factor -382*c**4 - 38088*c**2 - 482*c**4 - 6405*c**3 - 48668*c - 6097*c**3 + 2566*c**3.
-4*c*(6*c + 23)**3
Let a(j) be the second derivative of -j**4/42 + 7*j**3 - 766*j. Let a(i) = 0. What is i?
0, 147
Let p(m) be the first derivative of m**5/30 - m**4/6 - m**3/9 + m**2 - 20*m - 61. Let i(b) be the first derivative of p(b). Find s such that i(s) = 0.
-1, 1, 3
Let m(x) be the first derivative of x**3/3 + 853*x**2/4 + 213*x - 935. Factor m(k).
(k + 426)*(2*k + 1)/2
Factor -2*v**3 - 36 - 8*v**3 + 12*v**2 - 84*v**2 + 16*v**2 - 82*v.
-2*(v + 1)**2*(5*v + 18)
Let r(j) be the third derivative of -83*j**2 + 0 + 128/21*j**3 - 1331/210*j**6 + 0*j + 484/35*j**5 - 88/7*j**4. Suppose r(v) = 0. What is v?
4/11
Suppose -2*q + 20 = 3*q. Let l be 50/18 + q/18 - 1. Factor 4*s**2 - 3*s**2 + 4*s**l - 20*s - 25.
5*(s - 5)*(s + 1)
Factor -30*m**3 - 8736*m**2 + 4328*m**2 - 520*m - 336 + 4195*m**2 - m**4.
-(m + 1)*(m + 4)**2*(m + 21)
Suppose 94*h**4 - 1616*h - 22*h**5 - 2*h**5 + 1054*h**3 - 1246*h**2 + 560*h + 26*h**5 + 1152 = 0. Calculate h.
-24, -1, 1
Let o(l) be the first derivative of -5*l**6/6 + 13*l**5 + 15*l**4/4 - 205*l**3/3 + 65*l**2 - 11388. Let o(h) = 0. What is h?
-2, 0, 1, 13
Let m(u) be the second derivative of -4*u**6/45 + 71*u**5/15 - 35*u**4/9 + 1300*u + 3. Solve m(o) = 0.
0, 1/2, 35
Suppose 0 = y + 3*y - 8. Let q(t) = 8*t**2 + y*t + 6*t + 2*t - 4*t - 8*t**3. Let i(v) = -v**3 + v**2 + v. Let h(z) = -12*i(z) + 2*q(z). Let h(x) = 0. What is x?
0, 1
Factor 1/2*l**2 + 449/2*l + 447.
(l + 2)*(l + 447)/2
Let s(b) be the first derivative of -3*b**2 + 0*b + 89 - 3/5*b**3 + 3/20*b**4. Factor s(d).
3*d*(d - 5)*(d + 2)/5
Let u(y) be the second derivative of 2*y**6/5 - 7*y**5/5 - 3*y**4 + 14*y**3/3 + 12*y**2 - 398*y. Determine g so that u(g) = 0.
-1, -2/3, 1, 3
Let c = -2241834989/548 - -4090942. Let o = 3/274 + c. Solve -3/4 + 9/4*q + 3/4*q**3 - o*q**2 = 0.
1
Let 65/3*b**2 + 1/3*b**3 + 1024/3 + 1088/3*b = 0. What is b?
-32, -1
Let y(h) be the third derivative of h**7/840 - 23*h**6/120 - h**5/240 + 23*h**4/24 + 237*h**2 + h. Factor y(f).
f*(f - 92)*(f - 1)*(f + 1)/4
Factor -148/5*a**3 - 144/5*a - 2/5 + 294/5*a**2.
-2*(a - 1)**2*(74*a + 1)/5
Suppose 0 = 4*s + 3*t - 2, -2*s = 4*t + 4 - 0. Suppose d = v - 4, s*v + 8 = 4*v. Determine w so that -1/3*w**2 - 1/6*w + d*w**3 + 1/3*w**4 + 0 + 1/6*w**5 = 0.
-1, 0, 1
Let x = 273 + -285. Let p(n) = n**2 + 20*n + 100. Let a be p(x). Solve -2/17*d**a + 0 + 0*d + 0*d**2 + 8/17*d**3 = 0.
0, 4
Let a(s) be the third derivative of -21/8*s**3 + 0 + 1/80*s**5 + 0*s + 1/8*s**4 + 3*s**2. Factor a(i).
3*(i - 3)*(i + 7)/4
Let m = -2/314319 - -5029126/3457509. Solve 30/11*v**3 + 0 - 2/11*v**5 + 0*v + 12/11*v**4 + m*v**2 = 0 for v.
-1, 0, 8
Let h(v) be the first derivative of -5*v**4/4 + 785*v**3/3 - 385*v**2 - 1560*v - 4477. Determine j so that h(j) = 0.
-1, 2, 156
Let k = -27643/684 - -3139/76. Find b such that -2/9*b**4 - 2 - 8/3*b + k*b**3 + 4/9*b**2 = 0.
-1, 3
Let z(p) be the first derivative of -2*p**6/3 - 396*p**5/5 - 657*p**4 - 4772*p**3/3 + 588*p**2 + 6624*p + 6837. Let z(x) = 0. Calculate x.
-92, -3, -2, 1
Let c(w) be the third derivative of -w**5/540 - 97*w**4/27 - 75272*w**3/27 - 17*w**2 - 14. Factor c(h).
-(h + 388)**2/9
Let x(r) = r**3 + r**2 + r - 1. Let q(i) = 8*i + 3*i**3 - i**3 + 2*i**2 + i**3 + 4. Let v(s) = 3*q(s) - 12*x(s). Determine d so that v(d) = 0.
-2, 2
Let c be (493/51)/(2233/462). Let s = 1/572 + 175/572. Factor -2/13*l**c + s*l - 2/13.
-2*(l - 1)**2/13
Factor 4/5 - 6/5*h + 2/5*h**2.
2*(h - 2)*(h - 1)/5
Determine r, given that -335*r**2 - 676 + 2470 - 3134*r - 1115 - 763 - 9*r**3 - 596 = 0.
-20, -17, -2/9
Suppose -17*b + 1403 = 179. Determine p so that b*p**3 + 135*p - 3*p**3 + 210*p**2 + 20 + 26*p**3 = 0.
-1, -4/19
Let w(h) = -4*h**2 + 2*h. Let s(m) = -m**2. Let g = 37 - 5. Let x = g - 38. Let q(z) = x*s(z) + w(z). Factor q(l).
2*l*(l + 1)
Let m(s) = 3