b + 153 = 2*b. Let s = 52 - b. Let y(j) = j**2 - 4*j + 3. Let g(k) = k - 1. Let a(n) = s*y(n) + 2*g(n). Factor a(d).
(d - 1)**2
Let q(o) be the third derivative of o**5/30 - 1010*o**4/3 + 4080400*o**3/3 + 2*o**2 + 11*o - 15. Let q(j) = 0. Calculate j.
2020
Find j, given that 1174/9*j**2 - 176/9*j**3 + 0 - 16*j = 0.
0, 1/8, 72/11
Suppose -z - 5 = -6*z. Let i(j) = j + 9. Let a be i(z). Factor s - 6*s**3 + s + 8*s**2 + a*s + 2*s**3.
-4*s*(s - 3)*(s + 1)
Let h(u) = u**3 - 5*u**2 + 1. Let m be h(5). Let n be (1 - m)/(-1)*-1. Factor n*r**3 - 3 - 3*r**4 + 6 - 15*r**3 + 21 + 12*r - 18*r**2.
-3*(r - 1)*(r + 2)**3
Solve 0 + 4/3*a - 10/9*a**3 - 2/9*a**5 + 10/9*a**2 - 10/9*a**4 = 0 for a.
-3, -2, -1, 0, 1
Let b be (-88)/(-90) - 29/(725/(-20)). Factor 0 - 14/9*g**2 - b*g + 2/9*g**3.
2*g*(g - 8)*(g + 1)/9
Let 2*c**2 + 187*c**3 - 374 - 7*c**4 - 559*c + 15*c**4 - 9*c**4 + c**2 = 0. Calculate c.
-1, 2, 187
Let m(s) be the third derivative of -s**5/110 + 67*s**4/44 + 138*s**3/11 - 944*s**2. Factor m(w).
-6*(w - 69)*(w + 2)/11
Let j be (12/4 - 2) + 35. Suppose 0 = -6*p - 3*p + j. Factor 41*d**2 - 32*d**2 - p - 3*d**3 - 9*d + 6 + 1.
-3*(d - 1)**3
Let k be -1*(-2)/(-20)*(16324/1176 - 14). Let g(p) be the second derivative of 2*p + k*p**4 - 2/21*p**3 + 0 + 0*p**2. What is a in g(a) = 0?
0, 4
Let j(p) = 145*p**2 + 195*p + 385. Let u(z) = 173*z**2 + 194*z + 386. Let n(d) = 6*j(d) - 5*u(d). Let n(i) = 0. Calculate i.
-38, -2
Suppose 9*z - 66 = 3*z. Suppose 0 = -6*l + 259 + z. Let -40 + 7*a + l - a**2 - 3*a = 0. Calculate a.
-1, 5
Suppose 0 = 48*g - 37*g - 22. Let t(n) = n**3 + 7*n**2 + 6*n + 4. Let m be t(-6). Suppose -12*j**4 + 26*j**4 - 8*j - 18*j**4 + 8*j**3 + m*j**g = 0. Calculate j.
-1, 0, 1, 2
Factor -135/7*a**2 - 3/7*a + 135/7 + 3/7*a**3.
3*(a - 45)*(a - 1)*(a + 1)/7
Let c be (42/(-24))/(-2*112/64). Factor c*b**3 + 1369/2*b + 37*b**2 + 0.
b*(b + 37)**2/2
Solve 4/3 + 44/3*t**3 + 52/3*t + 92/3*t**2 = 0.
-1, -1/11
Let j(q) = 8*q**3 - 144*q**2 + 516*q + 4. Let y(p) = -9*p**3 + 144*p**2 - 517*p - 5. Let k(i) = -5*j(i) - 4*y(i). Determine v so that k(v) = 0.
0, 4, 32
Let l(d) be the second derivative of 24/7*d**2 - 26/21*d**3 + 1/70*d**5 + 1/42*d**4 + 30 + d. Factor l(o).
2*(o - 4)*(o - 1)*(o + 6)/7
Let p(l) be the first derivative of 7*l**5/10 - 93*l**4 + 3680*l**3 + 3200*l**2 - 140*l - 204. Let t(v) be the first derivative of p(v). Factor t(u).
2*(u - 40)**2*(7*u + 2)
Factor -704/7 + 360/7*s - 4/7*s**2.
-4*(s - 88)*(s - 2)/7
Let v(w) = 5*w**3 - 1263*w**2 + 7590*w - 11216. Let r(d) = 15*d**3 - 3790*d**2 + 22755*d - 33640. Let u(j) = 7*r(j) - 20*v(j). Suppose u(y) = 0. Calculate y.
3, 248
Suppose -o - 86 = -92. Factor y**3 + 161 - 13 - 40 - 63*y + o*y**2.
(y - 3)**2*(y + 12)
Factor -245/4 - 1/4*s**2 + 123/2*s.
-(s - 245)*(s - 1)/4
Factor 0*u + 0*u**2 + 0 - 2/9*u**4 - 12*u**3.
-2*u**3*(u + 54)/9
Solve -726*c**3 + 18723*c + 25200*c - 676*c**2 + 483153 + 33*c**4 - 7310*c**2 + 3*c**5 = 0 for c.
-11, 11
Let v = -5899963/15 - -393331. Solve -v*m**2 - 1922/15 - 124/15*m = 0.
-31
Let p(t) be the second derivative of 2*t**6/75 - 4*t**5/25 - 194*t**4/15 + 264*t**3/5 + 19602*t**2/5 - 17*t - 5. Let p(g) = 0. What is g?
-9, 11
What is u in 2391/4*u**2 - 1365/4*u**4 - 351/4*u - 513/2 + 363/4*u**3 - 3*u**5 = 0?
-114, -1, -3/4, 1
Let g(j) = -8*j**2 - 18*j + 32. Let i(c) = -c**2 + 2. Let u = 583 + -571. Let x(y) = u*i(y) - 2*g(y). Determine a so that x(a) = 0.
-10, 1
Let g = 57593/3 + -19195. Suppose -1/3*j - g*j**2 + 7/3*j**5 + 8/3*j**4 - 2*j**3 + 0 = 0. What is j?
-1, -1/7, 0, 1
Let p = 9043/3393 + 5/3393. Factor p*r - 7/3 - 1/3*r**2.
-(r - 7)*(r - 1)/3
Let t = 225242/5 - 45048. Factor 2/15*f**5 + 2/5*f**3 + 2/15*f**2 + 0 + 0*f + t*f**4.
2*f**2*(f + 1)**3/15
Suppose 901*k - 820*k - 301 - 2615 = 0. Let d(s) be the first derivative of -k + 6/11*s**3 + 6/11*s + 9/11*s**2 + 3/22*s**4. Solve d(i) = 0 for i.
-1
Let s(r) be the third derivative of -2*r**5/5 + 105*r**4/8 - 13*r**3/2 - 9204*r**2. Factor s(a).
-3*(a - 13)*(8*a - 1)
Let g(f) be the third derivative of -f**6/120 + f**5/3 - 4*f**4 + 2*f**2 - 2*f - 796. Suppose g(u) = 0. Calculate u.
0, 8, 12
Let v(u) be the third derivative of u**6/180 - u**5/15 - 7*u**4/36 + 3388*u**2. Find l, given that v(l) = 0.
-1, 0, 7
Let o(r) be the third derivative of -7*r**6/360 + 29*r**5/90 - 25*r**4/18 + 4*r**3/3 - 2928*r**2. Determine t so that o(t) = 0.
2/7, 2, 6
Let k = -16 + 25. Let v(t) = -t + 22. Let x be v(k). Solve -x + 11 - 28*f + 47 - 2*f + 5*f**2 = 0 for f.
3
Factor 1/2*c + 110 - 1/4*c**2.
-(c - 22)*(c + 20)/4
Let r(t) = -t**2 + 1. Let z(n) be the first derivative of -41/3*n**3 + 33/2*n**2 + 8*n - 22. Let b(f) = 2*r(f) - z(f). Factor b(v).
3*(v - 1)*(13*v + 2)
Let d(b) be the second derivative of -b**6/40 - 33*b**5/80 - 2*b**4 - 7*b**3/2 + 1079*b + 3. Factor d(o).
-3*o*(o + 2)**2*(o + 7)/4
Determine m so that -42*m**4 + 165/2 + 3/4*m**5 + 39*m**3 + 255/2*m**2 - 831/4*m = 0.
-2, 1, 55
Let v(n) = -8*n**2 + 10*n + 3. Let p(b) = 9*b**2 - 9*b - 6. Let r(a) = -6*a - 173. Let d be r(-28). Let s(i) = d*p(i) - 6*v(i). Factor s(k).
3*(k - 4)*(k - 1)
Suppose 188103*f + 7009*f - 3456*f**2 + 106*f**4 - 1620*f**3 - 1179648 - 202*f**4 + 38360*f + 177*f**4 = 0. What is f?
-12, 32/3
Let n(v) = -v**2 + 5*v - 3. Let f be n(3). Find m such that -5 + 5*m**2 - m + 12*m**f + 17*m**3 - 28*m**3 = 0.
-5, -1, 1
Let f = 2/3857 + 38544/50141. Factor f*w**2 - 72/13*w + 14/13.
2*(w - 7)*(5*w - 1)/13
Let b = 1163 + -764. Factor 138 + 150 - b*n + 63*n + 98*n**2.
2*(7*n - 12)**2
Let 6/7*r**2 - 6 - 36/7*r = 0. Calculate r.
-1, 7
Let l(t) be the first derivative of -t**4/10 + 8*t**3/3 + t**2/5 - 8*t - 3770. Determine s, given that l(s) = 0.
-1, 1, 20
Let w = -1224 + 44069/36. Let i(z) be the second derivative of 0 + 8/9*z**3 - 5/12*z**5 - w*z**4 - z - 2/3*z**2. Suppose i(q) = 0. What is q?
-1, 2/5
Let j(d) be the second derivative of d**6/4 + 33*d**5/20 - 8*d**4 - 3*d - 31. Factor j(l).
3*l**2*(l - 2)*(5*l + 32)/2
Let n(w) be the second derivative of 2*w**7/147 - 36*w**5/35 + 18*w**4/7 + 162*w**3/7 - 972*w**2/7 + 126*w. Solve n(f) = 0 for f.
-6, -3, 3
Let n(x) be the third derivative of -x**7/1680 - 7*x**6/480 - x**5/15 + 2*x**4/3 + 1022*x**2. Solve n(l) = 0.
-8, 0, 2
Let v(l) be the third derivative of 6*l**2 + 5 + 0*l + 0*l**4 + 0*l**6 - 1/630*l**7 - 2/9*l**3 + 1/36*l**5. Determine y so that v(y) = 0.
-2, -1, 1, 2
Let a(d) be the first derivative of d**3 - 81*d**2 - 1234. Factor a(h).
3*h*(h - 54)
Factor -154/9*z + 17 + 1/9*z**2.
(z - 153)*(z - 1)/9
Suppose 8 = -2*l, 6*l = p + 5*l - 19. Factor -19 - p*o - 7 + 134*o**2 - 135*o**2.
-(o + 2)*(o + 13)
Let l be -113*(5 + 836/(-168)) - -4. Let z = l - 47/84. Suppose 3*h + 9/4*h**2 + z = 0. What is h?
-1, -1/3
Let u(l) = -l**2 - 5*l + 31. Let r be u(-6). Factor 86*b**2 - 8 + 67*b**2 + 40*b**2 - r*b**2 + 100*b.
4*(3*b + 2)*(14*b - 1)
Let r(c) be the second derivative of c**4/3 - 4*c**3/3 - 30*c**2 - 6619*c. Factor r(m).
4*(m - 5)*(m + 3)
Let v(z) = 10*z**2 - 13*z - 59. Let l(g) = -3*g**2 + 4*g + 19. Let k(j) = -17*j + 176. Let x be k(10). Let b(a) = x*v(a) + 21*l(a). Factor b(p).
-3*(p - 5)*(p + 3)
Let v(y) be the first derivative of -8/3*y + 16/3*y**2 - 6/5*y**5 - 133 - 8/3*y**4 + 26/9*y**3. Find s such that v(s) = 0.
-2, -1, 2/9, 1
Let z(p) be the second derivative of -p**8/3920 + p**6/280 - p**5/140 - 7*p**3/6 - 89*p. Let q(j) be the second derivative of z(j). Solve q(d) = 0.
-2, 0, 1
Let i(q) be the first derivative of 8*q**3/39 + 309*q**2/13 + 154*q/13 + 17. Factor i(l).
2*(l + 77)*(4*l + 1)/13
Let r(b) be the third derivative of 0*b**4 - 8*b**2 + 0*b**3 + 1/735*b**7 + 0*b**5 - 1/420*b**6 + 1 + 0*b. Factor r(z).
2*z**3*(z - 1)/7
Let c(y) be the third derivative of -17*y**6/240 - 4*y**5/15 + 55*y**4/48 - y**3/2 - 6615*y**2. Factor c(m).
-(m - 1)*(m + 3)*(17*m - 2)/2
Solve 57*i**2 - 312*i + 3*i**4 + 170*i**2 + 175*i**2 - 5569*i**3 + 5476*i**3 = 0 for i.
0, 1, 4, 26
Let w = 7204 - 7200. Let o(f) be the first derivative of 3/4*f**w + 0*f + 20 + 0*f**2 - f**3. Factor o(j).
3*j**2*(j - 1)
Let s(i) be the third derivative of -i**8/840 + 23*i**7/525 - 47*i**6/150 - 43*i**5/15 - 481*i**4/60 - 169*i**3/15 - i**2 - 554. Factor s(g).
-2*(g - 13)**2*(g + 1)**3/5
Let p = 3325 + -3323. Let x(o) be the first derivative of -5/3*o**3 - 15