- 3*b**6/80 + 3*b**5/10 - 1083*b**2. Factor v(u).
u**2*(u - 12)*(u - 6)/4
Find c, given that -303*c**3 + 33*c**5 - 63*c - c**2 - 27*c**5 - 111*c**4 - 6*c**2 - 242*c**2 = 0.
-1, -1/2, 0, 21
Factor -1945*s**2 + 6*s**3 - 148313*s - 145919*s - s**3 + 292282*s.
5*s*(s - 390)*(s + 1)
Suppose 20 = 9*a - 4*a. Suppose -5*o + 3*o = -w - 8, 13 = o + a*w. Solve 81*i**2 - 6*i + o*i + 7*i + 0*i = 0 for i.
-2/27, 0
Let n(t) be the first derivative of t**5/4 + 7*t**4/4 - 8*t**2 + 4*t + 60. Let p(f) be the first derivative of n(f). Factor p(k).
(k + 1)*(k + 4)*(5*k - 4)
Let m = -14 + 17. Factor 51*b**3 - 48*b**3 - 3*b + 6 - 9*b**2 - m*b**4 + 6*b**4.
3*(b - 1)**2*(b + 1)*(b + 2)
Let t(r) be the first derivative of 2*r**3/9 + 620*r**2 + 576600*r - 3876. Factor t(p).
2*(p + 930)**2/3
Let h(q) be the first derivative of -12*q + 1 + q**3 + 9/2*q**2. Factor h(g).
3*(g - 1)*(g + 4)
Let v = 1597 + -1581. Let n be (1/(-2))/(((-195)/168)/13). Factor -72/5*g**2 - 32/5 - 4/5*g**4 + n*g**3 + v*g.
-4*(g - 2)**3*(g - 1)/5
Determine c so that 4*c**3 + 489 + 12306*c + 9768*c + 1219 - 20094*c + 276*c**2 = 0.
-61, -7, -1
Let a be (63/(-14))/(1/((-8)/3)). Suppose a*z = 3 + 9. Factor 22*n - n**2 - z - 6 - 114.
-(n - 11)**2
Let f(n) = 55*n**4 + 17*n**3 + 71*n**2 - 17*n - 62. Let p(j) = 21*j**4 + 6*j**3 + 24*j**2 - 6*j - 21. Let s(k) = 3*f(k) - 8*p(k). Solve s(g) = 0 for g.
-2, -1, 1, 3
Let i be (-11338)/51021 - ((-47)/9 - -1). Suppose 8/5 + 1/5*c**3 - 22/5*c - c**i + 1/5*c**5 + 17/5*c**2 = 0. What is c?
-2, 1, 4
Suppose -336/5 - 42/5*h**2 + 76*h - 2/5*h**3 = 0. What is h?
-28, 1, 6
Let t(p) be the first derivative of 5*p**3/3 + 1200*p**2 - 2405*p - 588. Factor t(b).
5*(b - 1)*(b + 481)
Let l(s) be the third derivative of -s**5/12 - 1845*s**4/8 + 2*s**2 - 398*s. Determine k so that l(k) = 0.
-1107, 0
Let n(t) = 9*t**4 - 15*t**3 - 60*t**2 + 25*t + 51. Let d(y) = 8*y**4 - 16*y**3 - 60*y**2 + 24*y + 52. Let w(b) = 5*d(b) - 4*n(b). Suppose w(s) = 0. What is s?
-2, -1, 1, 7
Let l(g) be the second derivative of g**5/150 + 26*g**4/45 + 92*g**3/15 + 8053*g. Let l(z) = 0. What is z?
-46, -6, 0
Let g = 857 - 853. Let a(o) be the second derivative of 0*o**2 + 7/4*o**5 - 5/6*o**3 + 5/6*o**g + 0 + 2/3*o**6 - 25*o. Factor a(z).
5*z*(z + 1)**2*(4*z - 1)
Let d(f) be the first derivative of f**4/16 - 4*f**3 + 45*f**2/8 + 47*f/2 + 2704. Factor d(o).
(o - 47)*(o - 2)*(o + 1)/4
Factor 345/4*z**2 + 36*z + 101/4*z**3 - 27 + 2*z**4.
(z + 1)*(z + 6)**2*(8*z - 3)/4
Let p(z) be the third derivative of -z**11/332640 + z**9/60480 - 11*z**5/12 + 69*z**2. Let d(i) be the third derivative of p(i). Determine g so that d(g) = 0.
-1, 0, 1
Let d be -9*(-3)/(36/(-32))*30/(-990). Factor 16/11*k - 6/11*k**2 - d.
-2*(k - 2)*(3*k - 2)/11
Let m(p) = p**4 + p**3 - 4*p**2 - 1. Let q(c) = -13*c**4 + 118*c**3 - 171*c**2 + 46*c + 38. Let t(w) = 6*m(w) + q(w). Factor t(j).
-(j - 16)*(j - 1)**2*(7*j + 2)
Let v(x) be the third derivative of 3*x**8/280 + 67*x**7/75 + 1534*x**6/75 + 338*x**5/75 - 1561*x**2 - x. Determine d, given that v(d) = 0.
-26, -1/9, 0
Factor 325*d - 25/2*d**3 - 169 - 573/4*d**2 - 1/4*d**4.
-(d - 1)**2*(d + 26)**2/4
Let y(p) = 6*p**3 - 60*p**2 + 105*p - 27. Let w be (-150)/(-35) + 14/(-49). Let k(n) = 3*n**3 - 30*n**2 + 52*n - 12. Let q(x) = w*y(x) - 9*k(x). Factor q(c).
-3*c*(c - 8)*(c - 2)
Let l(t) be the third derivative of 1/15*t**5 + 11/6*t**4 - t**2 - 2 + 0*t + 20/3*t**3. Factor l(d).
4*(d + 1)*(d + 10)
Let o = 49383/5 - 345621/35. Factor 348/7*x + o + 2523/7*x**2.
3*(29*x + 2)**2/7
Let d(l) be the first derivative of -2*l**3/15 - 277*l**2 - 2768*l/5 - 9198. Factor d(u).
-2*(u + 1)*(u + 1384)/5
Let k(x) be the third derivative of x**6/40 + 65*x**5/2 + 162*x**4 - 214*x**2 - 12*x. Find m such that k(m) = 0.
-648, -2, 0
Let g(u) = 2*u**2 - 69*u - 511. Let y be g(41). Let m(k) be the first derivative of 0*k + 5/9*k**3 - k**2 - y + 1/12*k**4. Factor m(h).
h*(h - 1)*(h + 6)/3
Let l(g) = 214*g - 640. Let v be l(3). Let q(x) be the second derivative of -5*x**v - 1/12*x**4 + 7/6*x**3 + 0 - 20*x. Factor q(f).
-(f - 5)*(f - 2)
Let f be (5/20 + 0)*18/(1 - -8). Let b(r) be the second derivative of 13*r + 0 + 0*r**2 - 1/4*r**4 - 3/20*r**5 + f*r**3 + 1/10*r**6. Factor b(t).
3*t*(t - 1)**2*(t + 1)
Let f = -79 - -207. Suppose 15*q + 17*q - f = 0. Suppose 17/8*a**2 - 3/2 - 2*a - 1/4*a**q + 1/8*a**3 = 0. What is a?
-3, -1/2, 2
Let t(a) be the second derivative of -a**5/4 - 125*a**4/4 - 2405*a**3/2 - 6845*a**2/2 + 520*a + 2. Factor t(f).
-5*(f + 1)*(f + 37)**2
Let j(k) = 12*k**2 - 1197*k + 45. Let y(z) = -z**2 + 5*z - 3. Let l(w) = -j(w) - 15*y(w). Factor l(g).
3*g*(g + 374)
Let t(o) be the second derivative of 1/24*o**4 + 189*o - 13/12*o**3 - 15/2*o**2 + 0. Factor t(k).
(k - 15)*(k + 2)/2
Let z(y) be the second derivative of y - 10*y**3 + 0*y**2 + 5/12*y**4 + 153. Factor z(v).
5*v*(v - 12)
Find w, given that -150 + 155*w - 1/4*w**4 - 103/2*w**2 + 25/4*w**3 = 0.
2, 3, 10
Let t(c) be the second derivative of c**4/3 - 340*c**3 + 3880*c. Find k such that t(k) = 0.
0, 510
Let l(o) be the second derivative of o**4/3 + 32*o**3/3 - 34*o**2 + 11*o - 51. Solve l(b) = 0.
-17, 1
Let u(r) be the third derivative of 0 + 2*r + 5/56*r**7 - 49/2*r**3 + 7/16*r**6 - 51/80*r**5 - 35/4*r**4 - 40*r**2. Find b such that u(b) = 0.
-2, -7/5, 2
Let c(h) = -21*h + 88. Let w be c(4). Factor 246*m**5 - 249*m**5 - w*m**4 - 3*m**3 - 2*m**4.
-3*m**3*(m + 1)**2
Let v(f) be the third derivative of 0*f**3 + 23/12*f**6 - 8/3*f**5 + 0*f + 0 + 1/14*f**7 + 67*f**2 + 0*f**4. Let v(g) = 0. What is g?
-16, 0, 2/3
Suppose -72 = -807*v + 808*v + 5*x, -2*x = 3*v + 21. Factor 1/2*q**3 + 0 + v*q + 5/2*q**2.
q*(q + 2)*(q + 3)/2
Let y(f) be the second derivative of -25/2*f**3 + 2 + 35/2*f**2 - 1/4*f**5 + 15/4*f**4 + 16*f. What is j in y(j) = 0?
1, 7
Let v(q) = -4*q**2 + 25*q + 26. Let s be v(7). Suppose -4*c - c + 4*b = -22, 0 = 3*c + s*b + 9. Determine r, given that -18/5 + 3*r - 3/5*r**c = 0.
2, 3
Let q be (4 - (-9 - -11))/(-7 + ((-96)/(-9) - 3)). Suppose 2*w**4 - 32/13*w**2 + 8/13*w + 0 - 8/13*w**5 - 6/13*w**q = 0. Calculate w.
-1, 0, 1/4, 2
Suppose 2116 - 202 + 1256 = 207*b + 427*b. Factor 0*t - 3/7*t**b - 3/7*t**4 + 0*t**2 + 6/7*t**3 + 0.
-3*t**3*(t - 1)*(t + 2)/7
Let d(c) be the second derivative of 3/2*c**2 + 20 + 0*c**3 - 3/16*c**4 + 3*c + 3/80*c**5. Factor d(j).
3*(j - 2)**2*(j + 1)/4
Let r = -165 - -183. Suppose -14*v + 10 = -r. Suppose -3/5*z**4 - 6/5 - 3/5*z**3 + 3/5*z + 9/5*z**v = 0. Calculate z.
-2, -1, 1
Let k(h) be the first derivative of 25*h**3/3 + 21*h**2/2 - 4*h + 1266. Solve k(n) = 0 for n.
-1, 4/25
Let y(k) be the second derivative of -169/2*k**2 + 13/6*k**3 - 1/48*k**4 + 0 - 78*k. Factor y(r).
-(r - 26)**2/4
Solve 0*n**2 - 4688*n + 3*n**2 - 4482*n - n**2 + 8982*n = 0 for n.
0, 94
Let p be -5*(-132)/60 - (-1467)/(-135). Let d(y) be the second derivative of 0 - 7/15*y**3 + 2/5*y**2 - p*y**4 + 12*y. Solve d(m) = 0.
-2, 1/4
Factor -24*l**3 + 0*l - 2/3*l**4 + 0 + 0*l**2.
-2*l**3*(l + 36)/3
Factor 3435 - 30905/2*b - 45/2*b**2.
-5*(b + 687)*(9*b - 2)/2
Let s(k) be the first derivative of k**6/2 - 6*k**5/5 - 81*k**4/4 + 108*k**3 - 162*k**2 + 6115. Factor s(l).
3*l*(l - 3)**2*(l - 2)*(l + 6)
Let h(z) be the first derivative of z**4/10 - 62*z**3/15 + 84*z**2/5 - 2433. What is i in h(i) = 0?
0, 3, 28
Let d(x) be the third derivative of -x**5/60 + 23*x**4/8 - 295*x**3/3 - 2*x**2 + 9*x - 136. Factor d(k).
-(k - 59)*(k - 10)
Let n = -470 - -657. Factor 3*i**4 + 0*i**4 + 197*i**3 - n*i**3 + 2*i**4.
5*i**3*(i + 2)
Let m(o) be the first derivative of 2*o**6/15 - 98*o**5/25 + 56*o**4/5 - 88*o**3/15 - 5216. Find d such that m(d) = 0.
0, 1/2, 2, 22
Let o(n) be the first derivative of n**6/10 - 3*n**5/20 - n**4/2 + 64*n - 1. Let m(p) be the first derivative of o(p). Factor m(x).
3*x**2*(x - 2)*(x + 1)
Let f = 180 - 177. Solve 21*l**4 + 15*l**2 - 1984*l**f + 2032*l**3 + 21*l**2 + 3*l**5 = 0 for l.
-3, -2, 0
Let h be 1*(-12)/54 - 9004/(-18). Determine l, given that 355*l + 952*l + 4*l**5 + 424*l**3 - h - 1160*l**2 - 7*l - 68*l**4 = 0.
1, 5
Let f(g) be the second derivative of g**5/60 - g**4/6 - 19*g**3/18 + 4*g**2 - 3042*g. Factor f(y).
(y - 8)*(y - 1)*(y + 3)/3
Let k(p) be the third derivative of p**8/1344 + p**7/420 - p**6/30 - 19*p**5/120 + 5*p**4/32 + 3*p**3/2 - 