1
Let w(a) = -12*a**2 - 6264*a + 6287. Let t(i) = 9*i**2 + 4698*i - 4715. Let j(n) = -11*t(n) - 8*w(n). Factor j(c).
-3*(c - 1)*(c + 523)
Let h(w) = 7*w**3 - 116*w**2 + 280*w + 18. Let p be h(3). Suppose -4/3*j**p + 800/3 - 158/3*j**2 - 1520/3*j = 0. What is j?
-20, 1/2
Let r = 67746 - 67746. Determine m, given that 12/7*m**2 - 57/7*m**4 + 33/7*m**3 + r*m + 12/7*m**5 + 0 = 0.
-1/4, 0, 1, 4
Factor 27 - 32282406*y**4 + 9234*y - 301850*y**2 + 1351430*y**2 + 39294766*y**3 - 8071201*y**4.
-(y - 1)*(343*y + 3)**3
Let i(v) be the third derivative of v**6/420 + 607*v**5/70 - 635*v**2 + v + 5. Factor i(w).
2*w**2*(w + 1821)/7
Find h, given that 14*h**2 - 10*h - 1/2*h**4 - 7/2*h**3 + 0 = 0.
-10, 0, 1, 2
Let g = 117310 - 1055789/9. Factor g*q**3 - 4/9 + 8/9*q - 5/9*q**2.
(q - 2)**2*(q - 1)/9
Let l be 31/(-124) + 1/4. Let h(n) be the third derivative of 0*n + l + 1/20*n**5 - 18*n**2 - 5/8*n**4 + 2*n**3. What is c in h(c) = 0?
1, 4
Let t(p) be the first derivative of 60*p - 3/2*p**4 + 123/2*p**2 + p**3 + 150. Factor t(i).
-3*(i - 5)*(i + 4)*(2*i + 1)
Let z(t) be the second derivative of -5*t**5/36 - 5*t**4/12 - t**3/2 - 15*t**2 - 42*t. Let r(i) be the first derivative of z(i). Factor r(d).
-(5*d + 3)**2/3
Let o = 242407/22722 + -13/7574. Solve -31/3*n**3 + 32/3 - 22/3*n**2 - 1/3*n**5 - 10/3*n**4 + o*n = 0 for n.
-4, -2, -1, 1
Let f be 54/(-8) + (-3)/(-4). Let a(r) = -37*r**3 + 36*r**3 - r**2 - 2 + 1. Let v(u) = u**4 - 9*u**3 - 6*u**2 - 6. Let x(i) = f*a(i) + v(i). Factor x(m).
m**3*(m - 3)
Determine f so that 134*f**3 - 2647*f + 10935 - 188*f - 139*f**3 + 163*f**2 - 418*f**2 = 0.
-27, 3
Let p(k) be the third derivative of -k**6/10 + 1409*k**5/15 + 2824*k**4/9 + 1256*k**3/3 - 2444*k**2. Factor p(s).
-4*(s - 471)*(3*s + 2)**2/3
Let z(s) be the third derivative of 0*s + 2*s**2 + 1/12*s**6 + 0*s**7 - 5/336*s**8 - 69 - 5/24*s**4 + 0*s**3 + 0*s**5. What is h in z(h) = 0?
-1, 0, 1
Let f(q) = 4*q**2 + 75*q - 47. Let k be f(-26). Let r = -705 + k. Factor 0 - 1/3*s - 1/3*s**r.
-s*(s + 1)/3
Let i be (-2 - 52/(-20)) + (-168)/(-70). Let q be -1*i/(-27) - (-28)/126. Factor 0 - q*s + 5/3*s**2.
s*(5*s - 1)/3
Solve -704/7*m - 1028/7*m**2 - 340/7*m**3 - 16/7 = 0.
-2, -1, -2/85
Let q be (-49)/(-14) - 4/(-8). Let l(n) = n**3 - 7*n**2 + 8*n - 9. Let v be l(6). Factor -2/3*y + 1/3 - 1/3*y**q + 0*y**2 + 2/3*y**v.
-(y - 1)**3*(y + 1)/3
Suppose 3*v - 99 = -111, -3*c + 2*v + 98 = 0. Suppose 7*n = 26 + c. Let -n*k**2 - 16*k - 4/3*k**3 - 32/3 = 0. Calculate k.
-2
Let j be -11 + (-2147)/(-5) + (-72)/270. Factor 2/15*i**2 + j + 224/15*i.
2*(i + 56)**2/15
Let s(a) = -a**3 + 146*a**2 - 377*a. Let t(i) = -295*i**2 + 755*i. Let z(o) = -5*s(o) - 2*t(o). Solve z(j) = 0.
0, 3, 25
Let c(f) = -2140*f + 992999. Let z be c(464). Determine j so that 6 - 105*j**4 + 225/4*j**5 + 117/2*j**2 + z*j - 219/4*j**3 = 0.
-2/5, -1/3, 1, 2
Let n(b) = -b**3 + 2*b**2 + b. Let v be n(2). Determine m so that v*m + 3*m - 6*m - 5*m**2 + 6*m = 0.
0, 1
Suppose -5*g + 44 = 2*k + 14, 4*k = -4*g + 36. Let i = -10269/4 - -2569. Factor 1/4*u**g + 0 + 11/4*u**2 - 5/4*u - i*u**3.
u*(u - 5)*(u - 1)**2/4
Let q(i) be the first derivative of -9 - 45/2*i**2 + 5/4*i**4 + 0*i**3 + 0*i. Factor q(y).
5*y*(y - 3)*(y + 3)
Suppose -9 = 280*w + 270*w - 553*w. Factor 0 + 1/3*x**4 - 2*x**2 - 1/3*x**w + 0*x.
x**2*(x - 3)*(x + 2)/3
Let s be -3 + (1 + 0)/((-3)/27). Let t be s/(-3) + 1122/(-391). What is u in 0 + t*u**2 - 8/23*u + 26/23*u**3 - 8/23*u**4 = 0?
-1, 0, 1/4, 4
Let g(o) be the third derivative of -o**5/30 + 7*o**4/4 - 110*o**3/3 + 3*o**2 + 34. Factor g(t).
-2*(t - 11)*(t - 10)
Let s be 21/((-22)/(242/(-33))) + 50/(-8). Factor -s*y**2 + 0*y + 1 + 1/4*y**3.
(y - 2)**2*(y + 1)/4
Factor -3142/5*u - 314 - 2/5*u**3 - 1574/5*u**2.
-2*(u + 1)**2*(u + 785)/5
Let h(n) = 2*n - n**4 - 33*n**3 + 32*n**3 - 5*n + 7*n - 5*n. Let w(i) = 5*i**5 - 5*i**3 + 20*i**2 + 30*i. Let p(v) = 10*h(v) + w(v). Factor p(b).
5*b*(b - 2)**2*(b + 1)**2
Let r be 3/6*(-6 + 6) - 96. Let v = r - -101. Find z, given that -1/3*z**3 - 1/3*z**4 + 1/3*z**2 + 0*z + 1/3*z**v + 0 = 0.
-1, 0, 1
Suppose 56*u**2 + 3*u**3 + 20*u**2 - 2331*u - 5*u**3 + 10584 + 74*u**2 - u**3 = 0. What is u?
8, 21
Let t(s) = s**3 - 60*s**2 - 327*s + 18562. Let r be t(61). Determine m, given that -10946/3*m**2 - 6*m**4 + r*m + 292*m**3 - 384 = 0.
1/3, 24
Let c(g) = g**3 + g**2 + g + 1. Let i(q) = -9*q - 91. Let p be i(-10). Let m(u) = -9*u**3 + 15*u**2 - 39*u + 9. Let d(x) = p*m(x) - 6*c(x). Solve d(s) = 0.
1, 5
Let x = -143068 + 143072. Solve 60/7*b**3 + 500/7*b + 4/7*b**x + 0 + 300/7*b**2 = 0.
-5, 0
Let q(v) be the first derivative of v**6/6 + 15*v**5/4 - 5*v**4/12 - 25*v**3/2 + 230*v - 138. Let y(p) be the first derivative of q(p). What is x in y(x) = 0?
-15, -1, 0, 1
Let b(z) = 7*z**2 - 2*z + 22. Let u be 3 + 3 - (-4 + 5). Let m(q) = -6*q**2 + 3*q - 21. Let p(h) = u*b(h) + 6*m(h). Factor p(v).
-(v - 4)**2
Suppose 0 = -56*h + 198 - 534. Let t(k) = 12 + 27 - k**2 + 0*k**2 - 36*k. Let m(g) = 35*g - 40. Let j(v) = h*m(v) - 5*t(v). Factor j(o).
5*(o - 3)**2
Let m(l) = 5*l + 34. Let t be m(-14). Let k be (14/(-21))/(21/t). Find q such that -4/7 + 2/7*q**3 + 10/7*q - k*q**2 = 0.
1, 2
Let t(r) be the first derivative of r**4/12 - 26*r**3/9 + 20*r**2/3 + 64*r + 1579. Factor t(n).
(n - 24)*(n - 4)*(n + 2)/3
Let t = 136576 - 409714/3. What is p in 1/3*p**2 - t - 5/3*p = 0?
-2, 7
Let v = 3570 - 3567. Let l(y) be the third derivative of 0*y + 1/40*y**6 - 11*y**2 + 0 + 0*y**v + 1/4*y**4 - 3/20*y**5. Let l(r) = 0. Calculate r.
0, 1, 2
Suppose -15 = -3*t - 4*v, 0 = t + 7*v - 5*v - 5. Factor -2*x**t + 1360*x**2 + 4*x**4 - 1360*x**2 - 2*x**3.
-2*x**3*(x - 1)**2
Let h = 4201 + -8395/2. Let u(m) be the first derivative of 4*m + h*m**4 + 11*m**2 + 4 + 32/3*m**3. Factor u(i).
2*(i + 1)**2*(7*i + 2)
Let k be ((-49)/4 + 11)/(2/(-72)). Suppose 4*t = -s + 6, 5*s + 16*t - 11*t = k. Find j such that -s*j**3 - 20/3*j**4 - 20/3*j**2 - 5/3*j**5 + 0 - 5/3*j = 0.
-1, 0
Let x be 103/55 + 704/(-440). Find o such that -4/11*o**2 - 1/11*o**3 + 0 - x*o = 0.
-3, -1, 0
Let j be (5/(30/4))/((-3)/(-18)). Suppose 2*h = j*n + 4*h - 14, -n + 3*h - 7 = 0. Solve n*u**2 + 60*u - 64*u - 4*u**2 + 6 = 0.
-3, 1
Let w be 1905/24 + (-3)/8. Suppose -1 - 4 = 5*k, h = -2*k + w. Factor 64*a**2 + 14*a**3 + 140*a + h + a**4 + 19 - 28*a**2 + 33*a**2.
(a + 2)**2*(a + 5)**2
Factor 0 - 1896/5*d**4 - 3/5*d**5 - 301458/5*d**3 - 119448*d**2 - 59535*d.
-3*d*(d + 1)**2*(d + 315)**2/5
Factor 16/9*h**3 + 8/3*h**2 + 0 + 0*h + 2/9*h**4.
2*h**2*(h + 2)*(h + 6)/9
Let w(k) = 5*k**4 + 28*k**3 - 30*k**2 - 31*k - 42. Let d(r) = 8*r**4 + 43*r**3 - 45*r**2 - 46*r - 60. Let i(j) = 7*d(j) - 10*w(j). Factor i(y).
3*y*(y - 1)*(y + 4)*(2*y + 1)
Let i(w) = -59115*w + 118232. Let q be i(2). What is r in -6050/13 - 2/13*r**q + 220/13*r = 0?
55
Let z(w) = -w**2 - 541*w + 1290. Let y(s) = 12*s**2 + 6005*s - 14190. Let r(p) = -2*y(p) - 23*z(p). Factor r(h).
-(h - 430)*(h - 3)
Let a = -1159616/5 + 231928. What is u in 9/5*u**4 + 1/5*u**5 - a*u - 16/5 + 7/5*u**2 + 23/5*u**3 = 0?
-4, -1, 1
Let k(v) be the third derivative of 0*v + 4/45*v**5 - 4/45*v**6 + 93*v**2 + 0 + 7/36*v**4 + 1/9*v**3. Factor k(f).
-2*(f - 1)*(4*f + 1)**2/3
Let y = 2344 + -2336. Let v(i) be the first derivative of -4/3*i**2 + 2/27*i**3 + 19 + y*i. Factor v(j).
2*(j - 6)**2/9
Let p be (-4)/27*77/((-1694)/66). Factor 2/9*g**3 - p*g**2 + 0 + 0*g + 2/9*g**4.
2*g**2*(g - 1)*(g + 2)/9
Factor 853*b**2 - 410*b + 88*b**3 - 32*b**4 - 949*b**2 + 446*b + 4*b**5.
4*b*(b - 3)**2*(b - 1)**2
Determine q so that 395*q + 5/2*q**4 - 300 - 35*q**3 - 125/2*q**2 = 0.
-4, 1, 2, 15
Let b be (-18864)/(-64) - 1/(-4). Suppose -6*w + b = -w. Let 2*p**3 - w*p + 2*p**2 + 61*p + 2*p**2 = 0. Calculate p.
-1, 0
Let l be (-3)/3 - (-12)/9*3. Factor 2948 - 21*v - 2978 + 0*v**2 - l*v**2.
-3*(v + 2)*(v + 5)
Let r(w) = 36*w - 324. Let f be r(9). Let b(x) be the first derivative of 1/2*x**4 + 2/5*x**5 + 0*x**3 + 0*x**2 + f*x + 4. Factor b(h).
2*h**3*(h + 1)
Let t = -12966 - -12966. Let 3/4*p**3 - 1/4*p**5 + t*p**4 + 0 + 1/2*p**2 + 0*p = 0. What is p?
-1, 0, 2
Let c = 176 - 174. Factor c*x**2 - 12*x**2 + 7*x**2 - 15*x + 10 + 8*x**2.
5*(x - 2)*(x - 1)
Let m(s) = -3*s**2 - 29*s - 66. Let k = -2265 - -2260. Let n be m(k). Factor 0 + 0*p - 1/5*p**5 - 2/5*p**2