z**2 - 9/16*z**4. Factor u(v).
-3*v*(v - 3)*(v + 2)*(v + 4)/4
Let t be 1/((-56)/(-16)) + 133749/(-98). Let g = -1363 - t. Factor 3/2*z**5 - 3*z**3 - 3/2 + g*z - 3/2*z**4 + 3*z**2.
3*(z - 1)**3*(z + 1)**2/2
Let z be 62031/9300 - (-2)/25. Factor 36*i**2 - 16*i**3 + z + 135/4*i.
-(i - 3)*(8*i + 3)**2/4
Let 666*n - 49*n**2 + 2*n**3 + 524*n + 11*n**2 - 48*n**2 - 5202 = 0. Calculate n.
9, 17
Solve 35*c - 675*c**2 + 195*c**2 + 1116 + 53*c + 476*c**2 = 0.
-9, 31
Solve 56/13 + 22/13*t**2 + 64/13*t + 2/13*t**3 = 0.
-7, -2
Let b(y) be the third derivative of 50*y**2 + 0*y - 7/240*y**5 + 23/96*y**4 + 0 - 1/4*y**3. Factor b(c).
-(c - 3)*(7*c - 2)/4
Let l be (903/(-35) - -5) + -1. Let t = l + 773/35. Factor 4/7*r**2 - t*r**3 - 2/7*r + 0.
-2*r*(r - 1)**2/7
Suppose t - 63 = -61. Factor 12*j - 63*j - 4*j**t - 52 - 5*j.
-4*(j + 1)*(j + 13)
Factor 1400 + 1285*r + 195*r - 28*r**3 + 91*r**2 - 37*r**2 - 2*r**4.
-2*(r - 7)*(r + 1)*(r + 10)**2
Let q(a) be the third derivative of -a**6/1080 - 4*a**5/135 - 55*a**4/216 + 4*a**3/3 - 6*a**2 - 311. Factor q(r).
-(r - 1)*(r + 8)*(r + 9)/9
Let y(h) be the second derivative of 3/5*h**5 - 4/15*h**6 + 1/21*h**7 + 1/3*h**3 + 0 - 9*h + 0*h**2 - 2/3*h**4. Factor y(a).
2*a*(a - 1)**4
Let u(h) be the third derivative of -2/75*h**5 + 0 - 14/15*h**3 + 0*h + 10*h**2 + 1/2*h**4. Factor u(c).
-4*(c - 7)*(2*c - 1)/5
Let h(r) = -3*r**4 + 4*r**3 - 3*r**2 + r + 11. Let b = -21 + 19. Let w(i) = -i**4 + 2*i**3 - 2*i**2 + 5. Let m(n) = b*h(n) + 5*w(n). Solve m(s) = 0.
-3, -1, 1
Factor 94*a + 8497*a**2 - 5*a**4 - 100 - 35*a**3 - 8512*a**2 + 61*a.
-5*(a - 1)**2*(a + 4)*(a + 5)
Let h(p) be the first derivative of 41*p**6/27 + 488*p**5/45 + 439*p**4/18 + 448*p**3/27 - 4*p**2/3 + 1284. What is d in h(d) = 0?
-3, -2, -1, 0, 2/41
Let a(n) = 30*n**3 - 1300*n**2 - 1318*n + 2612. Let l(m) = 11*m**3 - 433*m**2 - 439*m + 870. Let w(p) = 3*a(p) - 8*l(p). Factor w(h).
2*(h - 219)*(h - 1)*(h + 2)
Factor 3085*n - 208 - 132 - n**2 - n**2 - 3007*n.
-2*(n - 34)*(n - 5)
Let y(a) be the first derivative of -13*a**4/2 + 130*a**3/3 + 56*a**2 - 151. Let f(s) = -77*s**3 + 389*s**2 + 336*s. Let i(h) = 6*f(h) - 17*y(h). Factor i(b).
-4*b*(b - 7)*(5*b + 4)
Let x = -204274 - -204276. Let -1/3*q**x - 6*q - 27 = 0. What is q?
-9
Let m = 24 - -7. Let j be (-3)/2 + 14/4. Factor f - 18*f**2 - 14*f**j + m*f**2.
-f*(f - 1)
Suppose 82*h + 37*h - 1008 = -60*h - 650. Factor -255/4*m - 63/2 - 3/4*m**3 - 33*m**h.
-3*(m + 1)**2*(m + 42)/4
Suppose -37/3*a**4 - 287/3*a**3 - 467/3*a**2 + 0 - 72*a - 1/3*a**5 = 0. Calculate a.
-27, -8, -1, 0
Let d be 2/8 + 1*(-92)/(-16). Suppose -d*i + 17 = -1. Factor -3*f**3 - 3*f**2 + 2*f + i + 4*f - 3*f.
-3*(f - 1)*(f + 1)**2
Let f be (-2)/7*(-17 - -13)*14/10. Let s(g) be the first derivative of -f*g - 98/15*g**3 + 19 + 28/5*g**2. Factor s(z).
-2*(7*z - 2)**2/5
Let y be (1 - 2)/(10/(-1120)). What is n in 40 + 64*n**2 + 5*n**3 + y*n + 29*n**3 + 47*n**2 - 5*n**2 - 2*n**4 - 2*n**5 = 0?
-2, -1, 5
Let g = -447255 - -447255. Factor g + 13*t + 1/2*t**2.
t*(t + 26)/2
Let j(z) = 2*z**2 - 7. Let c(t) = -4456*t + 1241010. Let d(p) = -c(p) - 2*j(p). Factor d(g).
-4*(g - 557)**2
Factor -270/13 - 10/13*q**2 + 104*q.
-2*(q - 135)*(5*q - 1)/13
Let j be (3 - (3 - 3)) + 17. Suppose -6*q = -q + j, 4*q = -4*z. Factor 12*m**2 - 10*m**2 - 4 + z.
2*m**2
Find z, given that 144/5 - 14/5*z**3 + 32*z**2 - 402/5*z = 0.
3/7, 3, 8
Find k such that 66631*k - 752*k**3 + 243 - 65146*k - 89*k**3 + 2001*k**2 = 0.
-9/29, 3
Let z = 90 - 87. Factor -4*t + 4*t**z + 346 - 346.
4*t*(t - 1)*(t + 1)
Let b(u) be the first derivative of -u**5/55 + u**4/4 - 19*u**3/33 + 9*u**2/22 + 1107. Find v such that b(v) = 0.
0, 1, 9
Let t(x) be the third derivative of -x**5/140 - 69*x**4/14 - 275*x**3/14 - 3*x**2 - 1696. Factor t(i).
-3*(i + 1)*(i + 275)/7
Solve 1/6*i**2 - 40/3 - 1/3*i = 0 for i.
-8, 10
Suppose 2/3*b**2 + 2350/3 - 160*b = 0. What is b?
5, 235
Let r(o) be the third derivative of o**5/75 - 313*o**4/30 + 1244*o**3/15 - 2*o**2 - 820*o. Solve r(u) = 0.
2, 311
Solve -31612/3*w**2 + 17956/3*w - 2560/3 + 147*w**3 = 0 for w.
2/7, 640/9
Let h(a) be the first derivative of 4/3*a - 221 + 8*a**2 + 89/9*a**3 - 19/4*a**4. Suppose h(o) = 0. Calculate o.
-1/3, -2/19, 2
Let x(b) be the third derivative of b**5/20 - 35*b**4/8 - 100*b**3 + 981*b**2. Solve x(y) = 0 for y.
-5, 40
Let k(s) be the third derivative of s**5/60 + 1933*s**4/12 + 3736489*s**3/6 + 1315*s**2. Factor k(i).
(i + 1933)**2
Let x(l) = -2*l**3 - 502*l**2 - 1068*l - 9. Let n(i) = 4*i**3 + 1008*i**2 + 2136*i + 17. Let d(m) = -18*n(m) - 34*x(m). Let d(o) = 0. What is o?
-267, -2, 0
Let g(n) = 75*n - 15. Let o be g(1). Find x, given that o*x - 43*x**4 - 36*x**2 + 55*x**4 - 9*x**3 - 9*x - 18 = 0.
-2, 3/4, 1
Suppose 9*z - 4 = 14. Let n(q) = q**4 + q**3 - q**2 - 1. Let k(m) = 4*m**4 + 2*m**3 - 2*m**2 - 2. Let v(h) = z*n(h) - k(h). Factor v(a).
-2*a**4
Let c = -192 + 194. Let 89*k + 46*k - 1445 - 3*k**c + 35*k - 2*k**2 = 0. What is k?
17
Let p(n) = -6*n**4 - 10*n**3 + 10*n**2. Let w(l) = l**4 + l**3 + l**2. Let h = -31 + 33. Let g(d) = h*w(d) + p(d). Factor g(q).
-4*q**2*(q - 1)*(q + 3)
Let a(b) = -4 - 12*b + 0 + 3 + 13*b. Let y be a(3). Factor 0*n - n**y - 3*n + 88*n**3 - 77*n**3 - 7*n**4.
-n*(n - 1)**2*(7*n + 3)
Let n = 15066 + -15062. Suppose 0*p + 0 + 40/7*p**3 - 78/7*p**n + 8/7*p**2 = 0. Calculate p.
-2/13, 0, 2/3
Let j be (491 - -5)/(-1 - -3). Solve -5 + 2*l**2 + l**2 - 73*l + j + 19*l = 0.
9
Let s be -1 + 180 + -6 + 1. Let v be 1/3*464/s. Suppose -2/9*i**4 + 8/9*i - 8/9*i**3 + v - 2/3*i**2 = 0. Calculate i.
-2, -1, 1
Let z(x) be the third derivative of -x**5/15 + 235*x**4/6 - 932*x**3/3 - 4*x**2 + 3*x + 240. Determine n so that z(n) = 0.
2, 233
Let v = 54/5635 + 50499/22540. Factor 1/4*z**5 + v*z + 11/2*z**3 + 6*z**2 + 0 + 2*z**4.
z*(z + 1)**2*(z + 3)**2/4
Let p(t) be the first derivative of -1/4*t**4 - 9/2*t**2 + 2*t**3 + 4*t + 20. Solve p(x) = 0 for x.
1, 4
Let h be (7 + 1 - (0 + 5)) + 15. Solve -2*m**4 + 48*m**2 - 17*m**3 + 31*m + 21*m + 29*m**3 + h = 0 for m.
-1, 9
Determine c, given that -53*c**4 - 54*c**4 + 15*c**2 + 8*c**3 - 48*c - 17*c**4 - 59*c**2 + 128*c**4 + 144 = 0.
-3, 2
Let z = -6781/72 + 848/9. Let r(n) be the third derivative of 1/105*n**7 - 1/20*n**5 + 1/120*n**6 - 17*n**2 - z*n**4 + 0 + 0*n + 1/6*n**3. Factor r(p).
(p - 1)*(p + 1)**2*(2*p - 1)
Determine h so that -9*h**2 + 44*h**2 - 349*h + 180*h - 150*h**3 + 174*h = 0.
-1/10, 0, 1/3
Let h(f) be the second derivative of -21*f**2 + 47/2*f**3 + 133*f - 141/20*f**5 + 21/4*f**4 - 1 - 7/10*f**6. Determine w, given that h(w) = 0.
-7, -1, 2/7, 1
Let l be (-142)/(-213)*(0 + -1 + 13). Suppose 40*h - 42*h + l = x, 2*h - 8 = -2*x. Factor 6/19*j**3 + 0*j + 4/19*j**4 + 0*j**2 - 2/19*j**5 + x.
-2*j**3*(j - 3)*(j + 1)/19
Let q = 23447/18 + -1893/2. Let z = -355 + q. Factor -2/9*b**2 - 4/3 + z*b.
-2*(b - 3)*(b - 2)/9
Let b(y) = -y**2 + 215*y - 196. Let r(i) = -4*i**2 + 640*i - 588. Let d(x) = -8*b(x) + 3*r(x). Factor d(m).
-4*(m - 49)*(m - 1)
Let u(z) be the third derivative of 5*z**6/48 + 299*z**5/120 + 263*z**4/48 - 11*z**3/12 + 100*z**2. Determine a, given that u(a) = 0.
-11, -1, 1/25
Let i(t) = -31*t**2 + 22*t**2 - 17 - 5*t - 27*t**2. Let j(g) = 9 + g - 5 - 1 + 6*g**2. Let c(w) = 6*i(w) + 34*j(w). Determine p, given that c(p) = 0.
0, 1/3
Let n(m) be the second derivative of -243/5*m**2 - 73 - 126/5*m**3 + 3*m - 5/2*m**4 - 2/25*m**5. Factor n(l).
-2*(l + 9)**2*(4*l + 3)/5
Let h be (2 - 344/215)/(3/5). Factor 0 + 4/3*t + h*t**3 - 2*t**2.
2*t*(t - 2)*(t - 1)/3
Suppose 57*z + 42 = 51*z. Let o be z + -164*(-9)/180. Let 48/5*d**2 + 9*d**3 + 9/5*d - o + 12/5*d**4 = 0. What is d?
-2, -1, 1/4
Factor -1293 + 4*p + 246*p - 6*p - 467 - 28*p - 4*p**2.
-4*(p - 44)*(p - 10)
Let d = 31 - 28. Solve -5*b**2 - 13*b**d + 4*b**2 - 3*b**4 + 9*b**3 + 0*b**2 = 0 for b.
-1, -1/3, 0
Suppose -4*l + 26 + 14 = 0. Let -18*n**4 - 10*n**3 + 53*n**4 - l*n**2 + 35*n**3 = 0. Calculate n.
-1, 0, 2/7
Let f(z) be the second derivative of -7*z**6/240 - 3*z**5/20 + 47*z**3/2 + 2*z - 32. Let y(u) be the second derivative of f(u). What is g in y(g) = 0?
-12/7, 0
Let d = -35 - -49. Suppose 15*c**4 + d*c**4 + 5*c**5 + 15*c**3 - 9*c**4 = 0. Calculate c.
-3, -1, 0
Let r(s) be the second derivative of -s**4/60 + 2*s**3/5 - 18*s**2/5