1)
Find g such that -3/4*g**4 + 0 + 0*g - 53/2*g**2 - 161/4*g**3 = 0.
-53, -2/3, 0
Factor -23660/9*o + 52*o**2 - 4/9*o**4 + 92/9*o**3 + 140608/9.
-4*(o - 13)**3*(o + 16)/9
Let x be (-1976)/(-1330) - (375/(-150))/((-70)/8). Suppose -22/5 - 68/5*y - x*y**2 = 0. Calculate y.
-11, -1/3
Let q(t) be the second derivative of t**7/126 + 37*t**6/180 - 103*t**5/40 + 395*t**4/72 - 125*t**3/36 - 4836*t. Let q(j) = 0. Calculate j.
-25, 0, 1/2, 1, 5
Let s(u) = 6*u**2 + u + 6. Let c(d) = 79*d**2 - 70*d + 468. Let t(v) = 2*c(v) - 26*s(v). Factor t(i).
2*(i - 78)*(i - 5)
Suppose -8/3*p + 173/3*p**3 + 35*p**5 - 14/3*p**2 + 0 + 464/3*p**4 = 0. Calculate p.
-4, -1/3, -2/7, 0, 1/5
Let f be 16/(-96) + 3245/(-6). Let r = -541 - f. Solve 0*u**2 + 3/5*u - 3/5*u**3 + r = 0 for u.
-1, 0, 1
Let v(t) be the first derivative of -27*t**6/10 - t**5/5 + 6*t**4 + 8*t**3/9 + 12*t**2 + 64. Let o(y) be the second derivative of v(y). Solve o(w) = 0.
-2/3, -1/27, 2/3
Let r = 3492 - 104759/30. Let q(g) be the third derivative of 0*g + 0*g**3 - 8*g**2 + 0*g**4 - r*g**5 - 1/60*g**6 + 0. Factor q(n).
-2*n**2*(n + 1)
Find v such that 98*v**3 - 64*v**3 + 126*v**3 - 541*v - 175*v**2 + 211*v + 5*v**4 = 0.
-33, -1, 0, 2
Let m(c) = -3*c. Let d(v) = 1105 - 58*v + 1906 - 744 + 233 - 45*v + v**2. Let q(x) = -d(x) + m(x). Find j, given that q(j) = 0.
50
Suppose 2*l - 16 = -12. Suppose 3 = -s, -6*r + 20 = -l*r - 4*s. Factor -12*w**3 + 107*w**r - 227*w**2 + 110*w**2 + 2*w.
-2*w*(w + 1)*(6*w - 1)
Let g(d) be the third derivative of -d**7/840 + 31*d**6/240 - 319*d**5/60 + 363*d**4/4 - 3588*d**2. Factor g(j).
-j*(j - 22)**2*(j - 18)/4
Let g(d) be the third derivative of -7*d**6/780 + d**5 - 448*d**4/13 - 1568*d**3/39 - 622*d**2. Factor g(q).
-2*(q - 28)**2*(7*q + 2)/13
Suppose 10*b - 17*b + 14 = 0. Determine h so that 85 + 104*h**b + 4*h - 99*h**2 - 94*h = 0.
1, 17
Factor 2657*g**2 - 5314*g**2 - 504*g + 2655*g**2 - 31752.
-2*(g + 126)**2
Let n = 2/2249 + 6467/314860. Let a(v) be the second derivative of -15/14*v**2 + 0 - 11/14*v**3 - 1/4*v**4 - n*v**5 - 15*v. Factor a(d).
-3*(d + 1)**2*(d + 5)/7
Let c be ((-115)/(-92) + (-92)/(-16))*6/14. Find a, given that 0*a + 0*a**2 + 6/5*a**5 + 0 - 72/5*a**c - 6/5*a**4 = 0.
-3, 0, 4
Let z(p) be the second derivative of -p**7/441 + 4*p**6/63 - 3*p**5/5 + 18*p**4/7 - 33*p**3/7 + 6166*p. Suppose z(j) = 0. Calculate j.
0, 3, 11
Let y(m) be the second derivative of 13*m**4/6 - 285*m**3 - 198*m**2 - 8234*m. Determine o so that y(o) = 0.
-3/13, 66
Suppose -y + 4 = -22. Let d = -23 + y. Find a such that 4 - 2*a**2 + 12*a**2 - d*a**2 - 6*a**2 + 5*a = 0.
-4, -1
Let j = 75108 + -75104. Factor 9/5 + 3*h**3 + 37/5*h**2 + 33/5*h + 2/5*h**j.
(h + 1)*(h + 3)**2*(2*h + 1)/5
Let z = -123 - -127. Let i be z/(-40)*6*-5. Suppose 2/13*o**2 + 2/13*o**i + 0 + 0*o = 0. Calculate o.
-1, 0
Let u(z) be the first derivative of z**6/36 + 13*z**5/30 + 61*z**4/24 + 41*z**3/6 + 15*z**2/2 - 885. Factor u(p).
p*(p + 2)*(p + 3)**2*(p + 5)/6
Let a(v) = 16*v**3 - 25*v**3 + 10*v**3. Let o(x) = -2*x**5 + 24*x**4 - 82*x**3 + 120*x**2 - 50*x. Let b(f) = 10*a(f) - o(f). Factor b(d).
2*d*(d - 5)**2*(d - 1)**2
Let x(a) be the second derivative of a**4/42 - 11*a**3/7 + 1186*a. Suppose x(k) = 0. What is k?
0, 33
Determine k so that 46/7*k**2 - 2/7*k**3 + 170/7 - 214/7*k = 0.
1, 5, 17
Let s(c) = -3*c**2 - 66*c - 61. Let b be s(-21). Let l be (0 - 1/b)*72/(-12). Factor 2/3*k + 0 + 2/3*k**l - 4/3*k**2.
2*k*(k - 1)**2/3
Let j(c) = -30*c**2 - 71*c - 20. Let y(f) = -120*f**2 - 285*f - 81. Let d be 11 - (-10)/(-25)*5. Let s(w) = d*j(w) - 2*y(w). Factor s(n).
-3*(n + 2)*(10*n + 3)
Let -545*r**2 + 650*r**3 + 693*r**2 - 654*r**3 = 0. Calculate r.
0, 37
Let s(w) be the third derivative of -25*w**8/2688 - 23*w**7/112 + 81*w**6/160 + 137*w**5/120 + 5*w**4/8 - 2*w**2 - 86. Find z such that s(z) = 0.
-15, -2/5, 0, 2
Suppose 82/3*f**2 - 38/3 - 44/3*f = 0. What is f?
-19/41, 1
Solve -1015*w - 1428*w + 613*w + 0*w**2 + 1825 + 5*w**2 = 0.
1, 365
Let z(a) be the first derivative of -5/12*a**3 - 2*a**2 - 4 - 3/4*a. What is t in z(t) = 0?
-3, -1/5
Suppose 4*u = 3*t + 15 + 3, -5*t - 19 = -3*u. Factor -5*z**u - 47*z + 5*z**4 + 40*z + 27*z - 50*z**2 + 120.
5*(z - 3)*(z - 2)*(z + 2)**2
Let s(d) = -d - 16. Let v be s(-20). Let y be 1/v - (-7 - (-58)/8). Factor -1/12*x**2 + y + 0*x.
-x**2/12
Let h = 10 + -35. Let y = -21 - h. Determine d so that -16*d**y + 4*d**5 - 4*d**2 - 4*d**2 + 6*d**3 + 14*d**3 = 0.
0, 1, 2
Let r(i) = 4*i**2 - 13*i + 12. Let q be r(2). Let g be ((-5)/q)/((-6)/(-24)*-5). Determine c so that -3/2*c**3 + 0*c + 0 + 9/4*c**g - 3/4*c**4 = 0.
-3, 0, 1
Solve -1880*w - 131175*w**4 + 2835*w**5 - 96790*w**3 + 3831*w**2 - 24997*w**2 - 2294*w**2 = 0.
-2/7, -2/9, 0, 47
Let o(j) = 6*j**3 + 440*j**2 + 29400*j + 686004. Let m(f) = -13*f**3 - 885*f**2 - 58800*f - 1372009. Let n(v) = 8*m(v) + 18*o(v). Solve n(g) = 0.
-70
Let h be -9 + 8 - (-24)/1. Let z(u) = -2*u + 49. Let b be z(h). What is g in -7*g**3 + 7*g**b + 4*g**3 - 3*g**2 - g**2 = 0?
0, 1
Let q(y) be the second derivative of y**6/90 - y**5/5 - 79*y**4/36 - 17*y**3/3 - 1466*y. Find t, given that q(t) = 0.
-3, -2, 0, 17
Suppose -5 = c - 2*b - 10, -c - 5*b + 40 = 0. What is v in 48*v**2 - 175 - 43*v**2 + c*v - 25 = 0?
-8, 5
Factor 2/5*a**4 + 2*a**3 - 18/5*a + 6/5*a**2 + 0.
2*a*(a - 1)*(a + 3)**2/5
Let w(x) = -14*x**3 + 22*x**2 - 26*x + 12. Let p(z) = -2*z**3 + z**2. Let t = 956 + -950. Let o(m) = t*p(m) - w(m). Factor o(q).
2*(q - 6)*(q - 1)**2
Suppose -3*q + 4*q = 2. Suppose -2*d - 11*v = -10*v, -16 = 4*v. Factor -2*i**2 - 2*i - 2*i**3 - 4*i**q + 10*i**d.
-2*i*(i - 1)**2
Suppose 32*q - 313 + 121 = 0. Let o(r) be the second derivative of 5/12*r**4 + 0 + 5/3*r**3 + q*r - 15/2*r**2. Factor o(t).
5*(t - 1)*(t + 3)
Let f = -1803/152 + 242/19. Let a(c) be the first derivative of -28 - 1/12*c**3 - f*c**2 - 3/2*c. Factor a(g).
-(g + 1)*(g + 6)/4
Suppose -128*p = -393*p. Factor -9*s**2 + 21/2*s**3 + 0*s - 3/2*s**4 + p.
-3*s**2*(s - 6)*(s - 1)/2
Let w be 24 + -22 + -5 + 7. Let x(r) be the third derivative of -3*r**2 - 1/168*r**8 + 0*r - 1/105*r**7 + 0*r**3 + 0*r**w + 0 + 0*r**5 + 0*r**6. Factor x(n).
-2*n**4*(n + 1)
Let w(a) be the third derivative of a**5/210 + 10*a**4/21 + 30*a**2 + 10. Factor w(q).
2*q*(q + 40)/7
Let y(j) be the second derivative of 110 - 10*j**2 + 5/2*j**3 - 2*j + 5/12*j**4. Solve y(d) = 0 for d.
-4, 1
Determine n, given that -422500/3*n - 4/3*n**4 - 868*n**3 + 0 - 141700*n**2 = 0.
-325, -1, 0
Let -4*p**2 - 435*p + 22*p**2 - 3*p**2 - 16*p**2 + 1314 = 0. Calculate p.
-438, 3
Let u(g) be the first derivative of g**5/25 + 3919*g**4/40 + 853471*g**3/10 + 558169381*g**2/20 + 278445077*g/10 - 2570. Factor u(w).
(w + 653)**3*(2*w + 1)/10
Let i(f) be the first derivative of -3*f**6/5 - 168*f**5/25 - 271*f**4/10 - 736*f**3/15 - 44*f**2 - 96*f/5 - 3272. Suppose i(j) = 0. What is j?
-4, -3, -1, -2/3
Let y = -35/2774 - -100039/13870. What is f in -4/5*f**2 + y - 32/5*f = 0?
-9, 1
Find j such that -18820*j**3 + 126*j + 42*j**2 + 28 + 24 + 18816*j**3 = 0.
-2, -1/2, 13
Let v(j) be the first derivative of -3*j**5/10 + 3*j**4/2 + 2*j**3 - 12*j**2 + 966. Factor v(s).
-3*s*(s - 4)*(s - 2)*(s + 2)/2
Let n = -10333/11 - -2819/3. Let q(x) be the first derivative of 8/11*x - 3 + n*x**3 - 12/11*x**2. Solve q(l) = 0 for l.
2/5, 2
Let y(h) be the first derivative of -h**3/5 + 33*h**2/2 - 162*h/5 + 842. Factor y(b).
-3*(b - 54)*(b - 1)/5
Let l be 84/9*5/((-40)/(-12)). Let z be (15/(-35))/((-12)/l). Let z*c**2 + 1/2*c**4 - 3/2*c**3 - 1 + 3/2*c = 0. Calculate c.
-1, 1, 2
Let a = 178785483/328348 - -3/328348. Factor a - 115*w**2 + 7491/4*w + 7/4*w**3.
(w - 33)**2*(7*w + 2)/4
Factor 266*t + 46*t**3 - 162*t**2 - 2*t**4 - 84*t - 223*t**2 + 140*t**3 + 19*t**2.
-2*t*(t - 91)*(t - 1)**2
Let o(y) = 127*y - 294*y + 27*y + 4*y**2. Let r(w) = -2*w**2 + 70*w. Let n(i) = -4*o(i) - 7*r(i). Factor n(b).
-2*b*(b - 35)
Factor -26064*u**2 + 4*u**3 + 6563844 + 6553596*u - 26715*u**2 + 42535*u**2.
4*(u - 1281)**2*(u + 1)
Let g = -127960 + 127963. Find p such that 16 + 0*p - 1/2*p**g - 3*p**2 = 0.
-4, 2
Let a be (((-52)/12 + 5)*48)/2. Suppose 6*q**2 - 17*q**2 - 2*q**4 - 5*q**2 + 36*q**3 + 24*q**4 - 36*q + a - 22*q**2 = 0. What is q?
-2, -1, 4/11, 1
Let k(h) = h**3 + 152*h**2 + 956*h - 8553. Let v be k(-145). 