**2 - 28 - 24*a. Solve i(w) = 0 for w.
-1, 2/7, 1, 3
Suppose -40*f + 138 = 3*i, 19*i - 22*i + 15 = -f. Determine q so that 0 + 0*q + 3*q**2 - 1/3*q**f = 0.
0, 9
Find d, given that 2*d**4 + 15*d**3 - 6*d**4 + d**4 - 51*d + 179*d**2 + 2*d**4 - 142*d**2 = 0.
-3, 0, 1, 17
Let p(s) be the third derivative of -s**7/5460 - s**6/780 - s**5/390 + 31*s**3/3 + 66*s**2. Let a(n) be the first derivative of p(n). Let a(b) = 0. Calculate b.
-2, -1, 0
Let n = 2068 + -279178/135. Let y(x) be the third derivative of 1/540*x**6 + 0 + 0*x + n*x**5 + 1/27*x**4 - 6*x**2 + 0*x**3. Find i, given that y(i) = 0.
-2, 0
Let t(o) = 2*o**3 - 3*o**2 + 3*o. Suppose -9*r - 8 = -8*r. Let i = r + 11. Let v(l) = -5*l**3 + 5*l**2 - 5*l. Let a(x) = i*v(x) + 5*t(x). What is j in a(j) = 0?
0
Let c = 3719 - 3711. Let q(l) be the first derivative of -92/5*l**5 + 0*l + 8 - 16/3*l**3 - c*l**2 + 7/2*l**6 + 28*l**4. What is k in q(k) = 0?
-2/7, 0, 2/3, 2
Let u(m) = -22*m**2 + 553*m - 73. Let d be u(25). Let y(t) be the first derivative of 2*t**3 - 32*t - 1/4*t**4 + 0*t**d + 14. Determine c so that y(c) = 0.
-2, 4
Let r be 5346/6435 + 28/(-910). Factor -6/5 + 2/5*z**2 + r*z.
2*(z - 1)*(z + 3)/5
Let y(t) be the second derivative of -5*t**6/8 + 19*t**5/12 - 10*t**3/3 + 11*t**2 - 2*t + 3. Let j(l) be the first derivative of y(l). Factor j(p).
-5*(p - 1)*(3*p - 2)*(5*p + 2)
Let c(u) be the first derivative of 141 - 864*u - 22/5*u**5 - 240*u**3 + 46*u**4 + 648*u**2 + 1/6*u**6. Let c(k) = 0. What is k?
2, 6
Suppose -50 = -5*s + 5*d, -2*s - 2239*d + 2235*d = 28. Factor s + 14/9*n**2 + 10/3*n + 2/9*n**3.
2*(n + 1)*(n + 3)**2/9
Let p(o) be the third derivative of o**8/23520 - o**7/2205 + o**6/504 - o**5/210 - 43*o**4/24 + 82*o**2. Let a(j) be the second derivative of p(j). Factor a(w).
2*(w - 2)*(w - 1)**2/7
Let d(o) be the third derivative of -o**6/288 - o**5/16 - 5*o**4/12 - 5*o**3/3 + 8*o**2. Let r(j) be the first derivative of d(j). Determine c so that r(c) = 0.
-4, -2
Factor 26/5*m**2 - 68/5*m - 2/5*m**3 - 96/5.
-2*(m - 8)*(m - 6)*(m + 1)/5
Suppose -7*j + 14 = 4*y - 5*j, j = 1. Let g be 2 + (-1 - -6) - 7. Factor 4*x**2 + 1/3*x**4 + 2*x**y + g + 8/3*x.
x*(x + 2)**3/3
Find j such that -113 + 116*j**2 - 84 + j - 32*j**3 + 11*j + 20*j - 2*j**4 + 83 = 0.
-19, -1, 1, 3
Let r(w) be the second derivative of w**4/108 - 350*w**3/27 + 61250*w**2/9 - 1354*w. Factor r(i).
(i - 350)**2/9
Let q(p) be the third derivative of -p**8/1176 + 34*p**7/735 + 157*p**6/210 + 30*p**5/7 + 333*p**4/28 + 18*p**3 + 5*p**2 - 386. Suppose q(h) = 0. What is h?
-3, -1, 42
Suppose -1/2*r**2 - 1/4*r**3 + 3/4*r + 0 = 0. What is r?
-3, 0, 1
Let h be ((-741)/(-60) - -2) + 48/(-80). Let x = h - 49/4. Factor z + 1/2*z**3 - x*z**2 + 0.
z*(z - 2)*(z - 1)/2
Let v(i) = 65*i**3 + 5*i**2 - i + 1. Let f be v(-2). Let r = f - -1496/3. Let r*u**2 - u + 2/3*u**5 - 2/3 + 3*u**4 + 13/3*u**3 = 0. What is u?
-2, -1, 1/2
Let r = -2/11693 - -11723/175395. Let h(x) be the second derivative of -1/10*x**2 - r*x**4 + 22*x + 1/6*x**3 + 0. Factor h(f).
-(f - 1)*(4*f - 1)/5
Let b be (59 + 7 - 2)*1. Suppose -240*n = -256*n + b. Factor -11/2*a**2 - 3/4 - 9/2*a**3 - 13/4*a - 1/4*a**5 - 7/4*a**n.
-(a + 1)**4*(a + 3)/4
Let i(x) be the second derivative of -x**7/252 - x**6/1980 - 61*x**4/6 - 196*x. Let a(j) be the third derivative of i(j). Factor a(y).
-2*y*(55*y + 2)/11
Let -i**3 + 4*i**3 - 48*i + 69*i**2 - 296 + 6*i**2 + 177*i + 89 = 0. Calculate i.
-23, -3, 1
Suppose -5*c + 18 = -17. Suppose c = 2*l - 3*t, t = -l - 4*t - 3. Factor -w + 43*w**2 - 3*w**4 + l*w**3 - 64*w**2 + 13*w**3 + 10*w.
-3*w*(w - 3)*(w - 1)**2
Find d such that 24*d + 2*d**2 + 116 - 16*d**3 - 232 - 30*d**2 + 20*d**4 + 116 = 0.
-6/5, 0, 1
Let i(d) be the second derivative of 56/15*d**3 + 11 - 784/5*d**2 - 1/30*d**4 + 5*d. Suppose i(u) = 0. Calculate u.
28
Suppose -38 + 23 = 5*c. Let l(v) = -29*v**2 + 89*v + 6. Let j(z) = 28*z**2 - 88*z - 4. Let g(o) = c*j(o) - 4*l(o). Find m such that g(m) = 0.
-1/8, 3
Let b(x) be the second derivative of x**4/30 - 27*x**3/5 - 166*x**2/5 - 2*x - 30. Factor b(g).
2*(g - 83)*(g + 2)/5
Let g be -4*(-6)/8 - (-2 - 31). Factor 18 + g*c - 2*c**2 - 67 - c**2 - 11.
-3*(c - 10)*(c - 2)
Let c(g) = -2*g**3 - 109*g**2 + 4437*g - 25188. Let w(i) = i**3 - 6*i**2 + i - 4. Let t(m) = c(m) + 3*w(m). Factor t(n).
(n - 60)**2*(n - 7)
Let x be -1 + 0 - 16/(-14). Let t = -6039034/7 + 862720. Factor -1/7*n**2 + t - x*n.
-(n - 2)*(n + 3)/7
Let c(r) = r**3 - 3*r**2 + 378*r - 1937. Let h be c(5). What is u in 3/5*u**3 + 18/5*u - h*u**2 + 0 = 0?
0, 2, 3
Suppose -4*x - w - 43 = -58, 2*w = -2. Let a(s) be the first derivative of -3/2*s**2 + 0*s + 2/3*s**3 + 39 + 1/4*s**x. Find u, given that a(u) = 0.
-3, 0, 1
Let d = 14/2309 - -6871/9236. Factor -d*h**2 + 6 - 3/2*h.
-3*(h - 2)*(h + 4)/4
Let m be 7/(-14)*4/(-3). Let q = -105332 + 105332. Determine s, given that 0*s - 4*s**4 - 8*s**3 - 16/3*s**2 - m*s**5 + q = 0.
-2, 0
Let j = 371 + -367. Suppose 4*o - j = -2*f, -4*f = 4*o - 8*f - 16. Factor -46/9*c - 14/9*c**o - 4/3.
-2*(c + 3)*(7*c + 2)/9
Let k(t) be the first derivative of t**6 - 21*t**5/5 + 3*t**4/2 + 3*t**3 + 3264. Suppose k(p) = 0. What is p?
-1/2, 0, 1, 3
Let u be -39*(-1)/6 + (-8)/(-16). Let z be u/(-4)*(-94)/329. Find x such that -x - z*x**2 + 0 = 0.
-2, 0
Let g = 3092957/5 - 618589. Solve 0 + 4/5*i**2 + g*i = 0 for i.
-3, 0
Let u be ((-28)/105 + (-76)/(-2850))*-35. Factor 39/5 + 3/5*k**2 + u*k.
3*(k + 1)*(k + 13)/5
Let t(f) = 2*f**3 + 7*f**2 + 2*f + 3. Let y(s) = -10 - 20*s**2 + 3*s**3 - 4*s**3 - 5*s - 4*s**3. Let b = 949 + -939. Let k(z) = b*t(z) + 3*y(z). Factor k(i).
5*i*(i + 1)**2
Let q be ((-3)/9)/(5 + 553/(-21)). Let w = q + 47/64. Let w*x**2 + 0 + 3/4*x**3 - 3/2*x = 0. What is x?
-2, 0, 1
Let n(k) be the second derivative of -k**7/13860 - k**6/660 - 2*k**5/165 + 31*k**4/6 - k**3/6 - 18*k - 3. Let x(y) be the third derivative of n(y). Factor x(s).
-2*(s + 2)*(s + 4)/11
Let x = 3302/131 + -42664/1703. Determine c so that 20/13*c**2 + x*c**3 + 0 + 18/13*c = 0.
-9, -1, 0
Let j(b) = 1032*b**2 + 1028*b + 30. Let v(g) = 1031*g**2 + 1027*g + 47. Let l(x) = 6*j(x) - 4*v(x). Factor l(y).
4*(y + 1)*(517*y - 2)
Let t be ((-18)/(-9) - -9) + -7. Suppose 5*a - 36 = 2*a. Determine c so that a*c**2 + 6 - 2*c**4 + 0*c**t + 3*c**4 - 10*c - 6*c**3 - 3 = 0.
1, 3
Let h(m) be the third derivative of -19*m**5/30 + 25*m**4/8 + m**3/3 - 114*m**2 + 8. Let h(x) = 0. What is x?
-1/38, 2
Let p be (3 - 47/4) + -1 + 10. Factor -4 + 15/4*t + p*t**2.
(t - 1)*(t + 16)/4
Let d(w) = -30*w - 274. Let m be d(12). Let u = m + 3317/5. Factor -u - 3/5*n**2 - 42/5*n.
-3*(n + 7)**2/5
Let f(b) = 8*b**4 + 2*b**3 - 110*b**2 - 182*b - 72. Let q(w) = 7*w**4 - w**3 - 111*w**2 - 181*w - 73. Let r(p) = -5*f(p) + 6*q(p). Factor r(d).
2*(d - 13)*(d + 1)**2*(d + 3)
Determine i, given that -1/6*i**3 + 0 - 321602/3*i + 802/3*i**2 = 0.
0, 802
Let w(i) be the first derivative of i**3/30 + i**2/20 - 6*i/5 - 340. Solve w(k) = 0 for k.
-4, 3
Suppose 91*b + 3*p = 87*b - 21, 9*b - 3*p - 21 = 0. Factor b - 9/7*n - 6/7*n**2 + 3/7*n**3.
3*n*(n - 3)*(n + 1)/7
Solve 99*x + 228*x + 118*x**3 + 118*x + 2*x**5 + 118*x**3 + 624*x**2 - 48*x**4 - 107*x = 0.
-1, 0, 13
Suppose -69*d + 81*d - 24 = 0. Let a(y) be the second derivative of -3/4*y**d + 0 + 15*y - 1/12*y**4 - 7/12*y**3. Factor a(u).
-(u + 3)*(2*u + 1)/2
Solve -4/5*u**3 + 0 - 3952/5*u - 284/5*u**2 = 0.
-52, -19, 0
Let u be 2387/(-441) + 6 - (86/86 - (-6)/(-7)). Determine x, given that 0*x + 0 + 0*x**2 + u*x**4 + 16/9*x**3 - 2/9*x**5 = 0.
-2, 0, 4
Suppose -2488772*l - 3202*l**4 + 4*l**3 + 14031948*l + 153228*l**2 + 3204*l**4 + 326094722 + 900*l**3 = 0. What is l?
-113
Factor -1196/7 - 4/7*i**2 - 144/7*i.
-4*(i + 13)*(i + 23)/7
Let u be (-1)/(4/(-6))*528/72. Suppose -c = 5*m - 66, 0*m + c = m - 18. Solve 6 - u*f + 22*f**3 - 6*f**3 + 2*f**2 + f - m*f**3 = 0.
-3, 1
Let o be (7624/(-10))/(32/64). Let l = -1520 - o. Determine c, given that 0 - 3/5*c**5 + l*c**2 + 12/5*c**3 - 6/5*c**4 + 0*c = 0.
-2, 0, 2
Let a = -31 + 28. Let x(w) = w**2 + 3*w + 2. Let r be x(a). Determine m, given that 27*m + 2*m**3 + 9*m + 4*m**3 - 12*m**r - 5*m**3 = 0.
0, 6
Suppose 28*a = 5*x + 81, -2*a - 3*a - 15 = 5*x. What is f in -27*f**4 - 12/5*f**a + 72/5*f**3 + 0 + 0*f + 15*f**5 = 0?
0, 2/5, 1
Let o(f) be the secon