22. Suppose -7*s = -3*s - w. Factor -s*v**3 + 4*v**2 + 2*v**2 + 0*v**2 - 4*v.
-2*v*(v - 2)*(v - 1)
Let s = 2 + 1. Suppose 7 = 3*q + r - 6, -s*r = 5*q - 23. Solve -4*k**2 + 2*k**2 - q*k - 3 + 3 = 0 for k.
-2, 0
Factor 57*j**4 - 4*j**3 + 25*j**4 - 86*j**4 + 64*j**2 - 80*j.
-4*j*(j - 2)**2*(j + 5)
Let g(l) = -2*l. Let n be g(-3). Suppose -t + 34 = 16*t. Factor -q - 2*q + 3*q**t + n - 6*q.
3*(q - 2)*(q - 1)
Let o be 3/(-5) + -3 + (-832)/(-120). Factor -2*w**2 - 4/3 - o*w.
-2*(w + 1)*(3*w + 2)/3
Let i(v) be the second derivative of -1/120*v**5 + 1/36*v**4 + 5*v + 0*v**2 + 0 + 0*v**3. Suppose i(a) = 0. Calculate a.
0, 2
Let m(c) be the first derivative of -2*c**3/9 - 25*c**2/3 + 52*c/3 - 170. Suppose m(r) = 0. What is r?
-26, 1
Factor 21*f + 5*f + 18*f**3 - 80 + 156 - 40*f**2 - 80.
2*(f - 1)**2*(9*f - 2)
Suppose -2*n = -5*k - 0*n + 110, -2*k = -5*n - 23. Suppose 0 = k*f - 30 - 42. Factor 2/3*d**2 + 2/9*d + 2/9*d**4 + 0 + 2/3*d**f.
2*d*(d + 1)**3/9
Let u(v) = v**2 - 52*v - 245. Let a(f) = 6*f**2 - 207*f - 981. Let p(t) = -2*a(t) + 9*u(t). Factor p(g).
-3*(g + 9)**2
Let 1/3*x**5 + 0*x + 0*x**4 + 0 + 2*x**2 - 7/3*x**3 = 0. Calculate x.
-3, 0, 1, 2
Determine y so that -3/4*y + 9/8*y**2 - 9/8*y**4 + 3/8*y**3 + 0 + 3/8*y**5 = 0.
-1, 0, 1, 2
Let o(u) = -3*u**3 + 2*u**2 - 2*u - 2. Let s be o(-1). Find n, given that -s*n**2 + 6*n**2 - 4*n - 4*n + 0*n**2 = 0.
0, 8
What is p in 40/7*p**2 - 2/7*p**4 + 0 + 2/7*p**3 + 0*p = 0?
-4, 0, 5
Factor -32*w - 110*w**3 - 16*w**2 + 55*w**3 + 53*w**3.
-2*w*(w + 4)**2
Suppose -54 = 12*f - 2*f - 28*f. Determine k, given that 4/5 + 32/5*k**2 - 36/5*k**4 - 16/5*k**5 + 24/5*k - 8/5*k**f = 0.
-1, -1/4, 1
Let z(m) be the second derivative of m**4/3 - 4*m**3/3 + 2*m**2 + 57*m. Let z(b) = 0. Calculate b.
1
Let o be (779/205 - (-1)/5) + -2. Let c(w) be the third derivative of 0*w + 1/1080*w**6 - w**o + 1/27*w**3 + 0 + 0*w**5 - 1/72*w**4. Factor c(s).
(s - 1)**2*(s + 2)/9
Let l(q) be the third derivative of q**7/630 - 11*q**5/180 + q**4/4 - 4*q**3/9 + 64*q**2. Let l(a) = 0. What is a?
-4, 1, 2
Let r(x) = x**2 - 8*x + 9. Let c be r(6). Let o(d) = d**2 + d - 2. Let g be o(c). Find n, given that -4*n**3 + n**2 + 4*n**3 - 2*n + g*n**3 - 3*n**4 = 0.
-2/3, 0, 1
Let d(a) be the third derivative of a**5/20 + 3*a**4/8 - 2*a**3 - 2*a**2 - 3*a. Factor d(q).
3*(q - 1)*(q + 4)
Let i = -138 + 144. Let x(r) be the first derivative of 0*r + 7 + 0*r**2 - 9/4*r**4 - 1/2*r**i + 9/5*r**5 + r**3. Solve x(j) = 0.
0, 1
Let n(h) = h**3 + 14*h**2 - 5*h + 6. Let v be n(-13). Let d be 642/v*1 + 2/16. Determine x, given that -4/5 - 2*x**2 - d*x = 0.
-1, -2/5
Factor -16/5*p - 2/15*p**2 - 46/15.
-2*(p + 1)*(p + 23)/15
Let k be ((-1)/2)/(7/(-28)). Suppose 8*z**2 + 7*z**k + 9*z**3 - 9*z**2 = 0. What is z?
-2/3, 0
Let n(f) be the second derivative of f**5/25 + 7*f**4/15 + 22*f**3/15 + 2*f**2 - 72*f. Determine l, given that n(l) = 0.
-5, -1
Let u(r) = 7*r**3 + 5*r**3 - 2 + 10*r - 6*r - 2*r**2. Let g(p) = -p**3 - p**2 - p + 1. Suppose 3*o + 2 = 5*o. Let k(d) = o*u(d) + 6*g(d). Factor k(h).
2*(h - 1)**2*(3*h + 2)
Let t(i) = 3*i**4 + 51*i**3 + 243*i**2 + 195*i - 3. Let l(w) = w**2 + w - 1. Let z(q) = 3*l(q) - t(q). Find d such that z(d) = 0.
-8, -1, 0
Solve 0 + 2*d**3 + 6/5*d**2 - 4/5*d = 0.
-1, 0, 2/5
Let v(g) = g**3 + 9*g**2 + g + 11. Let y be v(-9). Let f be (-2)/((-1)/y*2). Determine p so that 2 - 2*p + f - 5*p**2 + 6*p - 7*p**3 + 4*p**3 = 0.
-2, -2/3, 1
Let j(h) = 23 + 0*h + 4*h - 3*h - 32. Let g be j(12). Factor -2*i**4 + 3*i**2 - g*i**4 - i - i**3 + 4*i**4 - 2 + 2*i**3.
-(i - 2)*(i - 1)*(i + 1)**2
Find p such that 10/3*p**2 - 16/9*p**3 + 2/9*p**4 + 0*p + 0 = 0.
0, 3, 5
Suppose x = 5*p - 6, 4*p - 3*p = 5*x - 18. Suppose p*d = -5*a - d + 19, 2*d - 12 = -3*a. Factor 1/4*c**a + 1/2*c + 0.
c*(c + 2)/4
Let y = -2264 - -15860/7. Solve 2/7*h**3 + 4/7 + 4/7*h**4 + 2/7*h - y*h**2 = 0.
-2, -1/2, 1
Let h(d) be the second derivative of -d**6/15 + 9*d**5/25 + 83*d**4/30 - 4*d**3 - 36*d**2/5 + 2*d - 88. Suppose h(g) = 0. Calculate g.
-3, -2/5, 1, 6
Factor 567*c**5 + 24*c**4 + 12*c**3 - 569*c**5 - 34*c**4.
-2*c**3*(c - 1)*(c + 6)
Let l(f) be the second derivative of 6*f + 1/3*f**3 - 1/20*f**5 + 1/12*f**4 + 0 + 0*f**2. Determine v, given that l(v) = 0.
-1, 0, 2
What is o in 2/11*o**3 - 256/11*o**2 + 0*o + 0 = 0?
0, 128
Let g = 14 + 1. Let r = 19 - g. Factor -2*o**2 + 0 - r*o + 0*o**2 - 2.
-2*(o + 1)**2
Let t(q) be the first derivative of -4*q**3/3 - 126*q**2 + 256*q + 239. Factor t(s).
-4*(s - 1)*(s + 64)
Factor 0*h**3 + 327*h**2 - 5321 - 8549*h - 196*h - 3*h**3 - 3754 + 0*h**3.
-3*(h - 55)**2*(h + 1)
Let r(p) be the third derivative of p**6/120 + 4*p**5/15 - 35*p**4/24 + 3*p**3 - 112*p**2. Factor r(n).
(n - 1)**2*(n + 18)
Let v(t) = t**2 + 6*t - 11. Let g be v(-8). Suppose 0 = f - l - 3, 2*f + 2 = -l + g. Factor f*k - k**2 + 3*k**2 - k - k**2.
k*(k + 1)
Factor 58/7*y**3 + 0 + 0*y - 4/7*y**2.
2*y**2*(29*y - 2)/7
Suppose 0 = -5*v - 9*w + 12*w + 34, v = -5*w - 10. Let r(j) be the second derivative of 2/21*j**3 + 0 - 13*j + 0*j**2 + 2/21*j**4 + 1/35*j**v. Factor r(s).
4*s*(s + 1)**2/7
Let d(i) = 124*i**3 + 5028*i**2 - 3112*i - 2052. Let z(t) = -50*t**3 - 2011*t**2 + 1245*t + 821. Let k(j) = -5*d(j) - 12*z(j). Factor k(r).
-4*(r - 1)*(r + 51)*(5*r + 2)
Let i be (-70)/(-24) - 2104/789. Factor 9/2*w**3 + 0 - i*w**4 + 54*w - 27*w**2.
-w*(w - 6)**3/4
Let a(u) = -18*u**2 - 57*u + 85. Let x(o) = 100*o**2 + 312*o - 468. Let w(k) = 28*a(k) + 5*x(k). Factor w(i).
-4*(i - 1)*(i + 10)
Let n(y) be the first derivative of y**5 + 35*y**4/4 + 10*y**3 - 35. Factor n(i).
5*i**2*(i + 1)*(i + 6)
Suppose -6*n - 2*r - 57 = -3*n, 2*r - 90 = 4*n. Let p = -18 - n. Solve -5 + 15 + p*m**2 - 7 + 6*m = 0 for m.
-1
Let o(r) = 3*r**3 + r**2 + r + 1. Let y(d) = -3*d**5 + 21*d**4 + 24*d**3 - 72*d**2 - 45*d + 9. Let q(w) = -9*o(w) + y(w). Find c such that q(c) = 0.
-1, 0, 3, 6
Suppose -3*b + 7*b - 16 = 4*p, 0 = 5*b + 3*p - 12. Let h be 4 - (1 - 3/b). Solve -1 + 49*v**5 - 2*v**h - 47*v**5 + 1 = 0 for v.
0, 1
Let z = 56 - 28. Let a be (3/10)/((-7)/z - -1). Factor 2/5*c**3 - 4/5*c**2 + 0 + a*c.
2*c*(c - 1)**2/5
Let k(o) be the third derivative of -o**7/735 + o**6/21 - 23*o**5/35 + 13*o**4/3 - 35*o**3/3 + 41*o**2 - 4. Suppose k(f) = 0. What is f?
1, 5, 7
Let z(s) be the second derivative of -5*s**4/24 + 115*s**3/3 - 2645*s**2 - 188*s. Suppose z(q) = 0. Calculate q.
46
Let i = -6988/13 + 538. Suppose -2/13*y**3 + 0*y**2 + i*y + 4/13 = 0. Calculate y.
-1, 2
Suppose 4*u - 3*u + 24 = -5*g, -5*u - g = 24. Let o be ((-6)/u)/((-3)/(-6)). Suppose -3/2 - 3/2*q**2 - o*q = 0. What is q?
-1
Let w be 2/8 + 285/12. Suppose z - 5*g = 0, -7*z + w = -2*z - g. Let 3*a - 3*a - z*a - 3*a**2 + 2*a = 0. What is a?
-1, 0
Let i(h) be the second derivative of -h**7/98 - 3*h**6/14 - 36*h**5/35 + 16*h**4/7 - h - 6. Find l, given that i(l) = 0.
-8, 0, 1
Determine u, given that 1/3*u**2 - 34 + 49/3*u = 0.
-51, 2
Let b(x) = -x + 3*x - 3 + x**3 + 3*x + 7*x**2. Let l be b(-6). Find a, given that 4 - 19*a**2 + 6*a**3 - 3*a - 6*a**l + 11*a + 7*a**3 = 0.
-2/7, 1, 2
Let i be 738/54 - (-120)/(-10). Solve -1/3 - 10/3*l**2 + 5/3*l + 10/3*l**3 + 1/3*l**5 - i*l**4 = 0.
1
Let y = -221/5 + 45. Let l(f) be the first derivative of -y*f**5 + 5 + 0*f + 5/2*f**4 + 0*f**2 - 4/3*f**3. Let l(w) = 0. What is w?
0, 1/2, 2
Let t = 543 - 535. Let s(o) be the first derivative of 0*o**2 + t + 3/10*o**5 - o**3 + 0*o**4 + 3/2*o. Let s(u) = 0. What is u?
-1, 1
Let w be 3/(-12)*-12 - 0. Let 0 + 1/2*t**2 + 1/2*t**5 - 1/2*t**w - 1/2*t**4 + 0*t = 0. Calculate t.
-1, 0, 1
Let g be (-6)/33 - (5100/22 - -2). Let p = -229 - g. Solve 15/2*k - p - 5/2*k**2 = 0 for k.
1, 2
Determine b, given that -1/2*b**3 + 0*b - 7/2*b**2 + 0 = 0.
-7, 0
Let w be (-219)/(-195) - (-17)/221. Solve -14/15*h**3 - 2*h**2 + 0 - 2/15*h**4 - w*h = 0 for h.
-3, -1, 0
Factor 3*r**2 - 36*r**4 - 26*r**4 - r**5 + 63*r**4 + 5*r**3.
-r**2*(r - 3)*(r + 1)**2
Solve 80/3*s**2 + 64/3*s + 0 + 8*s**3 - 4/3*s**4 - 2/3*s**5 = 0.
-2, 0, 4
Find s, given that -265*s**4 + 100*s**2 - 40*s + 430*s**3 + 106*s**5 - 137*s**5 - 194*s**5 = 0.
-2, -2/5, 0, 2/9, 1
Factor -2/13*z**2 + 0 + 22/13*z.
-2*z*(z - 11)/13
Let h(v) be the second derivative of 10*v + 0*v**2 - 2/85*v**5 + 1/34*v**4 + 0*v**3 + 0 - 1/255*v**6 + 2/357*v**7. Factor h(w).