3 - 8. Factor m(s).
-s*(s + 1)/7
Solve 4/5*a**2 - 696/5*a + 30276/5 = 0 for a.
87
Factor -17672 - 2673*c - c**3 + 186*c**2 - 4786*c - 1001*c.
-(c - 94)**2*(c + 2)
Factor 33*q**2 - 2*q**3 - 16*q**2 - 41*q**2 + 26*q.
-2*q*(q - 1)*(q + 13)
Factor -41212040 - 1649*s**2 + 5*s**3 + 128093*s + 254672*s + 229295*s - 1381*s**2.
5*(s - 202)**3
Suppose -2*h = -3*h + 2. Let q(t) = -t**3 - t**2 + 2*t + 2. Let y be q(-2). Let -6*f - 4 - 6*f**2 + y*f**2 + 2*f**h = 0. What is f?
-2, -1
Let v be (-3)/((-24)/22)*(-18)/(-99). Solve 1/8*f**4 + 1/8 + v*f**3 + 3/4*f**2 + 1/2*f = 0.
-1
Let y(t) be the third derivative of t**5/20 - 5*t**4/4 + 21*t**3/2 - 34*t**2 - 4*t. Let y(b) = 0. What is b?
3, 7
Let n = 708 + -1413/2. Let q(m) be the second derivative of -5*m + 1/4*m**4 - n*m**2 + 0 - 1/2*m**3 + 3/20*m**5. Factor q(z).
3*(z - 1)*(z + 1)**2
Let w(v) = -v**3 - v**2 - v + 1. Suppose -13*n = -12*n - 2. Let k(x) = -4*x**3 + 2 + 6 - 2*x - 2*x**n - 9 + 3. Let p(u) = -k(u) + 3*w(u). Factor p(i).
(i - 1)**2*(i + 1)
Let u = -209 + 650/3. Let v = u + -97/15. Determine r so that -4/5 - v*r - 2/5*r**2 = 0.
-2, -1
Let b(w) be the first derivative of -w**8/17640 + 2*w**3/3 + 9. Let t(r) be the third derivative of b(r). Factor t(q).
-2*q**4/21
Suppose 7 = 6*d + 1. Let m(k) = -2*k + k + 6*k**2 + 2*k + 3*k - 12 + 7*k**3. Let i(f) = -f**3 + f**2 + 1. Let p(b) = d*m(b) + 4*i(b). Solve p(v) = 0.
-2, 2/3
Suppose 26*c - 24*c = 4. Factor p + 6 + p + 3*p - p - c*p**2.
-2*(p - 3)*(p + 1)
Let q(p) = 35*p**4 - 50*p**3 - 15*p**2. Let n(k) = 7*k**2 - 7*k**3 + k**4 - 9*k**2 + 4*k**4. Let a(h) = 15*n(h) - 2*q(h). Factor a(b).
5*b**3*(b - 1)
Let a(b) = -83*b**4 + 660*b**3 - 603*b**2 - 640*b - 127. Let z(u) = 41*u**4 - 330*u**3 + 301*u**2 + 320*u + 64. Let w(n) = -4*a(n) - 7*z(n). Factor w(k).
5*(k - 6)*(k - 2)*(3*k + 1)**2
Factor -45441 - 2*a**2 + 976*a - 28463 - 45168.
-2*(a - 244)**2
Let q(f) be the first derivative of f**6/60 + f**5/50 - f**4/20 - f**3/15 + f**2/20 + f/10 + 4. Factor q(a).
(a - 1)**2*(a + 1)**3/10
Let j = -3 + 4. Suppose 0 = -u - j, c + 8 = 2*c - 4*u. Suppose -2*l + c*l + 7*l**3 + 4 - 4 + 9*l**2 = 0. Calculate l.
-1, -2/7, 0
Suppose -183*q = -168 - 198. Solve 2/3*d**q + 2*d + 0 = 0 for d.
-3, 0
Let f = -22 - -24. Factor -f*o**4 - 11*o**2 - 4*o**4 + o**4 + 2*o - 2*o**4 + 16*o**3.
-o*(o - 1)**2*(7*o - 2)
Determine d so that -d**3 - d**5 - 8*d**3 - 6*d**2 - 20 - 14*d**3 + 17*d**2 + 9*d**4 + 24*d = 0.
-1, 1, 2, 5
Suppose -36 = 8*k - 20*k. Factor -1756 + 6*d + 1756 + k*d**2.
3*d*(d + 2)
Let q = 14 - 119. Let z be -3 + (q/(-25) - 1). Suppose -1/5*o - z + 1/5*o**2 + 1/5*o**3 = 0. What is o?
-1, 1
Let a(v) be the third derivative of -5*v**5/3 - 5*v**4/24 + 5*v**3/6 - 14*v**2 + 7*v. Factor a(k).
-5*(4*k + 1)*(5*k - 1)
Factor 2/3*i**2 + 110450/3 - 940/3*i.
2*(i - 235)**2/3
Let o(h) be the first derivative of h**6/120 - h**4/2 + 5*h**3 + 3. Let a(j) be the third derivative of o(j). Factor a(t).
3*(t - 2)*(t + 2)
Let n = -5891/7 - -324439/385. Let d = n + -8/11. Solve d*t**2 + 0 - 2/5*t = 0 for t.
0, 1
Let k be 0 - 5*4/10. Let a be 18/5 - (5 + k). Factor 6/5*q + 0 + a*q**4 - 6/5*q**3 - 3/5*q**2.
3*q*(q - 2)*(q - 1)*(q + 1)/5
Let i(u) be the first derivative of -u**5/15 + u**4/2 + u**2 - 19. Let o(l) be the second derivative of i(l). Suppose o(g) = 0. What is g?
0, 3
Let k be -5*12/50*(-30)/9. Let o be (k/60*-6)/((-6)/20). Factor -2*j + 2/3 + 2/3*j**5 + o*j**2 - 2*j**4 + 4/3*j**3.
2*(j - 1)**4*(j + 1)/3
Let n(v) be the second derivative of v**4/4 + 103*v**3 + 31827*v**2/2 + 363*v. Factor n(l).
3*(l + 103)**2
Let u = 1132/763 + -6/109. Let k be 0/(12 + -9 - (2 - 1)). What is z in -2*z**3 + k - 16/7*z**2 + u*z**4 + 8/7*z = 0?
-1, 0, 2/5, 2
Let h(p) be the second derivative of -p**4/12 + 11*p**3/6 + p**2 + 2*p. Let x be h(11). Factor -1/2*w**3 + 1/2*w + w**x - 1.
-(w - 2)*(w - 1)*(w + 1)/2
Suppose 0 = -4*s - s - 45. Let m be 2 + -2 + s/(-3). Factor -5*i + 6*i + m*i**2 - 4*i**2 - i**3 + 1.
-(i - 1)*(i + 1)**2
Let j(n) = -15*n**2 - 4*n. Let w(o) = 5*o**2 + o. Let t = 12 + -23. Let k(p) = t*w(p) - 4*j(p). Factor k(u).
5*u*(u + 1)
Let c(t) be the first derivative of 5*t**3/3 - 135*t**2/2 - 450*t - 670. Let c(z) = 0. What is z?
-3, 30
Let y(c) be the first derivative of 0*c - 20 + 0*c**3 - 1/6*c**4 + 0*c**2 + 1/5*c**5 - 1/18*c**6. Factor y(s).
-s**3*(s - 2)*(s - 1)/3
Let v = 587/2072 - 41/259. Factor 5/8 - v*l**2 - 1/2*l.
-(l - 1)*(l + 5)/8
Suppose 914*b + 247*b - 71879 + 16162 - 1883 - 201*b - 4*b**2 = 0. What is b?
120
Suppose -14*b + 4 = k - 12*b, -3 = k - 5*b. Let j(y) be the first derivative of 4/21*y**3 + 2/7*y - 4 - 3/7*y**k. Let j(t) = 0. Calculate t.
1/2, 1
Let k(r) be the second derivative of 0 + 32*r + 0*r**2 + 0*r**3 + 1/70*r**5 - 1/42*r**4. Determine t, given that k(t) = 0.
0, 1
Let i(a) be the second derivative of -2*a**7/525 + a**6/50 - 2*a**4/15 + 15*a**2 - a. Let r(k) be the first derivative of i(k). Factor r(j).
-4*j*(j - 2)**2*(j + 1)/5
Suppose 88*w - 17*w + 4 - 217 = 0. What is j in 0*j + 0*j**2 + 1/10*j**5 - 1/5*j**w - 1/10*j**4 + 0 = 0?
-1, 0, 2
Let f(k) be the second derivative of -k**5/10 + 104*k**4 - 43264*k**3 + 8998912*k**2 + 645*k. Solve f(j) = 0 for j.
208
Let w(c) be the second derivative of -c**4/90 - 2*c**3/3 + 87*c. Factor w(z).
-2*z*(z + 30)/15
Let s(h) be the third derivative of -h**7/8820 - h**6/252 - 5*h**4/8 + 3*h**2. Let t(f) be the second derivative of s(f). Factor t(v).
-2*v*(v + 10)/7
Let z(c) = -c**2 + 2*c - 2. Let w(g) = -5*g**5 + 70*g**4 - 165*g**3 - 566*g**2 - 308*g - 12. Let a(o) = w(o) - 6*z(o). Find r such that a(r) = 0.
-1, 0, 8
Let r(t) be the first derivative of -t**5/20 + 3*t**4/4 - 3*t**3 + 81. Solve r(u) = 0.
0, 6
Let r(n) be the first derivative of n**6/24 + n**5/5 - 11*n**4/16 - 13*n**3/6 + 8*n**2 - 8*n - 14. Determine q so that r(q) = 0.
-4, 1, 2
Suppose -540 = 7*j + 2*j. Let t be ((-28)/j + -1)*(-3)/4. Factor 3/5*w + t + 1/5*w**2.
(w + 1)*(w + 2)/5
Let m be (1 + 7/(-3))*-3. Let q(g) = 31*g**3 + 495*g**2 - 40*g - 384. Let i be q(-16). Factor 0*x**3 - 5/3*x**m + 0*x + i + 5/3*x**2.
-5*x**2*(x - 1)*(x + 1)/3
Suppose 0 = -4*d + 3*k + 39, -204*d + 203*d - 2*k - 15 = 0. Find m, given that -36/5*m**2 + 432/5*m + 1/5*m**d - 1728/5 = 0.
12
Suppose -a + 14 + 52 = 3*x, -2*a + 172 = -4*x. Let r be (-46)/(-21) - a/91. Factor -r - 2*f - 2/3*f**2.
-2*(f + 1)*(f + 2)/3
Let u(d) be the third derivative of -1/210*d**5 + 1/42*d**4 + 0*d + 0 + 0*d**3 + 46*d**2. Solve u(h) = 0 for h.
0, 2
Suppose 4*p - 3 = -3*y, 5*p - 12 = 3*y - 4*y. What is b in 3*b - p*b**3 + 3/2*b**2 - 3/2 = 0?
-1, 1/2, 1
Let y(a) be the first derivative of a**8/336 - a**7/56 - a**6/24 + 7*a**5/24 + 5*a**4/4 - 37*a**3/3 + 12. Let u(b) be the third derivative of y(b). Factor u(f).
5*(f - 3)*(f - 2)*(f + 1)**2
Suppose 0 = -124*h + 121*h + 15. Suppose 2*b + h*q = 0, 3*b = -q - 0*q. Solve 1/3*a**4 - 1/3*a - 1/3*a**2 + b + 1/3*a**3 = 0 for a.
-1, 0, 1
Suppose -146*h + 142*h = 0. Let l(d) be the third derivative of -1/240*d**5 + 0 + 4*d**2 + 0*d**4 + h*d + 0*d**3. Let l(x) = 0. Calculate x.
0
Suppose -8*h - 3*h - 6*h = 0. Let b(a) be the third derivative of 2*a**2 + 0*a**5 + 0*a**6 + 0*a**3 + 0*a + 0 + h*a**4 - 1/840*a**7 - 1/1344*a**8. Factor b(l).
-l**4*(l + 1)/4
Let u(f) be the third derivative of -5/48*f**8 + 5/3*f**3 + 7/12*f**6 - 35/24*f**4 - 1/3*f**5 + f**2 + 0*f + 1/21*f**7 + 0. Let u(t) = 0. Calculate t.
-1, 2/7, 1
Let o = 6/103 + 461/927. Let f(w) be the second derivative of o*w**4 + 0 - 4/9*w**3 + 0*w**2 + 2/45*w**6 - 3*w - 4/15*w**5. Factor f(g).
4*g*(g - 2)*(g - 1)**2/3
Let v(b) be the first derivative of -b**4/24 + 13*b**3/18 - 4*b**2 + 6*b + 547. What is s in v(s) = 0?
1, 6
Let i(j) = 4*j - 28. Let w be i(-7). Let z be (2*(-6)/w)/(4/14). Factor z*y**5 + 3/2*y**3 + 0 + 0*y**2 + 0*y - 9/4*y**4.
3*y**3*(y - 2)*(y - 1)/4
Let w(p) be the first derivative of 1/22*p**4 + 6 + 0*p + 4/33*p**3 + 1/11*p**2. What is k in w(k) = 0?
-1, 0
Let n(i) = i**2 - 4. Let h = -127 + 130. Let s(o) = -2*o**2 + 7. Let b be (-2)/4*20/(-2). Let v(a) = b*n(a) + h*s(a). Find d, given that v(d) = 0.
-1, 1
Let c = 2/8311 - -33226/74799. Solve -1/3*p - c + 1/9*p**2 = 0.
-1, 4
Let v(r) be the second derivative of 0*r**2 - 1/24*r**4 + 4*r + 1/120*r**5 + 0 + 1/18*r**3. Determine h so that v(h) = 0.
0, 1, 2
Suppo