9. Factor -p*i**2 - 10*i**2 - 4*i**4 + 46*i**2 + 22*i**3 - 70*i**3.
-4*i**2*(i + 6)**2
Let z(h) be the first derivative of -h**6/2 - 306*h**5/5 - 2025*h**4 - 5000*h**3 - 632. Determine t so that z(t) = 0.
-50, -2, 0
Factor -3/2*x**3 - 14112*x + 252*x**2 + 263424.
-3*(x - 56)**3/2
Suppose r = 88 - 8. Suppose 3*v + v**2 - r + 82 + 0*v**2 = 0. Calculate v.
-2, -1
Suppose 4*d = 5*z - 10*z + 28, z - 5 = -d. Suppose 9*f = z*f. Factor f*c - 1/4*c**2 + 0.
-c**2/4
Let p(n) = -n + 1. Let q be p(9). Let g be (6/12)/((-2)/q). Factor -2*t**4 + 2*t**2 + t**2 - 2*t**3 + 4*t**3 - t**g - 2*t**5.
-2*t**2*(t - 1)*(t + 1)**2
Let g be ((-121)/4 - -30)/((-2)/32). Solve -16/7*x**3 + 0*x + 16/7*x**2 + 0 - 4/7*x**g + 4/7*x**5 = 0 for x.
-2, 0, 1, 2
Let q(p) be the third derivative of -p**5/120 + 23*p**4/48 + 80*p**2. Let q(w) = 0. Calculate w.
0, 23
Find o, given that 3/2*o - 15/2*o**4 + 15*o**2 - 3*o**3 + 3/2*o**5 - 15/2 = 0.
-1, 1, 5
Let s(b) be the third derivative of b**6/600 + b**5/60 + b**4/15 + 2*b**3/15 + 213*b**2. Factor s(d).
(d + 1)*(d + 2)**2/5
Let a(q) = -335*q**3 + 1310*q**2 - 600*q - 480. Let w(o) = 28*o**3 - 109*o**2 + 50*o + 40. Let h(t) = -3*a(t) - 35*w(t). Determine m so that h(m) = 0.
-2/5, 1, 4
Suppose 3*u - 900 = -2*t, -7*u + 1516 = -2*u - 2*t. Factor -15*x**3 + 2*x**4 + 27*x**2 + x - u + 308 + x**4 - 22*x.
3*(x - 2)*(x - 1)**3
Let g be ((-1040)/(-104) - 110/12)/(10/6). Factor 0*l - g*l**2 - 1/2*l**3 + 0 + l**4.
l**2*(l - 1)*(2*l + 1)/2
Let f = 30946 + -30943. Factor 0 + 5*y**2 - 5/3*y**f - 10/3*y.
-5*y*(y - 2)*(y - 1)/3
Find l such that -22*l - 10*l**2 - 11*l**2 + 25*l**2 - 2*l**2 = 0.
0, 11
Let v(f) be the second derivative of -5*f**4/12 - 10*f**3/3 + 225*f**2/2 - 84*f. Determine n, given that v(n) = 0.
-9, 5
Let j(h) = -30 + 92*h - 85*h + 11. Let m be j(3). Factor -2/3*a**3 + 0*a**m + 2*a + 4/3.
-2*(a - 2)*(a + 1)**2/3
Let -2/7*m**2 + 0 + 2/7*m**3 + 0*m = 0. What is m?
0, 1
Suppose 0 = -5*h - 3*v + 39, -5*h + 66 = -5*v + 11. Factor h*j**2 - 2*j**3 - j**3 - 5*j - j.
-3*j*(j - 2)*(j - 1)
Let c(l) be the first derivative of -l**6/80 + l**5/20 + l**4/16 - l**3/2 - 5*l**2/2 - 12. Let q(k) be the second derivative of c(k). Factor q(o).
-3*(o - 2)*(o - 1)*(o + 1)/2
Let a(i) = 6*i**2 + i**2 - 7*i - 8*i**2 - 6. Let u be a(-6). Factor 1/6*o**2 + 0 + u*o.
o**2/6
Find q, given that 79*q**2 - 45*q - 5*q**5 - 19*q**2 - 233*q**3 + 243*q**3 - 20*q**4 = 0.
-3, 0, 1
Let m(o) be the first derivative of -49*o**6/8 + 399*o**5/4 + 3159*o**4/16 - 25*o**3/4 - 114*o**2 + 45*o - 235. Find n, given that m(n) = 0.
-1, 2/7, 15
Let k(j) = -55*j**2 + 35*j - 180. Let r(d) = 2*d**2 + 1. Let c(n) = -k(n) - 30*r(n). Factor c(m).
-5*(m - 3)*(m + 10)
Let o(f) be the first derivative of 6*f**4 - 37*f**3/3 + 3*f**2/2 + 5*f + 4. Let y(s) = 60*s**3 - 92*s**2 + 8*s + 12. Let c(x) = -12*o(x) + 5*y(x). Factor c(a).
4*a*(a - 1)*(3*a - 1)
Let u = -22 + -50. Let k be ((-296)/u)/(2/12). Determine r so that 8/3 + 6*r**4 + 20*r**3 + 40/3*r + k*r**2 = 0.
-1, -2/3
Suppose -4*w**2 + 65 - 4*w + 36*w - 26 + 41 + 0*w**2 = 0. Calculate w.
-2, 10
Let f(o) = 17*o**4 + 101 - 6*o + 4*o**3 - 101 + 3*o**2. Let v(j) = -6*j**4 - j**3 - j**2 + 2*j. Let r(q) = 4*f(q) + 11*v(q). Find m such that r(m) = 0.
-2, -1, 0, 1/2
Let a(z) be the second derivative of z**7/105 - z**6/30 - z**5/10 + 3*z**2 - 12*z. Let g(m) be the first derivative of a(m). Let g(p) = 0. What is p?
-1, 0, 3
Let q(t) = -2*t**4 + 4*t**3 - 6*t**2 + t + 1. Let v(c) = c**4 + c**2 + c - 1. Let l(x) = -q(x) - v(x). Factor l(z).
z*(z - 2)*(z - 1)**2
Let d = 15 + -10. Suppose 4*p - 21 = -3*u + 4*u, p + 21 = -d*u. Find f such that 20/13*f**2 + 2/13*f**5 + 2/13 + 20/13*f**3 + 10/13*f**p + 10/13*f = 0.
-1
Let p = 63 - 755/12. Let b(f) be the third derivative of p*f**5 + 0 + 1/2*f**3 + 4*f**2 + 1/120*f**6 + 7/24*f**4 + 0*f. Determine v, given that b(v) = 0.
-3, -1
Let z = -1/51 - -157/204. Let r = 2043/20 - 507/5. Solve -r*y**2 + 3/4*y - z*y**3 + 3/4 = 0.
-1, 1
Suppose -d = -4*d + 15. Let v = -78 + 79. Factor d + v + 3 - 2*p**2 - 1.
-2*(p - 2)*(p + 2)
Let v(a) be the second derivative of a**9/7560 + a**8/2100 + a**7/2100 - 5*a**3/6 + 5*a. Let l(n) be the second derivative of v(n). Find r such that l(r) = 0.
-1, 0
Suppose 4*z = -u + 73 - 59, 5*u - 25 = -5*z. Let a(x) be the first derivative of -1/4*x**4 + 2*x - 1 + 0*x**3 + 3/2*x**u. Factor a(k).
-(k - 2)*(k + 1)**2
Let q(u) be the first derivative of -3185*u**6/33 + 15274*u**5/55 + 2719*u**4/11 + 1880*u**3/33 + 24*u**2/11 + 573. Find d such that q(d) = 0.
-2/7, -2/65, 0, 3
Let v be 2*2 + 188*(-1 + 3). Let f be v/70 + (-4)/(-7) + -3. Factor 0 + 3*g**f + 0*g - 3/4*g**2.
3*g**2*(4*g - 1)/4
Let m be (-9 - 1)/(4/(-180) - 0). Let d be 1/3 - 10/m*6. Factor 0*l**2 + 0 + 0*l**3 - d*l**4 + 0*l.
-l**4/5
Let y(b) = b**2 - 179*b + 184. Let d(r) = 4*r**2 - 356*r + 367. Let i(a) = 2*d(a) - 5*y(a). Factor i(t).
3*(t - 1)*(t + 62)
Let i(l) be the second derivative of 5*l**5/4 + 5*l**4/2 - 115*l**3/6 + 30*l**2 + 268*l. Factor i(q).
5*(q - 1)*(q + 3)*(5*q - 4)
Let d be -8 - (-3 - 5) - -3. Let j(b) be the first derivative of -7 + 4/3*b + 1/3*b**2 - 2/9*b**d. Factor j(r).
-2*(r - 2)*(r + 1)/3
Let f = -67 + 57. Let q = f + 74/7. Solve 0 - q*m**2 + 4/7*m + 1/7*m**3 = 0.
0, 2
Let b = 43782/38297 - 2/5471. Factor 8/7*y - 4/7*y**3 - 6/7*y**2 + b + 2/7*y**4.
2*(y - 2)**2*(y + 1)**2/7
Let x = -23884 - -23889. Find f such that 4/5 + 4/5*f**4 - 2/5*f**x - 8/5*f**2 - 2/5*f + 4/5*f**3 = 0.
-1, 1, 2
Let t(f) be the third derivative of f**8/560 + f**7/140 + f**6/120 - 2*f**3 + 10*f**2. Let p(g) be the first derivative of t(g). Suppose p(k) = 0. Calculate k.
-1, 0
Solve -16/5 - 12/5*f + 4/5*f**2 = 0.
-1, 4
Let j(v) = 27*v**2 - 183*v - 225. Let p(m) = -7*m**2 + 46*m + 57. Let a(g) = -4*j(g) - 15*p(g). Factor a(k).
-3*(k - 15)*(k + 1)
Let n(v) be the third derivative of -1/120*v**6 + 1/60*v**5 + 1/24*v**4 + 8*v**2 + 0 + 0*v - 1/6*v**3. Factor n(o).
-(o - 1)**2*(o + 1)
Let u = -122 - -124. Let a(c) be the first derivative of -8/9*c - 5 - 4/9*c**u - 2/27*c**3. Determine b so that a(b) = 0.
-2
Let b(h) = -4*h**3 - 473*h**2 - 18267*h - 237271. Let a(k) = 2*k**3 + 237*k**2 + 9135*k + 118635. Let s(w) = -5*a(w) - 3*b(w). Factor s(v).
2*(v + 39)**3
Let b(j) be the second derivative of -j**7/21 - 9*j**6/5 + j - 72. Let b(r) = 0. What is r?
-27, 0
Let p = -3134 - -3143. Factor p*y + 27/4 + 3*y**2.
3*(2*y + 3)**2/4
Let y(o) be the first derivative of -45 - 6*o**2 - 2/5*o**5 + 7/3*o**3 + 4*o + 3/4*o**4. What is z in y(z) = 0?
-2, 1/2, 1, 2
Let u(s) be the third derivative of s**5/330 - 5*s**4/132 - 2*s**3/11 + 410*s**2. Factor u(w).
2*(w - 6)*(w + 1)/11
Let r be (-122)/1403 + (-4900)/(-276) + -3. Determine t, given that -r*t**2 - 16/3*t + 4/3 - 8*t**3 = 0.
-1, 1/6
Let l(i) be the second derivative of i**3/6 + 4*i. Let a be l(3). Factor 5*w**3 - 3*w**4 + 6*w**2 - w**a - 4*w**3 - 3.
-3*(w - 1)**2*(w + 1)**2
Let b(o) be the third derivative of 73*o**5/80 - 37*o**4/8 + o**3/2 + o**2 - 14. Determine d so that b(d) = 0.
2/73, 2
Let q(g) be the third derivative of g**9/22680 + g**8/1680 + g**7/420 + g**6/270 + g**4/24 - 4*g**2. Let k(z) be the second derivative of q(z). Factor k(p).
2*p*(p + 1)**2*(p + 4)/3
Let d = -56209/5 - -11281. Find c such that 48*c**3 + 0 - 504/5*c**4 - 32/5*c**2 + 0*c + d*c**5 = 0.
0, 2/7, 2
Let p(f) be the third derivative of 1/200*f**6 - 31*f**2 + 0*f + 0*f**3 + 1/1050*f**7 + 1/120*f**4 + 1/100*f**5 + 0. What is o in p(o) = 0?
-1, 0
Let n(r) be the first derivative of -r**6/5 + 12*r**5/25 - 4*r**3/5 + 3*r**2/5 + 119. Factor n(m).
-6*m*(m - 1)**3*(m + 1)/5
Let r be 4/10*5/(-301). Let u = 1194/1505 - r. Find j, given that -4/5 + 0*j + u*j**2 = 0.
-1, 1
Let p(a) = 39*a**4 + 12*a**3 - 39*a**2 - 66*a - 27. Let s(d) = -6*d + 3*d**4 + d - 3*d**2 - 2 + 45*d**3 - 44*d**3. Let w(n) = 2*p(n) - 27*s(n). Factor w(m).
-3*m*(m - 1)*(m + 1)**2
Let l(w) = -3*w + 40. Let g be l(15). Let a(c) = -c**2 + 3*c - 12. Let i(x) = -x - 1. Let p(r) = g*a(r) + 15*i(r). Factor p(q).
5*(q - 3)**2
Let p = -37/399 + 643/1197. Suppose 0 - p*r**2 - 32/9*r = 0. What is r?
-8, 0
Let m(d) be the third derivative of d**5/180 - 7*d**4/12 + 49*d**3/2 + 33*d**2. Let m(i) = 0. Calculate i.
21
Let s = -5775 + 17333/3. Factor -2*d**2 + 0*d**3 - 1 + 1/3*d**4 + s*d.
(d - 1