2)/8
Let w(p) be the third derivative of 2*p**5 - 92*p**2 + 13/120*p**6 + 1/630*p**7 + 0*p + 0*p**3 + 0 - 50/9*p**4. Factor w(j).
j*(j - 1)*(j + 20)**2/3
Let o be (-1 - -6*(-5)/(-40))*-88. Factor -o*c**3 - 21*c**3 + 67*c**3 + 5*c**4 - 680 - 330*c**2 - 29*c**3 + 10*c**4 + 900*c.
5*(c - 2)**3*(3*c + 17)
Let z(g) be the second derivative of -g**4/78 + 44*g**3/13 - 20*g**2 - 62*g - 6. Factor z(c).
-2*(c - 130)*(c - 2)/13
Let w = -165014/9 + 18336. Solve w*y - 4/9 - 2/3*y**2 = 0 for y.
2/3, 1
Let h(t) = 2*t**2 + 79*t + 431. Let m be h(-33). Let w(j) be the first derivative of -7/6*j**4 + 16 + 8/3*j + 16/3*j**m + 10/9*j**3. Let w(d) = 0. What is d?
-1, -2/7, 2
Let p(c) be the third derivative of -17/6*c**3 - 9*c**2 - 1/450*c**6 + 0*c**5 + 0 + 1/30*c**4 + 0*c. Let r(a) be the first derivative of p(a). Factor r(s).
-4*(s - 1)*(s + 1)/5
Let z(w) be the second derivative of -w**4/30 + 722*w**3/15 - 130321*w**2/5 - 80*w + 2. Find b such that z(b) = 0.
361
Let p = 357 + 505. Let m = p - 859. Suppose -1/2*a**4 + 3/2*a**m - 3/2*a**2 + 1/2*a + 0 = 0. What is a?
0, 1
Let r(b) be the second derivative of -2/15*b**3 + 32*b + 1/75*b**6 - 5 - 1/30*b**4 + 0*b**2 + 1/25*b**5. Factor r(f).
2*f*(f - 1)*(f + 1)*(f + 2)/5
Factor 246*f - 198*f - 268*f**2 - 458*f - 294*f - 88 - 20*f**3 - 152.
-4*(f + 3)*(f + 10)*(5*f + 2)
Let d = -9668 + 58009/6. Let v(u) be the second derivative of -6*u + 0 + 5/12*u**4 - 1/10*u**5 - d*u**3 - u**2. Suppose v(y) = 0. What is y?
-1/2, 1, 2
Suppose m - 5 = -2*p, 2*m + 10*p - 7*p - 10 = 0. Let h(n) be the third derivative of 1/210*n**m + 22*n**2 + 0 + 1/28*n**4 + 0*n**3 + 0*n. Factor h(q).
2*q*(q + 3)/7
Let v(q) be the second derivative of -q**6/30 + 2*q**5/5 + q**4/12 - 34*q**3/3 + 42*q**2 + 2*q - 12. Factor v(p).
-(p - 7)*(p - 2)**2*(p + 3)
Suppose -68 = 10*d + 152, 2*t - 126 = d. Determine f so that -3328*f + 2/5*f**4 + 8706/5*f**2 + 8192/5 - t*f**3 = 0.
1, 64
Let u = -5710 - -5712. Let g(o) be the first derivative of 8 + 0*o**3 + 0*o**u - 1/5*o**5 + 1/10*o**4 + 0*o. Factor g(l).
-l**3*(5*l - 2)/5
Let l(c) = 2*c - 3. Let y(r) be the third derivative of r**5/30 + 11*r**4/12 + 32*r**3/3 + 8*r**2 + 8*r. Let b(v) = 4*l(v) + y(v). Solve b(s) = 0.
-13, -2
Let -34/9*j - 4/3 - 14/9*j**2 = 0. Calculate j.
-2, -3/7
Let o(d) = 10*d**2 + 14*d + 4. Let j(r) = -4*r - 50. Let w be j(-11). Let k(a) = -29*a**2 - 41*a - 12. Let m(p) = w*k(p) - 17*o(p). Factor m(g).
4*(g + 1)**2
Let n(w) = -2*w**3 + w**2 + w - 8. Let f be n(-2). Let r(i) be the first derivative of 12 + 5/2*i**4 - f*i**2 - 5*i**3 + i**5 + 20*i. Factor r(x).
5*(x - 1)**2*(x + 2)**2
Let h(w) be the second derivative of -3/2*w**2 + 1/24*w**3 - 2*w + 1/48*w**4 - 6. Factor h(a).
(a - 3)*(a + 4)/4
Let m(d) = 4*d**2 + 4*d - 2. Let o(x) = 13*x**2 - 13*x + 8. Let y(b) = -3*b**2 + 3*b - 2. Let l(h) = -2*o(h) - 9*y(h). Let j(u) = 15*l(u) - 5*m(u). Factor j(n).
-5*(n - 1)*(n + 8)
Let o(n) be the third derivative of 8/525*n**7 + 23/60*n**4 + 0*n + 8 - 24*n**2 + 17/75*n**5 + 2/5*n**3 + 2/25*n**6 + 1/840*n**8. Solve o(g) = 0.
-3, -2, -1
Let a(y) = 616*y**2 + 240*y - 2. Let s(k) = 209*k**2 + 80*k. Let p(i) = -2*a(i) + 7*s(i). Factor p(h).
(7*h + 2)*(33*h + 2)
Factor 416/3 + 308/3*k - 36*k**2.
-4*(k + 1)*(27*k - 104)/3
Let w = -18696 - -37393/2. Factor w*b**2 + 3 + 5/2*b.
(b + 2)*(b + 3)/2
Factor 4806/5*g + 3/5*g**2 - 4809/5.
3*(g - 1)*(g + 1603)/5
Suppose 5*s - 5*q - 5 = -15, -4*s = q - 2. Let n(k) be the second derivative of 4/3*k**3 + 13*k + s*k**2 + 0 + 1/6*k**4. Determine j so that n(j) = 0.
-4, 0
Let j(y) be the second derivative of y**4/42 + 13*y**3/21 - 114*y**2/7 - 992*y. Determine b so that j(b) = 0.
-19, 6
Let y be 5/(15/8) + 820/615. Let a(z) be the first derivative of -6/55*z**5 + 10 - 3/22*z**y + 0*z - 1/33*z**6 + 0*z**2 - 2/33*z**3. What is h in a(h) = 0?
-1, 0
Suppose -7 = 4*v + 5*u, 5*v + 2*u + 5 = -3*u. Let i be v + (17 - 15) + 18/(-8). Factor 1/2*n**4 - 1/2 + 1/4*n**5 - 1/2*n**3 - i*n - 2*n**2.
(n - 2)*(n + 1)**4/4
Factor 0 - 3/2*i**4 + 4935/2*i**3 - 2027049/2*i**2 - 2031987/2*i.
-3*i*(i - 823)**2*(i + 1)/2
Let i = -99 - -101. Let z = i + 2. Factor 0 - 1/4*f**2 + 0*f - 3/4*f**z + 1/4*f**5 + 3/4*f**3.
f**2*(f - 1)**3/4
Determine h, given that -79*h**3 + 194*h**3 - 257*h**2 - 4*h**5 - h**5 + 107*h**2 + 40*h**4 = 0.
-3, 0, 1, 10
Factor 87474*m - 21*m**2 + 90 - 87441*m + 22*m**2.
(m + 3)*(m + 30)
Let c(b) = 4*b**4 + 11*b**3 + 23*b**2 + 16*b + 3. Let o(m) = -m**4 + m**2 - 1. Let r(v) = c(v) + 3*o(v). Suppose r(t) = 0. Calculate t.
-8, -2, -1, 0
Let w(m) be the third derivative of m**8/84 - 2*m**7/105 - 3*m**6/10 + 3*m**5/5 + 2492*m**2. Factor w(t).
4*t**2*(t - 3)*(t - 1)*(t + 3)
Solve -365*k**3 + 64 - 2209*k**2 + 80*k**4 - 316*k - 9*k**4 + 2749*k**2 + 6*k**5 = 0.
-16, 1/2, 2/3, 1, 2
Let u be (-306)/20790*-25 - (1 - 16/22). Let u*y**5 + 80/7*y**3 + 352/7*y + 12/7*y**4 + 192/7 + 736/21*y**2 = 0. Calculate y.
-6, -2
Let i(l) be the second derivative of -l**4/54 - 7*l**3/27 - 2*l**2/3 - 26*l + 5. Factor i(k).
-2*(k + 1)*(k + 6)/9
Suppose 6*i - 8*i = 0. Suppose 0 = 3*f + 4*g - 25, i = 5*f + 5*g - 12 - 23. Find q, given that 2*q**4 - q**5 - 6*q**3 + 5*q**f + 0*q**3 = 0.
0, 1
Factor -16/7*w - 2/7*w**2 + 78.
-2*(w - 13)*(w + 21)/7
Let l be 365/(-146)*(0 - 8/9)*3. Let g(o) be the first derivative of -2*o**2 + 12 - 3*o**4 + 36/5*o**5 + 0*o - l*o**3. Determine m, given that g(m) = 0.
-1/3, 0, 1
Let a(i) be the second derivative of i**4/48 - 49*i**3/3 + 4802*i**2 - i - 132. Determine l, given that a(l) = 0.
196
Let w be (-351)/65 - (-9)/(-15). Let v be (-5 + (-279)/(-54))/((-2)/w). Let -1/4*r**3 + 1/8*r**4 + 1/2 - 3/8*r**2 + v*r = 0. Calculate r.
-1, 2
Let a(b) be the third derivative of -b**8/50400 - b**7/12600 + b**6/150 - 23*b**5/12 + 88*b**2. Let o(f) be the third derivative of a(f). Factor o(h).
-2*(h - 3)*(h + 4)/5
Let y(q) be the second derivative of 1/40*q**4 + 24*q - 12*q**2 + 0 + 0*q**3 + 9/100*q**5. Let m(k) be the first derivative of y(k). Let m(c) = 0. What is c?
-1/9, 0
Let w = 20707/237 + -6876/79. Find x, given that -2/3*x + 0 + w*x**2 + 1/3*x**3 = 0.
-2, 0, 1
Let i(a) be the first derivative of 6/65*a**5 - 4/13*a**3 + 66 + 1/13*a**2 - 1/13*a**4 + 1/39*a**6 + 6/13*a. Solve i(v) = 0.
-3, -1, 1
Let l(g) be the second derivative of -g**7/70 - g**6/40 + 3*g**5/20 + g**4/8 - g**3 + 16*g**2 - 3*g + 2. Let s(o) be the first derivative of l(o). Factor s(f).
-3*(f - 1)**2*(f + 1)*(f + 2)
Factor 27*z**2 + 1007*z**3 - 580*z - 947*z**3 + 581*z**2 - 88.
4*(z - 1)*(z + 11)*(15*z + 2)
Let 891*o - 24669 - 980*o**5 + 24669 - 795*o**2 + 234*o - 14845*o**3 + 25095*o**4 = 0. What is o?
-1/4, 0, 3/7, 25
Let g(o) be the second derivative of o**4/6 + 31*o**3 - 388*o**2 + 437*o + 3. Solve g(m) = 0 for m.
-97, 4
Let r(a) = -4*a**4 - 6*a**3 - 8*a + 5. Let v(j) = j**4 + j**3 - j**2 + j - 1. Suppose 0*t = 15*t + 15. Let f(p) = t*r(p) - 5*v(p). Determine b so that f(b) = 0.
-1, 0, 3
Let n(f) = 2*f**2 - 5*f + 6. Let o be n(11). Suppose 2*a - o = y + 344, 0 = -3*a + y + 804. Factor -4*z + 2*z**4 + 267 - a - 6*z**2.
2*z*(z - 2)*(z + 1)**2
Let j = -770 + 3081/4. Let o(i) be the second derivative of 0 + 3*i + 0*i**3 + 3/2*i**2 - j*i**4. What is n in o(n) = 0?
-1, 1
Let w(h) be the first derivative of h**9/10584 - h**8/5880 - h**7/2940 + h**6/1260 - 53*h**3 + 8. Let o(d) be the third derivative of w(d). Factor o(v).
2*v**2*(v - 1)**2*(v + 1)/7
Solve -1/3*v**2 - 772/3*v - 1540/3 = 0 for v.
-770, -2
Let l(p) be the third derivative of -p**10/1285200 + p**9/51408 - 5*p**8/34272 + 61*p**5/60 + 196*p**2. Let r(o) be the third derivative of l(o). Factor r(c).
-2*c**2*(c - 5)**2/17
Let l = 4/24935 + 99728/74805. Factor -7*r**3 - l + 8*r - 29/3*r**2.
-(r + 2)*(3*r - 1)*(7*r - 2)/3
Let h(d) = -4*d**2 + 43*d + 16. Let z be h(11). Factor -39*m + 250*m**z - 29*m**2 - 245*m**5 - 21*m - 20 - 26*m**2 + 15*m**4 - 5*m**3.
5*(m - 2)*(m + 1)**3*(m + 2)
Factor -3732*p + 47*p**2 + 20 - 86*p**3 + 77*p**2 + 24*p**4 + 3651*p - p**5.
-(p - 20)*(p - 1)**4
Let d be 146/374 + (-1518)/187 + (0 - -8). Solve -2/11*z - d + 1/11*z**2 = 0.
-1, 3
Factor 4*q**4 + 246*q**2 - 312*q**2 + 366*q**2 + 500*q + 60*q**3.
4*q*(q + 5)**3
Let u be (-2)/(-9) - ((-1284)/54 + 4). Factor -45*v + u*v + 14*v + 30 + v**2 + 0*v**2.
(v - 6)*(v - 5)
Suppose 3071*k + 3970*k**2 