w**2 - 16*w - 7. Factor b(n).
(n - 1)*(n + 2)*(n + 34)
Let p(f) be the second derivative of -f**7/112 + 7*f**6/20 + 171*f**5/40 + 289*f**4/16 + 589*f**3/16 + 315*f**2/8 + 2480*f + 2. Find l such that p(l) = 0.
-3, -2, -1, 35
Factor 14*f**3 - 1312*f**2 + 229065 + 300223 + 103540*f - 10*f**3 - 216532 + 356580.
4*(f - 167)**2*(f + 6)
Let m(u) be the second derivative of u**4/12 - 3*u**3/2 - 95*u**2 - u + 427. What is w in m(w) = 0?
-10, 19
Solve -1314*u**2 + 1402*u**2 - 8*u - 4*u + 8*u**4 + 63*u**3 = 0.
-6, -2, 0, 1/8
Let d(t) = 4*t**3 - 1858*t**2 + 213987*t - 53361. Let f(o) = -o**2 + 9*o. Let g(w) = -2*d(w) + 18*f(w). Determine k so that g(k) = 0.
1/4, 231
Factor -55*z**2 - 393*z**2 - 7*z**3 + 8*z**3 + 113*z**2 - 6*z**3 - 2975*z - 7125.
-5*(z + 5)**2*(z + 57)
Suppose 6*c + 10*c - 132 = 124. Let n(t) be the first derivative of -2/27*t**3 + 0*t - c + 0*t**2. Factor n(z).
-2*z**2/9
Suppose -11377552*c = -11377558*c. Factor 0*p + 11/2*p**2 + c - 1/2*p**3.
-p**2*(p - 11)/2
Factor 542/9*y - 76/9*y**2 - 2/9*y**3 + 616/9.
-2*(y - 7)*(y + 1)*(y + 44)/9
Suppose 6 = -3*p - 2*d - 3*d, 12 = 3*p - d. Factor -11*r**p + 10 + 41*r**3 + 15*r - 14*r**3 - 60*r**2 + 19*r**3.
5*(r - 1)**2*(7*r + 2)
Let a(q) be the second derivative of -1/22*q**4 - 15123/11*q**2 - 3*q + 4 + 142/11*q**3. Let a(x) = 0. Calculate x.
71
Factor 1/5*z**2 - 44/5*z + 228/5.
(z - 38)*(z - 6)/5
Let g(k) = -4*k + 1 + 1 + 42. Let u be g(9). Solve 2 - 4*y**5 + 2 - 8*y**3 - 19*y + u*y**2 + 20*y + 11*y - 12*y**4 = 0.
-1, 1
Let o be (3/9)/(5/60). Factor 42*z**5 - 35*z**3 - 14*z**o - 43*z**5 + 130*z**2 - 152*z**2.
-z**2*(z + 1)*(z + 2)*(z + 11)
Let a = -2179319/11 + 198123. Solve 0 + 4/11*y**2 + 30/11*y**4 + 0*y - a*y**3 = 0.
0, 2/15, 1
Let g(v) be the third derivative of v**5/150 + 9*v**4/20 - 124*v**3/15 - 1236*v**2. Factor g(n).
2*(n - 4)*(n + 31)/5
Factor -13225/9 + 1/9*s**4 + 1150/9*s + 56*s**2 - 46/9*s**3.
(s - 23)**2*(s - 5)*(s + 5)/9
Let j(p) be the first derivative of -7*p**4 - 1/3*p**6 - 16/3*p**3 - 14/5*p**5 + 0*p + 181 + 0*p**2. Solve j(k) = 0 for k.
-4, -2, -1, 0
Let x(z) be the second derivative of z**4/6 + 8*z**3/3 - 3*z**2/2 + 11*z. Let q be x(-20). Factor q*m**4 + 9*m - 21*m**2 + 2 + 15*m**3 - 2 - 480*m**4.
-3*m*(m - 3)*(m - 1)**2
Let p(m) be the first derivative of 4/5*m**5 + 1/6*m**6 + 1/2*m**4 - 1 - 4/3*m**3 - 3/2*m**2 + 0*m. Solve p(l) = 0.
-3, -1, 0, 1
Let l(q) be the first derivative of -q**6/45 + q**5/30 + 5*q**4/9 + 8*q**3/9 + 11*q + 159. Let n(j) be the first derivative of l(j). Factor n(z).
-2*z*(z - 4)*(z + 1)*(z + 2)/3
Let t(c) be the second derivative of -c**7/84 + c**6/6 - 7*c**5/8 + 25*c**4/12 - 2*c**3 - 8200*c. Let t(p) = 0. Calculate p.
0, 1, 2, 3, 4
Suppose -9*l = -15*l + 18. Determine n so that 9*n**4 - 56*n**3 + 12*n**l + 1168*n - 4*n**4 + 832*n + 1800*n**2 - 151*n**3 = 0.
-1, 0, 20
Let -3/2*g**3 + 1/2*g**5 + 2*g - 2*g**2 + 0 + g**4 = 0. Calculate g.
-2, 0, 1
Factor 8/19*i**2 - 474/19*i + 580/19.
2*(i - 58)*(4*i - 5)/19
Let f(g) be the third derivative of -g**8/3696 - g**7/210 - g**6/132 - 2948*g**2. Factor f(r).
-r**3*(r + 1)*(r + 10)/11
Let j(m) be the second derivative of m**4/6 + 28*m**3/9 - 20*m**2/3 - 180*m. Factor j(a).
2*(a + 10)*(3*a - 2)/3
Let o(b) be the second derivative of 1/315*b**7 - 2/45*b**4 + 1/25*b**5 + 110*b + 1/45*b**6 + 0 + 0*b**2 - 8/45*b**3. Factor o(n).
2*n*(n - 1)*(n + 2)**3/15
Factor -11/2*i**2 + 73/4*i - 25/2 - 1/4*i**3.
-(i - 2)*(i - 1)*(i + 25)/4
Determine p, given that 331/2*p**2 + 477/4*p**3 - 23/2 + 117/4*p - 11/2*p**4 = 0.
-1, -1/2, 2/11, 23
Let j = -210 - -219. Suppose -j*o = 9*o. Suppose -4/9*n + 2*n**2 - 8/9*n**3 + o = 0. Calculate n.
0, 1/4, 2
Let u be 4 - (-89 + -3)*(-6)/(-4). Let x = u + -134. Factor -5*h**4 + 9*h**3 - 45*h**2 + 8*h**3 + 38*h**2 + h**5 - x*h**3 + 2*h.
h*(h - 2)*(h - 1)**3
Let y(j) be the third derivative of -1/140*j**7 - 1/2*j**4 + 0*j + 23/120*j**5 + 3/80*j**6 - 7*j**2 - 1/672*j**8 - 3*j**3 - 12. Let y(z) = 0. What is z?
-3, -1, 2
Let 0 - 2/9*a + 38/9*a**3 - 16/9*a**2 - 20/9*a**4 = 0. Calculate a.
-1/10, 0, 1
Determine r, given that -3/2*r**5 + 11/6*r**4 + 0 + 17/3*r**3 - 22/3*r**2 + 4/3*r = 0.
-2, 0, 2/9, 1, 2
Let m(a) be the second derivative of a**4/3 - 194*a**3/3 - 808*a**2 - 2654*a. Factor m(r).
4*(r - 101)*(r + 4)
Let d be (11 - (-637)/(-39))*(-28)/8. Solve -52/3 - 4/3*s**2 - d*s = 0 for s.
-13, -1
Let j(p) = 16*p**2 + 136*p + 240. Let a(t) = t**2 - t + 4. Let z(l) = -20*a(l) + j(l). Factor z(h).
-4*(h - 40)*(h + 1)
Let u(h) be the third derivative of -h**8/672 + h**7/42 + 7*h**6/60 - h**5/3 - 2*h**4 - 9*h**2 + 1. Let u(f) = 0. Calculate f.
-2, 0, 2, 12
Let m be (510/40 - 14)*-4. Let c(i) be the second derivative of 10*i**2 - 5/4*i**m - 1/6*i**6 + 0 - 5/4*i**4 + 25/6*i**3 + 21*i. Factor c(w).
-5*(w - 1)*(w + 1)**2*(w + 4)
Let k(p) = -17*p**3 + 134*p**2 + 3555*p + 17796. Let w(g) = 20*g**3 - 135*g**2 - 3555*g - 17790. Let l(u) = -5*k(u) - 4*w(u). Let l(o) = 0. Calculate o.
-9, 44
Let w = 269 + -1344. Let r be ((-86)/w)/((-1)/(-10)). Factor r*x + 0 - 1/5*x**2.
-x*(x - 4)/5
Let t(y) = y**3 + 15*y**2 + 2. Suppose -179*i = -192*i - 195. Let x be t(i). Factor -1/2*z**x + 0 + 4*z.
-z*(z - 8)/2
Let b = -12 + 14. Suppose b*l - 4*l = -8. Factor 9*u + 100 + 16*u + 15*u + l*u**2 + 0*u.
4*(u + 5)**2
Let k(l) be the first derivative of -207646/7*l + 111 + 1/14*l**4 + 6627/7*l**2 - 94/7*l**3. Factor k(t).
2*(t - 47)**3/7
Let u(d) be the third derivative of 0 + 11/36*d**4 - 1/180*d**5 + 0*d**3 + d**2 - 29*d. Let u(l) = 0. What is l?
0, 22
Suppose -16 = -3*m - m, 186 = 3*o + 3*m. Determine g so that -399*g**3 + 15*g**3 - 243*g**3 + 278*g**2 + 42*g**3 - 20*g - o*g**2 + 605*g**5 - 220*g**4 = 0.
-1, 0, 2/11, 1
Let q(x) = x**2 - 10*x - 3. Let j(p) = -20*p - 5. Let d = -123 - -120. Let b(n) = d*j(n) + 5*q(n). Solve b(r) = 0 for r.
-2, 0
Let m(h) be the second derivative of 0 - 9*h**2 + 1/20*h**5 - h**3 - 7*h + 1/8*h**4. Let j(l) be the first derivative of m(l). Let j(k) = 0. What is k?
-2, 1
Let z be 64/132 - (-4)/22. Let u(f) be the second derivative of 0 + 1/5*f**5 + 16*f - 16*f**2 - 8/3*f**3 + z*f**4. Find c such that u(c) = 0.
-2, 2
Let y(x) = -7*x**4 - 33*x**3 - 2001*x**2 - 9936*x - 13608. Let k(i) = 2*i**4 + 8*i**3 + 500*i**2 + 2484*i + 3402. Let l(p) = 15*k(p) + 4*y(p). Factor l(d).
2*(d - 21)*(d + 3)**2*(d + 9)
Factor 5/3*q**3 + 125/3*q**2 + 145*q + 105.
5*(q + 1)*(q + 3)*(q + 21)/3
Let y = -670 + 672. Factor 138*s**y + 6*s**3 - 39*s - 144*s**2 - 30 - 3*s**3.
3*(s - 5)*(s + 1)*(s + 2)
Let w(x) be the first derivative of x**7/2520 - 7*x**5/360 - x**4/12 - 5*x**3/3 - 8*x + 22. Let j(y) be the third derivative of w(y). Let j(l) = 0. Calculate l.
-2, -1, 3
Let w(j) = -j**3 + 2*j. Let o(k) = -9*k**3 - 14*k**2 + 513*k + 510. Let v(h) = -o(h) + 8*w(h). Factor v(l).
(l - 17)*(l + 1)*(l + 30)
Let i = 88047 - 88045. Factor 84/13*u + 2/13*u**i + 882/13.
2*(u + 21)**2/13
Solve -36/7*k + 160/7 + 2/7*k**2 = 0 for k.
8, 10
Let k(a) be the third derivative of 0 + 1/30*a**5 + 0*a + 16/3*a**3 + 31*a**2 - 2/3*a**4. Solve k(q) = 0.
4
Let s = 48/41233 + 82034/371097. Solve -4/9*q**2 + 28/9*q**3 - 14/9*q**5 + s*q**4 + 2/9 - 14/9*q = 0 for q.
-1, 1/7, 1
Let r = -61 + 86. Suppose -7*q + 2*q = -r. Factor 29 - 174*v + 158*v - 13 - v**2 + q*v**2.
4*(v - 2)**2
Let r(v) be the first derivative of -3*v**4/2 + 178*v**3/3 - 142*v**2 + 112*v - 9018. Factor r(z).
-2*(z - 28)*(z - 1)*(3*z - 2)
Let u(h) be the second derivative of 0*h**3 + 1/5*h**6 + 0*h**2 + 0 + 1/42*h**7 - 78*h + 9/20*h**5 + 1/3*h**4. Suppose u(z) = 0. What is z?
-4, -1, 0
Let x = 61033/3 - 20662. Let v = 321 + x. Suppose 10/3*c**2 - v*c**3 - 8/3 + 2/3*c**5 + 8/3*c - 2/3*c**4 = 0. Calculate c.
-2, -1, 1, 2
Suppose 24*c - 21*c = 81. Factor -375 + c*k + 3*k**2 + 170 + 175.
3*(k - 1)*(k + 10)
Let r(c) be the second derivative of c**5/15 - 19*c**4/9 - 44*c**3/9 + 80*c**2/3 - 2445*c - 2. Suppose r(i) = 0. Calculate i.
-2, 1, 20
Suppose -13*p + 260 = 26. Suppose p*r + 9 = 21*r. Solve 0*f + 0*f**r + 1/3*f**4 + 0 - 4/3*f**2 = 0.
-2, 0, 2
Find b such that 0 + 2/17*b**4 + 160/17*b**2 - 200/17*b + 38/17*b**3 = 0.
-10, 0, 1
Let k be 20/(-16)*4/(-10)*4. Factor 4 - 8 + 4*m**k + 24 + 24*m.
4*(m + 1)*(m + 5)
Let p(i) = i**4 + 19*i**3 - 27*i**2 - 34*i + 41. Let h(g) = 2*g**4 + 28*g**3 - 40*g**