- 47. Let z(w) = d*r(w) - 44*c(w). Factor z(h).
-4*(h - 1)*(h + 1)*(h + 22)
Let f(h) = -h**2 - h. Suppose -w = -31 + 12. Suppose -w*l - 6 = -17*l. Let r(d) = -d**3 - 4*d**2 - 2*d + 1. Let b(q) = l*f(q) + r(q). Factor b(k).
-(k - 1)*(k + 1)**2
Let k = 406 - 399. Determine d so that -k*d**3 + 5*d**5 - 3*d**3 + 4863*d - 4858*d = 0.
-1, 0, 1
Let s(v) be the first derivative of 6 - 1/120*v**6 + 0*v + 0*v**3 - 1/24*v**4 - 1/30*v**5 - 11*v**2. Let d(z) be the second derivative of s(z). Factor d(j).
-j*(j + 1)**2
Let l(r) be the first derivative of r**6/6 + 8*r**5/5 - 5*r**4/4 - 112*r**3/3 - 106*r**2 - 112*r + 2263. What is c in l(c) = 0?
-7, -2, -1, 4
Let y(x) = x**3 - 2*x + 1. Let t(k) = -10*k**3 + 524*k**2 + 360*k - 4. Let c(m) = -t(m) - 4*y(m). Find g, given that c(g) = 0.
-2/3, 0, 88
Let w = -6605 - -6605. Let h(g) be the second derivative of -3/10*g**4 + w*g**5 + 4/5*g**3 - 9/10*g**2 + 1/50*g**6 + 0 - g. Let h(p) = 0. Calculate p.
-3, 1
Factor -7*l**3 + 32515*l**2 - 20*l - l**4 - 32539*l**2 - 2*l**3.
-l*(l + 2)**2*(l + 5)
Suppose 54*d**2 + 4*d**2 + 1153*d + 3397*d - 1760 - 160*d - 33*d**2 = 0. What is d?
-176, 2/5
Suppose -20*v**4 - 16*v**2 + 62*v**3 + 6*v**3 + 16*v**4 - 68*v**5 + 20*v**4 = 0. Calculate v.
-1, 0, 4/17, 1
Determine x so that -9600 + 9760*x + 2/3*x**3 - 482/3*x**2 = 0.
1, 120
Factor 2/21*a**2 - 1000/21*a + 125000/21.
2*(a - 250)**2/21
Let j(d) be the third derivative of -d**5/135 - 91*d**4/54 + 184*d**3/27 + 2*d**2 - 25. Factor j(r).
-4*(r - 1)*(r + 92)/9
Find h such that 100/3 + 6*h**3 - 26/3*h**2 - 2/3*h**4 - 30*h = 0.
-2, 1, 5
Let a(r) be the third derivative of 0 - 1/660*r**6 - 3*r**2 - 1/110*r**5 + 4*r + 0*r**3 + 5/66*r**4. Factor a(b).
-2*b*(b - 2)*(b + 5)/11
Let p(a) be the third derivative of a**7/525 + 3*a**6/100 + 2*a**5/15 + a**4/5 - 187*a**2. Find l such that p(l) = 0.
-6, -2, -1, 0
Let p = 310/181 + 441/905. Factor -p*n - 2 - 1/5*n**2.
-(n + 1)*(n + 10)/5
Let -145/4*a**4 + 4*a + 9/2*a**5 + 0 - 77*a**2 + 92*a**3 = 0. Calculate a.
0, 1/18, 2, 4
Factor 0 - 421/3*k**2 - 418*k - 1/3*k**3.
-k*(k + 3)*(k + 418)/3
Let l = 306350 - 919048/3. Factor l*c**4 + 0*c**3 + 1/3*c**5 - 1/3*c + 0 - 2/3*c**2.
c*(c - 1)*(c + 1)**3/3
Let h(q) be the first derivative of 96/7*q + 189 - 15/7*q**3 - 3/28*q**4 + 27/7*q**2. Suppose h(o) = 0. Calculate o.
-16, -1, 2
Suppose 3*y = 60*y. Let a(s) be the third derivative of -1/336*s**8 + 0*s**4 + y*s**3 + 0 + 0*s**5 + 0*s + 35*s**2 + 1/60*s**6 - 1/210*s**7. Factor a(d).
-d**3*(d - 1)*(d + 2)
Let h(w) = 14 + 5*w + 6*w**2 - w**2 + 9*w. Let r(u) = -147*u + 84*u + 99 + 95*u + 36*u**2 + 67*u. Let q(t) = 15*h(t) - 2*r(t). Factor q(p).
3*(p + 2)**2
Let h(k) be the first derivative of 5*k**4/4 - 1625*k**3/3 + 66420*k**2 - 131220*k + 1431. Factor h(a).
5*(a - 162)**2*(a - 1)
Let f = 15/8 + -41/24. Let s = -62/79 - -265/237. Suppose 1/6*n + s - f*n**2 = 0. What is n?
-1, 2
Let y(d) = 107506*d - 215009. Let t be y(2). Factor -11/5*m**2 + 7/10*m**t - 5/2*m + 2/5.
(m - 4)*(m + 1)*(7*m - 1)/10
Let m(w) be the first derivative of 5*w**4/4 - 1690*w**3/3 + 1351. Factor m(n).
5*n**2*(n - 338)
Suppose -728 + 1018 = -54*a + 560. Factor -1/2*s**a + 0*s**2 + 0*s + 5/2*s**3 + 0 + 2*s**4.
-s**3*(s - 5)*(s + 1)/2
Let n(t) be the second derivative of t**8/1344 - t**7/126 - 5*t**6/144 - t**4/4 + 11*t**3/6 - 43*t. Let v(d) be the third derivative of n(d). Factor v(a).
5*a*(a - 5)*(a + 1)
Let l(n) be the third derivative of n**7/840 - n**6/120 - 3*n**5/40 - 5*n**4/24 + 28*n**3/3 + 72*n**2. Let a(j) be the first derivative of l(j). Factor a(m).
(m - 5)*(m + 1)**2
Let w(c) be the second derivative of c**5/25 - c**4/3 + 4*c**3/5 - 306*c - 3. Solve w(x) = 0 for x.
0, 2, 3
Let x(k) be the second derivative of -k**6/900 - 3*k**5/100 - 7*k**4/30 - 113*k**3/6 + 10*k + 2. Let v(i) be the second derivative of x(i). Factor v(w).
-2*(w + 2)*(w + 7)/5
Let k(a) be the third derivative of -a**8/1680 + 19*a**7/1050 - 7*a**6/60 - a**5/15 + 37*a**4/15 - 112*a**3/15 - 126*a**2 - 38. Find i, given that k(i) = 0.
-2, 1, 2, 4, 14
Let s(p) be the second derivative of 3*p**5/40 + 377*p**4/36 - 14*p**3/3 - 29*p - 11. Determine q so that s(q) = 0.
-84, 0, 2/9
Factor 2/3*s**2 - 200 + 296/3*s.
2*(s - 2)*(s + 150)/3
Let o(x) be the first derivative of 5*x**3/3 - 3*x**2/2 - 2*x - 49. Let p(i) = 10*i**2 - 5*i - 5. Let h(k) = 7*o(k) - 3*p(k). Suppose h(c) = 0. What is c?
1/5, 1
Suppose a = -149 + 152. Let j(x) be the first derivative of -11 - 1/28*x**4 + 11/21*x**a - 36/7*x - 12/7*x**2. Factor j(k).
-(k - 6)**2*(k + 1)/7
Suppose 281*f + 868 - 1711 = 0. Factor -21/2*s + 15/4*s**2 + 0 + 3/4*s**f.
3*s*(s - 2)*(s + 7)/4
Let n(j) be the third derivative of -85*j**2 + 0 + 0*j + 1/60*j**6 - 5/9*j**4 + 4/3*j**3 + 1/90*j**5. Factor n(t).
2*(t - 2)*(t + 3)*(3*t - 2)/3
Let t(d) be the second derivative of -3/4*d**5 + 35/6*d**3 - 14*d - 2 - 25/3*d**4 + 0*d**2. Suppose t(v) = 0. Calculate v.
-7, 0, 1/3
Let p be (-2)/(-12) - 222/(-396). Let k = -4084 - -44926/11. Solve p*y**3 + k*y**5 - 4/11 - 4/11*y**2 + 8/11*y**4 - 10/11*y = 0 for y.
-2, -1, 1
Let n(s) be the third derivative of s**5/12 - 1615*s**4/24 + 48*s**2 - 6. Find c such that n(c) = 0.
0, 323
Let r(j) be the first derivative of 3/2*j**6 - 165 + 103/4*j**4 - 12*j - 57/5*j**5 - 19/3*j**3 - 28*j**2. Determine q so that r(q) = 0.
-1/3, 2, 3
Suppose -5*w = -3*j - 8279 - 3560, 3*j = -w + 2375. Factor w*z - 2369*z + z**3 - 4*z**4.
-z**3*(4*z - 1)
Let u(b) be the first derivative of 2/75*b**5 + 0*b - 174 - 7/15*b**2 + 7/30*b**4 - 2/45*b**3. Find p such that u(p) = 0.
-7, -1, 0, 1
Let r(v) be the first derivative of v**4/5 - 868*v**3/15 + 4576*v**2 + 29040*v + 870. Factor r(f).
4*(f - 110)**2*(f + 3)/5
Let s(c) be the third derivative of -c**5/120 + 55*c**4/12 - 73*c**3/4 + 274*c**2 + 2*c - 4. Find h, given that s(h) = 0.
1, 219
Let w(b) be the first derivative of 64*b + 4/3*b**3 - 34*b**2 - 35. Let w(g) = 0. What is g?
1, 16
Let q(y) = 9*y - 1. Let i be q(3). Suppose -2*v + 81 = 31. Find r, given that -8*r + 3 + 5*r**2 + v*r**3 + r - i*r**3 = 0.
1, 3
Let y(i) = i**4 + i**3 - 6. Let q(r) = -r**4 + 19*r**3 + 73*r**2 + 87*r + 46. Let t(j) = 3*q(j) + 6*y(j). Solve t(f) = 0.
-17, -2, -1
Let z(p) be the first derivative of p**4/26 - 202*p**3/39 + 200*p**2 - 5000*p/13 - 361. Factor z(d).
2*(d - 50)**2*(d - 1)/13
Let s(t) be the first derivative of 5*t**6/6 + 74*t**5 + 1425*t**4/4 + 1760*t**3/3 + 350*t**2 - 1515. Determine d, given that s(d) = 0.
-70, -2, -1, 0
Let x(k) be the third derivative of -k**8/1344 - 29*k**7/280 - 65*k**6/48 - 719*k**5/120 - 423*k**4/32 - 395*k**3/24 - 4*k**2 + k + 3. What is l in x(l) = 0?
-79, -5, -1
Factor -3/7*j**2 + 0 + 1545/7*j.
-3*j*(j - 515)/7
Factor 215/6 + 5/2*p**2 - 325/3*p.
5*(p - 43)*(3*p - 1)/6
Solve 1442*t**3 + 185*t**5 + 303*t**3 - 1605*t + 1100*t**4 - 325*t**3 + 52 - 1190*t**2 + 38 = 0 for t.
-3, -1, 2/37, 1
Let d be -4 + 1 + 2 - -601. Let v be 10/14*240/d. Factor -1/7*o + 0 - 1/7*o**3 + v*o**2.
-o*(o - 1)**2/7
Let x be (-2)/25 - 4590/(-1125). Let -22*t**5 - 22*t**3 - 4*t**x + 46*t**3 - 8*t - 2372*t**2 + 2340*t**2 + 42*t**3 = 0. Calculate t.
-2, -2/11, 0, 1
Let v = 17727 - 11119. Let c be (32/18 - 2) + v/1062. What is g in 12*g**2 + 15/2*g**3 + c*g + 0 + 3/2*g**4 = 0?
-2, -1, 0
Let c(m) be the first derivative of -3*m**5/20 - 37*m**4/4 - 18*m**3 + 57*m - 26. Let b(i) be the first derivative of c(i). Factor b(d).
-3*d*(d + 1)*(d + 36)
Let n(p) be the first derivative of -5*p**4/4 + 690*p**3 - 106080*p**2 - 432640*p + 4380. Let n(d) = 0. Calculate d.
-2, 208
Let k(i) be the second derivative of -3*i**5/20 - i**4 + 2772*i - 2. Suppose k(p) = 0. What is p?
-4, 0
Let u be -11 - ((-15 - 3) + 26 + -19 - (9 - 5)). Suppose -18/5*j + 0 + 3*j**3 + 21/5*j**2 - 21/5*j**u + 3/5*j**5 = 0. Calculate j.
-1, 0, 1, 6
Let d(w) be the third derivative of 75*w**2 - 1/36*w**4 + 1/315*w**7 - 1/504*w**8 - 1/45*w**5 + 0 + 1/9*w**3 + 0*w + 1/90*w**6. Solve d(z) = 0 for z.
-1, 1
Let o(a) be the first derivative of -a**8/2940 + a**7/735 + a**6/42 - 6*a**5/35 - 3*a**3 - 5*a + 170. Let z(b) be the third derivative of o(b). Factor z(w).
-4*w*(w - 3)**2*(w + 4)/7
Let d(a) = -2*a**2 + 14*a + 1383. Let v be d(-23). Let n(m) be the first derivative of -6*m - 2/5*m**v + 18/5*m**2 + 23. Factor n(c).
-6*(c - 5)*(c - 1)/5