 8 - 2. Let x(b) = -6*b**2 - 10*b + 1. Let c(l) = 6*l**2 + 10*l - 2. Let a(p) = f*c(p) + 4*x(p). Factor a(k).
4*(k + 2)*(3*k - 1)
Let y(q) = -8*q + 4. Let b be y(-11). Suppose 27*k - b = -11. Factor 2/11*s**k - 2/11*s**2 - 2/11*s + 2/11.
2*(s - 1)**2*(s + 1)/11
Let o(s) be the third derivative of 1/20*s**5 + 0*s + 1/40*s**6 + 0 - 1/2*s**3 - 1/8*s**4 - 11*s**2. Factor o(i).
3*(i - 1)*(i + 1)**2
Let u(p) be the second derivative of p**6/180 - p**4/18 + 22*p + 2. Determine y, given that u(y) = 0.
-2, 0, 2
Let f(b) be the second derivative of -5*b**7/42 - 4*b**6/3 - 11*b**5/2 - 10*b**4 - 15*b**3/2 - 74*b. Factor f(x).
-5*x*(x + 1)**2*(x + 3)**2
Let i(t) be the first derivative of t**4/20 - 2*t**3/5 - 31*t**2/10 + 36*t/5 - 399. Factor i(a).
(a - 9)*(a - 1)*(a + 4)/5
Let y(v) be the third derivative of 31*v**6/120 + v**5 - v**4/6 - 44*v**2 + 2*v. Factor y(n).
n*(n + 2)*(31*n - 2)
Let x(j) = 3*j**3 - 57*j**2 - 779*j + 841. Let z(w) = 5*w**3 - 57*w**2 - 777*w + 841. Let t(i) = -3*x(i) + 2*z(i). Solve t(y) = 0.
-29, 1
Let x(i) be the first derivative of -i**6/960 + i**5/240 - i**4/192 + i**2/2 + 14. Let v(y) be the second derivative of x(y). Suppose v(a) = 0. What is a?
0, 1
Let i(j) = 2*j**2 + 1. Let w(k) = 13*k**2 + 144*k - 5177. Let c(d) = -35*i(d) + 5*w(d). Suppose c(p) = 0. Calculate p.
72
Suppose 2*s + s - 5*v = -13, -v + 6 = -4*s. Let l(x) = x**3 - x**2 - 1. Let m(c) = 8*c**2 - 8*c + 4. Let w(k) = s*m(k) - 4*l(k). Solve w(g) = 0.
-2, 0, 1
Suppose 40 = d + 3*d. Suppose -5*s - d = -7*s. Find f such that 0*f**4 - 2*f**5 + f**3 + 3*f**s + 2*f**4 = 0.
-1, 0
Find b, given that 0*b**2 + 0*b + 4/5*b**4 - 2/5*b**3 - 2/5*b**5 + 0 = 0.
0, 1
Let d = 14 + -9. Let x(h) be the second derivative of -h + 0*h**2 + 5/36*h**4 + 1/20*h**d + 1/9*h**3 + 0. Let x(b) = 0. What is b?
-1, -2/3, 0
Let o(d) = -529*d**3 - 7850*d**2 + 1369*d - 60. Let f(r) = -529*r**3 - 7849*r**2 + 1370*r - 60. Let b(x) = 7*f(x) - 6*o(x). Find t, given that b(t) = 0.
-15, 2/23
Let p(f) be the second derivative of -f**6/105 + f**5/7 - 17*f**4/42 + 8*f**3/21 - 170*f. Suppose p(o) = 0. What is o?
0, 1, 8
Let b(a) be the second derivative of -5*a**4 + 0 + 0*a**2 + 51/20*a**5 + 24*a + 2*a**3 - 2/5*a**6. Factor b(y).
-3*y*(y - 2)**2*(4*y - 1)
Let v(q) be the second derivative of -q**6/75 + 6*q**5/25 - q**4 + 28*q**3/15 - 9*q**2/5 + 2*q + 165. Factor v(i).
-2*(i - 9)*(i - 1)**3/5
Let r(a) be the third derivative of -a**8/560 + a**7/70 - a**6/50 + 530*a**2. Factor r(f).
-3*f**3*(f - 4)*(f - 1)/5
Let d(a) be the first derivative of -a**8/420 + a**7/70 + a**3/3 + 10. Let n(f) be the third derivative of d(f). Let n(z) = 0. Calculate z.
0, 3
Let n(s) = -80*s - 77. Let t be n(-1). Suppose 36/5*v**t - 2*v**4 + 8/5*v**2 - 12/5*v - 24/5*v**5 + 2/5 = 0. Calculate v.
-1, 1/4, 1/3, 1
Suppose -28 = -44*u + 17*u + 13*u. Factor -1/6*r**4 - 1/6*r**3 + 0 + 0*r + 0*r**u.
-r**3*(r + 1)/6
Let v(t) be the first derivative of 3*t**7/455 + 7*t**6/780 - t**5/195 + 8*t**2 - 5. Let w(s) be the second derivative of v(s). Determine f so that w(f) = 0.
-1, 0, 2/9
Let z(y) be the third derivative of -y**6/30 + 2*y**5/5 - 15*y**4/8 + 9*y**3/2 - y**2 + 33. Let z(n) = 0. What is n?
3/2, 3
Let c = 66711 - 133421/2. Let q = 8 + -15/2. Factor 1/2*z**2 - c + q*z - 1/2*z**3.
-(z - 1)**2*(z + 1)/2
What is l in 31*l**4 - 25*l**4 + 33*l**3 + 12 + 60*l + 6*l**3 - 15*l**5 + 93*l**2 - 27*l**4 = 0?
-1, -2/5, 2
Let g = -61 + 489/8. Let h(l) be the first derivative of 9/16*l**4 + g*l**2 + 3 + 0*l + 1/2*l**3. Factor h(w).
w*(3*w + 1)**2/4
Suppose -2*y = 3*d - 16, 4*y - 9 = -2*d + 3*y. Factor -3 + 49*r**d + 3 - 45*r**2 + 8*r.
4*r*(r + 2)
Let i(m) be the second derivative of 0 + 1/16*m**4 + 1/4*m**3 + 6*m + 3/8*m**2. Factor i(z).
3*(z + 1)**2/4
Factor -29/6*g - 5 + 1/6*g**2.
(g - 30)*(g + 1)/6
Let h(u) be the first derivative of 2*u**7/945 - u**6/90 + 2*u**4/27 + 11*u**2 + 27. Let r(t) be the second derivative of h(t). Determine y so that r(y) = 0.
-1, 0, 2
Factor 50/13 - 148/13*j - 6/13*j**2.
-2*(j + 25)*(3*j - 1)/13
Let c(m) be the third derivative of -m**7/1785 - 2*m**6/255 - 23*m**2 - 2*m. What is b in c(b) = 0?
-8, 0
Let s be 0*1/(2 - 0). Suppose -3*j + 102*j - 348 = -17*j. Find d, given that -3/5*d + s*d**2 + 6/5*d**j + 0*d**4 + 0 - 3/5*d**5 = 0.
-1, 0, 1
Let c = -37 + 39. Factor 2*b + 3*b**3 + 6*b**c - 5*b - 13*b**2 + 18*b**4 - 11*b**2.
3*b*(b - 1)*(b + 1)*(6*b + 1)
Let s(w) be the second derivative of 1/15*w**5 - 2*w + 0*w**3 + 0 + 5/2*w**2 + 1/6*w**4. Let i(n) be the first derivative of s(n). Let i(x) = 0. Calculate x.
-1, 0
Let d(p) be the second derivative of 49*p**5/190 - 259*p**4/38 + 1144*p**3/19 - 2704*p**2/19 + 135*p. Factor d(u).
2*(u - 1)*(7*u - 52)**2/19
Suppose -5*n = -10 - 0. Suppose 2 + 34 = 12*w. Factor -5*b**n - 4*b - w*b**3 + 11*b**2 + b.
-3*b*(b - 1)**2
Let n(w) = w - w**3 - 136*w**4 - 1 + 1 + w**2 + 135*w**4. Let j(d) = 4*d**5 + 4*d**4 + 13*d**3 - 10*d**2 - 11*d. Let q(b) = 4*j(b) + 44*n(b). Factor q(u).
4*u**2*(u - 1)**2*(4*u + 1)
Suppose 0 = -o + 3*o - 6. Factor -13*m - o - 64*m**2 - 39*m + 4*m - 6.
-(8*m + 3)**2
Let w(l) be the first derivative of l**6/18 + 2*l**5/5 + l**4/3 - 2*l**3/3 - 5*l**2/6 - 6. Factor w(y).
y*(y - 1)*(y + 1)**2*(y + 5)/3
Suppose -508*w + 521*w - 39 = 0. Determine n, given that -27*n - 1/4*n**w + 9/2*n**2 + 54 = 0.
6
Suppose 0 = -l + 2*a - 2, -2*a + 2 = 6*l - l. Let m(x) be the second derivative of 1/30*x**4 + l*x**3 + 0 + 0*x**2 + 0*x**5 - 7*x - 1/75*x**6. Factor m(u).
-2*u**2*(u - 1)*(u + 1)/5
Let t(i) be the third derivative of -i**5/12 - 5*i**4/24 + 5*i**3 + 33*i**2. What is u in t(u) = 0?
-3, 2
Let a(p) be the third derivative of 0*p**4 + 1/480*p**5 + 1/2880*p**6 + 0 + 0*p + 6*p**2 - 5/6*p**3. Let f(v) be the first derivative of a(v). Factor f(g).
g*(g + 2)/8
Let b(o) = -7*o**2 + 96*o. Let f(z) = z**2 + 2*z. Let l(p) = -b(p) - 2*f(p). Factor l(g).
5*g*(g - 20)
Factor -6 + 58/13*w + 22/13*w**2 - 2/13*w**3.
-2*(w - 13)*(w - 1)*(w + 3)/13
Let r = -2094 - -6283/3. Find j such that -j - r*j**2 - 2/3 = 0.
-2, -1
Let n be 6*(-3 + 46/12). Suppose 5*w - n = 3*k, 14 = 5*k + 5*w - 31. What is l in -3*l**2 + 7*l - l - 15*l**3 + 9*l**k + 3*l**4 + 0*l**3 = 0?
-1, 0, 2/3, 1
Let z = 9 + -5. Suppose 0 = -z*v + 5 + 7. Solve 1 - b - 25/4*b**2 + 25/4*b**v = 0 for b.
-2/5, 2/5, 1
Suppose 0 = -2*a + 2*i + 14, 2*a + 4*i + 16 = -0*i. Factor 10*m + 28*m**4 - 8*m**4 - 35*m**a + 0*m - 25*m**3.
5*m*(m - 2)*(m + 1)*(4*m - 1)
Let c = -22 + 4. Let z be (-134)/(-12) - (-5 + (-102)/c). Let -3*g**2 - 21/2*g + 3 + z*g**3 = 0. What is g?
-1, 2/7, 1
Let f(y) be the second derivative of -10*y + 0 + 1/7*y**3 - 1/70*y**5 + 2/7*y**2 + 0*y**4. Factor f(w).
-2*(w - 2)*(w + 1)**2/7
Factor 384/7 - 80/7*n - 4/7*n**2.
-4*(n - 4)*(n + 24)/7
Solve -3/2*h + 2*h**2 + 0 - 1/2*h**3 = 0 for h.
0, 1, 3
Let o be (-16*(-26)/(-9152))/((-1)/8). Suppose 8/11*i**3 + 0 + o*i - 10/11*i**2 - 2/11*i**4 = 0. Calculate i.
0, 1, 2
Suppose 563*q - 2*h = 561*q - 4, 3*h = q + 12. Suppose -2/5 + 8/5*w + 8/5*w**q - 12/5*w**2 - 2/5*w**4 = 0. What is w?
1
Find i, given that -7 + 17/2*i - 3/2*i**2 = 0.
1, 14/3
Let d(g) be the third derivative of 0*g + 1/330*g**5 + 1/11*g**3 + 8 - 1/33*g**4 + g**2. Find u, given that d(u) = 0.
1, 3
Suppose -r + 18 = -4*b - 6, -4*r + 2*b = -26. Let g be -1 + 2 - r/4. Solve -1/2*t - 1/2*t**2 + g = 0 for t.
-1, 0
Suppose 4*j - 4*d = 32, 2*j - 4*d = d + 31. Factor 0*k + 0 - 1/3*k**2 + 1/3*k**j.
k**2*(k - 1)/3
Suppose -3*a - 11 = o, -3*o - 1 = -2*o + a. Let w(z) be the second derivative of 49/10*z**5 + 343/15*z**6 - 35*z**o + 2*z + 0 + 76/3*z**3 - 8*z**2. Factor w(h).
2*(h + 1)*(7*h - 2)**3
Let a(o) = -190*o**2 - 3345*o - 3430. Let p(g) = -7*g**2 - 124*g - 127. Let j(k) = -2*a(k) + 55*p(k). Factor j(v).
-5*(v + 1)*(v + 25)
Let k(x) be the third derivative of x**5/120 - 7*x**4/12 + 49*x**3/3 - 48*x**2. Factor k(g).
(g - 14)**2/2
Factor -322 + 4*o**2 - 43 + 90*o + 89 + o - 11*o.
4*(o - 3)*(o + 23)
Let b(a) = -2*a - 10. Let i be b(-7). Factor -96*x**3 + 106*x**3 + 2*x**i - 3*x**4 - 4*x**4.
-5*x**3*(x - 2)
Suppose -g + 2 = -2*i - 2, -2*g - 5*i = -17. Let r be (-2)/4*-12 - g. Determine o so that 0*o - 1/10*o**3 + 1/10*o**2 + r = 0.
0, 1
Let m(d) be the first derivative of 5*d**3/3 - 25*d**2 + 80*d + 249. Suppose m(f) = 0. Calculate f.
2, 