13). Let y(b) be the third derivative of 0*b**w - 1/105*b**7 - 1/60*b**6 + 0*b - 3*b**2 + 1/30*b**5 + 1/12*b**4 + 0. Factor y(s).
-2*s*(s - 1)*(s + 1)**2
Let s(a) be the second derivative of a**6/240 + a**5/120 - a**4/24 - a**2/2 - 2*a. Let r(t) be the first derivative of s(t). Factor r(y).
y*(y - 1)*(y + 2)/2
Let m(t) be the third derivative of -t**5/80 - 5*t**4/16 - 21*t**3/8 - 14*t**2 - t. Find z, given that m(z) = 0.
-7, -3
Let l be 4/10 - 13/(-5). Suppose 8 = l*u + u. Factor -2*i**u - 15*i**4 + 0*i + 3*i**2 + 16*i**3 - 2*i + 4*i**5 - 4*i**2.
i*(i - 2)*(i - 1)**2*(4*i + 1)
Let z(s) = -15*s**3 - 26*s**2 + 5*s + 4. Let y = 17 - 6. Let j(d) = -30*d**3 - 51*d**2 + 10*d + 9. Let n(a) = y*z(a) - 6*j(a). Factor n(l).
5*(l + 1)**2*(3*l - 2)
Let y(d) be the third derivative of -5*d**8/336 + 2*d**7/21 - d**6/8 + 4*d**2. Factor y(w).
-5*w**3*(w - 3)*(w - 1)
Let 22*b - 44381*b**2 - 10*b - 4*b**4 + b**5 - 13*b**3 + 44385*b**2 = 0. What is b?
-2, -1, 0, 1, 6
Let v(l) = 12*l**4 + 9*l**3 + 3*l**2. Let i = 24 + -21. Let o(r) = -r**5 - 11*r**4 - 9*r**3 - 3*r**2. Let x(s) = i*o(s) + 2*v(s). Let x(g) = 0. Calculate g.
-1, 0
Let c be 2 - (-1 + -2) - 3. Find k, given that -3*k - 77*k**2 - 35*k - 21*k**3 - 16*k - 22*k**c + 24 = 0.
-4, -1, 2/7
Let f(p) = 2*p**4 - p**2. Let o(n) = 15*n**4 + 105*n**3 + 858*n**2 - 972*n. Let r(b) = -6*f(b) + o(b). Factor r(v).
3*v*(v - 1)*(v + 18)**2
Let t be (-24)/(-16)*(0 - -40). Let y be 5/(-2)*(-48)/t. Factor 4*c**3 - y*c**4 - 4 + 4*c**4 - 4*c + 0*c**4 + 2.
2*(c - 1)*(c + 1)**3
Let i(d) be the first derivative of -4*d**4/7 + 4*d**3/3 + 4*d**2/7 + 82. Let i(x) = 0. What is x?
-1/4, 0, 2
Let m(t) = -6*t**3 + 18*t**2 - 48*t + 30. Let y(n) = -14*n**3 + 36*n**2 - 96*n + 59. Let d(s) = 5*m(s) - 2*y(s). Solve d(o) = 0 for o.
1, 4
Suppose -9*h + 6*h = -6. Suppose 34 - 34 = h*j. Factor 8/5*l + 4/5*l**2 + j.
4*l*(l + 2)/5
Let d = -2296 + 18401/8. Let y(u) be the first derivative of -3/2*u + 3/4*u**2 - 7 + 9/2*u**3 + d*u**4 + 6/5*u**5. Let y(r) = 0. What is r?
-1, 1/4
Let j = 101/3690 + -2/123. Let q(d) be the third derivative of 6*d**2 + 1/27*d**3 + 0*d + j*d**5 + 0 - 1/36*d**4 - 1/540*d**6. Determine f so that q(f) = 0.
1
Let u(w) = -w. Let f(m) = m**2 + 16*m - 13. Let c(s) = f(s) + 4*u(s). Let g(l) = 2*l**2 + 12*l - 14. Let q(d) = -2*c(d) + 3*g(d). Factor q(v).
4*(v - 1)*(v + 4)
Let -5/6*z**4 - 95/3*z**2 + 0 - 205/6*z**3 + 200/3*z = 0. What is z?
-40, -2, 0, 1
Let u(h) = 5*h**2 - 4*h + 10. Let s(x) = -6*x**2 + 4*x - 11. Let w(g) = -6*s(g) - 7*u(g). Let f(a) = 1. Let k(t) = 4*f(t) + w(t). Factor k(p).
p*(p + 4)
Solve -4*a + 16/3*a**2 + 0 - 16/3*a**4 + 4*a**3 = 0.
-1, 0, 3/4, 1
Let u(f) be the third derivative of -7*f**6/360 - 29*f**5/360 - f**4/9 - f**3/36 - 4*f**2 - 2. Solve u(g) = 0 for g.
-1, -1/14
Let h be -3 + (12 - 9/(-3)). Suppose h = -d + 4*d. Suppose d*l + 8 - 2*l**4 + 4*l - 8*l**3 - 6*l**2 + 0*l**4 = 0. Calculate l.
-2, -1, 1
Suppose -3*d + 19 = 2*u, -2*u = -u + 5*d - 27. Let -x + x**u - 1 - 3 + 6 - 4 = 0. Calculate x.
-1, 2
Let d(u) be the second derivative of 0*u**2 - 5/4*u**4 + 3/4*u**5 + 0 - 3*u - 1/6*u**6 + 5/6*u**3. Factor d(c).
-5*c*(c - 1)**3
Let h(d) be the first derivative of 64*d**5/25 - 3*d**4/5 - 64*d**3/5 - 46*d**2/5 + 24*d/5 + 266. Determine q, given that h(q) = 0.
-1, 3/16, 2
Let l(q) = -q**2 - 6*q + 2. Let v be l(-6). Let m(k) = 6*k**2 - 4*k + 4*k + v*k**3 + 3*k. Let i(a) = a**3. Let x(s) = -i(s) - m(s). Let x(d) = 0. What is d?
-1, 0
Suppose 3*b = -9, -b + 7 + 15 = 5*l. Suppose -w**4 - 4*w**l + 9*w**4 + 4*w**2 + 4*w**4 - 12*w**3 = 0. What is w?
0, 1
Let u(k) be the first derivative of -1/3*k**4 + 0*k**2 + 0*k**3 + 1/9*k**6 - 29 + 0*k - 2/15*k**5. Let u(w) = 0. Calculate w.
-1, 0, 2
Let x(i) be the second derivative of i**5/180 - i**4/108 - 2*i**3/27 + 2*i**2/9 + 29*i. Suppose x(d) = 0. Calculate d.
-2, 1, 2
Let m = 47 + 95. Let x = -94 + m. Factor -12*g**4 - 27*g**2 + 15*g**2 - x*g**2 - 8 - 8*g - 44*g**3 - 28*g.
-4*(g + 1)**3*(3*g + 2)
Let a(c) = 37*c**2 - 21*c + 19. Let l(g) = -5*g**2 + g - 1. Let y(w) = -2*a(w) - 14*l(w). What is n in y(n) = 0?
1, 6
Let p(h) = 2*h + 4 - 35*h + 3*h**2 + h**3 + 5*h. Let r be p(4). What is n in 4/7*n**r - 4/7*n**5 + 4/7*n**3 - 4/7*n**2 + 0 + 0*n = 0?
-1, 0, 1
Let m be ((40/(-250)*-5)/(9/345))/4. Determine x so that -m*x + 10/3 - 5/3*x**2 = 0.
-5, 2/5
Let u = -215 + 220. Suppose 5*h - 14 = -4. Solve 3*b**4 - b + u*b**2 - h*b**3 + 3*b + 9*b**3 - b = 0 for b.
-1, -1/3, 0
Let r be 47/9 - (-36 - -40) - 1. Let m(g) be the second derivative of -r*g**3 + 2*g - 5/18*g**4 + 0*g**2 + 0. What is a in m(a) = 0?
-2/5, 0
Suppose -o - 5 = -10. Determine x so that -x**5 + 22*x**4 - 8*x**2 - x**o - 16*x**4 = 0.
-1, 0, 2
Let q(b) = -b**3 + 14*b**2 - 13*b + 5. Let m be q(13). Determine d so that 5*d**2 - d - m*d - 3*d**2 - 5*d**2 = 0.
-2, 0
Let m be 6/(-4) - 65/(-10). Factor -8*z + 6*z**3 - 8*z**4 + 38*z**m - 36*z**5 + 9*z**2 - z**2.
2*z*(z - 2)**2*(z - 1)*(z + 1)
Let q(t) = -t**2 - 6*t - 6. Let o be q(-4). Suppose -3*x = -2*v + 26 - 5, 9 = -o*v - 3*x. What is p in p**3 - 2*p**4 - v*p**3 + 4*p**3 = 0?
0, 1
Let i(o) be the second derivative of o**8/11760 + o**7/4410 - o**6/630 + o**4/2 + 12*o. Let n(m) be the third derivative of i(m). Factor n(b).
4*b*(b - 1)*(b + 2)/7
Let o(n) be the first derivative of n**3/3 - 9*n**2 + 32. Determine v so that o(v) = 0.
0, 18
Let s(a) be the third derivative of 3*a**8/224 - a**7/28 - 11*a**6/240 + 11*a**5/120 - a**4/24 - 5*a**2 + 11*a. Suppose s(r) = 0. Calculate r.
-1, 0, 1/3, 2
Factor -2/3*t**3 + 58/3*t**2 + 392/3 - 448/3*t.
-2*(t - 14)**2*(t - 1)/3
Let a(m) = -9*m**4 + 35*m**3 + 3*m**2 - 20*m + 11. Let d(b) = -4*b**4 + 18*b**3 + 2*b**2 - 9*b + 5. Let c(i) = -3*a(i) + 5*d(i). Find r, given that c(r) = 0.
-1, 1, 8/7
Let t(m) = 15*m**3 - 5*m**2 - 5*m + 5. Let v(z) = 8*z**3 - 3*z**2 - 3*z + 3. Let n(l) = -3*t(l) + 5*v(l). Let n(h) = 0. Calculate h.
0
Let 0 + 62/21*f**3 + 0*f - 2/21*f**5 + 0*f**4 - 20/7*f**2 = 0. Calculate f.
-6, 0, 1, 5
Suppose -33*j + 6*j**2 + 21*j + 29*j**3 + 16*j - 27*j**3 = 0. Calculate j.
-2, -1, 0
Let q(w) be the first derivative of -w**4/22 + 8*w**3/33 - 5*w**2/11 + 4*w/11 - 625. Find s, given that q(s) = 0.
1, 2
Factor 8*q**2 + 7*q**4 - q**3 - 15*q**4 + 4*q**4 - 3*q**3.
-4*q**2*(q - 1)*(q + 2)
Let w be (16/(-4))/4*-3. Determine c so that 2 - 14*c + 45*c**2 + 18 - 5*c**4 - 5*c**w - 41*c = 0.
-4, 1
Let j(w) be the third derivative of -w**7/1260 + w**6/270 + 11*w**3/6 - 3*w**2. Let i(r) be the first derivative of j(r). Factor i(q).
-2*q**2*(q - 2)/3
Let s be (-8050)/(-8800) - (-9)/(-48). Find r such that 16/11*r**2 + 0 + s*r - 10/11*r**3 = 0.
-2/5, 0, 2
Factor -4*x + 11/3 + 1/3*x**2.
(x - 11)*(x - 1)/3
Let -l**4 + 3*l**4 + 2*l**3 + 0*l**4 + 12*l**3 + 20*l**2 = 0. What is l?
-5, -2, 0
Let s(a) be the third derivative of a**5/510 - a**4/68 - 10*a**3/51 - 11*a**2 + 2*a. Factor s(g).
2*(g - 5)*(g + 2)/17
Let w be (4 + -7)/(2 + -1). Let i be ((-3)/w)/(21/9). Factor 3/7*j + 0 + 6/7*j**2 + i*j**3.
3*j*(j + 1)**2/7
Let g be ((-42)/(-15) + -4)/(4/(-10)). Suppose 2/3 + 2*b**2 - 2*b - 2/3*b**g = 0. What is b?
1
Let o = 5083 - 5080. Factor 115*q**o - 1 + 16*q**5 - 241/4*q**2 - 76*q**4 + 13*q.
(q - 2)**2*(4*q - 1)**3/4
Find c such that 2/5*c + 6/5 - 8/5*c**2 = 0.
-3/4, 1
Let v be (-8)/(-14) + (-3)/(-336)*-106. Let z = v + 5/8. Factor 1 - i + z*i**2.
(i - 2)**2/4
Let c(l) = -35*l**4 + 37*l**3 + 53*l**2 - 24*l. Let y(f) = 18*f**4 - 18*f**3 - 27*f**2 + 12*f. Let v(j) = -3*c(j) - 5*y(j). Factor v(u).
3*u*(u - 2)*(u + 1)*(5*u - 2)
Let q(i) = 71*i - 779. Let t be q(11). Let a(s) be the first derivative of -8/11*s + 7 - 2/33*s**3 - 4/11*s**t. Factor a(c).
-2*(c + 2)**2/11
Let j(s) = -6*s**2 + s - 1. Let f(g) = -70*g**2 - 8*g - 60. Let a(c) = f(c) - 12*j(c). Factor a(m).
2*(m - 12)*(m + 2)
Let f(p) be the second derivative of -p**4/72 + 7*p**3/6 - 147*p**2/4 + 8*p + 12. Determine g, given that f(g) = 0.
21
Factor -20/3*o**2 + 20/3 + 2/3*o**3 - 2/3*o.
2*(o - 10)*(o - 1)*(o + 1)/3
Let b(t) = -t**2 - 9*t - 10. Let p be b(-4). Let j be -3*(-2 + (0 - 2)). Factor 4*m**3 - 4*m**3 + p*m**3 + 36*m**2 + 5*m**3 + j*m.
3*m*(m + 2)*(5*m + 2)
Let o(r) be the first derivative of r**5/180 - r**4/36 - 5*r**2/2 - 6. Let j(n) be the second derivative of o(n). Factor j(y).
y*(y