iven that -1/7*d**2 - 25/7 - i*d = 0.
-5
Let r(o) be the first derivative of -2*o**5/5 - 5*o**4 - 34*o**3/3 - 8*o**2 + 8. Find t such that r(t) = 0.
-8, -1, 0
Let o(b) = 3*b**2 - 9*b + 18. Let s(c) = 4*c**2 - 10*c + 21. Let z(k) = 5*o(k) - 4*s(k). Factor z(x).
-(x - 1)*(x + 6)
Let a(q) = q**3 - 9*q**2 - 50*q + 452. Let h be a(7). Suppose 2/3*p + 0 + 1/3*p**5 + 1/3*p**h - 1/3*p**2 - p**3 = 0. What is p?
-2, -1, 0, 1
Let t be (19 - (-111)/(-6))*(-8)/(-12). Factor -8/3 + t*s**3 + 20/3*s - 17/6*s**2.
(s - 4)**2*(2*s - 1)/6
Let v(g) be the third derivative of 0*g + 0*g**3 + 0 - 1/525*g**7 + 0*g**4 - 9*g**2 - 1/150*g**5 - 1/150*g**6. Factor v(i).
-2*i**2*(i + 1)**2/5
Let y(a) be the first derivative of -5*a**4/4 - 5*a**3 - 15*a**2/2 - 5*a - 152. Suppose y(o) = 0. Calculate o.
-1
Let r(l) = 12 + 3*l - 14 + l. Let o be r(1). What is x in -7*x + 15*x + 9*x**3 + 6*x**4 - 17*x**3 + 8 - 14*x**o = 0?
-1, -2/3, 1, 2
Suppose -2*o + 33 = -3*l, 8 - 41 = -3*o - l. Suppose 19*z**2 + 2*z**4 + 5*z**2 - 20*z - o*z**3 + 6 + 0*z = 0. Calculate z.
1, 3
Let p(y) be the third derivative of -1/60*y**6 + 25*y**2 - 1/10*y**5 + 0 + 0*y - 1/3*y**3 - 1/4*y**4. Factor p(b).
-2*(b + 1)**3
Suppose -58*y + 25 = -53*y. Suppose 0*w - 3*w - 15 = -a, -y*a + 4*w + 20 = 0. Factor a*n**3 + 1/7*n**4 + 1/7*n**5 + 0 + 0*n**2 + 0*n.
n**4*(n + 1)/7
Let c(y) = -9*y**2 + 75*y. Let w(j) = 8*j**2 - 72*j. Let g(u) = 5*c(u) + 6*w(u). Factor g(p).
3*p*(p - 19)
Let i(w) be the third derivative of -w**7/280 + 39*w**6/160 + w**5/80 - 39*w**4/32 + 110*w**2. Suppose i(p) = 0. What is p?
-1, 0, 1, 39
Let c be (-6)/5*(0 - 200/15). Let l be c + -12 + (42/4)/(-3). Find m, given that l*m**2 + 2*m + 2 = 0.
-2
Let o(u) be the second derivative of -2*u**7/21 - 4*u**6/15 + 2*u**5/5 + 8*u**4/3 + 14*u**3/3 + 4*u**2 + 107*u. Factor o(f).
-4*(f - 2)*(f + 1)**4
Let r = -13/139 - -178/417. Determine k so that k + r*k**2 + 2/3 = 0.
-2, -1
Factor 6*o**3 - 40/3 + 128/3*o - 38*o**2.
2*(o - 5)*(3*o - 2)**2/3
Let o be 11/(-66)*-12 + 3. Let f(m) be the first derivative of 0*m + o + 1/7*m**2 + 2/21*m**3. Determine k so that f(k) = 0.
-1, 0
Let x(z) be the first derivative of -3*z**2 + 1/18*z**3 + 1/180*z**5 - 1/36*z**4 + 0*z - 3. Let a(c) be the second derivative of x(c). Solve a(u) = 0.
1
Solve -1/2*j**4 + 1/2*j**2 + 0*j**3 + 0*j + 0 = 0 for j.
-1, 0, 1
Let t(i) = -11*i**3 - i**2 + 18*i + 1. Let z(n) = -6*n**3 + 10*n. Let y(j) = 4*t(j) - 7*z(j). Factor y(h).
-2*(h - 1)*(h + 1)*(h + 2)
Factor -2/5 - 3/5*g**2 + 1/5*g**4 - 1/5*g**3 + g.
(g - 1)**3*(g + 2)/5
Let s = -2436 + 2441. Find k, given that 130/3*k**4 + 20/3*k - 45*k**3 + 0 - 35/3*k**s + 20/3*k**2 = 0.
-2/7, 0, 1, 2
Let t = 86 + -82. Let s(v) be the second derivative of t*v + 1/6*v**4 + 2/3*v**3 + v**2 + 0. Factor s(q).
2*(q + 1)**2
Let q be (-7 - (-133)/21)*-3. Let v be 0 + -2 + (-7)/(-2). Let -v*m**q - 27/2 + 9*m = 0. Calculate m.
3
Let g(b) be the first derivative of 22*b**3/15 - 3*b**2 + 8*b/5 - 369. Factor g(v).
2*(v - 1)*(11*v - 4)/5
Factor -3/2*v + 3*v**2 - 5 - 1/2*v**3.
-(v - 5)*(v - 2)*(v + 1)/2
Let o(q) be the third derivative of -q**6/60 - q**5/10 + 3*q**4/4 - 5*q**3/3 - 88*q**2. Let o(b) = 0. Calculate b.
-5, 1
Let z(v) = 3*v**4 + 2*v**3 + v. Let i(j) = -j**5 + 10*j**4 + 23*j**3 - 4*j**2 - 16*j. Let t(d) = -i(d) + 4*z(d). Find h such that t(h) = 0.
-5, -1, 0, 2
Let w(y) be the third derivative of y**6/60 - 7*y**5/30 + 5*y**4/6 + 46*y**2 - 2*y. Factor w(m).
2*m*(m - 5)*(m - 2)
Suppose -84 = -9*x + 285. Factor -19*m - 5*m**2 - 12*m - 245 - x*m + 2*m.
-5*(m + 7)**2
Let i(x) be the third derivative of x**6/96 + 2*x**5/15 + 19*x**4/32 + 3*x**3/4 - 76*x**2. Factor i(z).
(z + 3)**2*(5*z + 2)/4
Let t(v) be the second derivative of 2*v**6/15 + 44*v**5/5 + 484*v**4/3 + 5*v - 6. Solve t(f) = 0 for f.
-22, 0
Let f = 43075/129207 - 2/43069. Factor 2/3*t**2 - 1/3 - 1/3*t**4 - f*t**5 - 1/3*t + 2/3*t**3.
-(t - 1)**2*(t + 1)**3/3
Let b(y) be the first derivative of -5*y**3/3 + 3*y**2/2 + 2*y + 29. Factor b(i).
-(i - 1)*(5*i + 2)
Let v(k) be the first derivative of k**9/1512 + k**8/840 - k**7/420 - k**6/180 + 13*k**3/3 - 26. Let j(x) be the third derivative of v(x). Factor j(u).
2*u**2*(u - 1)*(u + 1)**2
Suppose -8 = -3*s + v, -5*s + 24 = 2*v - v. Suppose -a + 15 = s*a. Factor 12 + 4*z - 12 + 8*z**a + 10*z**2 + 2*z**4.
2*z*(z + 1)**2*(z + 2)
Let l(j) be the third derivative of 0*j**5 + 6*j**2 + 0*j**3 - 1/90*j**6 + 0*j + 1/315*j**7 + 0*j**4 + 0. Suppose l(p) = 0. Calculate p.
0, 2
Let h(q) be the third derivative of q**5/30 - 5*q**4/2 - 136*q**3/3 + 21*q**2 + 3. Let h(f) = 0. Calculate f.
-4, 34
Factor -55 - 11 - 3*f**2 + 18 + 24*f - 48*f.
-3*(f + 4)**2
Factor -8/3*i**4 + 4/3*i - 2/3 + 2*i**2 - 8/3*i**3.
-2*(i + 1)**2*(2*i - 1)**2/3
Let s = -25847/142 + -105/71. Let y = -182 - s. Let -3/2*w**2 + 3/2 + y*w**3 - 3/2*w = 0. What is w?
-1, 1
Let n(i) be the first derivative of i**5/40 + 29*i**4/32 + 28*i**3/3 + 49*i**2/4 + 35. Factor n(s).
s*(s + 1)*(s + 14)**2/8
Let g(w) = 7*w**2 - 30*w - 37. Let x(v) = 85*v**2 - 360*v - 445. Let n(u) = -25*g(u) + 2*x(u). Factor n(b).
-5*(b - 7)*(b + 1)
Let m(s) be the third derivative of -3*s**8/784 + 2*s**7/245 + s**6/70 - 5*s**2 + 7*s. Factor m(j).
-3*j**3*(j - 2)*(3*j + 2)/7
Suppose 0 = -0*p + p - 13. Factor p*a**2 - 16*a**2 - 6*a**3 - 3*a**4 - 3*a**4 + 3*a**4.
-3*a**2*(a + 1)**2
Suppose -5*q + 85 - 540 = 0. Let f = q - -183/2. Factor f - 1/2*b**2 + 2*b - 2*b**3.
-(b - 1)*(b + 1)*(4*b + 1)/2
Let q(s) be the first derivative of -s**5/25 - s**4/5 - 2*s**3/5 - 2*s**2/5 - s/5 + 113. Find b, given that q(b) = 0.
-1
Let c(a) be the third derivative of a**8/168 + 17*a**7/21 + 235*a**6/6 + 1943*a**5/3 - 46255*a**4/12 + 24389*a**3/3 - 14*a**2 - 3. Find g such that c(g) = 0.
-29, 1
Determine r, given that 1/4*r + r**2 + 0 + 3/4*r**3 = 0.
-1, -1/3, 0
Let g(a) be the second derivative of -a**5/75 - a**4/20 + 2*a**3/15 - a**2/2 + 7*a. Let p(f) be the first derivative of g(f). Let p(m) = 0. What is m?
-2, 1/2
Factor 121*a**2 + 4 - 235*a**2 + 15*a**4 - 35*a**3 + 129*a**2 - 6 + 15*a - 8.
5*(a - 1)**3*(3*a + 2)
Let b(t) = -t**2 + 8*t + 2. Let w be b(8). Factor -4/19 + 2/19*p + 2/19*p**w.
2*(p - 1)*(p + 2)/19
Let i(q) = 5*q**2 + 8*q. Let w(r) = -2*r + 9. Let b be w(4). Let o(f) = -f - 1 - 10*f**2 + 1 - 14*f + b. Let k(j) = -9*i(j) - 4*o(j). Factor k(d).
-(d + 2)*(5*d + 2)
Let k(o) be the second derivative of o**7/7560 + o**6/540 - o**5/72 + o**4/4 + 7*o. Let y(g) be the third derivative of k(g). Let y(v) = 0. Calculate v.
-5, 1
Let 9/5 + 1/5*q**2 - 6/5*q = 0. What is q?
3
Suppose 0 = -w - 2 + 3. Let l be -2 + w - (-20)/5. Factor 5*v**4 + 4*v**l + 2*v**5 + v**2 - 2*v + 0*v + 2*v.
v**2*(v + 1)**2*(2*v + 1)
Let g(j) be the first derivative of -j**6/30 - 3*j**5/25 - j**4/20 + j**3/5 + j**2/5 + 17. Find f such that g(f) = 0.
-2, -1, 0, 1
Let z(j) = 0*j**2 + j + 4*j**2 + 2*j + 3. Let w = -181 + 185. Let y(d) = -3*d**2 - 2*d - 3. Let q(m) = w*z(m) + 5*y(m). Factor q(h).
(h - 1)*(h + 3)
Let v(o) = o**4 - o**3 - o**2 - 2*o - 1. Let u(w) = w**5 - 14*w**4 + 26*w**3 - 4*w**2 - 9*w + 24. Let n(k) = -u(k) - 6*v(k). Find i, given that n(i) = 0.
-1, 1, 2, 3
Let w(j) be the second derivative of 0*j**3 - 3/70*j**7 + 1/25*j**5 - 12*j - 1/30*j**4 + 0*j**2 + 0 + 3/100*j**6. Solve w(g) = 0 for g.
-2/3, 0, 1/2, 2/3
Let l(g) = -g**3 - 12*g**2 - g - 12. Suppose -3*h - p = -2*h + 8, h = -4*p + 4. Let o be l(h). Factor o - 2*j**2 + 2 + 3*j**2 + 3*j.
(j + 1)*(j + 2)
Let b(r) = -r**3 + 13*r**2 + 14*r + 2. Let i be b(14). Determine l, given that 5*l**3 - 7*l**3 + 4*l**2 - 5 + i*l + 1 = 0.
-1, 1, 2
Let a be 2*1*(-9)/6. Let z be -1 + a/12*-7. Solve 3/4*p**2 + 0 + z*p = 0 for p.
-1, 0
Let t(g) be the second derivative of g**4/4 - 7*g**3/2 + 18*g**2 + 2*g + 18. Find h such that t(h) = 0.
3, 4
Let p(a) be the first derivative of -3*a**4/10 - 28*a**3/15 - 7*a**2/5 + 8*a/5 + 143. Let p(t) = 0. Calculate t.
-4, -1, 1/3
Let d(c) be the second derivative of 0*c**2 - 4*c + 1/60*c**5 + 0 - 1/18*c**3 + 0*c**4. Factor d(t).
t*(t - 1)*(t + 1)/3
Suppose -21 - 21 = -3*c. Let n be 112/(-98)*c/(-10). Factor 48/5*k - 12/5*k**3 + n*k**2 - 32/5.
-4*(k - 2)*(k + 2)*(3*k - 2)/5
Let x = -2324/5 + 465. Let y(c) be the first derivative of x*c**5 + 5 - 1/3*c**3 + 1/6*c**6 - 1/4*c**4 + 0*c + 0*c**2. Solve y(z) = 