 5. Suppose j(o) = 0. What is o?
-2, 0
Factor -10/3*u**4 + 0 - 2/3*u**5 + 0*u - 4*u**3 + 0*u**2.
-2*u**3*(u + 2)*(u + 3)/3
Solve 5*m**4 - 48 - 85*m - 30*m**3 - 8*m**4 - 99*m**2 - 35*m = 0 for m.
-4, -1
Let g(u) = 6 - 12*u + 0 + 3*u. Let s(q) = -q**2 + 18*q - 12. Let b be 1/5 - 32/10. Let n(z) = b*s(z) - 5*g(z). Find y such that n(y) = 0.
1, 2
Let t(c) be the third derivative of -c**11/498960 + c**9/90720 + c**5/20 - c**2. Let h(g) be the third derivative of t(g). Suppose h(x) = 0. Calculate x.
-1, 0, 1
Let z(t) = t**2 - 7*t + 12. Let u be z(5). Factor 4/9 + 8/9*j**u + 2/9*j**3 + 10/9*j.
2*(j + 1)**2*(j + 2)/9
Let u(t) = 4*t**2 - 17*t + 3. Let s(h) = 2*h**2 - 8*h + 2. Let r(l) = -5*s(l) + 2*u(l). Find a such that r(a) = 0.
1, 2
Factor 2*n**4 - 5*n**4 - 4*n + 2*n + 2*n**3 + n**4 + 2*n**2.
-2*n*(n - 1)**2*(n + 1)
Let p(d) = -d**2 + 1. Let a be p(0). Let w be (-2)/4*(1 - a). What is r in 1/2*r**2 + 0*r**3 + 1/4*r**5 + w - 1/2*r**4 - 1/4*r = 0?
-1, 0, 1
Let m(i) = -2*i + 7. Let v be m(7). Let b = 11 + v. Suppose -4*r**3 - b*r**2 + 4*r**3 + 2*r**4 + 2 = 0. Calculate r.
-1, 1
Let v = 8 - 5. Factor t + t**2 - 5*t**3 + 9*t**v - 1 - 5*t**3.
-(t - 1)**2*(t + 1)
Let w(v) be the second derivative of v**6/165 - 3*v**5/110 + v**4/33 - 22*v. Determine j, given that w(j) = 0.
0, 1, 2
Let a(g) be the first derivative of g**4/6 - 4*g + 2. Let i(f) be the first derivative of a(f). Factor i(w).
2*w**2
Let v(f) be the third derivative of -f**5/660 + f**4/88 - 26*f**2. Factor v(w).
-w*(w - 3)/11
Let l(n) be the first derivative of -3*n**4/4 - 3*n**3 + 3*n**2/2 + 9*n + 5. Find p such that l(p) = 0.
-3, -1, 1
Suppose 2*z + 6*y + 21 = y, -3*z + 3*y = -21. Factor 2*s**2 - s**z - 3*s + 2*s**3 - 1 + s**3 + 0*s**3.
(s - 1)*(s + 1)*(3*s + 1)
Let f = 1066 - 2173/2. Let w = f + 21. Factor -3/4*p + 1/4*p**2 + w.
(p - 2)*(p - 1)/4
Let i(y) be the first derivative of y**8/1400 + y**7/420 + y**6/450 + y**3 - 2. Let n(k) be the third derivative of i(k). Factor n(q).
2*q**2*(q + 1)*(3*q + 2)/5
Solve 3/5*i**2 + 3/5*i**3 + 0 + 0*i = 0.
-1, 0
Let w be (-3 + 104/36)*-6. Let o(c) be the first derivative of 0*c + w*c**3 - c**2 - 2. Factor o(z).
2*z*(z - 1)
Let c(x) = -x**2 + x - 1. Let v(r) = 2*r**4 + 15*r**2 - 19*r + 3. Let f(s) = 3*c(s) + v(s). Let o(i) = i**3 - i**2. Let d(p) = f(p) - 12*o(p). Factor d(j).
2*j*(j - 2)**3
Let l(u) be the second derivative of u**7/1680 + u**6/96 + u**5/20 + 5*u**4/12 - 6*u. Let v(y) be the third derivative of l(y). Solve v(i) = 0.
-4, -1
Let p(b) be the first derivative of -b**4/20 - 2. Factor p(z).
-z**3/5
Let v(n) be the second derivative of -n**4/3 - 4*n**3/3 + 16*n**2 + 4*n - 4. Factor v(p).
-4*(p - 2)*(p + 4)
Let p(j) = 3*j**3 + 2. Let b(x) = -16*x**3 - 11. Suppose -2*w + 5*v = 22, 2*v + 5 = -3*w - 9. Let u(d) = w*b(d) - 33*p(d). Let u(y) = 0. What is y?
0
Let c(r) be the second derivative of -r**8/560 - r**7/280 + r**6/60 - 4*r**3/3 - 3*r. Let f(w) be the second derivative of c(w). Factor f(j).
-3*j**2*(j - 1)*(j + 2)
Suppose -1931 = -5*o - 26. Let m = -2659/7 + o. Find h, given that -2/7 + m*h**3 - 12/7*h**2 + 8/7*h - 2/7*h**4 = 0.
1
Let u = -1 + 1. Suppose -y + 21 = 2*y. Find t, given that u - 5*t**2 + 0 - 2*t + y*t**3 = 0.
-2/7, 0, 1
Suppose 7*i + 120 = 3*i. Let z be (-6)/15 + (-22)/i. Suppose -z*w + 2/3*w**2 + 0 = 0. Calculate w.
0, 1/2
Let x(i) be the second derivative of 1/30*i**5 + 1/12*i**3 + 0 + 1/2*i**2 - 1/12*i**4 - 2*i. Let a(d) be the first derivative of x(d). Solve a(w) = 0.
1/2
Suppose 5*b = -2*x + 62, -b + 16 = 2*x + 2*x. Factor 2*k**2 - 4*k - 21 - 3*k**2 + b - 2*k.
-(k + 3)**2
Let l(z) be the second derivative of -z**6/120 - z**5/40 + z**4/12 + z**3/12 - 3*z**2/8 + z. Determine a, given that l(a) = 0.
-3, -1, 1
Suppose 0 = 19*y + 113 - 170. Factor -7*g**2 + y*g**3 + 16/3*g - 4/3.
(g - 1)*(3*g - 2)**2/3
Let l be (2/5)/((-6)/(-60)). Suppose x**3 - x**l + x**2 - x**2 - 2*x + x + x**2 = 0. Calculate x.
-1, 0, 1
Let x(t) = t**2 - 1. Let o be x(-2). Determine k, given that 0*k**4 - 6*k**o + 3*k**4 + 2 - 2 = 0.
0, 2
Let z(s) be the first derivative of -s**5/210 + s**4/28 - 2*s**3/21 + 2*s**2 - 1. Let l(u) be the second derivative of z(u). Determine a, given that l(a) = 0.
1, 2
Let w be (1 + 1)*(-9)/(-2). Let z = -9 + w. Factor z - 2/3*i**2 - 1/3*i**3 - 1/3*i.
-i*(i + 1)**2/3
Suppose j - 4 + 2 = 0. Let q be j/((-1 + 2)/1). Suppose 2*m**2 + 2*m + q + 6 + 5*m + m = 0. Calculate m.
-2
Suppose -4*z + j = -16, -9 = z + 2*j + j. Let m(w) be the first derivative of 1/4*w**4 - 1/2*w**2 + 0*w - 2 + 0*w**z. Solve m(c) = 0 for c.
-1, 0, 1
Let s be 36/(-12) + (1 - -4). Determine q, given that 0 - 15/4*q**s - 3*q**3 - 3/4*q**4 - 3/2*q = 0.
-2, -1, 0
Let y be 4*((-15)/(-6) - 2). Suppose -6 = -4*b + y. Suppose -2 + 2*l**5 - 2*l**2 - b*l - 4*l + 4*l**3 - 2*l**2 + 6*l**4 = 0. What is l?
-1, 1
Let j(i) be the third derivative of i**5/15 + i**4/6 - 4*i**3/3 - 2*i**2. Suppose j(r) = 0. What is r?
-2, 1
Let m be 1/(-4) - 871/312. Let z = m - -35/8. Factor 7/3*x**2 + 2/3*x + z*x**3 - 1/3.
(x + 1)**2*(4*x - 1)/3
Let q(d) be the third derivative of 0*d**4 + 0*d**3 + 0*d + 1/120*d**5 + 1/240*d**6 + 0 + 3*d**2. Factor q(i).
i**2*(i + 1)/2
Let l = 7/4 - 3/2. Suppose 3*f - 6 = 0, 6 = 5*x - 4*f - 6. Factor -l - 1/4*m**x + 0*m + 0*m**3 + 1/2*m**2.
-(m - 1)**2*(m + 1)**2/4
Let n(y) = -y**3 - 10*y**2 - 11*y - 1. Let d be n(-9). Suppose 4*l = -9 + d. Suppose 0*m**l - 2/5*m + 0 + 2/5*m**3 = 0. Calculate m.
-1, 0, 1
Let s(w) = 4*w - 2. Let k be s(2). What is x in -3*x**5 + 4*x**4 - 6*x**2 + 3 + k*x**3 + 2*x**4 - 3*x - 4*x**4 + x**4 = 0?
-1, 1
Let m(r) = 4*r + 6*r**2 - 2*r**4 + r**4 - r**4 - 6. Let j(s) = 8*s**4 - s**3 - 24*s**2 - 17*s + 25. Let b(x) = 2*j(x) + 9*m(x). Factor b(g).
-2*(g - 1)**2*(g + 1)*(g + 2)
Let b = 18 + -13. Let f(l) be the first derivative of -4/3*l**b - 1/18*l**3 + 0*l - 4/3*l**6 - 1 + 0*l**2 - 11/24*l**4. Factor f(n).
-n**2*(3*n + 1)*(4*n + 1)**2/6
Let b(k) = 3*k**2 - 11*k + 5. Let y(s) = -s + 1. Let c(q) = -b(q) + 5*y(q). Determine r, given that c(r) = 0.
0, 2
Factor 0 - 49/4*a**4 + 9*a + 133/4*a**3 - 30*a**2.
-a*(a - 1)*(7*a - 6)**2/4
Let u(y) = y**2 - 5*y + 3. Let b be u(4). Let x be b/(-4) + (-25)/(-20). Factor 1/2 + 1/2*a**5 - x*a + a**3 + a**2 - 3/2*a**4.
(a - 1)**4*(a + 1)/2
Let l = 13 - 11. Find n such that -1/4*n**l + 0 + 0*n = 0.
0
Let b be 109/(-24) - 8/(-12). Let g = 171/40 + b. Suppose 0*l + 0*l**3 - g*l**2 + 2/5*l**4 + 0 = 0. Calculate l.
-1, 0, 1
What is v in -40*v**2 - 35*v - 3 - 3 - 15*v**3 + 0 - 4 = 0?
-1, -2/3
Determine l so that 1/3*l**3 + 1/3*l + 0 + 2/3*l**2 = 0.
-1, 0
Let g(n) = -4*n - 4. Let l be g(-2). Let d(r) be the second derivative of -2*r + 1/2*r**2 + 0 - 1/2*r**3 + 1/4*r**l - 1/20*r**5. Factor d(m).
-(m - 1)**3
Let t(q) be the second derivative of -q**5/20 - q**4/12 + q**3/3 + 5*q. Let t(p) = 0. Calculate p.
-2, 0, 1
Solve -96/5*n**3 - 128/5*n + 176/5*n**2 + 32/5 + 18/5*n**4 = 0.
2/3, 2
Let i(f) be the second derivative of 5*f + 0 - 1/6*f**4 + 0*f**2 - 1/3*f**3. Factor i(r).
-2*r*(r + 1)
Find m such that -2 + 8*m**4 - m + 0*m**4 - 8*m**4 - m**4 + m**3 + 3*m**2 = 0.
-1, 1, 2
Let z(d) be the second derivative of -d**8/20160 - d**7/1512 - d**6/270 - d**5/90 + d**4/3 + 3*d. Let m(w) be the third derivative of z(w). Factor m(o).
-(o + 1)*(o + 2)**2/3
Suppose -x - 400 + 406 = 0. Let n(w) be the third derivative of 0*w**4 + 0*w**3 + 1/60*w**x - 2*w**2 + 0*w + 0 + 0*w**5. Factor n(t).
2*t**3
Let h(d) be the third derivative of -1/72*d**4 + 0 + 4*d**2 + 0*d**3 - 1/630*d**7 + 1/180*d**5 + 0*d + 1/360*d**6. Find z, given that h(z) = 0.
-1, 0, 1
Factor 2 + 5*m**3 - 12 - 5*m + m**2 + 9*m**2.
5*(m - 1)*(m + 1)*(m + 2)
Let q(f) be the second derivative of f**10/6048 + 17*f**9/15120 + f**8/420 + f**7/630 + 2*f**4/3 - 2*f. Let s(c) be the third derivative of q(c). Factor s(w).
w**2*(w + 1)*(w + 2)*(5*w + 2)
Suppose -20 = 5*p, 2*p = -5*g + p + 11. Suppose -u - 4 = -g*u. Factor u*b**5 + 0*b**3 - 2*b**3 + 0*b**2 + b**4 - b**2.
b**2*(b - 1)*(b + 1)*(2*b + 1)
Let a(w) = 4*w**4 - 8*w**2 + 4. Let u(h) = 7*h**4 - h**3 - 15*h**2 + h + 8. Let r(b) = -11*a(b) + 6*u(b). Find m, given that r(m) = 0.
-2, -1, 1
Let a(r) be the third derivative of -r**8/756 - 2*r**7/315 - r**6/270 + r**5/45 + r**4/27 + 22*r**2. Determine b, given that a(b) = 0.
-2