h). Factor g(p).
-5*p*(p - 2)*(p - 1)*(p + 1)
Let c(g) = -10*g - 80. Let i(b) = -40*b - 318. Let w(l) = -9*c(l) + 2*i(l). Let j be w(-8). Factor 18*a**4 + j*a**5 + 9*a**2 + a + 97/4*a**3 + 0.
a*(a + 2)**2*(4*a + 1)**2/4
Let f(x) be the third derivative of -x**6/45 + x**5/20 + 5*x**4/24 - x**3/9 + x**2 - 33*x. Factor f(z).
-(z - 2)*(z + 1)*(8*z - 1)/3
Let 2*o**2 + 6/5*o - 18/5 + 2/5*o**3 = 0. Calculate o.
-3, 1
Suppose -3*n - 2*c = 0, 11*n = 9*n - 5*c. Factor 1/5*l**2 - 1/5*l + n.
l*(l - 1)/5
Let x(l) = 5*l**4 - 20*l**3 + 21*l**2 + 6*l - 6. Let h(i) = 5*i**4 - 20*i**3 + 20*i**2 + 5*i - 5. Let r(w) = -6*h(w) + 5*x(w). Solve r(a) = 0.
0, 1, 3
Let o(q) be the third derivative of -q**6/80 + q**5/10 - 5*q**4/16 + q**3/2 - 95*q**2. Find k, given that o(k) = 0.
1, 2
Let u be (30/(-40))/(-2 + (-39)/(-24)). Factor x - 8 + 2*x + 33*x - 12*x**u - 4*x**2.
-4*(x - 2)*(4*x - 1)
Let m(b) be the second derivative of b**8/30240 + 2*b**7/2835 - b**6/3240 - 2*b**5/135 - 5*b**4/3 - 2*b. Let v(z) be the third derivative of m(z). Factor v(c).
2*(c - 1)*(c + 1)*(c + 8)/9
Let l(j) = j**2. Let p(s) = 24*s**2 + 16 - 5*s**2 + 16*s + s**2. Let h(b) = b**3 + 9*b**2 + 15*b + 8. Let v be h(-7). Let o(c) = v*p(c) - 16*l(c). Factor o(g).
4*(g + 2)**2
Let x(j) be the first derivative of -7/3*j**3 + 8 + 7*j + 3/2*j**4 + 1/15*j**6 - 1/2*j**5 + 2*j**2. Let z(i) be the first derivative of x(i). Factor z(h).
2*(h - 2)*(h - 1)**3
Let b(x) = 4 - 20*x**2 - 11*x**3 - 6 + 24*x**2 - 4 + 6*x. Let u(m) = 21*m**3 - 9*m**2 - 11*m + 11. Let s(o) = 11*b(o) + 6*u(o). Factor s(y).
5*y**2*(y - 2)
Let o be (96/20)/4*5. Let m be 7/(-2)*o*(-22)/231. Determine p so that 0 + 4/3*p**m + 0*p = 0.
0
Let d be (-6)/8 + (-575)/(-100). Let -163*v + 0*v**d + 163*v + v**5 = 0. Calculate v.
0
Suppose 10*v = 4*v + 24. Suppose -x + 7 = r - 0, 4*x = 4*r + v. Find k, given that 4/3*k**r + 0*k**2 - 16/3*k + 0 = 0.
-2, 0, 2
Suppose 0 = -z + 12*z - 7*z. Let i(s) be the first derivative of -1/12*s**4 - 2 + 1/15*s**5 + 1/6*s**2 - 1/9*s**3 + z*s. Factor i(a).
a*(a - 1)**2*(a + 1)/3
Suppose 0 = 4*b - 3*m - 31, b - 4*b + 15 = -5*m. Let p = 61 + -56. Factor 2*f + b - p*f - 2*f + 0*f**2 - 5*f**2.
-5*(f - 1)*(f + 2)
Let b = -1 - -3. Suppose 97 + 29 = 21*a. Find u, given that -4 - a*u**2 + 2*u**2 + 3*u**2 + 3*u**2 + b*u = 0.
-2, 1
Let c(b) = -7*b**4 + 4*b**3 + 3*b**2 - 4*b - 4. Let v(p) = -1 - 457*p - p**4 + 0 + 456*p + p**3. Let d(h) = c(h) - 4*v(h). Factor d(i).
-3*i**2*(i - 1)*(i + 1)
Let p(q) be the third derivative of 0 + 1/40*q**6 + 20*q**2 - 5/8*q**4 + 0*q + 1/20*q**5 + 3/2*q**3. Let p(z) = 0. What is z?
-3, 1
Suppose -4/5*t**4 + 0*t + 0 + 0*t**2 + 16/5*t**3 = 0. Calculate t.
0, 4
Let b(p) be the second derivative of 4/9*p**3 + 1/45*p**6 + 0 + 1/3*p**4 + 2/15*p**5 + 5*p + 1/3*p**2. Suppose b(t) = 0. What is t?
-1
Let u = 1452 + -1452. What is j in u*j + 0 - 1/5*j**3 + 4/5*j**2 = 0?
0, 4
Let h(v) be the second derivative of v**4/78 + 436*v**3/39 + 47524*v**2/13 + 133*v - 1. Suppose h(m) = 0. What is m?
-218
Suppose -17*q + 52*q = 35. Let t(f) be the first derivative of -q + 2/9*f**3 + 0*f**2 + 0*f + 2/15*f**5 - 1/3*f**4. Factor t(n).
2*n**2*(n - 1)**2/3
Let d(k) = k. Let x(l) = l**2 - 159*l. Let y(i) = 4*d(i) + x(i). Solve y(s) = 0.
0, 155
Factor -44*m**2 + 322*m - 2*m**4 - 98 - 229*m - 24*m**3 + 75*m.
-2*(m - 1)**2*(m + 7)**2
Let v be (3*(-1)/(-6))/((-40)/(-240)). Factor -z + 2/5 + 4/5*z**2 - 1/5*z**v.
-(z - 2)*(z - 1)**2/5
Suppose 40*i - 38*i = -24. Let x be (30/44 - -1) + i/8. Suppose -x*f**2 - 10/11*f - 8/11 = 0. What is f?
-4, -1
Let p(t) be the second derivative of -t**5/20 + t**4/2 - 5*t**3/6 - 4*t. Let k be p(5). Let k + m + 1/2*m**2 = 0. What is m?
-2, 0
Let g(m) = 38*m**3 - 37*m**2 - 19*m + 30. Let s(n) = -455*n**3 + 445*n**2 + 230*n - 360. Let j(d) = 35*g(d) + 3*s(d). Factor j(i).
-5*(i - 1)**2*(7*i + 6)
Let i(a) be the first derivative of a**5/12 - 5*a**4/18 + 5*a**3/18 + a**2/2 + 17. Let p(f) be the second derivative of i(f). Factor p(v).
5*(v - 1)*(3*v - 1)/3
Let z = 100 - 97. Let r be (z/((-6)/(-2)))/(3/12). Factor 6/7*u**3 + 2/7*u**r + 0 + 0*u + 4/7*u**2.
2*u**2*(u + 1)*(u + 2)/7
Let c(s) = s**4 + s**3 - s**2 + s - 1. Let y(m) = 8*m**4 + 5*m**3 - 8*m**2 + 13*m - 9. Let b(a) = 18*c(a) - 2*y(a). Factor b(w).
2*w*(w - 1)*(w + 1)*(w + 4)
Let a be 1/(-630)*-5041 + -8. Let q(d) be the third derivative of 0 + 1/180*d**5 - 3*d**2 + 0*d - a*d**7 - 1/72*d**4 + 1/360*d**6 + 0*d**3. Factor q(g).
-g*(g - 1)**2*(g + 1)/3
Let q be ((-1)/24)/((-93)/744). Solve q*m + 1/3*m**2 - 2/3 = 0.
-2, 1
Let h be (2/7 + 0)/2. Let i(g) = g**3 - 20*g**2 - 17*g - 79. Let q be i(21). Factor 0 + h*v**q - 2/7*v**3 + 1/7*v + 0*v**2 + 0*v**4.
v*(v - 1)**2*(v + 1)**2/7
Let z(h) be the second derivative of h**6/120 - h**5/30 + h**4/24 - 4*h**2 - 5*h. Let s(t) be the first derivative of z(t). What is x in s(x) = 0?
0, 1
Let p(l) be the first derivative of -l**4/27 + 2*l**3/9 - 21*l - 3. Let q(i) be the first derivative of p(i). Factor q(c).
-4*c*(c - 3)/9
Factor -136*s**2 - 5668*s**3 + 48 + 5656*s**3 + 5*s - 9*s + 104*s.
-4*(s - 1)*(s + 12)*(3*s + 1)
Find g, given that -3*g**2 + 3*g - 319*g + 5*g**2 + 2*g**2 = 0.
0, 79
Let u = -247 - -249. Let a(y) be the first derivative of -y**3 + 9/4*y**4 + 0*y + 8 - 9/5*y**5 + 0*y**u + 1/2*y**6. Determine o, given that a(o) = 0.
0, 1
Let i(p) = -4*p - 2. Let t be i(-2). Let a(s) be the first derivative of -9*s - s**3 + t*s**2 - 1 - 1 + 1. Suppose a(l) = 0. What is l?
1, 3
Factor 68*h - 5*h**3 + 52*h + 206 + 14 - 105*h**2.
-5*(h - 2)*(h + 1)*(h + 22)
Let d(s) be the third derivative of s**5/20 + 5*s**4/4 - 11*s**3/2 + 54*s**2. Factor d(h).
3*(h - 1)*(h + 11)
Suppose -35*g + 8 = -31*g. Let u(l) be the third derivative of 0 - 1/210*l**5 - 1/21*l**3 - 3*l**g + 0*l - 1/42*l**4. Factor u(f).
-2*(f + 1)**2/7
Let i(j) = 15*j**4 + 96*j**3 - 30*j**2 - 11*j - 11. Let x(p) = -2*p**2 + 8*p**2 - 3*p**4 + 2*p - 13 + 15 - 19*p**3. Let h(u) = 6*i(u) + 33*x(u). Solve h(r) = 0.
-6, 0, 1/3
Suppose -i + 2*i + 6*i = 3*i. Determine m, given that -4/3*m**3 + 0*m**2 + 2*m**4 + 0 + i*m = 0.
0, 2/3
Let x(s) be the first derivative of s**4/2 - 12*s**3 + 60*s**2 - 112*s - 69. Factor x(q).
2*(q - 14)*(q - 2)**2
Let a(i) = i**4 + i**2 + i + 1. Let n(m) = -2*m**5 + 9*m**4 + 2*m**3 + 5*m**2 + 7*m + 7. Let y(z) = 14*a(z) - 2*n(z). Let y(x) = 0. Calculate x.
-1, 0, 1
Suppose -f = 1, -z + 1 = -4*z - 4*f. Let s(m) = 25*m**4 + 30*m**3 - 25*m**2 - 30. Let b(t) = t**4 + t**3 - t**2 - 1. Let v(r) = z*s(r) - 30*b(r). Factor v(q).
-5*q**2*(q - 1)*(q + 1)
Let o be 3/(-4) - (-135)/36. Factor 5*n**2 + 5*n**4 - 13*n**3 + 127*n - 127*n + o*n**3.
5*n**2*(n - 1)**2
Suppose h - g = 4*g + 23, 2*g + 14 = 2*h. Let n be ((-3)/6)/((-4)/24). Solve -2*b**4 - 11*b**2 - n*b - 5*b**4 - 3*b**3 + b - 13*b**h = 0 for b.
-1, -2/7, 0
Let n(h) = 5*h - 400. Let q be n(0). Let y be 2/8 + (-4)/(q/15). Factor 2/5*b + y*b**2 - 4/5.
2*(b - 1)*(b + 2)/5
Determine t, given that -3721 + 2817*t**2 + 122*t - 5626*t**2 + 2808*t**2 = 0.
61
Let n(k) = -97*k + 391. Let t be n(4). Factor 2/9*q**4 - 10/9*q**2 + 2/3*q**t + 4/9*q + 0 - 2/9*q**5.
-2*q*(q - 1)**3*(q + 2)/9
Let f(x) = -x**3 + 6*x**2 - 5*x + 5. Let i be f(2). Suppose -n = 3*b - i, b - 5*n - 3 = -10. Factor 0 - 4*p**2 - 4/3*p**4 + 4*p**b + 4/3*p.
-4*p*(p - 1)**3/3
Factor 34*l**3 + 336*l + 3 - 19*l**3 + 171*l**2 + 105.
3*(l + 2)*(l + 9)*(5*l + 2)
Let z(l) be the second derivative of -l**6/900 - l**5/300 + 25*l**3/6 + 36*l. Let m(n) be the second derivative of z(n). Let m(i) = 0. Calculate i.
-1, 0
Let j(m) be the second derivative of m**5/4 - 5*m**4/12 - 25*m**3/6 - 15*m**2/2 - 7*m - 3. Factor j(g).
5*(g - 3)*(g + 1)**2
Let j = -13233 + 2911309/220. Let k = -1/44 + j. Factor 3/5*h**5 - k*h + 8/5*h**4 + 0*h**2 + 0 + 6/5*h**3.
h*(h + 1)**3*(3*h - 1)/5
Let a be (59/(-8) - (-20 - -13))*-8. Factor 4/3*u**a - 4/3*u - 1/3 + 1/3*u**2.
(u - 1)*(u + 1)*(4*u + 1)/3
Let s(j) be the second derivative of -1/60*j**5 + 0 + 14*j + j**2 + 1/6*j**4 - 11/18*j**3. Factor s(n).
-(n - 3)*(n - 2)*(n - 1)/3
What is m in 6/13*m**4 + 0 - 2/13*m**3 - 6/13*m**2 + 2/13*m = 0?
-1, 0, 1/3, 1
Factor -182*i**3 + 111*i**2 + 169/2*i**4 + 1/2 - 14*i.
(i - 1)**2*(13*i - 1)**2/2
Let c be (2 + 39/(-18))/((-18)/60). Let t(u) be the first derivative of -4/3*u**2 - 1/1