2. Suppose g(c) = 0. Calculate c.
-3, 5
Let w(t) be the first derivative of 11*t**7/3360 + t**6/72 + 7*t**5/480 - t**4/48 - t**3 - 13. Let p(z) be the third derivative of w(z). Factor p(l).
(l + 1)**2*(11*l - 2)/4
Let l(h) = -2*h**3 + h**2 - h. Let r(p) = -5*p**3 - 5*p**2 - 12*p. Let y(b) = -3*l(b) + r(b). Determine v, given that y(v) = 0.
-1, 0, 9
Factor 2*k**2 - 23852 + 23904 + 7*k - 61*k.
2*(k - 26)*(k - 1)
Let q(l) be the first derivative of -l**7/336 - l**6/96 + l**5/12 - 5*l**4/32 - 11*l**3/3 + 5. Let g(y) be the third derivative of q(y). Factor g(f).
-5*(f - 1)*(f + 3)*(2*f - 1)/4
Let l be -16 + ((-10500)/(-45))/14. Factor 0 - 1/6*n**2 - l*n.
-n*(n + 4)/6
Let r(j) = 4*j**2 + 106*j + 3. Let v(g) = -2*g**2 - 106*g - 2. Let a(m) = -2*r(m) - 3*v(m). Find u, given that a(u) = 0.
0, 53
Suppose 8 = b + 3*c, -2 = -3*c + 4. Factor -n - b - 11*n - n - 11*n**2.
-(n + 1)*(11*n + 2)
Let x(h) = h**2 + 45*h + 78. Let m(t) = -5*t**2 - 226*t - 388. Let w(f) = 2*m(f) + 11*x(f). Factor w(s).
(s + 2)*(s + 41)
Let s be (-1007)/(-21) + -1*(-6)/(-21). Let v = 48 - s. Suppose 0*l + 0 + v*l**3 + 1/3*l**4 - 1/3*l**5 - 1/3*l**2 = 0. What is l?
-1, 0, 1
Let c be (12/(-14))/((-2)/266). Let b be (c/(-18) - -3) + (-1 - -5). Factor 2/9*n**4 + 2/9*n**2 + 2/3*n - 4/9 - b*n**3.
2*(n - 2)*(n - 1)**2*(n + 1)/9
Suppose 5*c = -4*k + 2, 3*c + 0*k = 2*k + 10. Suppose -4*d - t + 1 = -c*d, -3*d = 2*t. Factor 3/4*v**d + 6*v + 12.
3*(v + 4)**2/4
Let 828*d**2 - 24*d**3 + 105/2 + 837/2*d = 0. Calculate d.
-1/4, 35
Let h be 264/28 - 11/(462/18). Let q(y) be the third derivative of 0*y**3 + 0*y**4 - 1/120*y**5 + 0*y**6 + 0 + 1/420*y**7 + h*y**2 + 0*y. Factor q(s).
s**2*(s - 1)*(s + 1)/2
Let -3/2*p**4 + 0 - 45/2*p**2 + 0*p - 12*p**3 = 0. Calculate p.
-5, -3, 0
Let l(w) = -116*w - 691. Let y be l(-6). Factor 5/2 - 5*k**3 + 5/2*k**y + 5/2*k**4 + 5/2*k - 5*k**2.
5*(k - 1)**2*(k + 1)**3/2
Let l(t) be the first derivative of t**3/15 - 29*t**2/5 + 456. Factor l(h).
h*(h - 58)/5
Let j = -11 - -18. Suppose 0 = m - 9 + j. Suppose -5*p - 3*p + 11*p - 3*p**m = 0. What is p?
0, 1
Let x(g) = -4*g**2 + 12*g - 21. Let j be x(2). Let t(v) = 8*v + 104. Let l be t(j). Factor l - 1/3*c**2 + 0*c.
-c**2/3
Let x = -151 + 216. Let f be x/(-13)*2/(-5). Suppose -s**2 - 7*s - f*s**2 + 4*s = 0. What is s?
-1, 0
Let f(q) be the third derivative of q**8/28 - 34*q**7/105 + q**6 - 4*q**5/5 - 4*q**4/3 + 204*q**2. Factor f(c).
4*c*(c - 2)**3*(3*c + 1)
Suppose 0 = 3*a - 3*u - 21, 12 = 4*a - 3*u - 13. Suppose a*z - 5 - 3 = 4*q, -2*z + 4 = -4*q. Factor 0*m - z*m**3 + 0 - 4/5*m**2 - 8/5*m**4 - 2/5*m**5.
-2*m**2*(m + 1)**2*(m + 2)/5
Let i(v) be the second derivative of 4*v - 9/2*v**2 + 0 + 1/30*v**5 - 1/135*v**6 - 1/18*v**4 + 1/27*v**3. Let p(k) be the first derivative of i(k). Factor p(z).
-2*(z - 1)**2*(4*z - 1)/9
Let p(k) = 3*k + 57. Let u be p(-18). Let c(w) be the first derivative of 2/11*w + 2 - 2/11*w**2 + 2/33*w**u. Solve c(i) = 0 for i.
1
Let n(c) be the third derivative of -c**8/48 + 4*c**7/105 + c**6/24 - c**5/10 - 224*c**2. Determine k, given that n(k) = 0.
-6/7, 0, 1
Let a(p) = 2*p**2 + 2*p. Let q(h) be the first derivative of 2*h**3/3 + 3*h**2/2 + 12. Let d(v) = -5*a(v) + 4*q(v). Factor d(j).
-2*j*(j - 1)
Let o = 22 - 19. Let p(f) be the second derivative of 1/30*f**5 - 1/30*f**6 + 1/18*f**4 + 1/6*f**2 - 5*f + 1/126*f**7 + 0 - 1/6*f**o. Factor p(d).
(d - 1)**4*(d + 1)/3
Suppose -3*a - 1 - 18 = -5*d, 3*a = 2*d - 13. Factor -186*g**4 - 3*g**2 + 4*g - 9*g**d + 11*g**3 + 183*g**4.
-g*(g - 2)*(g - 1)*(3*g - 2)
Let l(q) be the first derivative of q**8/1680 - q**7/210 + q**6/72 - q**5/60 + 10*q**3/3 + 3. Let w(y) be the third derivative of l(y). Factor w(i).
i*(i - 2)*(i - 1)**2
What is n in -22*n - 10*n + 487*n**3 - 4*n**4 - 491*n**3 + 40*n**2 = 0?
-4, 0, 1, 2
Let f be 14 + -1 + 0 + 1. Determine p, given that f*p - p**4 - 2*p**3 - 14*p + 4*p**3 = 0.
0, 2
Solve 4*t**2 - 63*t + 11664 - 147*t - 50*t - 58*t - 114*t = 0.
54
Find f such that -152/3*f**2 - 100/3 - 12/5*f**4 + 70*f + 2/15*f**5 + 244/15*f**3 = 0.
1, 2, 5
Let h(k) = -k**3 + 4*k**2 - 7*k + 14. Let r be h(3). Determine a, given that 6*a**2 + 9*a**2 - 6*a**r - 2*a**2 + 2*a = 0.
-2/7, 0
Let l = -25 + 27. Suppose 2*g + 5*g**3 - 7*g**l + 6 - 1 - 2 - 3*g = 0. What is g?
-3/5, 1
Let r(i) be the first derivative of i**6/3 - 28*i**5/5 + 13*i**4/2 + 168*i**3 + 324*i**2 - 816. Suppose r(f) = 0. Calculate f.
-2, 0, 9
Let w(p) be the first derivative of 3*p**4/4 - 78*p**3 + 450*p**2 - 888*p + 608. Factor w(m).
3*(m - 74)*(m - 2)**2
Let y be (52/(-78))/(2/(-12)). Let b be 6 + (-9)/(18/y). Find w, given that 2*w**3 + 2/3*w**2 - 2*w + 2/3*w**b - 4/3 = 0.
-2, -1, 1
Let k(w) be the first derivative of 3*w - 6*w**2 - 3*w**4 + 3/5*w**5 + 6*w**3 - 30. Find y, given that k(y) = 0.
1
Suppose 2*v + 15 = -t - 3*v, 2*t + 4*v + 12 = 0. Suppose 517*k = -3*z + 521*k + 26, -17 = -z + 3*k. Factor -8/13 + 2/13*c**z + t*c.
2*(c - 2)*(c + 2)/13
Let c = 25 - 12. Suppose -5 = -9*w + c. Find s, given that 0 - 2/3*s**w - 2/9*s**4 - 2/3*s**3 - 2/9*s = 0.
-1, 0
Let t(o) be the first derivative of 21 + 1/5*o**2 - 1/15*o**3 + 3/5*o. Suppose t(s) = 0. Calculate s.
-1, 3
Let r = 48 - 45. Solve -4*y**2 - 8*y + 2*y**r + 5*y**3 - 3*y**3 = 0 for y.
-1, 0, 2
Suppose -5*p = -20, 4*t - 3*p = 4 + 4. Let o be 146*t/(-150) - -5. Factor 0 - o*f**2 + 2/15*f.
-2*f*(f - 1)/15
Let l = 52 + -466/9. Solve -l - 2/9*z + 2/9*z**2 + 2/9*z**3 = 0.
-1, 1
Let z(r) be the second derivative of -1/200*r**6 + 0*r**2 + 2/3*r**3 - 1/100*r**5 + 0 + 2*r + 1/40*r**4. Let f(x) be the second derivative of z(x). Factor f(p).
-3*(p + 1)*(3*p - 1)/5
Let j(w) be the first derivative of 2/3*w**2 + 5/3*w - 25 - 1/9*w**3. Suppose j(y) = 0. What is y?
-1, 5
Factor 1/6*b**2 - 10 - 2/3*b.
(b - 10)*(b + 6)/6
Factor 212/5*w - 8 + 44/5*w**2.
4*(w + 5)*(11*w - 2)/5
Let o(t) = 24*t**2 + 117*t + 13. Let f(r) = 15*r**2 + 58*r + 6. Let i(a) = 10*f(a) - 4*o(a). Factor i(l).
2*(l + 2)*(27*l + 2)
Let f(n) = n**3 - n**2 - 1. Let v(w) = 5*w**4 + 105*w**3 + 445*w**2 + 870*w + 480. Let u(k) = -15*f(k) + v(k). Suppose u(z) = 0. Calculate z.
-11, -3, -1
Suppose -7 = -2*q + 3*q + 2*r, -5*q - r = -10. Suppose 0*k = q*k - 6. Factor 15*o**3 - 1 - 5*o**k + 5*o**5 - 3 + 4 - 15*o**4.
5*o**2*(o - 1)**3
Let k(h) be the first derivative of 2*h**6/7 - 8*h**5/7 - 30*h**4/7 + 80*h**3/21 + 54*h**2/7 - 40*h/7 - 141. Determine p, given that k(p) = 0.
-2, -1, 1/3, 1, 5
Let g(s) be the third derivative of -s**8/840 - 2*s**7/525 + s**6/75 + s**5/75 - s**4/20 - 25*s**2. Suppose g(l) = 0. Calculate l.
-3, -1, 0, 1
Let p(f) be the second derivative of 0 + 7*f + 1/140*f**5 + 2/7*f**2 + 1/42*f**4 - 1/6*f**3. Find z, given that p(z) = 0.
-4, 1
Factor -2*a**5 - 28*a**2 + 3*a**4 - a**4 + a**5 + 28*a**2 + 8*a**3.
-a**3*(a - 4)*(a + 2)
Let p(h) be the second derivative of h**7/168 - h**6/60 - 3*h**5/80 + h**4/12 + h**3/6 + 43*h. Find j such that p(j) = 0.
-1, 0, 2
Let z be 18/15 + (-26)/30. Find q, given that -8*q**2 - 512/3 + z*q**3 + 64*q = 0.
8
Factor -104*d + 2 + 8*d**2 + 32*d + 40*d + 42*d.
2*(d + 1)*(4*d + 1)
Let g(v) be the second derivative of v**3/3 - 4*v**2 - 3*v. Let z be g(6). Solve 5*n**4 + 8*n - n**z - 8*n**3 + 0 - 4 = 0.
-1, 1
Let u(i) be the second derivative of -22*i + 0*i**4 + 0*i**2 + 1/70*i**6 + 0 - 3/70*i**5 + 0*i**3. Factor u(q).
3*q**3*(q - 2)/7
Let m = 17 - 13. Factor m*f - 2 - 9*f + 5*f**2 - 3 + 5*f**3.
5*(f - 1)*(f + 1)**2
Let z(f) be the third derivative of 0*f + 1/9*f**4 - 19*f**2 + 8/9*f**3 + 0 + 1/360*f**6 - 7/180*f**5. Factor z(w).
(w - 4)**2*(w + 1)/3
Let 8*f**4 + 36*f**2 - 291*f**5 - f**4 + 48*f**3 - f**4 + 3*f**4 + 288*f**5 = 0. Calculate f.
-2, -1, 0, 6
Let m be (-34)/(-10) + 2/(-5). Solve 16*d + 8 + 5*d**2 - d + m - 1 = 0.
-2, -1
Let v(i) be the third derivative of -i**5/510 + 5*i**4/204 - 4*i**3/51 + 21*i**2. Factor v(c).
-2*(c - 4)*(c - 1)/17
Suppose 0 = -4*d - 32, -243*i + 238*i + 2*d + 16 = 0. Factor 0 - 1/3*h**3 + 4/3*h**2 + i*h.
-h**2*(h - 4)/3
Let b(x) be the first derivative of -x**5/4 + 5*x**4/6 - 5*x**3/6 + 16*x - 19. Let m(z) be the first derivative of b(z). Factor m(r).
-5*r*(r - 1)**2
Let p(g) = g**2 - g - 4. Let w(f) = 2*f**2 - 34*f - 70. Let r(n) = -3*p(n) + w(n). Suppose r(d) = 0. What is d?
-29, -2
Let n be (-70)/112 + 85/40 + 0. Dete