(c). Find r such that q(r) = 0.
-702, -1
Let x = -64899742/21 + 3091241. Let t = x - 777. Suppose 2/21*d**3 - t*d - 2/7*d**2 + 0 + 2/7*d**4 = 0. What is d?
-1, -1/3, 0, 1
Let s(y) be the third derivative of 0*y**3 + 1/40*y**6 + 2 - 82*y**2 + 1/10*y**5 + 0*y - y**4. Factor s(q).
3*q*(q - 2)*(q + 4)
Let a(y) be the first derivative of y**4/16 + 7*y**3/12 - 7*y**2/2 + 5*y + 910. Let a(g) = 0. What is g?
-10, 1, 2
Let l(m) be the second derivative of 0 + 0*m**2 - 48*m - 1/6*m**4 - m**3. Find n such that l(n) = 0.
-3, 0
Suppose 11 = -2*a + 13, -2*a + 1124 = 3*t. Solve t - 438 - 11*k + 35*k + 4*k**2 = 0.
-8, 2
Factor 392/3*o**2 + 0*o + 1/3*o**5 + 140/3*o**3 - 26/3*o**4 + 0.
o**2*(o - 14)**2*(o + 2)/3
Let s(f) be the first derivative of f**4/2 - 22*f**3 + 216*f**2 - 800*f + 3121. Factor s(y).
2*(y - 25)*(y - 4)**2
Let b(p) be the first derivative of -36/5*p**5 - 8*p**4 - 84 + 4/3*p**6 + 56/3*p**3 - 20*p + 12*p**2. Determine x so that b(x) = 0.
-1, 1/2, 1, 5
Let u(i) be the first derivative of 2*i**3/3 + 139*i**2 - 280*i - 7. Let u(b) = 0. What is b?
-140, 1
Let r be -4 + (-84)/(-16) - (-102)/(-120). Let a be (4/(-20))/(2/(-6)). Factor a*n + 1/5*n**2 + r.
(n + 1)*(n + 2)/5
Factor -5/7*c + 92 - 1/7*c**2.
-(c - 23)*(c + 28)/7
Let b(g) be the first derivative of g**5/60 + g**4/2 + 10*g**3/3 + 63*g**2/2 + 176. Let d(w) be the second derivative of b(w). Factor d(u).
(u + 2)*(u + 10)
Let v(p) = -2*p**2 - 30*p. Let q(u) = 5*u**2 + 91*u. Suppose 2*g + 62 = -4*k, 2*k + 0*k + 22 = -4*g. Let x(d) = k*v(d) - 6*q(d). Let x(a) = 0. Calculate a.
0, 9
Let j(l) be the first derivative of -81 + 1/12*l**4 - 96*l + 16*l**2 + 22/9*l**3. What is i in j(i) = 0?
-12, 2
Let j(b) be the first derivative of 162 + 20/3*b**3 + 0*b + 0*b**2 - 5*b**4 + b**5. Factor j(i).
5*i**2*(i - 2)**2
Let x(k) = k**2 - k - 5. Let j be x(4). Let u(a) = -2*a**2 + 16*a - 10. Let g be u(j). Factor -2*m + 0*m**2 + 4*m + g*m**3 + 2*m - 8*m**2.
4*m*(m - 1)**2
Factor 22/3*p**3 + 32/3*p + 0 + 18*p**2.
2*p*(p + 1)*(11*p + 16)/3
Let s(z) be the third derivative of -z**5/42 - 2*z**4/7 - 16*z**3/21 + 100*z**2 + 4*z. Determine p, given that s(p) = 0.
-4, -4/5
Suppose 1673*k + 3007 - 2300*k**2 - 1457 + 2212*k - 15*k**3 = 0. Calculate k.
-155, -1/3, 2
Let w(s) = 12*s**4 + 1155*s**3 + 8118*s**2 + 90*s. Let m(f) = f**4 + 105*f**3 + 738*f**2 + 8*f. Let u(v) = 45*m(v) - 4*w(v). Factor u(z).
-3*z**2*(z - 41)*(z + 6)
Suppose -24 = 94*a - 106*a. Factor -11*o**5 - 116*o**a + 7*o**4 + o**3 - 146 - 270*o + 12*o**5 - 70 + 17*o**2.
(o - 4)*(o + 2)*(o + 3)**3
Let 206/3*h**2 + 16*h**3 + 2/3*h**4 + 104*h + 152/3 = 0. Calculate h.
-19, -2, -1
Let j(g) = -18*g**3 - 112*g**2 + 322*g - 220. Let t(x) = 4*x**3 + 22*x**2 - 64*x + 44. Let v(z) = -3*j(z) - 14*t(z). Factor v(n).
-2*(n - 11)*(n - 2)*(n - 1)
Let n(s) be the first derivative of -286*s**3/51 + 8*s**2/17 + 3032. Factor n(u).
-2*u*(143*u - 8)/17
Let j(w) = -9*w**2 - 698*w. Let v(y) = -20*y**2 - 1395*y. Let o(g) = -5*j(g) + 2*v(g). Determine t, given that o(t) = 0.
-140, 0
Let n(m) be the first derivative of -2*m**3/3 + 2560*m**2 - 3276800*m - 1286. Solve n(i) = 0.
1280
Let w(i) be the second derivative of -i**4/12 - 267*i**3 - 641601*i**2/2 + 1884*i. Factor w(d).
-(d + 801)**2
Let k(n) be the first derivative of 1/5*n**4 + 0*n**2 - 2/25*n**5 - 51 - 2/15*n**3 + 0*n. Determine s, given that k(s) = 0.
0, 1
Suppose -24/5*r - 1/5*r**3 + 144 - 19/5*r**2 = 0. What is r?
-12, 5
Let g(h) be the first derivative of 289*h**4/24 - 17*h**3/3 + h**2 + 27*h + 174. Let p(y) be the first derivative of g(y). Factor p(l).
(17*l - 2)**2/2
Let d(p) be the third derivative of -3*p**5/40 - 35*p**4/32 - 2*p**3 + 5*p**2 - 87*p. Factor d(w).
-3*(2*w + 1)*(3*w + 16)/4
Let c(k) = k**2 + 8*k - 5. Suppose -9*t + 25 = 106. Let i be c(t). Suppose -i*j**4 - 51*j**2 - 76*j**2 + 31*j**2 + 64*j + 36*j**3 = 0. What is j?
0, 1, 4
Let d(j) = -3*j**5 + 2*j**4 - 3*j**3 + 4*j**2 - 2. Let a(p) = -7*p**5 + 4*p**4 - 7*p**3 + 10*p**2 - 5. Let n(b) = -4*a(b) + 10*d(b). Factor n(y).
-2*y**3*(y - 1)**2
Let y(x) = -5*x**2 + 45*x + 230. Let q(p) = -p - 5. Let k = -323 - -348. Let m(o) = k*q(o) + y(o). Factor m(s).
-5*(s - 7)*(s + 3)
Let r(a) = 49*a + 3. Let p be r(0). What is q in -8*q**2 + 136*q**2 - 1445*q + q**p + 5541*q = 0?
-64, 0
Let n(r) be the second derivative of -r**6/90 - 11*r**5/20 - 8*r**4 - 128*r**3/9 - 78*r. Factor n(i).
-i*(i + 1)*(i + 16)**2/3
Let l(z) be the second derivative of z**5/40 + 67*z**4/24 - 52*z**3/3 + 35*z**2 - 2248*z. Let l(s) = 0. Calculate s.
-70, 1, 2
Suppose -16 = 16*x - 18*x. Let h = x + -6. Solve -7*t**4 + 6*t**2 + 3*t**4 - 12*t**2 + 16*t**3 - 10*t**h = 0.
0, 2
Suppose 4*l + 5*l - 90 = 0. Factor v**2 - 2*v + 9*v**2 + 26*v - 15*v**3 + l + 11*v.
-5*(v - 2)*(v + 1)*(3*v + 1)
Let y(c) be the first derivative of c**3/4 + 135*c**2/8 + 348*c - 4868. Find d such that y(d) = 0.
-29, -16
Let f(t) be the first derivative of -5*t**3 + 0*t - 3/5*t**5 - 3*t**2 - 3*t**4 + 109. Determine l so that f(l) = 0.
-2, -1, 0
Let n be -9*9/(-486) + (-23)/(-6). Let a(k) be the second derivative of 3/14*k**7 - 4/5*k**6 + 0*k**n + 0*k**2 + 0 + 15*k - 1/2*k**3 + 9/10*k**5. Factor a(x).
3*x*(x - 1)**3*(3*x + 1)
Let c(q) be the second derivative of 84*q + 0 + 0*q**2 + 25/6*q**3 + 1/210*q**7 + 9/10*q**5 - 8/75*q**6 - 10/3*q**4. Let c(l) = 0. What is l?
0, 1, 5
Let i(v) be the first derivative of -v**6/135 + v**5/9 - 37*v**4/54 + 20*v**3/9 - 4*v**2 - 31*v - 105. Let q(g) be the first derivative of i(g). Factor q(x).
-2*(x - 3)**2*(x - 2)**2/9
Let z(x) be the first derivative of -5*x**5/6 + 35*x**4/8 - 95*x**3/18 + 5*x**2/4 + 253. Find d such that z(d) = 0.
0, 1/5, 1, 3
Let v(a) be the third derivative of -a**7/1260 - a**6/720 + a**5/12 + a**2 + 104*a. Suppose v(g) = 0. Calculate g.
-6, 0, 5
Find f such that -3*f + 3*f**2 + 185*f**3 - 9*f + 13*f**2 - 81*f**3 - 108*f**3 = 0.
0, 1, 3
Let m(w) be the second derivative of -w**4/48 - 17*w**3/6 - 1413*w. Factor m(s).
-s*(s + 68)/4
Suppose -a - 5*x = 0, 0*a + x - 76 = -4*a. Let g be 4/(a/25)*204/15. Factor -g + 20*l**2 + 4*l + 28 + 20 - 4*l**3.
-4*(l - 5)*(l - 1)*(l + 1)
Let b be (-3)/65*((-3660)/(-488))/(18/(-8)). Determine d, given that -2/13*d**3 - 2/13 + b*d + 2/13*d**2 = 0.
-1, 1
Let a(k) be the second derivative of -3025*k**7/42 - 341*k**6/6 + 404*k**5/5 + 50*k**4/3 - 56*k**3/3 - 8*k**2 - 2606*k + 2. Find i, given that a(i) = 0.
-1, -2/11, 2/5
Let 2/5*u**5 - 102*u**2 - 42/5*u**4 + 46*u**3 + 488/5*u - 168/5 = 0. What is u?
1, 2, 3, 14
Find w, given that -18*w**2 + 122*w**4 + 9*w - 1 + 12*w**5 - 162*w**4 - 6*w**2 - 7*w**2 + 51*w**3 = 0.
1/3, 1/2, 1
Let k = 148 + -142. Let c be k + (402/(-42) - -9). What is i in 0 + 6/7*i**5 - 22/7*i**2 + c*i**3 - 26/7*i**4 + 4/7*i = 0?
0, 1/3, 1, 2
Let p(l) be the first derivative of 255/7*l**2 - 26 - 578/7*l + 22/7*l**3 + 1/14*l**4. Factor p(m).
2*(m - 1)*(m + 17)**2/7
Let w = 7411/42 + -2461/14. Let z(v) be the first derivative of 23 - w*v**3 - 14*v + 8*v**2. Let z(k) = 0. What is k?
1, 7
Let s(j) be the third derivative of 43*j**5/180 + 118*j**4/9 - 22*j**3/9 + 1292*j**2. Find x, given that s(x) = 0.
-22, 2/43
Let f(k) = 12*k**3 + 27498*k**2 - 8427219*k + 859578459. Let x(c) = -c**3 - 2750*c**2 + 842722*c - 85957846. Let g(b) = 2*f(b) + 21*x(b). Factor g(j).
3*(j - 306)**3
Let j(l) be the first derivative of 25*l**4/4 + 465*l**3 + 552*l**2 + 220*l + 2075. Factor j(h).
(h + 55)*(5*h + 2)**2
Factor -640*w**3 + 1038*w**3 + 2601*w**5 + 3042 - 4719*w + 1120*w**3 - 2600*w**5 + 236*w**2 - 78*w**4.
(w - 39)**2*(w - 1)**2*(w + 2)
Factor -l**3 - 158*l**2 - 4567*l - 34656 + 1943*l - 4064*l.
-(l + 6)*(l + 76)**2
Let a = -17/4373 + 39391/8746. Factor 3/2*t**3 - 5 - a*t + 2*t**2.
(t + 1)*(t + 2)*(3*t - 5)/2
Suppose 13*s - 125 = -4*l, -l = -s - 5 + 12. Let 0*i**3 + 0 - 3/2*i + 3*i**l + 3/2*i**5 - 3*i**4 = 0. What is i?
-1, 0, 1
Let l(z) be the second derivative of 0*z**4 + 1/45*z**6 - 9*z + 1/30*z**5 + 0*z**3 + 16 + 0*z**2. Factor l(i).
2*i**3*(i + 1)/3
Let u(p) be the second derivative of p**4/21 + 208*p**3/21 + 206*p**2/7 + 916*p. Determine h so that u(h) = 0.
-103, -1
Let f be 31/(155/(-30)) + 33*3/12. Factor -15/4*y**2 - f*y**3 + 0 - 1/4*y**4 - 7/4*y.
-y*(y + 1)**2*(y + 7)/4
Factor -58/3 - 1/6*o**2 + 10*o.
-(o - 58)*(o - 2)/6
Let x(c) = 2*c**4