Math / Algebra

QuestionWrite in factored form. a) $f(x)=x^{2}-7 x-18$ c) $h(x)=4 x^{2}-25$ b) $g(x)=-2 x^{2}+17 x-8$ d) $y=6 x^{2}+13 x-5$

Studdy Solution

STEP 1

1. Each quadratic expression can be factored into the form $(ax + b)(cx + d)$ .
2. We will use methods such as factoring by grouping or using the quadratic formula to assist in finding the factors.

STEP 2

1. Factor the quadratic expression $f(x)=x^{2}-7x-18$ .
2. Factor the quadratic expression $g(x)=-2x^{2}+17x-8$ .
3. Factor the quadratic expression $h(x)=4x^{2}-25$ .
4. Factor the quadratic expression $y=6x^{2}+13x-5$ .

STEP 3

For $f(x)=x^{2}-7x-18$ , find two numbers that multiply to $-18$ and add to $-7$ . These numbers are $-9$ and $2$ .
$f(x) = (x - 9)(x + 2)$

STEP 4

For $g(x)=-2x^{2}+17x-8$ , multiply the leading coefficient $-2$ and the constant term $-8$ to get $16$ . Find two numbers that multiply to $16$ and add to $17$ . These numbers are $16$ and $1$ .
Rewrite the middle term using these numbers:
$g(x) = -2x^{2} + 16x + x - 8$
Factor by grouping:
$g(x) = -2x(x - 8) + 1(x - 8)$
$g(x) = (-2x + 1)(x - 8)$

STEP 5

For $h(x)=4x^{2}-25$ , recognize it as a difference of squares:
$h(x) = (2x)^{2} - (5)^{2}$
$h(x) = (2x - 5)(2x + 5)$

STEP 6

For $y=6x^{2}+13x-5$ , multiply the leading coefficient $6$ and the constant term $-5$ to get $-30$ . Find two numbers that multiply to $-30$ and add to $13$ . These numbers are $15$ and $-2$ .
Rewrite the middle term using these numbers:
$y = 6x^{2} + 15x - 2x - 5$
Factor by grouping:
$y = 3x(2x + 5) - 1(2x + 5)$
$y = (3x - 1)(2x + 5)$

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QuestionWrite in factored form. a) $f(x)=x^{2}-7 x-18$ c) $h(x)=4 x^{2}-25$ b) $g(x)=-2 x^{2}+17 x-8$ d) $y=6 x^{2}+13 x-5$

Studdy Solution

STEP 1

1. Each quadratic expression can be factored into the form $(ax + b)(cx + d)$ .
2. We will use methods such as factoring by grouping or using the quadratic formula to assist in finding the factors.

STEP 2

1. Factor the quadratic expression $f(x)=x^{2}-7x-18$ .
2. Factor the quadratic expression $g(x)=-2x^{2}+17x-8$ .
3. Factor the quadratic expression $h(x)=4x^{2}-25$ .
4. Factor the quadratic expression $y=6x^{2}+13x-5$ .

STEP 3

For $f(x)=x^{2}-7x-18$ , find two numbers that multiply to $-18$ and add to $-7$ . These numbers are $-9$ and $2$ .
$f(x) = (x - 9)(x + 2)$

STEP 4

STEP 5

For $h(x)=4x^{2}-25$ , recognize it as a difference of squares:
$h(x) = (2x)^{2} - (5)^{2}$
$h(x) = (2x - 5)(2x + 5)$

STEP 6

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QuestionWrite in factored form. a) f(x)=x2−7x−18f(x)=x^{2}-7 x-18f(x)=x2−7x−18 c) h(x)=4x2−25h(x)=4 x^{2}-25h(x)=4x2−25 b) g(x)=−2x2+17x−8g(x)=-2 x^{2}+17 x-8g(x)=−2x2+17x−8 d) y=6x2+13x−5y=6 x^{2}+13 x-5y=6x2+13x−5

Studdy Solution

STEP 1

1. Each quadratic expression can be factored into the form (ax+b)(cx+d)(ax + b)(cx + d)(ax+b)(cx+d).2. We will use methods such as factoring by grouping or using the quadratic formula to assist in finding the factors.

STEP 2

STEP 3

For f(x)=x2−7x−18f(x)=x^{2}-7x-18f(x)=x2−7x−18, find two numbers that multiply to −18-18−18 and add to −7-7−7. These numbers are −9-9−9 and 222.f(x)=(x−9)(x+2) f(x) = (x - 9)(x + 2) f(x)=(x−9)(x+2)

STEP 4

STEP 5

For h(x)=4x2−25h(x)=4x^{2}-25h(x)=4x2−25, recognize it as a difference of squares:h(x)=(2x)2−(5)2 h(x) = (2x)^{2} - (5)^{2} h(x)=(2x)2−(5)2h(x)=(2x−5)(2x+5) h(x) = (2x - 5)(2x + 5) h(x)=(2x−5)(2x+5)

STEP 6

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWrite in factored form. a) $f(x)=x^{2}-7 x-18$ c) $h(x)=4 x^{2}-25$ b) $g(x)=-2 x^{2}+17 x-8$ d) $y=6 x^{2}+13 x-5$

1. Each quadratic expression can be factored into the form $(ax + b)(cx + d)$ .
2. We will use methods such as factoring by grouping or using the quadratic formula to assist in finding the factors.

For $f(x)=x^{2}-7x-18$ , find two numbers that multiply to $-18$ and add to $-7$ . These numbers are $-9$ and $2$ .
$f(x) = (x - 9)(x + 2)$

For $h(x)=4x^{2}-25$ , recognize it as a difference of squares:
$h(x) = (2x)^{2} - (5)^{2}$
$h(x) = (2x - 5)(2x + 5)$